Subgroups — C₂×#10618719 #13006424

Order 1280.

9542 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618719	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66045	C₂	1	2	yes	maximal, complemented
4	C₂×#66038	C₂	1	2	yes	maximal, complemented
5	C₂×#66017	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66008	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66000	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#65988	C₂	1	2	yes	maximal, complemented
9	C₂×#65987	C₂	1	2	yes	maximal, complemented
10	C₂×#65987	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65964	C₂	1	2	yes	maximal, complemented
12	C₂×#65978	C₂	1	2	yes	maximal, complemented
13	C₂×#65924	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×D₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×D₄×D₂₀	C₂	1	2	yes	maximal, complemented
16	C₂×#65894	C₂	1	2	yes	maximal, complemented
17	C₂×#65861	C₂	1	2	yes	maximal, complemented
18	C₂×#65859	C₂	1	2	yes	maximal, complemented
19	C₂×#65824	C₂	1	2	yes	maximal, complemented
20	C₂²×#4028	C₂	1	2	yes	maximal, complemented
21	C₂⁵×D₅	C₂²	1	1	yes	characteristic, complemented
22	C₂³×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₂²×#713	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
26	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
27	C₂²×#709	C₂²	1	2	yes	complemented
28	C₂³×D₂₀	C₂²	1	2	yes	complemented
29	C₂³×D₂₀	C₂²	1	2	yes	complemented
30	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
31	C₅×#551	C₂²	1	16	yes	complemented
32	C₂×C₅×#126	C₂²	1	2	yes	complemented
33	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#123	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#123	C₂²	1	2	yes	complemented
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₅×#120	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
39	C₂×C₅×#117	C₂²	1	2	yes	complemented
40	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂×#4099	C₂²	1	1	yes	characteristic, complemented
42	C₂×#4093	C₂²	1	1	yes	characteristic, complemented
43	C₂×#4093	C₂²	1	2	yes	complemented
44	C₂×#4086	C₂²	1	1	yes	characteristic, complemented
45	C₂×#4085	C₂²	1	2	yes	complemented
46	C₂×#4083	C₂²	1	2	yes	complemented
47	C₂×#4083	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4083	C₂²	1	1	yes	characteristic, complemented
49	C₂×#4076	C₂²	1	2	yes	complemented
50	C₂×#4076	C₂²	1	2	yes	complemented
51	C₂×#4075	C₂²	1	2	yes	complemented
52	C₂×#4075	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
54	C₂²×#685	C₂²	1	2	yes	complemented
55	C₂²×#685	C₂²	1	2	yes	complemented
56	#66045	C₂²	1	32	yes	complemented
57	#66038	C₂²	1	32	yes	complemented
58	#66017	C₂²	1	16	yes	complemented
59	#66008	C₂²	1	16	yes	complemented
60	#66000	C₂²	1	16	yes	complemented
61	#65988	C₂²	1	32	yes	complemented
62	#65987	C₂²	1	16	yes	complemented
63	#65987	C₂²	1	32	yes	complemented
64	#65978	C₂²	1	32	yes	complemented
65	#65964	C₂²	1	32	yes	complemented
66	#65924	C₂²	1	16	yes	complemented
67	D₅×#120	C₂²	1	16	yes	complemented
68	#65894	C₂²	1	32	yes	complemented
69	D₄×D₂₀	C₂²	1	32	yes	complemented
70	#65861	C₂²	1	32	yes	complemented
71	#65859	C₂²	1	32	yes	complemented
72	C₂×#4044	C₂²	1	2	yes	complemented
73	C₂×#4044	C₂²	1	2	yes	complemented
74	C₂×#4042	C₂²	1	2	yes	complemented
75	C₂×#4041	C₂²	1	2	yes	complemented
76	C₂×#4041	C₂²	1	2	yes	complemented
77	C₂×#4041	C₂²	1	2	yes	complemented
78	C₂×#4041	C₂²	1	2	yes	complemented
79	C₂×#4041	C₂²	1	2	yes	complemented
80	C₂×#4041	C₂²	1	2	yes	complemented
81	C₂×#4041	C₂²	1	2	yes	complemented
82	C₂×#4040	C₂²	1	2	yes	complemented
83	C₂×#4040	C₂²	1	2	yes	complemented
84	C₂×#4040	C₂²	1	2	yes	complemented
85	C₂×#4040	C₂²	1	2	yes	complemented
86	C₂×#4040	C₂²	1	2	yes	complemented
87	C₂×#4039	C₂²	1	2	yes	complemented
88	C₂×#4031	C₂²	1	2	yes	complemented
89	C₂×#4031	C₂²	1	2	yes	complemented
90	#65824	C₂²	1	32	yes	complemented
91	C₂×#4030	C₂²	1	2	yes	complemented
92	C₂×#4030	C₂²	1	2	yes	complemented
93	C₂×#4030	C₂²	1	2	yes	complemented
94	C₂×#4030	C₂²	1	2	yes	complemented
95	C₂×#4030	C₂²	1	2	yes	complemented
96	C₂×#4029	C₂²	1	2	yes	complemented
97	C₂×#4028	C₂²	1	2	yes	—
98	C₂×#4028	C₂²	1	2	yes	complemented
99	C₂×#4028	C₂²	1	2	yes	complemented
100	C₂×#4028	C₂²	1	2	yes	complemented
101	C₂×#4028	C₂²	1	2	yes	complemented
102	C₂×#4028	C₂²	1	2	yes	complemented
103	C₂×#4028	C₂²	1	2	yes	complemented
104	C₂×#4028	C₂²	1	2	yes	complemented
105	C₂×#4028	C₂²	1	2	yes	complemented
106	C₂×#4028	C₂²	1	1	yes	characteristic, complemented
107	C₂×#4028	C₂²	1	2	yes	complemented
108	C₂×#4028	C₂²	1	2	yes	complemented
109	C₂×#4028	C₂²	1	1	yes	characteristic, complemented
110	C₂×#4028	C₂²	1	2	yes	complemented
111	C₂×#4028	C₂²	1	2	yes	complemented
112	C₂×#4028	C₂²	1	32	yes	complemented
113	C₂×#4027	C₂²	1	2	yes	complemented
114	C₂×#4027	C₂²	1	2	yes	complemented
115	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₂×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂×#4024	C₂²	1	2	yes	complemented
120	C₂×#4022	C₂²	1	2	yes	complemented
121	C₂×#4021	C₂²	1	2	yes	complemented
122	C₂×#4021	C₂²	1	2	yes	complemented
123	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
124	C₂×#4020	C₂²	1	2	yes	complemented
125	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
126	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
127	C₂×#3532	—	5	1	no	maximal, Sylow
128	C₂⁵×C₅	C₂³	1	1	yes	characteristic
129	C₂⁴×D₅	—	4	4	no	—
130	C₂⁴×D₅	—	4	8	no	—
131	C₂⁴×D₅	C₂³	1	2	yes	—
132	C₂⁴×D₅	C₂³	1	1	yes	characteristic
133	C₂⁴×D₅	C₂³	1	2	yes	—
134	C₂⁴×D₅	C₂³	1	1	yes	characteristic
135	C₂⁴×D₅	C₂³	1	2	yes	—
136	C₂⁴×D₅	C₂³	1	1	yes	characteristic
137	C₂⁴×D₅	C₂³	1	8	yes	complemented
138	C₂⁴×D₅	C₂³	1	1	yes	characteristic, complemented
139	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	C₂³	1	2	yes	—
141	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅	C₂³	1	2	yes	—
143	C₂³×C₄×C₅	C₂³	1	2	yes	—
144	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
145	C₂²×C₂²⋊D₅	—	4	8	no	—
146	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
149	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
152	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
153	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
154	C₂²×C₂²⋊D₅	C₂³	1	16	yes	complemented
155	C₂²×C₂²⋊D₅	C₂³	1	2	yes	complemented
156	C₂³×Dic₅	C₂³	1	2	yes	—
157	C₂×#713	—	4	4	no	—
158	C₂×#713	C₂³	1	8	yes	complemented
159	C₂×D₄×D₅	—	4	4	no	—
160	C₂×D₄×D₅	—	4	8	no	—
161	C₂×D₄×D₅	—	4	8	no	—
162	C₂×D₄×D₅	C₂³	1	16	yes	complemented
163	C₂×D₄×D₅	C₂³	1	8	yes	complemented
164	C₂×D₄×D₅	C₂³	1	16	yes	complemented
165	C₂×#709	—	4	8	no	—
166	C₂×#709	C₂³	1	16	yes	complemented
167	C₂²×D₂₀	—	4	4	no	—
168	C₂²×D₂₀	—	4	8	no	—
169	C₂²×D₂₀	—	4	8	no	—
170	C₂²×D₂₀	C₂³	1	2	yes	—
171	C₂²×D₂₀	C₂³	1	2	yes	—
172	C₂²×D₂₀	C₂³	1	2	yes	—
173	C₂²×D₂₀	C₂³	1	2	yes	—
174	C₂²×D₂₀	C₂³	1	2	yes	—
175	C₂²×D₂₀	C₂³	1	2	yes	—
176	C₂²×D₂₀	C₂³	1	1	yes	characteristic
177	C₂²×D₂₀	C₂³	1	2	yes	—
178	C₂²×D₂₀	C₂³	1	2	yes	—
179	C₂²×D₂₀	C₂³	1	2	yes	—
180	C₂²×D₂₀	C₂³	1	16	yes	complemented
181	C₂²×D₂₀	C₂³	1	16	yes	complemented
182	C₂²×D₂₀	C₂³	1	8	yes	complemented
183	C₂²×D₂₀	C₂³	1	2	yes	complemented
184	C₂²×D₂₀	C₂³	1	1	yes	characteristic, complemented
185	C₂²×D₂₀	C₂³	1	2	yes	complemented
186	C₂²×D₂₀	C₂³	1	2	yes	complemented
187	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₅	C₂³	1	2	yes	—
189	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
190	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
191	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
192	C₂²×C₄×D₅	C₂³	1	2	yes	complemented
193	C₂²×Dic₁₀	C₂³	1	2	yes	complemented
194	C₅×#126	C₂³	1	16	yes	complemented
195	C₅×#124	C₂³	1	8	yes	complemented
196	C₅×#123	C₂³	1	8	yes	complemented
197	C₅×#123	C₂³	1	16	yes	complemented
198	C₅×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₅×#120	C₂³	1	8	yes	—
200	C₄×C₅×D₄	C₂³	1	16	yes	complemented
201	C₅×#117	C₂³	1	16	yes	complemented
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
203	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
204	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
205	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
213	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
214	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
216	C₂×C₄²×C₅	C₂³	1	2	yes	complemented
217	#4099	C₂³	1	8	yes	complemented
218	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
219	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
221	#4093	C₂³	1	16	yes	complemented
222	#4093	C₂³	1	8	yes	complemented
223	#4086	C₂³	1	8	yes	complemented
224	#4085	C₂³	1	16	yes	complemented
225	#4083	C₂³	1	16	yes	complemented
226	#4083	C₂³	1	8	yes	complemented
227	#4083	C₂³	1	8	yes	complemented
228	#4076	C₂³	1	16	yes	complemented
229	#4076	C₂³	1	16	yes	complemented
230	#4075	C₂³	1	8	yes	complemented
231	#4075	C₂³	1	16	yes	complemented
232	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
233	C₂×#685	C₂³	1	2	yes	—
234	C₂×#685	C₂³	1	2	yes	—
235	C₂×#685	C₂³	1	2	yes	—
236	C₂×#685	C₂³	1	2	yes	—
237	C₂×#685	C₂³	1	2	yes	—
238	C₂×#685	C₂³	1	2	yes	—
239	C₂×#685	C₂³	1	2	yes	—
240	C₂×#685	C₂³	1	2	yes	—
241	C₂×#685	C₂³	1	2	yes	—
242	C₂×#685	C₂³	1	2	yes	—
243	C₂×#685	C₂³	1	2	yes	—
244	C₂×#685	C₂³	1	16	yes	complemented
245	C₂×#685	C₂³	1	16	yes	complemented
246	C₂×#685	C₂³	1	2	yes	complemented
247	C₂×#685	C₂³	1	2	yes	complemented
248	C₂×#685	C₂³	1	2	yes	complemented
249	C₂×#685	C₂³	1	2	yes	complemented
250	C₂×#685	C₂³	1	2	yes	complemented
251	C₂×#685	C₂³	1	2	yes	complemented
252	C₂×#685	C₂³	1	2	yes	complemented
253	C₂×C₄⋊Dic₅	C₂³	1	2	yes	complemented
254	C₂×#683	C₂³	1	2	yes	complemented
255	C₂×#683	C₂³	1	2	yes	complemented
256	C₂×#683	C₂³	1	2	yes	complemented
257	C₂×#683	C₂³	1	2	yes	complemented
258	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic, complemented
259	C₂×C₄×Dic₅	C₂³	1	2	yes	complemented
260	#4044	C₂³	1	16	yes	complemented
261	#4044	C₂³	1	16	yes	complemented
262	#4042	C₂³	1	16	yes	complemented
263	#4041	C₂³	1	16	yes	complemented
264	#4041	C₂³	1	16	yes	complemented
265	#4041	C₂³	1	16	yes	complemented
266	#4041	C₂³	1	16	yes	complemented
267	#4041	C₂³	1	16	yes	complemented
268	#4041	C₂³	1	16	yes	complemented
269	#4041	C₂³	1	16	yes	complemented
270	#4040	C₂³	1	16	yes	complemented
271	#4040	C₂³	1	16	yes	complemented
272	#4040	C₂³	1	16	yes	complemented
273	#4040	C₂³	1	16	yes	complemented
274	#4040	C₂³	1	16	yes	complemented
275	#4039	C₂³	1	16	yes	complemented
276	#4031	C₂³	1	16	yes	complemented
277	#4031	C₂³	1	16	yes	complemented
278	#4030	C₂³	1	16	yes	complemented
279	#4030	C₂³	1	16	yes	complemented
280	#4030	C₂³	1	16	yes	complemented
281	#4030	C₂³	1	16	yes	complemented
282	#4030	C₂³	1	16	yes	complemented
283	#4029	C₂³	1	16	yes	complemented
284	#4028	C₂³	1	16	yes	—
285	#4028	C₂³	1	16	yes	complemented
286	#4028	C₂³	1	16	yes	complemented
287	#4028	C₂³	1	16	yes	complemented
288	#4028	C₂³	1	16	yes	complemented
289	#4028	C₂³	1	16	yes	complemented
290	#4028	C₂³	1	16	yes	complemented
291	#4028	C₂³	1	16	yes	complemented
292	#4028	C₂³	1	16	yes	complemented
293	#4028	C₂³	1	8	yes	complemented
294	#4028	C₂³	1	16	yes	complemented
295	#4028	C₂³	1	16	yes	complemented
296	#4028	C₂³	1	16	yes	complemented
297	#4028	C₂³	1	16	yes	complemented
298	#4028	C₂³	1	8	yes	complemented
299	#4027	C₂³	1	16	yes	complemented
300	#4027	C₂³	1	16	yes	complemented
301	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
302	D₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
303	D₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
304	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
305	#4024	C₂³	1	16	yes	complemented
306	#4022	C₂³	1	16	yes	complemented
307	#4021	C₂³	1	16	yes	complemented
308	#4021	C₂³	1	16	yes	complemented
309	#4020	C₂³	1	8	yes	complemented
310	#4020	C₂³	1	16	yes	complemented
311	C₄×D₂₀	C₂³	1	16	yes	complemented
312	#4018	C₂³	1	8	yes	complemented
313	#3532	—	5	32	no	—
314	C₂×H(3,𝔽₄)	—	5	1	no	—
315	C₂×#560	—	5	2	no	—
316	C₂×#560	—	5	1	no	—
317	C₂×#551	—	5	2	no	—
318	C₂×#551	D₅	1	1	yes	characteristic, complemented
319	C₂×#546	—	5	2	no	—
320	C₂×#546	—	5	2	no	—
321	C₂×#546	—	5	2	no	—
322	C₂×D₄²	—	5	1	no	—
323	C₂×D₄²	—	5	2	no	—
324	C₂×#538	—	5	2	no	—
325	C₂×#538	—	5	2	no	—
326	C₂×#538	—	5	2	no	—
327	C₂×#535	—	5	1	no	—
328	C₂×#535	—	5	2	no	—
329	C₂×#534	—	5	2	no	—
330	C₂×#534	—	5	1	no	—
331	C₂²×#120	—	5	1	no	—
332	C₂²×#120	—	5	2	no	—
333	C₂⁴×C₅	—	2	8	no	—
334	C₂⁴×C₅	—	4	2	no	—
335	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
336	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
337	C₂⁴×C₅	C₂⁴	1	4	yes	—
338	C₂⁴×C₅	C₂⁴	1	2	yes	—
339	C₂³×D₅	—	2	8	no	—
340	C₂³×D₅	—	2	8	no	—
341	C₂³×D₅	—	2	8	no	—
342	C₂³×D₅	—	2	8	no	—
343	C₂³×D₅	—	2	4	no	—
344	C₂³×D₅	—	2	4	no	—
345	C₂³×D₅	—	4	16	no	—
346	C₂³×D₅	—	4	4	no	—
347	C₂³×D₅	—	4	4	no	—
348	C₂³×D₅	—	4	2	no	—
349	C₂³×D₅	—	4	4	no	—
350	C₂³×D₅	—	4	4	no	—
351	C₂³×D₅	—	4	4	no	—
352	C₂³×D₅	—	4	32	no	—
353	C₂³×D₅	—	4	4	no	—
354	C₂³×D₅	—	4	2	no	—
355	C₂³×D₅	—	4	4	no	—
356	C₂³×D₅	—	4	4	no	—
357	C₂³×D₅	—	4	4	no	—
358	C₂³×D₅	—	4	64	no	—
359	C₂³×D₅	C₂⁴	1	2	yes	—
360	C₂³×D₅	C₂⁴	1	1	yes	characteristic
361	C₂³×D₅	C₂⁴	1	2	yes	—
362	C₂³×D₅	C₂⁴	1	2	yes	—
363	C₂³×D₅	C₂⁴	1	1	yes	characteristic
364	C₂³×D₅	C₂⁴	1	8	yes	—
365	C₂³×D₅	C₂⁴	1	1	yes	characteristic
366	C₂³×D₅	C₂⁴	1	8	yes	—
367	C₂³×D₅	C₂⁴	1	4	yes	—
368	C₂³×D₅	C₂⁴	1	8	yes	—
369	C₂³×D₅	C₂⁴	1	4	yes	—
370	C₂³×D₅	C₂⁴	1	4	yes	—
371	C₂³×D₅	C₂⁴	1	4	yes	complemented
372	C₂×C₅×Q₈	—	4	2	no	—
373	C₂×C₅×Q₈	C₂⁴	1	4	yes	complemented
374	C₂×C₅×D₄	—	2	8	no	—
375	C₂×C₅×D₄	—	4	2	no	—
376	C₂×C₅×D₄	C₂⁴	1	8	yes	—
377	C₂×C₅×D₄	C₂⁴	1	4	yes	—
378	C₂²×C₄×C₅	—	2	8	no	—
379	C₂²×C₄×C₅	—	4	4	no	—
380	C₂²×C₄×C₅	—	4	2	no	—
381	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
382	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
383	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
388	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
389	C₂²×C₄×C₅	C₂⁴	1	4	yes	complemented
390	C₂×C₂²⋊D₅	—	2	8	no	—
391	C₂×C₂²⋊D₅	—	2	8	no	—
392	C₂×C₂²⋊D₅	—	2	8	no	—
393	C₂×C₂²⋊D₅	—	4	4	no	—
394	C₂×C₂²⋊D₅	—	4	2	no	—
395	C₂×C₂²⋊D₅	—	4	2	no	—
396	C₂×C₂²⋊D₅	—	4	4	no	—
397	C₂×C₂²⋊D₅	—	4	4	no	—
398	C₂×C₂²⋊D₅	—	4	4	no	—
399	C₂×C₂²⋊D₅	—	4	32	no	—
400	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
401	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
402	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
403	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
404	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
405	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
406	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
407	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
408	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	complemented
409	C₂²×Dic₅	—	4	4	no	—
410	C₂²×Dic₅	C₂⁴	1	2	yes	—
411	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅	C₂⁴	1	2	yes	—
413	C₂²×Dic₅	C₂⁴	1	2	yes	—
414	C₂²×Dic₅	C₂⁴	1	8	yes	—
415	#713	—	4	16	no	—
416	D₄×D₅	—	4	16	no	—
417	D₄×D₅	—	4	32	no	—
418	D₄×D₅	—	4	32	no	—
419	#709	—	4	32	no	—
420	C₂×D₂₀	—	2	8	no	—
421	C₂×D₂₀	—	2	8	no	—
422	C₂×D₂₀	—	4	16	no	—
423	C₂×D₂₀	—	4	32	no	—
424	C₂×D₂₀	—	4	4	no	—
425	C₂×D₂₀	—	4	4	no	—
426	C₂×D₂₀	—	4	4	no	—
427	C₂×D₂₀	—	4	4	no	—
428	C₂×D₂₀	—	4	4	no	—
429	C₂×D₂₀	—	4	4	no	—
430	C₂×D₂₀	—	4	32	no	—
431	C₂×D₂₀	—	4	4	no	—
432	C₂×D₂₀	—	4	2	no	—
433	C₂×D₂₀	—	4	4	no	—
434	C₂×D₂₀	—	4	4	no	—
435	C₂×D₂₀	—	4	4	no	—
436	C₂×D₂₀	—	4	2	no	—
437	C₂×D₂₀	C₂⁴	1	8	yes	—
438	C₂×D₂₀	C₂⁴	1	8	yes	—
439	C₂×D₂₀	C₂⁴	1	8	yes	—
440	C₂×D₂₀	C₂⁴	1	8	yes	—
441	C₂×D₂₀	C₂⁴	1	8	yes	—
442	C₂×D₂₀	C₂⁴	1	8	yes	—
443	C₂×D₂₀	C₂⁴	1	8	yes	—
444	C₂×D₂₀	C₂⁴	1	8	yes	—
445	C₂×D₂₀	C₂⁴	1	8	yes	—
446	C₂×D₂₀	C₂⁴	1	4	yes	—
447	C₂×D₂₀	C₂⁴	1	8	yes	complemented
448	C₂×D₂₀	C₂⁴	1	8	yes	complemented
449	C₂×D₂₀	C₂⁴	1	8	yes	complemented
450	C₂×D₂₀	C₂⁴	1	4	yes	complemented
451	C₂×C₄×D₅	—	2	4	no	—
452	C₂×C₄×D₅	—	4	4	no	—
453	C₂×C₄×D₅	—	4	4	no	—
454	C₂×C₄×D₅	—	4	4	no	—
455	C₂×C₄×D₅	—	4	4	no	—
456	C₂×C₄×D₅	—	4	4	no	—
457	C₂×C₄×D₅	C₂⁴	1	4	yes	—
458	C₂×C₄×D₅	C₂⁴	1	8	yes	—
459	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
460	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
461	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
462	C₂×C₄×D₅	C₂⁴	1	8	yes	complemented
463	C₂×Dic₁₀	—	4	4	no	—
464	C₂×Dic₁₀	C₂⁴	1	8	yes	complemented
465	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
466	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
467	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
468	C₅×C₄⋊C₄	C₂⁴	1	8	yes	complemented
469	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
471	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
473	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
474	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
475	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	complemented
476	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
477	C₄²×C₅	C₂⁴	1	4	yes	complemented
478	C₄²×C₅	C₂⁴	1	8	yes	complemented
479	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
480	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
481	C₂²⋊Dic₅	C₂⁴	1	4	yes	complemented
482	#685	C₂⁴	1	8	yes	—
483	#685	C₂⁴	1	8	yes	—
484	#685	C₂⁴	1	8	yes	—
485	#685	C₂⁴	1	8	yes	—
486	#685	C₂⁴	1	8	yes	—
487	#685	C₂⁴	1	8	yes	—
488	#685	C₂⁴	1	8	yes	—
489	#685	C₂⁴	1	8	yes	—
490	#685	C₂⁴	1	8	yes	—
491	#685	C₂⁴	1	8	yes	—
492	#685	C₂⁴	1	8	yes	—
493	#685	C₂⁴	1	8	yes	complemented
494	#685	C₂⁴	1	8	yes	complemented
495	#685	C₂⁴	1	8	yes	complemented
496	#685	C₂⁴	1	8	yes	complemented
497	#685	C₂⁴	1	8	yes	complemented
498	#685	C₂⁴	1	8	yes	complemented
499	#685	C₂⁴	1	8	yes	complemented
500	C₄⋊Dic₅	C₂⁴	1	8	yes	complemented
501	#683	C₂⁴	1	8	yes	complemented
502	#683	C₂⁴	1	8	yes	complemented
503	#683	C₂⁴	1	8	yes	complemented
504	#683	C₂⁴	1	8	yes	complemented
505	C₄×Dic₅	C₂⁴	1	4	yes	complemented
506	C₄×Dic₅	C₂⁴	1	8	yes	complemented
507	C₂⁶	—	5	1	no	—
508	C₂²×#41	—	5	1	no	—
509	C₂²×#41	—	5	2	no	—
510	C₂³×D₄	—	5	2	no	—
511	C₂³×D₄	—	5	1	no	—
512	C₂³×D₄	—	5	2	no	—
513	C₂³×D₄	—	5	2	no	—
514	C₂³×D₄	—	5	2	no	—
515	C₂³×D₄	—	5	2	no	—
516	C₂³×D₄	—	5	1	no	—
517	H(3,𝔽₄)	—	5	16	no	—
518	#560	—	5	32	no	—
519	#560	—	5	16	no	—
520	#551	—	5	32	no	—
521	#551	C₂×D₅	1	16	yes	complemented
522	#546	—	5	32	no	—
523	#546	—	5	32	no	—
524	#546	—	5	32	no	—
525	D₄²	—	5	16	no	—
526	D₄²	—	5	32	no	—
527	#538	—	5	32	no	—
528	#538	—	5	32	no	—
529	#538	—	5	32	no	—
530	#535	—	5	16	no	—
531	#535	—	5	32	no	—
532	#534	—	5	32	no	—
533	#534	—	5	16	no	—
534	C₂×#127	—	5	1	no	—
535	C₂×#127	—	5	1	no	—
536	C₂×#127	—	5	2	no	—
537	C₂×#126	—	5	2	no	—
538	C₂×#126	—	5	2	no	—
539	C₂×#126	—	5	2	no	—
540	C₂×#126	C₂×D₅	1	2	yes	complemented
541	C₂×#124	—	5	1	no	—
542	C₂×#124	—	5	2	no	—
543	C₂×#124	—	5	2	no	—
544	C₂×#124	—	5	2	no	—
545	C₂×#124	—	5	2	no	—
546	C₂×#124	—	5	2	no	—
547	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
548	C₂×#123	—	5	2	no	—
549	C₂×#123	—	5	1	no	—
550	C₂×#123	—	5	2	no	—
551	C₂×#123	—	5	2	no	—
552	C₂×#123	—	5	2	no	—
553	C₂×#123	—	5	2	no	—
554	C₂×#123	—	5	2	no	—
555	C₂×#123	—	5	2	no	—
556	C₂×#123	C₂×D₅	1	1	yes	characteristic, complemented
557	C₂×#123	C₂×D₅	1	2	yes	complemented
558	C₂×C₂²⋊Q₈	—	5	2	no	—
559	C₂×C₂²⋊Q₈	—	5	2	no	—
560	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
561	C₂×#121	—	5	2	no	—
562	C₂×#121	—	5	2	no	—
563	C₂×#121	—	5	2	no	—
564	C₂×#121	—	5	2	no	—
565	C₂×#121	—	5	2	no	—
566	C₂×#121	—	5	2	no	—
567	C₂×#121	—	5	2	no	—
568	C₂×#121	—	5	2	no	—
569	C₂×#121	—	5	2	no	—
570	C₂×#121	—	5	2	no	—
571	C₂×#121	—	5	2	no	—
572	C₂×#121	—	5	2	no	—
573	C₂×#121	—	5	2	no	—
574	C₂×#121	—	5	2	no	—
575	C₂×#121	—	5	2	no	—
576	C₂×#120	—	5	1	no	—
577	C₂×#120	—	5	2	no	—
578	C₂×#120	—	5	1	no	—
579	C₂×#120	—	5	1	no	—
580	C₂×#120	—	5	16	no	—
581	C₂×#120	—	5	2	no	—
582	C₂×#120	—	5	2	no	—
583	C₂×#120	—	5	2	no	—
584	C₂×#120	—	5	2	no	—
585	C₂×#120	—	5	2	no	—
586	C₂×#120	—	5	2	no	—
587	C₂×#120	—	5	2	no	—
588	C₂×#120	—	5	2	no	—
589	C₂×#120	—	5	1	no	—
590	C₂×#120	—	5	2	no	—
591	C₂×#120	—	5	2	no	—
592	C₂×#120	—	5	2	no	—
593	C₂×#120	—	5	32	no	—
594	C₂×#120	—	5	1	no	—
595	C₂×#120	—	5	2	no	—
596	C₂×#120	—	5	2	no	—
597	C₂×#120	C₂×D₅	1	1	yes	characteristic
598	C₂×C₄×D₄	—	5	2	no	—
599	C₂×C₄×D₄	—	5	2	no	—
600	C₂×C₄×D₄	—	5	2	no	—
601	C₂×C₄×D₄	—	5	2	no	—
602	C₂×C₄×D₄	—	5	2	no	—
603	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
604	C₂×#117	—	5	1	no	—
605	C₂×#117	C₂×D₅	1	2	yes	complemented
606	C₂²×C₂²⋊C₄	—	5	2	no	—
607	C₂²×C₂²⋊C₄	—	5	2	no	—
608	C₂²×C₂²⋊C₄	—	5	1	no	—
609	C₂²×C₂²⋊C₄	—	5	2	no	—
610	C₂²×C₂²⋊C₄	—	5	2	no	—
611	C₂²×C₂²⋊C₄	—	5	1	no	—
612	C₂²×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
613	C₂³×C₅	—	2	4	no	—
614	C₂³×C₅	—	2	4	no	—
615	C₂³×C₅	—	2	4	no	—
616	C₂³×C₅	—	2	16	no	—
617	C₂³×C₅	—	2	4	no	—
618	C₂³×C₅	—	2	2	no	—
619	C₂³×C₅	—	2	2	no	—
620	C₂³×C₅	—	4	4	no	—
621	C₂³×C₅	—	4	16	no	—
622	C₂³×C₅	H(5,𝔽₂)	1	8	yes	—
623	C₂³×C₅	C₂⁵	1	2	yes	—
624	C₂³×C₅	C₂⁵	1	2	yes	—
625	C₂³×C₅	C₂⁵	1	4	yes	—
626	C₂³×C₅	C₂⁵	1	1	yes	characteristic
627	C₂²×D₅	—	2	4	no	—
628	C₂²×D₅	—	2	4	no	—
629	C₂²×D₅	—	2	4	no	—
630	C₂²×D₅	—	2	4	no	—
631	C₂²×D₅	—	2	4	no	—
632	C₂²×D₅	—	2	4	no	—
633	C₂²×D₅	—	2	4	no	—
634	C₂²×D₅	—	2	2	no	—
635	C₂²×D₅	—	2	16	no	—
636	C₂²×D₅	—	2	4	no	—
637	C₂²×D₅	—	2	4	no	—
638	C₂²×D₅	—	2	4	no	—
639	C₂²×D₅	—	2	4	no	—
640	C₂²×D₅	—	2	4	no	—
641	C₂²×D₅	—	2	2	no	—
642	C₂²×D₅	—	2	16	no	—
643	C₂²×D₅	—	2	16	no	—
644	C₂²×D₅	—	2	16	no	—
645	C₂²×D₅	—	2	8	no	—
646	C₂²×D₅	—	2	8	no	—
647	C₂²×D₅	—	4	8	no	—
648	C₂²×D₅	—	4	8	no	—
649	C₂²×D₅	—	4	4	no	—
650	C₂²×D₅	—	4	8	no	—
651	C₂²×D₅	—	4	8	no	—
652	C₂²×D₅	—	4	8	no	—
653	C₂²×D₅	—	4	8	no	—
654	C₂²×D₅	—	4	4	no	—
655	C₂²×D₅	—	4	8	no	—
656	C₂²×D₅	—	4	8	no	—
657	C₂²×D₅	—	4	8	no	—
658	C₂²×D₅	—	4	32	no	—
659	C₂²×D₅	—	4	16	no	—
660	C₂²×D₅	—	4	32	no	—
661	C₂²×D₅	—	4	128	no	—
662	C₂²×D₅	—	4	16	no	—
663	C₂²×D₅	—	8	8	no	—
664	C₂²×D₅	—	8	16	no	—
665	C₂²×D₅	—	8	8	no	—
666	C₂²×D₅	H(5,𝔽₂)	1	4	yes	—
667	C₂²×D₅	C₂⁵	1	4	yes	—
668	C₂²×D₅	C₂⁵	1	2	yes	—
669	C₂²×D₅	C₂⁵	1	4	yes	—
670	C₂²×D₅	C₂⁵	1	4	yes	—
671	C₂²×D₅	C₂⁵	1	2	yes	—
672	C₂²×D₅	C₂⁵	1	2	yes	—
673	C₅×Q₈	—	4	4	no	—
674	C₅×D₄	—	2	16	no	—
675	C₅×D₄	—	4	4	no	—
676	C₂×C₄×C₅	—	2	4	no	—
677	C₂×C₄×C₅	—	2	2	no	—
678	C₂×C₄×C₅	—	2	4	no	—
679	C₂×C₄×C₅	—	2	4	no	—
680	C₂×C₄×C₅	—	2	4	no	—
681	C₂×C₄×C₅	—	2	4	no	—
682	C₂×C₄×C₅	—	2	16	no	—
683	C₂×C₄×C₅	—	4	8	no	—
684	C₂×C₄×C₅	—	4	4	no	—
685	C₂×C₄×C₅	C₂⁵	1	2	yes	—
686	C₂×C₄×C₅	C₂⁵	1	4	yes	—
687	C₂×C₄×C₅	C₂⁵	1	4	yes	—
688	C₂×C₄×C₅	C₂⁵	1	4	yes	—
689	C₂×C₄×C₅	C₂⁵	1	4	yes	—
690	C₂×C₄×C₅	C₂⁵	1	4	yes	—
691	C₂²⋊D₅	—	2	16	no	—
692	C₂²⋊D₅	—	2	16	no	—
693	C₂²⋊D₅	—	2	16	no	—
694	C₂²⋊D₅	—	4	8	no	—
695	C₂²⋊D₅	—	4	4	no	—
696	C₂²⋊D₅	—	4	4	no	—
697	C₂²⋊D₅	—	4	8	no	—
698	C₂²⋊D₅	—	4	8	no	—
699	C₂²⋊D₅	—	4	8	no	—
700	C₂×Dic₅	—	2	4	no	—
701	C₂×Dic₅	—	2	4	no	—
702	C₂×Dic₅	—	2	2	no	—
703	C₂×Dic₅	—	2	4	no	—
704	C₂×Dic₅	—	4	8	no	—
705	C₂×Dic₅	C₂⁵	1	4	yes	—
706	C₂×Dic₅	C₂⁵	1	4	yes	—
707	C₂×Dic₅	C₂⁵	1	4	yes	—
708	C₂×Dic₅	C₂⁵	1	2	yes	—
709	D₂₀	—	2	16	no	—
710	D₂₀	—	2	16	no	—
711	D₂₀	—	4	8	no	—
712	D₂₀	—	4	8	no	—
713	D₂₀	—	4	8	no	—
714	D₂₀	—	4	8	no	—
715	D₂₀	—	4	8	no	—
716	D₂₀	—	4	8	no	—
717	D₂₀	—	4	8	no	—
718	D₂₀	—	4	4	no	—
719	D₂₀	—	4	8	no	—
720	D₂₀	—	4	8	no	—
721	D₂₀	—	4	8	no	—
722	D₂₀	—	4	4	no	—
723	C₄×D₅	—	2	8	no	—
724	C₄×D₅	—	4	8	no	—
725	C₄×D₅	—	4	8	no	—
726	C₄×D₅	—	4	8	no	—
727	C₄×D₅	—	4	8	no	—
728	C₄×D₅	—	4	8	no	—
729	Dic₁₀	—	4	8	no	—
730	C₂⁵	—	5	2	no	—
731	C₂⁵	—	5	1	no	—
732	C₂⁵	—	5	2	no	—
733	C₂⁵	—	5	1	no	—
734	C₂⁵	—	5	2	no	—
735	C₂⁵	—	5	1	no	—
736	C₂⁵	—	5	8	no	—
737	C₂⁵	—	5	1	no	—
738	C₂⁵	—	20	8	no	—
739	C₂⁵	—	20	4	no	—
740	C₂⁵	C₂²×D₅	1	1	yes	characteristic
741	C₂×#41	—	5	8	no	—
742	C₂×#41	—	5	16	no	—
743	C₂×#41	—	20	8	no	—
744	C₂×#41	—	20	4	no	—
745	C₂²×Q₈	—	5	2	no	—
746	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
747	C₂²×D₄	—	5	2	no	—
748	C₂²×D₄	—	5	2	no	—
749	C₂²×D₄	—	5	2	no	—
750	C₂²×D₄	—	5	1	no	—
751	C₂²×D₄	—	5	2	no	—
752	C₂²×D₄	—	5	2	no	—
753	C₂²×D₄	—	5	1	no	—
754	C₂²×D₄	—	5	2	no	—
755	C₂²×D₄	—	5	16	no	—
756	C₂²×D₄	—	5	2	no	—
757	C₂²×D₄	—	5	8	no	—
758	C₂²×D₄	—	5	16	no	—
759	C₂²×D₄	—	5	16	no	—
760	C₂²×D₄	—	5	2	no	—
761	C₂²×D₄	—	5	2	no	—
762	C₂²×D₄	—	5	2	no	—
763	C₂²×D₄	—	5	2	no	—
764	C₂²×D₄	—	5	2	no	—
765	C₂²×D₄	—	5	2	no	—
766	C₂²×D₄	—	5	2	no	—
767	C₂²×D₄	—	5	2	no	—
768	C₂²×D₄	—	5	1	no	—
769	C₂²×D₄	—	5	2	no	—
770	C₂²×D₄	—	5	1	no	—
771	C₂²×D₄	—	5	2	no	—
772	C₂²×D₄	—	5	16	no	—
773	C₂²×D₄	—	5	16	no	—
774	C₂²×D₄	—	5	2	no	—
775	C₂²×D₄	—	5	2	no	—
776	C₂²×D₄	—	5	8	no	—
777	C₂²×D₄	—	20	8	no	—
778	C₂²×D₄	—	20	8	no	—
779	C₂²×D₄	—	20	4	no	—
780	C₂²×D₄	—	20	4	no	—
781	C₂²×D₄	—	20	8	no	—
782	C₂²×D₄	—	20	8	no	—
783	C₂²×D₄	—	20	8	no	—
784	C₂²×D₄	C₂²×D₅	1	2	yes	—
785	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
786	C₂³×C₄	—	5	2	no	—
787	C₂³×C₄	—	5	1	no	—
788	C₂³×C₄	—	5	2	no	—
789	C₂³×C₄	—	5	2	no	—
790	C₂³×C₄	—	5	2	no	—
791	C₂³×C₄	—	5	2	no	—
792	C₂³×C₄	—	5	2	no	—
793	C₂³×C₄	C₂²×D₅	1	2	yes	—
794	C₂³×C₄	C₂²×D₅	1	2	yes	—
795	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic, complemented
796	#127	—	5	8	no	—
797	#127	—	5	8	no	—
798	#127	—	5	16	no	—
799	#126	—	5	16	no	—
800	#126	—	5	16	no	—
801	#126	—	5	16	no	—
802	#126	C₂²×D₅	1	16	yes	complemented
803	#124	—	5	8	no	—
804	#124	—	5	16	no	—
805	#124	—	5	16	no	—
806	#124	—	5	16	no	—
807	#124	—	5	16	no	—
808	#124	—	5	16	no	—
809	#124	C₂²×D₅	1	8	yes	complemented
810	#123	—	5	16	no	—
811	#123	—	5	8	no	—
812	#123	—	5	16	no	—
813	#123	—	5	16	no	—
814	#123	—	5	16	no	—
815	#123	—	5	16	no	—
816	#123	—	5	16	no	—
817	#123	—	5	16	no	—
818	#123	C₂²×D₅	1	8	yes	complemented
819	#123	C₂²×D₅	1	16	yes	complemented
820	C₂²⋊Q₈	—	5	16	no	—
821	C₂²⋊Q₈	—	5	16	no	—
822	C₂²⋊Q₈	C₂²×D₅	1	16	yes	complemented
823	#121	—	5	16	no	—
824	#121	—	5	16	no	—
825	#121	—	5	16	no	—
826	#121	—	5	16	no	—
827	#121	—	5	16	no	—
828	#121	—	5	16	no	—
829	#121	—	5	16	no	—
830	#121	—	5	16	no	—
831	#121	—	5	16	no	—
832	#121	—	5	16	no	—
833	#121	—	5	16	no	—
834	#121	—	5	16	no	—
835	#121	—	5	16	no	—
836	#121	—	5	16	no	—
837	#121	—	5	16	no	—
838	#120	—	5	8	no	—
839	#120	—	5	16	no	—
840	#120	—	5	8	no	—
841	#120	—	5	8	no	—
842	#120	—	5	16	no	—
843	#120	—	5	16	no	—
844	#120	—	5	16	no	—
845	#120	—	5	16	no	—
846	#120	—	5	16	no	—
847	#120	—	5	16	no	—
848	#120	—	5	16	no	—
849	#120	—	5	16	no	—
850	#120	—	5	8	no	—
851	#120	—	5	16	no	—
852	#120	—	5	16	no	—
853	#120	—	5	16	no	—
854	#120	—	5	8	no	—
855	#120	—	5	16	no	—
856	#120	—	5	16	no	—
857	#120	C₂²×D₅	1	8	yes	—
858	C₄×D₄	—	5	16	no	—
859	C₄×D₄	—	5	16	no	—
860	C₄×D₄	—	5	16	no	—
861	C₄×D₄	—	5	16	no	—
862	C₄×D₄	—	5	16	no	—
863	C₄×D₄	C₂²×D₅	1	16	yes	complemented
864	#117	—	5	8	no	—
865	#117	C₂²×D₅	1	16	yes	complemented
866	C₂×C₄⋊C₄	—	5	2	no	—
867	C₂×C₄⋊C₄	—	5	2	no	—
868	C₂×C₄⋊C₄	—	5	2	no	—
869	C₂×C₄⋊C₄	—	5	2	no	—
870	C₂×C₄⋊C₄	—	5	2	no	—
871	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
872	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
873	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
874	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
875	C₂×C₂²⋊C₄	—	5	2	no	—
876	C₂×C₂²⋊C₄	—	5	1	no	—
877	C₂×C₂²⋊C₄	—	5	1	no	—
878	C₂×C₂²⋊C₄	—	5	2	no	—
879	C₂×C₂²⋊C₄	—	5	2	no	—
880	C₂×C₂²⋊C₄	—	5	2	no	—
881	C₂×C₂²⋊C₄	—	5	2	no	—
882	C₂×C₂²⋊C₄	—	5	2	no	—
883	C₂×C₂²⋊C₄	—	5	2	no	—
884	C₂×C₂²⋊C₄	—	5	2	no	—
885	C₂×C₂²⋊C₄	—	5	2	no	—
886	C₂×C₂²⋊C₄	—	5	2	no	—
887	C₂×C₂²⋊C₄	—	5	2	no	—
888	C₂×C₂²⋊C₄	—	5	2	no	—
889	C₂×C₂²⋊C₄	—	5	16	no	—
890	C₂×C₂²⋊C₄	—	5	16	no	—
891	C₂×C₂²⋊C₄	—	5	2	no	—
892	C₂×C₂²⋊C₄	—	5	2	no	—
893	C₂×C₂²⋊C₄	—	5	2	no	—
894	C₂×C₂²⋊C₄	—	5	2	no	—
895	C₂×C₂²⋊C₄	—	5	2	no	—
896	C₂×C₂²⋊C₄	—	5	2	no	—
897	C₂×C₂²⋊C₄	—	5	2	no	—
898	C₂×C₂²⋊C₄	—	5	8	no	—
899	C₂×C₂²⋊C₄	—	5	16	no	—
900	C₂×C₂²⋊C₄	—	5	16	no	—
901	C₂×C₂²⋊C₄	—	5	8	no	—
902	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
903	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
904	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
905	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
906	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
907	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
908	C₂×C₂²⋊C₄	C₂²×D₅	1	16	yes	complemented
909	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
910	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
911	C₂×C₄²	—	5	1	no	—
912	C₂×C₄²	—	5	2	no	—
913	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
914	C₂×C₄²	C₂²×D₅	1	2	yes	complemented
915	C₂²×C₅	—	2	4	no	—
916	C₂²×C₅	—	2	4	no	—
917	C₂²×C₅	—	2	16	no	—
918	C₂²×C₅	—	2	4	no	—
919	C₂²×C₅	—	2	4	no	—
920	C₂²×C₅	—	2	2	no	—
921	C₂²×C₅	—	2	2	no	—
922	C₂²×C₅	—	4	16	no	—
923	C₂²×C₅	—	4	4	no	—
924	C₂²×C₅	—	4	4	no	—
925	C₂²×C₅	C₂×H(5,𝔽₂)	1	8	yes	—
926	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
927	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
928	C₂²×C₅	C₂⁶	1	1	yes	characteristic
929	C₂×D₅	—	2	4	no	—
930	C₂×D₅	—	2	8	no	—
931	C₂×D₅	—	2	4	no	—
932	C₂×D₅	—	2	4	no	—
933	C₂×D₅	—	2	4	no	—
934	C₂×D₅	—	2	4	no	—
935	C₂×D₅	—	2	4	no	—
936	C₂×D₅	—	2	4	no	—
937	C₂×D₅	—	2	2	no	—
938	C₂×D₅	—	2	4	no	—
939	C₂×D₅	—	2	4	no	—
940	C₂×D₅	—	2	4	no	—
941	C₂×D₅	—	2	4	no	—
942	C₂×D₅	—	2	4	no	—
943	C₂×D₅	—	2	2	no	—
944	C₂×D₅	—	4	32	no	—
945	C₂×D₅	—	4	16	no	—
946	C₂×D₅	—	4	32	no	—
947	C₂×D₅	—	4	16	no	—
948	C₂×D₅	—	4	8	no	—
949	C₂×D₅	—	4	4	no	—
950	C₂×D₅	—	4	8	no	—
951	C₂×D₅	—	4	4	no	—
952	C₂×D₅	—	4	8	no	—
953	C₂×D₅	—	8	8	no	—
954	C₂×D₅	—	8	16	no	—
955	C₂×D₅	—	8	8	no	—
956	C₂×D₅	C₂×H(5,𝔽₂)	1	4	yes	—
957	C₄×C₅	—	2	4	no	—
958	C₄×C₅	—	2	2	no	—
959	C₄×C₅	—	2	4	no	—
960	C₄×C₅	—	2	4	no	—
961	C₄×C₅	—	2	4	no	—
962	C₄×C₅	—	2	4	no	—
963	Dic₅	—	2	4	no	—
964	Dic₅	—	2	4	no	—
965	Dic₅	—	2	2	no	—
966	Dic₅	—	2	4	no	—
967	C₂⁴	—	2	8	no	—
968	C₂⁴	—	4	2	no	—
969	C₂⁴	—	5	1	no	—
970	C₂⁴	—	5	2	no	—
971	C₂⁴	—	5	1	no	—
972	C₂⁴	—	5	2	no	—
973	C₂⁴	—	5	1	no	—
974	C₂⁴	—	5	2	no	—
975	C₂⁴	—	5	8	no	—
976	C₂⁴	—	5	4	no	—
977	C₂⁴	—	5	8	no	—
978	C₂⁴	—	5	4	no	—
979	C₂⁴	—	5	8	no	—
980	C₂⁴	—	5	4	no	—
981	C₂⁴	—	5	4	no	—
982	C₂⁴	—	10	8	no	—
983	C₂⁴	—	10	4	no	—
984	C₂⁴	—	10	4	no	—
985	C₂⁴	—	10	8	no	—
986	C₂⁴	—	10	8	no	—
987	C₂⁴	—	10	8	no	—
988	C₂⁴	—	20	4	no	—
989	C₂⁴	—	20	4	no	—
990	C₂⁴	—	20	4	no	—
991	C₂⁴	—	20	4	no	—
992	C₂⁴	—	20	4	no	—
993	C₂⁴	—	20	32	no	—
994	C₂⁴	—	20	2	no	—
995	C₂⁴	—	20	4	no	—
996	C₂⁴	—	20	4	no	—
997	C₂⁴	—	20	4	no	—
998	C₂⁴	—	20	4	no	—
999	C₂⁴	—	20	2	no	—
1000	C₂⁴	—	20	16	no	—
1001	C₂⁴	—	20	64	no	—
1002	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1003	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1004	C₂⁴	C₂³×D₅	1	4	yes	—
1005	C₂⁴	C₂³×D₅	1	2	yes	—
1006	#41	—	20	32	no	—
1007	#41	—	20	16	no	—
1008	C₂×Q₈	—	4	2	no	—
1009	C₂×Q₈	—	5	8	no	—
1010	C₂×Q₈	—	20	4	no	—
1011	C₂×Q₈	C₂³×D₅	1	4	yes	complemented
1012	C₂×D₄	—	2	8	no	—
1013	C₂×D₄	—	4	2	no	—
1014	C₂×D₄	—	5	8	no	—
1015	C₂×D₄	—	5	8	no	—
1016	C₂×D₄	—	5	8	no	—
1017	C₂×D₄	—	5	4	no	—
1018	C₂×D₄	—	5	8	no	—
1019	C₂×D₄	—	5	8	no	—
1020	C₂×D₄	—	5	4	no	—
1021	C₂×D₄	—	5	8	no	—
1022	C₂×D₄	—	5	8	no	—
1023	C₂×D₄	—	5	8	no	—
1024	C₂×D₄	—	5	8	no	—
1025	C₂×D₄	—	5	8	no	—
1026	C₂×D₄	—	5	8	no	—
1027	C₂×D₄	—	5	8	no	—
1028	C₂×D₄	—	5	8	no	—
1029	C₂×D₄	—	5	8	no	—
1030	C₂×D₄	—	5	8	no	—
1031	C₂×D₄	—	5	4	no	—
1032	C₂×D₄	—	5	8	no	—
1033	C₂×D₄	—	5	4	no	—
1034	C₂×D₄	—	5	8	no	—
1035	C₂×D₄	—	5	8	no	—
1036	C₂×D₄	—	5	8	no	—
1037	C₂×D₄	—	10	8	no	—
1038	C₂×D₄	—	10	8	no	—
1039	C₂×D₄	—	10	8	no	—
1040	C₂×D₄	—	10	8	no	—
1041	C₂×D₄	—	10	8	no	—
1042	C₂×D₄	—	20	4	no	—
1043	C₂×D₄	—	20	4	no	—
1044	C₂×D₄	—	20	4	no	—
1045	C₂×D₄	—	20	4	no	—
1046	C₂×D₄	—	20	32	no	—
1047	C₂×D₄	—	20	4	no	—
1048	C₂×D₄	—	20	4	no	—
1049	C₂×D₄	—	20	4	no	—
1050	C₂×D₄	—	20	4	no	—
1051	C₂×D₄	—	20	4	no	—
1052	C₂×D₄	—	20	2	no	—
1053	C₂×D₄	—	20	4	no	—
1054	C₂×D₄	—	20	2	no	—
1055	C₂×D₄	—	20	32	no	—
1056	C₂×D₄	—	20	16	no	—
1057	C₂×D₄	—	20	16	no	—
1058	C₂×D₄	—	20	4	no	—
1059	C₂×D₄	—	20	4	no	—
1060	C₂×D₄	—	20	4	no	—
1061	C₂×D₄	—	20	4	no	—
1062	C₂×D₄	—	20	2	no	—
1063	C₂×D₄	—	20	2	no	—
1064	C₂×D₄	—	20	32	no	—
1065	C₂×D₄	—	20	32	no	—
1066	C₂×D₄	—	20	32	no	—
1067	C₂×D₄	C₂³×D₅	1	8	yes	—
1068	C₂×D₄	C₂³×D₅	1	4	yes	—
1069	C₂²×C₄	—	2	8	no	—
1070	C₂²×C₄	—	4	4	no	—
1071	C₂²×C₄	—	4	2	no	—
1072	C₂²×C₄	—	5	2	no	—
1073	C₂²×C₄	—	5	2	no	—
1074	C₂²×C₄	—	5	2	no	—
1075	C₂²×C₄	—	5	1	no	—
1076	C₂²×C₄	—	5	8	no	—
1077	C₂²×C₄	—	5	4	no	—
1078	C₂²×C₄	—	5	8	no	—
1079	C₂²×C₄	—	5	8	no	—
1080	C₂²×C₄	—	5	8	no	—
1081	C₂²×C₄	—	5	8	no	—
1082	C₂²×C₄	—	5	8	no	—
1083	C₂²×C₄	—	10	4	no	—
1084	C₂²×C₄	—	20	4	no	—
1085	C₂²×C₄	—	20	4	no	—
1086	C₂²×C₄	—	20	4	no	—
1087	C₂²×C₄	—	20	4	no	—
1088	C₂²×C₄	—	20	4	no	—
1089	C₂²×C₄	—	20	4	no	—
1090	C₂²×C₄	C₂³×D₅	1	8	yes	—
1091	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1092	C₂²×C₄	C₂³×D₅	1	2	yes	—
1093	C₂²×C₄	C₂³×D₅	1	2	yes	—
1094	C₂²×C₄	C₂³×D₅	1	2	yes	—
1095	C₂²×C₄	C₂³×D₅	1	2	yes	—
1096	C₂²×C₄	C₂³×D₅	1	2	yes	—
1097	C₂²×C₄	C₂³×D₅	1	8	yes	—
1098	C₂²×C₄	C₂³×D₅	1	4	yes	complemented
1099	C₄⋊C₄	—	5	8	no	—
1100	C₄⋊C₄	—	5	8	no	—
1101	C₄⋊C₄	—	5	8	no	—
1102	C₄⋊C₄	—	5	8	no	—
1103	C₄⋊C₄	—	5	8	no	—
1104	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1105	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1106	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1107	C₄⋊C₄	C₂³×D₅	1	8	yes	complemented
1108	C₂²⋊C₄	—	5	8	no	—
1109	C₂²⋊C₄	—	5	4	no	—
1110	C₂²⋊C₄	—	5	4	no	—
1111	C₂²⋊C₄	—	5	8	no	—
1112	C₂²⋊C₄	—	5	8	no	—
1113	C₂²⋊C₄	—	5	8	no	—
1114	C₂²⋊C₄	—	5	8	no	—
1115	C₂²⋊C₄	—	5	8	no	—
1116	C₂²⋊C₄	—	5	8	no	—
1117	C₂²⋊C₄	—	5	8	no	—
1118	C₂²⋊C₄	—	5	8	no	—
1119	C₂²⋊C₄	—	5	8	no	—
1120	C₂²⋊C₄	—	5	8	no	—
1121	C₂²⋊C₄	—	5	8	no	—
1122	C₂²⋊C₄	—	5	8	no	—
1123	C₂²⋊C₄	—	5	8	no	—
1124	C₂²⋊C₄	—	5	8	no	—
1125	C₂²⋊C₄	—	5	8	no	—
1126	C₂²⋊C₄	—	5	8	no	—
1127	C₂²⋊C₄	—	5	8	no	—
1128	C₂²⋊C₄	—	5	8	no	—
1129	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1130	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1131	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1132	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1133	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1134	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1135	C₂²⋊C₄	C₂³×D₅	1	4	yes	complemented
1136	C₂²⋊C₄	C₂³×D₅	1	8	yes	complemented
1137	C₄²	—	5	4	no	—
1138	C₄²	—	5	8	no	—
1139	C₄²	C₂³×D₅	1	4	yes	complemented
1140	C₄²	C₂³×D₅	1	8	yes	complemented
1141	C₂×C₅	—	2	8	no	—
1142	C₂×C₅	—	4	2	no	—
1143	C₂×C₅	—	4	2	no	—
1144	C₂×C₅	#3532	1	4	yes	complemented
1145	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
1146	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1147	D₅	—	2	4	no	—
1148	D₅	—	4	4	no	—
1149	D₅	—	4	2	no	—
1150	D₅	—	4	4	no	—
1151	D₅	—	4	2	no	—
1152	D₅	—	4	4	no	—
1153	C₂³	—	2	4	no	—
1154	C₂³	—	2	4	no	—
1155	C₂³	—	2	4	no	—
1156	C₂³	—	2	16	no	—
1157	C₂³	—	2	4	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	2	no	—
1160	C₂³	—	4	4	no	—
1161	C₂³	—	4	16	no	—
1162	C₂³	—	5	4	no	—
1163	C₂³	—	5	2	no	—
1164	C₂³	—	5	4	no	—
1165	C₂³	—	5	2	no	—
1166	C₂³	—	5	4	no	—
1167	C₂³	—	5	2	no	—
1168	C₂³	—	5	4	no	—
1169	C₂³	—	10	16	no	—
1170	C₂³	—	10	8	no	—
1171	C₂³	—	10	8	no	—
1172	C₂³	—	10	4	no	—
1173	C₂³	—	10	4	no	—
1174	C₂³	—	10	4	no	—
1175	C₂³	—	10	4	no	—
1176	C₂³	—	10	4	no	—
1177	C₂³	—	10	4	no	—
1178	C₂³	—	10	16	no	—
1179	C₂³	—	10	16	no	—
1180	C₂³	—	10	4	no	—
1181	C₂³	—	10	4	no	—
1182	C₂³	—	10	4	no	—
1183	C₂³	—	10	4	no	—
1184	C₂³	—	10	4	no	—
1185	C₂³	—	10	2	no	—
1186	C₂³	—	10	4	no	—
1187	C₂³	—	10	2	no	—
1188	C₂³	—	10	16	no	—
1189	C₂³	—	20	8	no	—
1190	C₂³	—	20	8	no	—
1191	C₂³	—	20	8	no	—
1192	C₂³	—	20	8	no	—
1193	C₂³	—	20	8	no	—
1194	C₂³	—	20	4	no	—
1195	C₂³	—	20	8	no	—
1196	C₂³	—	20	8	no	—
1197	C₂³	—	20	8	no	—
1198	C₂³	—	20	8	no	—
1199	C₂³	—	20	4	no	—
1200	C₂³	—	20	32	no	—
1201	C₂³	—	20	32	no	—
1202	C₂³	—	20	16	no	—
1203	C₂³	—	20	128	no	—
1204	C₂³	—	20	16	no	—
1205	C₂³	—	40	16	no	—
1206	C₂³	—	40	8	no	—
1207	C₂³	—	40	8	no	—
1208	C₂³	#4149	1	8	yes	—
1209	C₂³	C₂⁴×D₅	1	2	yes	—
1210	C₂³	C₂⁴×D₅	1	2	yes	—
1211	C₂³	C₂⁴×D₅	1	4	yes	—
1212	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1213	Q₈	—	4	4	no	—
1214	Q₈	—	20	8	no	—
1215	D₄	—	2	16	no	—
1216	D₄	—	4	4	no	—
1217	D₄	—	10	16	no	—
1218	D₄	—	10	16	no	—
1219	D₄	—	10	16	no	—
1220	D₄	—	10	16	no	—
1221	D₄	—	10	16	no	—
1222	D₄	—	20	8	no	—
1223	D₄	—	20	8	no	—
1224	D₄	—	20	8	no	—
1225	D₄	—	20	8	no	—
1226	D₄	—	20	8	no	—
1227	D₄	—	20	8	no	—
1228	D₄	—	20	8	no	—
1229	D₄	—	20	8	no	—
1230	D₄	—	20	8	no	—
1231	D₄	—	20	4	no	—
1232	D₄	—	20	8	no	—
1233	D₄	—	20	4	no	—
1234	D₄	—	20	8	no	—
1235	D₄	—	20	8	no	—
1236	D₄	—	20	8	no	—
1237	D₄	—	20	8	no	—
1238	D₄	—	20	4	no	—
1239	D₄	—	20	4	no	—
1240	C₂×C₄	—	2	4	no	—
1241	C₂×C₄	—	2	4	no	—
1242	C₂×C₄	—	2	16	no	—
1243	C₂×C₄	—	2	4	no	—
1244	C₂×C₄	—	2	4	no	—
1245	C₂×C₄	—	2	4	no	—
1246	C₂×C₄	—	2	2	no	—
1247	C₂×C₄	—	4	8	no	—
1248	C₂×C₄	—	4	4	no	—
1249	C₂×C₄	—	5	4	no	—
1250	C₂×C₄	—	5	4	no	—
1251	C₂×C₄	—	5	4	no	—
1252	C₂×C₄	—	5	2	no	—
1253	C₂×C₄	—	10	8	no	—
1254	C₂×C₄	—	10	4	no	—
1255	C₂×C₄	—	10	4	no	—
1256	C₂×C₄	—	10	4	no	—
1257	C₂×C₄	—	10	2	no	—
1258	C₂×C₄	—	20	8	no	—
1259	C₂×C₄	—	20	8	no	—
1260	C₂×C₄	—	20	8	no	—
1261	C₂×C₄	—	20	8	no	—
1262	C₂×C₄	—	20	8	no	—
1263	C₂×C₄	—	20	8	no	—
1264	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1265	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1266	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1267	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1268	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1269	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1270	C₅	C₂×#3532	1	1	yes	characteristic, complemented, Sylow
1271	C₂²	—	2	4	no	—
1272	C₂²	—	2	4	no	—
1273	C₂²	—	2	16	no	—
1274	C₂²	—	2	4	no	—
1275	C₂²	—	2	4	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	4	16	no	—
1279	C₂²	—	4	4	no	—
1280	C₂²	—	4	4	no	—
1281	C₂²	—	5	4	no	—
1282	C₂²	—	10	4	no	—
1283	C₂²	—	10	8	no	—
1284	C₂²	—	10	4	no	—
1285	C₂²	—	10	4	no	—
1286	C₂²	—	10	4	no	—
1287	C₂²	—	10	4	no	—
1288	C₂²	—	10	4	no	—
1289	C₂²	—	10	4	no	—
1290	C₂²	—	10	4	no	—
1291	C₂²	—	10	4	no	—
1292	C₂²	—	10	4	no	—
1293	C₂²	—	10	4	no	—
1294	C₂²	—	10	2	no	—
1295	C₂²	—	10	4	no	—
1296	C₂²	—	10	2	no	—
1297	C₂²	—	20	32	no	—
1298	C₂²	—	20	32	no	—
1299	C₂²	—	20	16	no	—
1300	C₂²	—	20	16	no	—
1301	C₂²	—	20	8	no	—
1302	C₂²	—	20	4	no	—
1303	C₂²	—	20	8	no	—
1304	C₂²	—	20	4	no	—
1305	C₂²	—	20	8	no	—
1306	C₂²	—	40	16	no	—
1307	C₂²	—	40	8	no	—
1308	C₂²	—	40	8	no	—
1309	C₂²	C₂×#4149	1	8	yes	—
1310	C₂²	C₂×#4149	1	4	yes	—
1311	C₂²	D₅×H(5,𝔽₂)	1	2	yes	—
1312	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1313	C₄	—	2	4	no	—
1314	C₄	—	2	4	no	—
1315	C₄	—	2	4	no	—
1316	C₄	—	2	4	no	—
1317	C₄	—	2	4	no	—
1318	C₄	—	2	2	no	—
1319	C₄	—	10	4	no	—
1320	C₄	—	10	4	no	—
1321	C₄	—	10	4	no	—
1322	C₄	—	10	2	no	—
1323	C₂	—	2	8	no	—
1324	C₂	—	4	2	no	—
1325	C₂	—	4	2	no	—
1326	C₂	—	10	4	no	—
1327	C₂	—	20	4	no	—
1328	C₂	—	20	2	no	—
1329	C₂	—	20	4	no	—
1330	C₂	—	20	2	no	—
1331	C₂	—	20	4	no	—
1332	C₂	#10618719	1	4	yes	direct product factor
1333	C₂	C₂²×#4149	1	2	yes	—
1334	C₂	C₂×D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#551	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#551	D₅
hypocenter	C₅	C₂×#3532
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#551

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×#551	C₂	semidirect
2. #10618719	C₂	direct (N × H)
3. C₂×#66045	C₂	semidirect
4. C₂×#66038	C₂	semidirect
5. C₂×#66017	C₂	semidirect
6. C₂×#66008	C₂	semidirect
7. C₂×#66000	C₂	semidirect
8. C₂×#65988	C₂	semidirect
9. C₂×#65987	C₂	semidirect
10. C₂×#65987	C₂	semidirect
11. C₂×#65964	C₂	semidirect
12. C₂×#65978	C₂	semidirect
13. C₂×#65924	C₂	semidirect
14. C₂×D₅×#120	C₂	semidirect
15. C₂×D₄×D₂₀	C₂	semidirect
16. C₂×#65894	C₂	semidirect
17. C₂×#65861	C₂	semidirect
18. C₂×#65859	C₂	semidirect
19. C₂×#65824	C₂	semidirect
20. C₂²×#4028	C₂	semidirect
21. C₂⁵×D₅	C₂²	semidirect
22. C₂³×C₂²⋊D₅	C₂²	semidirect
23. C₂²×#713	C₂²	semidirect
24. C₂²×D₄×D₅	C₂²	semidirect
25. C₂²×D₄×D₅	C₂²	semidirect
26. C₂²×D₄×D₅	C₂²	semidirect
27. C₂²×#709	C₂²	semidirect
28. C₂³×D₂₀	C₂²	semidirect
29. C₂³×D₂₀	C₂²	semidirect
30. C₂³×D₂₀	C₂²	semidirect
31. C₅×#551	C₂²	semidirect
32. C₂×C₅×#126	C₂²	semidirect
33. C₂×C₅×#124	C₂²	semidirect
34. C₂×C₅×#123	C₂²	semidirect
35. C₂×C₅×#123	C₂²	semidirect
36. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×C₅×D₄	C₂²	semidirect
39. C₂×C₅×#117	C₂²	semidirect
40. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₂×#4099	C₂²	semidirect
42. C₂×#4093	C₂²	semidirect
43. C₂×#4093	C₂²	semidirect
44. C₂×#4086	C₂²	semidirect
45. C₂×#4085	C₂²	semidirect
46. C₂×#4083	C₂²	semidirect
47. C₂×#4083	C₂²	semidirect
48. C₂×#4083	C₂²	semidirect
49. C₂×#4076	C₂²	semidirect
50. C₂×#4076	C₂²	semidirect
51. C₂×#4075	C₂²	semidirect
52. C₂×#4075	C₂²	semidirect
53. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
54. C₂²×#685	C₂²	semidirect
55. C₂²×#685	C₂²	semidirect
56. #66045	C₂²	semidirect
57. #66038	C₂²	semidirect
58. #66017	C₂²	semidirect
59. #66008	C₂²	semidirect
60. #66000	C₂²	semidirect
61. #65988	C₂²	semidirect
62. #65987	C₂²	semidirect
63. #65987	C₂²	semidirect
64. #65978	C₂²	semidirect
65. #65964	C₂²	semidirect
66. #65924	C₂²	semidirect
67. D₅×#120	C₂²	semidirect
68. #65894	C₂²	semidirect
69. D₄×D₂₀	C₂²	semidirect
70. #65861	C₂²	semidirect
71. #65859	C₂²	semidirect
72. C₂×#4044	C₂²	semidirect
73. C₂×#4044	C₂²	semidirect
74. C₂×#4042	C₂²	semidirect
75. C₂×#4041	C₂²	semidirect
76. C₂×#4041	C₂²	semidirect
77. C₂×#4041	C₂²	semidirect
78. C₂×#4041	C₂²	semidirect
79. C₂×#4041	C₂²	semidirect
80. C₂×#4041	C₂²	semidirect
81. C₂×#4041	C₂²	semidirect
82. C₂×#4040	C₂²	semidirect
83. C₂×#4040	C₂²	semidirect
84. C₂×#4040	C₂²	semidirect
85. C₂×#4040	C₂²	semidirect
86. C₂×#4040	C₂²	semidirect
87. C₂×#4039	C₂²	semidirect
88. C₂×#4031	C₂²	semidirect
89. C₂×#4031	C₂²	semidirect
90. #65824	C₂²	semidirect
91. C₂×#4030	C₂²	semidirect
92. C₂×#4030	C₂²	semidirect
93. C₂×#4030	C₂²	semidirect
94. C₂×#4030	C₂²	semidirect
95. C₂×#4030	C₂²	semidirect
96. C₂×#4029	C₂²	semidirect
98. C₂×#4028	C₂²	semidirect
99. C₂×#4028	C₂²	semidirect
100. C₂×#4028	C₂²	semidirect
101. C₂×#4028	C₂²	semidirect
102. C₂×#4028	C₂²	semidirect
103. C₂×#4028	C₂²	semidirect
104. C₂×#4028	C₂²	semidirect
105. C₂×#4028	C₂²	semidirect
106. C₂×#4028	C₂²	semidirect
107. C₂×#4028	C₂²	semidirect
108. C₂×#4028	C₂²	semidirect
109. C₂×#4028	C₂²	semidirect
110. C₂×#4028	C₂²	semidirect
111. C₂×#4028	C₂²	semidirect
112. C₂×#4028	C₂²	semidirect
113. C₂×#4027	C₂²	semidirect
114. C₂×#4027	C₂²	semidirect
115. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
116. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
117. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
118. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
119. C₂×#4024	C₂²	semidirect
120. C₂×#4022	C₂²	semidirect
121. C₂×#4021	C₂²	semidirect
122. C₂×#4021	C₂²	semidirect
123. C₂×#4020	C₂²	semidirect
124. C₂×#4020	C₂²	semidirect
125. C₂×C₄×D₂₀	C₂²	semidirect
126. C₂×#4018	C₂²	semidirect
137. C₂⁴×D₅	C₂³	semidirect
138. C₂⁴×D₅	C₂³	semidirect
139. C₂²×C₅×Q₈	C₂³	semidirect
144. C₂³×C₄×C₅	C₂³	semidirect
154. C₂²×C₂²⋊D₅	C₂³	semidirect
155. C₂²×C₂²⋊D₅	C₂³	semidirect
158. C₂×#713	C₂³	semidirect
162. C₂×D₄×D₅	C₂³	semidirect
163. C₂×D₄×D₅	C₂³	semidirect
164. C₂×D₄×D₅	C₂³	semidirect
166. C₂×#709	C₂³	semidirect
180. C₂²×D₂₀	C₂³	semidirect
181. C₂²×D₂₀	C₂³	semidirect
182. C₂²×D₂₀	C₂³	semidirect
183. C₂²×D₂₀	C₂³	semidirect
184. C₂²×D₂₀	C₂³	semidirect
185. C₂²×D₂₀	C₂³	semidirect
186. C₂²×D₂₀	C₂³	semidirect
189. C₂²×C₄×D₅	C₂³	semidirect
190. C₂²×C₄×D₅	C₂³	semidirect
191. C₂²×C₄×D₅	C₂³	semidirect
192. C₂²×C₄×D₅	C₂³	semidirect
193. C₂²×Dic₁₀	C₂³	semidirect
194. C₅×#126	C₂³	semidirect
195. C₅×#124	C₂³	semidirect
196. C₅×#123	C₂³	semidirect
197. C₅×#123	C₂³	semidirect
198. C₅×C₂²⋊Q₈	C₂³	semidirect
200. C₄×C₅×D₄	C₂³	semidirect
201. C₅×#117	C₂³	semidirect
202. C₂×C₅×C₄⋊C₄	C₂³	semidirect
203. C₂×C₅×C₄⋊C₄	C₂³	semidirect
204. C₂×C₅×C₄⋊C₄	C₂³	semidirect
205. C₂×C₅×C₄⋊C₄	C₂³	semidirect
212. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
213. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
214. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
215. C₂×C₄²×C₅	C₂³	semidirect
216. C₂×C₄²×C₅	C₂³	semidirect
217. #4099	C₂³	semidirect
220. C₂×C₂²⋊Dic₅	C₂³	semidirect
221. #4093	C₂³	semidirect
222. #4093	C₂³	semidirect
223. #4086	C₂³	semidirect
224. #4085	C₂³	semidirect
225. #4083	C₂³	semidirect
226. #4083	C₂³	semidirect
227. #4083	C₂³	semidirect
228. #4076	C₂³	semidirect
229. #4076	C₂³	semidirect
230. #4075	C₂³	semidirect
231. #4075	C₂³	semidirect
232. C₄×C₂²⋊D₅	C₂³	semidirect
244. C₂×#685	C₂³	semidirect
245. C₂×#685	C₂³	semidirect
246. C₂×#685	C₂³	semidirect
247. C₂×#685	C₂³	semidirect
248. C₂×#685	C₂³	semidirect
249. C₂×#685	C₂³	semidirect
250. C₂×#685	C₂³	semidirect
251. C₂×#685	C₂³	semidirect
252. C₂×#685	C₂³	semidirect
253. C₂×C₄⋊Dic₅	C₂³	semidirect
254. C₂×#683	C₂³	semidirect
255. C₂×#683	C₂³	semidirect
256. C₂×#683	C₂³	semidirect
257. C₂×#683	C₂³	semidirect
258. C₂×C₄×Dic₅	C₂³	semidirect
259. C₂×C₄×Dic₅	C₂³	semidirect
260. #4044	C₂³	semidirect
261. #4044	C₂³	semidirect
262. #4042	C₂³	semidirect
263. #4041	C₂³	semidirect
264. #4041	C₂³	semidirect
265. #4041	C₂³	semidirect
266. #4041	C₂³	semidirect
267. #4041	C₂³	semidirect
268. #4041	C₂³	semidirect
269. #4041	C₂³	semidirect
270. #4040	C₂³	semidirect
271. #4040	C₂³	semidirect
272. #4040	C₂³	semidirect
273. #4040	C₂³	semidirect
274. #4040	C₂³	semidirect
275. #4039	C₂³	semidirect
276. #4031	C₂³	semidirect
277. #4031	C₂³	semidirect
278. #4030	C₂³	semidirect
279. #4030	C₂³	semidirect
280. #4030	C₂³	semidirect
281. #4030	C₂³	semidirect
282. #4030	C₂³	semidirect
283. #4029	C₂³	semidirect
285. #4028	C₂³	semidirect
286. #4028	C₂³	semidirect
287. #4028	C₂³	semidirect
288. #4028	C₂³	semidirect
289. #4028	C₂³	semidirect
290. #4028	C₂³	semidirect
291. #4028	C₂³	semidirect
292. #4028	C₂³	semidirect
293. #4028	C₂³	semidirect
294. #4028	C₂³	semidirect
295. #4028	C₂³	semidirect
296. #4028	C₂³	semidirect
297. #4028	C₂³	semidirect
298. #4028	C₂³	semidirect
299. #4027	C₂³	semidirect
300. #4027	C₂³	semidirect
301. D₅×C₂²⋊C₄	C₂³	semidirect
302. D₅×C₂²⋊C₄	C₂³	semidirect
303. D₅×C₂²⋊C₄	C₂³	semidirect
304. D₅×C₂²⋊C₄	C₂³	semidirect
305. #4024	C₂³	semidirect
306. #4022	C₂³	semidirect
307. #4021	C₂³	semidirect
308. #4021	C₂³	semidirect
309. #4020	C₂³	semidirect
310. #4020	C₂³	semidirect
311. C₄×D₂₀	C₂³	semidirect
312. #4018	C₂³	semidirect
318. C₂×#551	D₅	semidirect
371. C₂³×D₅	C₂⁴	semidirect
373. C₂×C₅×Q₈	C₂⁴	semidirect
389. C₂²×C₄×C₅	C₂⁴	semidirect
408. C₂×C₂²⋊D₅	C₂⁴	semidirect
447. C₂×D₂₀	C₂⁴	semidirect
448. C₂×D₂₀	C₂⁴	semidirect
449. C₂×D₂₀	C₂⁴	semidirect
450. C₂×D₂₀	C₂⁴	semidirect
459. C₂×C₄×D₅	C₂⁴	semidirect
460. C₂×C₄×D₅	C₂⁴	semidirect
461. C₂×C₄×D₅	C₂⁴	semidirect
462. C₂×C₄×D₅	C₂⁴	semidirect
464. C₂×Dic₁₀	C₂⁴	semidirect
465. C₅×C₄⋊C₄	C₂⁴	semidirect
466. C₅×C₄⋊C₄	C₂⁴	semidirect
467. C₅×C₄⋊C₄	C₂⁴	semidirect
468. C₅×C₄⋊C₄	C₂⁴	semidirect
475. C₅×C₂²⋊C₄	C₂⁴	semidirect
476. C₅×C₂²⋊C₄	C₂⁴	semidirect
477. C₄²×C₅	C₂⁴	semidirect
478. C₄²×C₅	C₂⁴	semidirect
481. C₂²⋊Dic₅	C₂⁴	semidirect
493. #685	C₂⁴	semidirect
494. #685	C₂⁴	semidirect
495. #685	C₂⁴	semidirect
496. #685	C₂⁴	semidirect
497. #685	C₂⁴	semidirect
498. #685	C₂⁴	semidirect
499. #685	C₂⁴	semidirect
500. C₄⋊Dic₅	C₂⁴	semidirect
501. #683	C₂⁴	semidirect
502. #683	C₂⁴	semidirect
503. #683	C₂⁴	semidirect
504. #683	C₂⁴	semidirect
505. C₄×Dic₅	C₂⁴	semidirect
506. C₄×Dic₅	C₂⁴	semidirect
521. #551	C₂×D₅	semidirect
540. C₂×#126	C₂×D₅	semidirect
547. C₂×#124	C₂×D₅	semidirect
556. C₂×#123	C₂×D₅	semidirect
557. C₂×#123	C₂×D₅	semidirect
560. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
603. C₂×C₄×D₄	C₂×D₅	semidirect
605. C₂×#117	C₂×D₅	semidirect
612. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
746. C₂²×Q₈	C₂²×D₅	semidirect
795. C₂³×C₄	C₂²×D₅	semidirect
802. #126	C₂²×D₅	semidirect
809. #124	C₂²×D₅	semidirect
818. #123	C₂²×D₅	semidirect
819. #123	C₂²×D₅	semidirect
822. C₂²⋊Q₈	C₂²×D₅	semidirect
863. C₄×D₄	C₂²×D₅	semidirect
865. #117	C₂²×D₅	semidirect
871. C₂×C₄⋊C₄	C₂²×D₅	semidirect
872. C₂×C₄⋊C₄	C₂²×D₅	semidirect
873. C₂×C₄⋊C₄	C₂²×D₅	semidirect
874. C₂×C₄⋊C₄	C₂²×D₅	semidirect
908. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
909. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
910. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
913. C₂×C₄²	C₂²×D₅	semidirect
914. C₂×C₄²	C₂²×D₅	semidirect
1011. C₂×Q₈	C₂³×D₅	semidirect
1098. C₂²×C₄	C₂³×D₅	semidirect
1104. C₄⋊C₄	C₂³×D₅	semidirect
1105. C₄⋊C₄	C₂³×D₅	semidirect
1106. C₄⋊C₄	C₂³×D₅	semidirect
1107. C₄⋊C₄	C₂³×D₅	semidirect
1135. C₂²⋊C₄	C₂³×D₅	semidirect
1136. C₂²⋊C₄	C₂³×D₅	semidirect
1139. C₄²	C₂³×D₅	semidirect
1140. C₄²	C₂³×D₅	semidirect
1144. C₂×C₅	#3532	semidirect
1270. C₅	C₂×#3532	semidirect
1332. C₂	#10618719	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#551	2
#10618719	2
C₂×#66045	2
C₂×#66038	2
C₂×#66017	2
C₂×#66008	2
C₂×#66000	2
C₂×#65988	2
C₂×#65987	2
C₂×#65964	2
C₂×#65978	2
C₂×#65924	2
C₂×D₅×#120	2
C₂×D₄×D₂₀	2
C₂×#65894	2
C₂×#65861	2
C₂×#65859	2
C₂×#65824	2
C₂²×#4028	2
C₂×#3532	5

Subgroups — C2×#10618719 #13006424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618719 #13006424