Subgroups — C₂×#10618073 #13006890

Order 1280.

8814 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618073	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66045	C₂	1	4	yes	maximal, complemented
4	C₂×#66032	C₂	1	2	yes	maximal, complemented
5	C₂×#66008	C₂	1	2	yes	maximal, complemented
6	C₂×#65987	C₂	1	4	yes	maximal, complemented
7	C₂×#65964	C₂	1	2	yes	maximal, complemented
8	C₂×#65943	C₂	1	2	yes	maximal, complemented
9	C₂×#65919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65911	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#65884	C₂	1	2	yes	maximal, complemented
12	C₂×D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₄×D₂₀	C₂	1	2	yes	maximal, complemented
14	C₂×#65887	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#65869	C₂	1	2	yes	maximal, complemented
16	C₂×#65859	C₂	1	2	yes	maximal, complemented
17	C₂²×#4020	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65813	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#713	C₂²	1	2	yes	complemented
20	C₂²×D₄×D₅	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₅	C₂²	1	2	yes	complemented
22	C₂²×#709	C₂²	1	2	yes	complemented
23	C₂³×D₂₀	C₂²	1	2	yes	complemented
24	C₂³×D₂₀	C₂²	1	2	yes	complemented
25	C₂³×D₂₀	C₂²	1	2	yes	complemented
26	C₂³×D₂₀	C₂²	1	2	yes	complemented
27	C₅×#529	C₂²	1	16	yes	complemented
28	C₂×C₅×#126	C₂²	1	2	yes	complemented
29	C₂×C₅×#125	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#124	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#123	C₂²	1	2	yes	complemented
32	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#121	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₂×C₅×#117	C₂²	1	2	yes	complemented
38	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
39	C₂×#4093	C₂²	1	2	yes	complemented
40	C₂×#4086	C₂²	1	2	yes	complemented
41	C₂×#4083	C₂²	1	4	yes	complemented
42	C₂×#4076	C₂²	1	1	yes	characteristic
43	C₂×#4076	C₂²	1	2	yes	complemented
44	C₂×#4076	C₂²	1	2	yes	complemented
45	C₂×#4075	C₂²	1	2	yes	complemented
46	C₂×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
47	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
48	#66045	C₂²	1	64	yes	complemented
49	#66032	C₂²	1	32	yes	complemented
50	#66008	C₂²	1	32	yes	complemented
51	#65987	C₂²	1	64	yes	complemented
52	#65964	C₂²	1	32	yes	complemented
53	#65943	C₂²	1	32	yes	complemented
54	#65919	C₂²	1	16	yes	complemented
55	#65911	C₂²	1	16	yes	complemented
56	#65887	C₂²	1	16	yes	complemented
57	#65884	C₂²	1	32	yes	complemented
58	D₄×D₂₀	C₂²	1	16	yes	complemented
59	D₄×D₂₀	C₂²	1	32	yes	complemented
60	#65869	C₂²	1	32	yes	complemented
61	#65859	C₂²	1	32	yes	complemented
62	C₂×#4041	C₂²	1	4	yes	complemented
63	C₂×#4041	C₂²	1	2	yes	complemented
64	C₂×#4041	C₂²	1	4	yes	complemented
65	C₂×#4041	C₂²	1	4	yes	complemented
66	C₂×#4041	C₂²	1	4	yes	complemented
67	C₂×#4041	C₂²	1	2	yes	complemented
68	C₂×#4040	C₂²	1	4	yes	complemented
69	C₂×#4040	C₂²	1	4	yes	complemented
70	C₂×#4040	C₂²	1	4	yes	complemented
71	C₂×#4040	C₂²	1	4	yes	complemented
72	C₂×#4039	C₂²	1	2	yes	complemented
73	C₂×#4039	C₂²	1	2	yes	complemented
74	C₂×#4030	C₂²	1	4	yes	complemented
75	C₂×#4030	C₂²	1	4	yes	complemented
76	C₂×#4030	C₂²	1	4	yes	complemented
77	C₂×#4030	C₂²	1	4	yes	complemented
78	C₂×#4028	C₂²	1	4	yes	complemented
79	C₂×#4028	C₂²	1	4	yes	complemented
80	C₂×#4028	C₂²	1	4	yes	complemented
81	C₂×#4028	C₂²	1	4	yes	complemented
82	C₂×#4028	C₂²	1	4	yes	complemented
83	C₂×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	#65813	C₂²	1	16	yes	complemented
85	C₂×#4022	C₂²	1	2	yes	complemented
86	C₂×#4021	C₂²	1	1	yes	characteristic, complemented
87	C₂×#4021	C₂²	1	2	yes	complemented
88	C₂×#4020	C₂²	1	1	yes	characteristic
89	C₂×#4020	C₂²	1	2	yes	complemented
90	C₂×#4020	C₂²	1	2	yes	complemented
91	C₂×#4020	C₂²	1	1	yes	characteristic, complemented
92	C₂×#4020	C₂²	1	2	yes	complemented
93	C₂×#4020	C₂²	1	2	yes	complemented
94	C₂×#4020	C₂²	1	16	yes	complemented
95	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
96	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
97	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
98	C₂×#4018	C₂²	1	2	yes	complemented
99	C₂×#4016	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
101	C₂×#3543	—	5	1	no	maximal, Sylow
102	C₂⁴×D₅	C₂³	1	4	yes	—
103	C₂⁴×D₅	C₂³	1	4	yes	—
104	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂³	1	2	yes	—
106	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂³	1	2	yes	—
111	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
112	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₅	C₂³	1	4	yes	—
115	C₂×#713	—	4	8	no	—
116	C₂×#713	C₂³	1	16	yes	complemented
117	C₂×D₄×D₅	—	4	8	no	—
118	C₂×D₄×D₅	—	4	16	no	—
119	C₂×D₄×D₅	C₂³	1	32	yes	complemented
120	C₂×D₄×D₅	C₂³	1	16	yes	complemented
121	C₂×#709	—	4	8	no	—
122	C₂×#709	C₂³	1	16	yes	complemented
123	C₂²×D₂₀	—	4	8	no	—
124	C₂²×D₂₀	—	4	8	no	—
125	C₂²×D₂₀	—	4	8	no	—
126	C₂²×D₂₀	—	4	8	no	—
127	C₂²×D₂₀	C₂³	1	2	yes	—
128	C₂²×D₂₀	C₂³	1	2	yes	—
129	C₂²×D₂₀	C₂³	1	1	yes	characteristic
130	C₂²×D₂₀	C₂³	1	2	yes	—
131	C₂²×D₂₀	C₂³	1	2	yes	—
132	C₂²×D₂₀	C₂³	1	2	yes	—
133	C₂²×D₂₀	C₂³	1	4	yes	—
134	C₂²×D₂₀	C₂³	1	4	yes	—
135	C₂²×D₂₀	C₂³	1	4	yes	—
136	C₂²×D₂₀	C₂³	1	2	yes	—
137	C₂²×D₂₀	C₂³	1	4	yes	—
138	C₂²×D₂₀	C₂³	1	4	yes	—
139	C₂²×D₂₀	C₂³	1	4	yes	—
140	C₂²×D₂₀	C₂³	1	16	yes	complemented
141	C₂²×D₂₀	C₂³	1	16	yes	complemented
142	C₂²×D₂₀	C₂³	1	16	yes	complemented
143	C₂²×D₂₀	C₂³	1	16	yes	complemented
144	C₂²×C₄×D₅	C₂³	1	2	yes	—
145	C₂²×C₄×D₅	C₂³	1	4	yes	—
146	C₂²×C₄×D₅	C₂³	1	4	yes	—
147	C₂²×C₄×D₅	C₂³	1	4	yes	—
148	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
149	C₅×#126	C₂³	1	16	yes	complemented
150	C₅×#125	C₂³	1	8	yes	complemented
151	C₅×#124	C₂³	1	8	yes	complemented
152	C₅×#123	C₂³	1	16	yes	complemented
153	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
154	C₅×#121	C₂³	1	8	yes	—
155	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
156	C₄×C₅×D₄	C₂³	1	16	yes	complemented
157	C₄×C₅×D₄	C₂³	1	8	yes	complemented
158	C₅×#117	C₂³	1	16	yes	complemented
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅	C₂³	1	2	yes	—
174	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
176	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
177	#4093	C₂³	1	16	yes	complemented
178	#4086	C₂³	1	16	yes	complemented
179	#4083	C₂³	1	32	yes	complemented
180	#4076	C₂³	1	8	yes	—
181	#4076	C₂³	1	16	yes	complemented
182	#4076	C₂³	1	16	yes	complemented
183	#4075	C₂³	1	16	yes	complemented
184	C₄×C₂²⋊D₅	C₂³	1	16	yes	complemented
185	C₂×#685	C₂³	1	2	yes	—
186	C₂×#685	C₂³	1	2	yes	—
187	C₂×#685	C₂³	1	2	yes	—
188	C₂×#685	C₂³	1	4	yes	—
189	C₂×#685	C₂³	1	4	yes	—
190	C₂×#685	C₂³	1	2	yes	—
191	C₂×#685	C₂³	1	4	yes	—
192	C₂×#685	C₂³	1	4	yes	—
193	C₂×#685	C₂³	1	4	yes	—
194	C₂×#685	C₂³	1	4	yes	—
195	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
197	#4070	C₂³	1	8	yes	complemented
198	C₂×#683	C₂³	1	2	yes	—
199	C₂×#683	C₂³	1	2	yes	—
200	C₂×#683	C₂³	1	2	yes	—
201	C₂×#683	C₂³	1	2	yes	—
202	C₂×C₄×Dic₅	C₂³	1	2	yes	—
203	#4041	C₂³	1	32	yes	complemented
204	#4041	C₂³	1	32	yes	complemented
205	#4041	C₂³	1	16	yes	complemented
206	#4041	C₂³	1	32	yes	complemented
207	#4041	C₂³	1	16	yes	complemented
208	#4041	C₂³	1	32	yes	complemented
209	#4040	C₂³	1	32	yes	complemented
210	#4040	C₂³	1	32	yes	complemented
211	#4040	C₂³	1	32	yes	complemented
212	#4040	C₂³	1	32	yes	complemented
213	#4039	C₂³	1	16	yes	complemented
214	#4039	C₂³	1	16	yes	complemented
215	#4030	C₂³	1	32	yes	complemented
216	#4030	C₂³	1	32	yes	complemented
217	#4030	C₂³	1	32	yes	complemented
218	#4030	C₂³	1	32	yes	complemented
219	#4028	C₂³	1	32	yes	complemented
220	#4028	C₂³	1	32	yes	complemented
221	#4028	C₂³	1	32	yes	complemented
222	#4028	C₂³	1	32	yes	complemented
223	#4028	C₂³	1	32	yes	complemented
224	D₅×C₂²⋊C₄	C₂³	1	32	yes	complemented
225	#4022	C₂³	1	16	yes	complemented
226	#4021	C₂³	1	8	yes	complemented
227	#4021	C₂³	1	16	yes	complemented
228	#4020	C₂³	1	8	yes	—
229	#4020	C₂³	1	16	yes	complemented
230	#4020	C₂³	1	8	yes	complemented
231	#4020	C₂³	1	16	yes	complemented
232	#4020	C₂³	1	16	yes	complemented
233	#4020	C₂³	1	16	yes	complemented
234	C₄×D₂₀	C₂³	1	8	yes	complemented
235	C₄×D₂₀	C₂³	1	16	yes	complemented
236	C₄×D₂₀	C₂³	1	16	yes	complemented
237	#4018	C₂³	1	16	yes	complemented
238	#4016	C₂³	1	8	yes	complemented
239	C₄×Dic₁₀	C₂³	1	8	yes	complemented
240	#3543	—	5	32	no	—
241	C₂×#560	—	5	4	no	—
242	C₂×#559	—	5	1	no	—
243	C₂×#550	—	5	1	no	—
244	C₂×#550	—	5	1	no	—
245	C₂×#546	—	5	2	no	—
246	C₂×#546	—	5	2	no	—
247	C₂×D₄²	—	5	2	no	—
248	C₂×D₄²	—	5	1	no	—
249	C₂×D₄²	—	5	2	no	—
250	C₂×#540	—	5	2	no	—
251	C₂×#540	—	5	2	no	—
252	C₂×#535	—	5	2	no	—
253	C₂×#535	—	5	2	no	—
254	C₂×#534	—	5	4	no	—
255	C₂²×#127	—	5	1	no	—
256	C₂×#529	—	5	1	no	—
257	C₂×#529	D₅	1	1	yes	characteristic, complemented
258	C₂⁴×C₅	C₂⁴	1	2	yes	—
259	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
260	C₂³×D₅	—	2	16	no	—
261	C₂³×D₅	—	4	8	no	—
262	C₂³×D₅	—	4	8	no	—
263	C₂³×D₅	—	4	8	no	—
264	C₂³×D₅	—	4	8	no	—
265	C₂³×D₅	—	4	8	no	—
266	C₂³×D₅	C₂⁴	1	4	yes	—
267	C₂³×D₅	C₂⁴	1	2	yes	—
268	C₂³×D₅	C₂⁴	1	4	yes	—
269	C₂³×D₅	C₂⁴	1	16	yes	—
270	C₂³×D₅	C₂⁴	1	16	yes	—
271	C₂×C₅×Q₈	—	2	4	no	—
272	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
273	C₂×C₅×D₄	—	2	8	no	—
274	C₂×C₅×D₄	—	2	4	no	—
275	C₂×C₅×D₄	C₂⁴	1	8	yes	—
276	C₂×C₅×D₄	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₅	—	2	4	no	—
278	C₂²×C₄×C₅	—	2	4	no	—
279	C₂²×C₄×C₅	—	2	4	no	—
280	C₂²×C₄×C₅	—	2	8	no	—
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂×C₂²⋊D₅	—	2	8	no	—
295	C₂×C₂²⋊D₅	—	4	8	no	—
296	C₂×C₂²⋊D₅	—	4	8	no	—
297	C₂×C₂²⋊D₅	—	4	8	no	—
298	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
299	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
300	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
301	C₂×C₂²⋊D₅	C₂⁴	1	16	yes	—
302	C₂²×Dic₅	C₂⁴	1	2	yes	—
303	C₂²×Dic₅	C₂⁴	1	2	yes	—
304	C₂²×Dic₅	C₂⁴	1	2	yes	—
305	#713	—	4	32	no	—
306	D₄×D₅	—	4	32	no	—
307	D₄×D₅	—	4	64	no	—
308	#709	—	4	32	no	—
309	C₂×D₂₀	—	2	8	no	—
310	C₂×D₂₀	—	2	4	no	—
311	C₂×D₂₀	—	2	8	no	—
312	C₂×D₂₀	—	2	8	no	—
313	C₂×D₂₀	—	2	8	no	—
314	C₂×D₂₀	—	4	32	no	—
315	C₂×D₂₀	—	4	32	no	—
316	C₂×D₂₀	—	4	32	no	—
317	C₂×D₂₀	—	4	8	no	—
318	C₂×D₂₀	—	4	8	no	—
319	C₂×D₂₀	—	4	8	no	—
320	C₂×D₂₀	—	4	4	no	—
321	C₂×D₂₀	—	4	8	no	—
322	C₂×D₂₀	—	4	4	no	—
323	C₂×D₂₀	—	4	32	no	—
324	C₂×D₂₀	—	4	8	no	—
325	C₂×D₂₀	—	4	8	no	—
326	C₂×D₂₀	C₂⁴	1	8	yes	—
327	C₂×D₂₀	C₂⁴	1	4	yes	—
328	C₂×D₂₀	C₂⁴	1	8	yes	—
329	C₂×D₂₀	C₂⁴	1	8	yes	—
330	C₂×D₂₀	C₂⁴	1	8	yes	—
331	C₂×D₂₀	C₂⁴	1	8	yes	—
332	C₂×D₂₀	C₂⁴	1	16	yes	—
333	C₂×D₂₀	C₂⁴	1	16	yes	—
334	C₂×D₂₀	C₂⁴	1	16	yes	—
335	C₂×D₂₀	C₂⁴	1	8	yes	—
336	C₂×D₂₀	C₂⁴	1	16	yes	—
337	C₂×D₂₀	C₂⁴	1	16	yes	—
338	C₂×D₂₀	C₂⁴	1	16	yes	—
339	C₂×C₄×D₅	—	2	8	no	—
340	C₂×C₄×D₅	—	4	8	no	—
341	C₂×C₄×D₅	—	4	8	no	—
342	C₂×C₄×D₅	—	4	8	no	—
343	C₂×C₄×D₅	C₂⁴	1	8	yes	—
344	C₂×C₄×D₅	C₂⁴	1	16	yes	—
345	C₂×C₄×D₅	C₂⁴	1	16	yes	—
346	C₂×C₄×D₅	C₂⁴	1	16	yes	—
347	C₂×Dic₁₀	—	2	4	no	—
348	C₂×Dic₁₀	C₂⁴	1	4	yes	—
349	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
350	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
351	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
352	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
353	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
354	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
355	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
356	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
357	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
358	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
359	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
360	C₄²×C₅	C₂⁴	1	4	yes	—
361	C₄²×C₅	C₂⁴	1	4	yes	—
362	C₄²×C₅	C₂⁴	1	4	yes	—
363	C₄²×C₅	C₂⁴	1	4	yes	—
364	C₄²×C₅	C₂⁴	1	8	yes	—
365	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
366	#685	C₂⁴	1	8	yes	—
367	#685	C₂⁴	1	8	yes	—
368	#685	C₂⁴	1	8	yes	—
369	#685	C₂⁴	1	16	yes	—
370	#685	C₂⁴	1	16	yes	—
371	#685	C₂⁴	1	8	yes	—
372	#685	C₂⁴	1	16	yes	—
373	#685	C₂⁴	1	16	yes	—
374	#685	C₂⁴	1	16	yes	—
375	#685	C₂⁴	1	16	yes	—
376	C₄⋊Dic₅	C₂⁴	1	4	yes	—
377	C₄⋊Dic₅	C₂⁴	1	4	yes	—
378	#683	C₂⁴	1	8	yes	—
379	#683	C₂⁴	1	8	yes	—
380	#683	C₂⁴	1	8	yes	—
381	#683	C₂⁴	1	8	yes	—
382	C₄×Dic₅	C₂⁴	1	8	yes	—
383	C₂²×#41	—	5	2	no	—
384	C₂²×#41	—	5	2	no	—
385	C₂³×D₄	—	5	4	no	—
386	C₂³×D₄	—	5	2	no	—
387	C₂³×D₄	—	5	2	no	—
388	C₂³×D₄	—	5	2	no	—
389	C₂³×D₄	—	5	2	no	—
390	C₂³×D₄	—	5	2	no	—
391	#560	—	5	64	no	—
392	#559	—	5	16	no	—
393	#550	—	5	16	no	—
394	#550	—	5	16	no	—
395	#546	—	5	32	no	—
396	#546	—	5	32	no	—
397	D₄²	—	5	32	no	—
398	D₄²	—	5	16	no	—
399	D₄²	—	5	32	no	—
400	#540	—	5	32	no	—
401	#540	—	5	32	no	—
402	#535	—	5	32	no	—
403	#535	—	5	32	no	—
404	#534	—	5	64	no	—
405	C₂×#127	—	5	2	no	—
406	C₂×#127	—	5	1	no	—
407	C₂×#127	—	5	2	no	—
408	C₂×#127	—	5	2	no	—
409	C₂×#127	—	5	1	no	—
410	C₂×#127	—	5	2	no	—
411	C₂×#127	—	5	2	no	—
412	C₂×#127	—	5	16	no	—
413	#529	—	5	16	no	—
414	#529	C₂×D₅	1	16	yes	complemented
415	C₂×#126	—	5	2	no	—
416	C₂×#126	C₂×D₅	1	2	yes	complemented
417	C₂×#125	—	5	1	no	—
418	C₂×#125	C₂×D₅	1	1	yes	characteristic, complemented
419	C₂×#124	—	5	2	no	—
420	C₂×#124	—	5	1	no	—
421	C₂×#124	—	5	2	no	—
422	C₂×#124	C₂×D₅	1	1	yes	characteristic, complemented
423	C₂×#123	—	5	2	no	—
424	C₂×#123	—	5	4	no	—
425	C₂×#123	—	5	4	no	—
426	C₂×#123	—	5	4	no	—
427	C₂×#123	—	5	4	no	—
428	C₂×#123	C₂×D₅	1	2	yes	complemented
429	C₂×C₂²⋊Q₈	—	5	1	no	—
430	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
431	C₂×#121	—	5	1	no	—
432	C₂×#121	—	5	2	no	—
433	C₂×#121	—	5	2	no	—
434	C₂×#121	—	5	4	no	—
435	C₂×#121	—	5	4	no	—
436	C₂×#121	—	5	4	no	—
437	C₂×#121	—	5	2	no	—
438	C₂×#121	—	5	2	no	—
439	C₂×#121	—	5	4	no	—
440	C₂×#121	—	5	4	no	—
441	C₂×#121	—	5	4	no	—
442	C₂×#121	—	5	4	no	—
443	C₂×#121	—	5	4	no	—
444	C₂×#121	C₂×D₅	1	1	yes	characteristic
445	C₂×#120	—	5	4	no	—
446	C₂×#120	—	5	4	no	—
447	C₂×#120	—	5	4	no	—
448	C₂×#120	—	5	4	no	—
449	C₂×#120	—	5	4	no	—
450	C₂×#120	—	5	4	no	—
451	C₂×C₄×Q₈	—	5	1	no	—
452	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
453	C₂×C₄×D₄	—	5	2	no	—
454	C₂×C₄×D₄	—	5	2	no	—
455	C₂×C₄×D₄	—	5	2	no	—
456	C₂×C₄×D₄	—	5	1	no	—
457	C₂×C₄×D₄	—	5	2	no	—
458	C₂×C₄×D₄	—	5	2	no	—
459	C₂×C₄×D₄	C₂×D₅	1	2	yes	complemented
460	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
461	C₂×#117	—	5	2	no	—
462	C₂×#117	C₂×D₅	1	2	yes	complemented
463	C₂²×C₂²⋊C₄	—	5	4	no	—
464	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
465	C₂³×C₅	—	2	2	no	—
466	C₂³×C₅	—	2	2	no	—
467	C₂³×C₅	—	2	4	no	—
468	C₂³×C₅	—	2	4	no	—
469	C₂³×C₅	—	2	4	no	—
470	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
471	C₂³×C₅	C₂⁵	1	4	yes	—
472	C₂³×C₅	C₂⁵	1	2	yes	—
473	C₂³×C₅	C₂⁵	1	1	yes	characteristic
474	C₂²×D₅	—	2	4	no	—
475	C₂²×D₅	—	2	8	no	—
476	C₂²×D₅	—	2	8	no	—
477	C₂²×D₅	—	2	8	no	—
478	C₂²×D₅	—	2	4	no	—
479	C₂²×D₅	—	2	8	no	—
480	C₂²×D₅	—	2	8	no	—
481	C₂²×D₅	—	2	8	no	—
482	C₂²×D₅	—	2	4	no	—
483	C₂²×D₅	—	2	32	no	—
484	C₂²×D₅	—	4	16	no	—
485	C₂²×D₅	—	4	16	no	—
486	C₂²×D₅	—	4	16	no	—
487	C₂²×D₅	—	4	16	no	—
488	C₂²×D₅	—	4	16	no	—
489	C₂²×D₅	—	8	32	no	—
490	C₂²×D₅	—	8	32	no	—
491	C₂²×D₅	C₂⁵	1	4	yes	—
492	C₂²×D₅	C₂⁵	1	8	yes	—
493	C₂²×D₅	C₂⁵	1	8	yes	—
494	C₅×Q₈	—	2	8	no	—
495	C₅×D₄	—	2	16	no	—
496	C₅×D₄	—	2	8	no	—
497	C₂×C₄×C₅	—	2	4	no	—
498	C₂×C₄×C₅	—	2	4	no	—
499	C₂×C₄×C₅	—	2	4	no	—
500	C₂×C₄×C₅	—	2	8	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	2	no	—
503	C₂×C₄×C₅	—	2	2	no	—
504	C₂×C₄×C₅	—	2	2	no	—
505	C₂×C₄×C₅	—	2	8	no	—
506	C₂×C₄×C₅	—	2	8	no	—
507	C₂×C₄×C₅	—	2	16	no	—
508	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
509	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
510	C₂×C₄×C₅	C₂⁵	1	2	yes	—
511	C₂×C₄×C₅	C₂⁵	1	2	yes	—
512	C₂×C₄×C₅	C₂⁵	1	2	yes	—
513	C₂×C₄×C₅	C₂⁵	1	2	yes	—
514	C₂×C₄×C₅	C₂⁵	1	4	yes	—
515	C₂×C₄×C₅	C₂⁵	1	4	yes	—
516	C₂×C₄×C₅	C₂⁵	1	4	yes	—
517	C₂×C₄×C₅	C₂⁵	1	2	yes	—
518	C₂×C₄×C₅	C₂⁵	1	2	yes	—
519	C₂²⋊D₅	—	2	16	no	—
520	C₂²⋊D₅	—	4	16	no	—
521	C₂²⋊D₅	—	4	16	no	—
522	C₂²⋊D₅	—	4	16	no	—
523	C₂×Dic₅	—	2	4	no	—
524	C₂×Dic₅	—	2	4	no	—
525	C₂×Dic₅	—	2	4	no	—
526	C₂×Dic₅	C₂⁵	1	4	yes	—
527	C₂×Dic₅	C₂⁵	1	4	yes	—
528	C₂×Dic₅	C₂⁵	1	4	yes	—
529	D₂₀	—	2	16	no	—
530	D₂₀	—	2	8	no	—
531	D₂₀	—	2	16	no	—
532	D₂₀	—	2	16	no	—
533	D₂₀	—	2	16	no	—
534	D₂₀	—	4	16	no	—
535	D₂₀	—	4	16	no	—
536	D₂₀	—	4	16	no	—
537	D₂₀	—	4	8	no	—
538	D₂₀	—	4	16	no	—
539	D₂₀	—	4	8	no	—
540	D₂₀	—	4	16	no	—
541	D₂₀	—	4	16	no	—
542	C₄×D₅	—	2	16	no	—
543	C₄×D₅	—	4	16	no	—
544	C₄×D₅	—	4	16	no	—
545	C₄×D₅	—	4	16	no	—
546	Dic₁₀	—	2	8	no	—
547	C₂⁵	—	5	4	no	—
548	C₂⁵	—	5	4	no	—
549	C₂×#41	—	5	16	no	—
550	C₂×#41	—	5	16	no	—
551	C₂×#41	—	20	8	no	—
552	C₂×#41	—	20	8	no	—
553	C₂²×Q₈	—	5	1	no	—
554	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
555	C₂²×D₄	—	5	2	no	—
556	C₂²×D₄	—	5	4	no	—
557	C₂²×D₄	—	5	4	no	—
558	C₂²×D₄	—	5	4	no	—
559	C₂²×D₄	—	5	32	no	—
560	C₂²×D₄	—	5	16	no	—
561	C₂²×D₄	—	5	2	no	—
562	C₂²×D₄	—	5	1	no	—
563	C₂²×D₄	—	5	2	no	—
564	C₂²×D₄	—	5	2	no	—
565	C₂²×D₄	—	5	2	no	—
566	C₂²×D₄	—	5	4	no	—
567	C₂²×D₄	—	5	4	no	—
568	C₂²×D₄	—	5	2	no	—
569	C₂²×D₄	—	5	4	no	—
570	C₂²×D₄	—	5	4	no	—
571	C₂²×D₄	—	5	4	no	—
572	C₂²×D₄	—	5	4	no	—
573	C₂²×D₄	—	5	2	no	—
574	C₂²×D₄	—	5	16	no	—
575	C₂²×D₄	—	5	16	no	—
576	C₂²×D₄	—	5	16	no	—
577	C₂²×D₄	—	5	16	no	—
578	C₂²×D₄	—	20	8	no	—
579	C₂²×D₄	—	20	8	no	—
580	C₂²×D₄	—	20	8	no	—
581	C₂²×D₄	—	20	8	no	—
582	C₂²×D₄	—	20	8	no	—
583	C₂²×D₄	—	20	16	no	—
584	C₂²×D₄	C₂²×D₅	1	2	yes	—
585	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
586	C₂³×C₄	—	5	2	no	—
587	C₂³×C₄	—	5	4	no	—
588	C₂³×C₄	—	5	4	no	—
589	C₂³×C₄	—	5	4	no	—
590	C₂³×C₄	C₂²×D₅	1	2	yes	—
591	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
592	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
593	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
594	#127	—	5	16	no	—
595	#127	—	5	16	no	—
596	#127	—	5	16	no	—
597	#127	—	5	8	no	—
598	#127	—	5	8	no	—
599	#127	—	5	16	no	—
600	#127	—	5	16	no	—
601	#126	—	5	16	no	—
602	#126	C₂²×D₅	1	16	yes	complemented
603	#125	—	5	8	no	—
604	#125	C₂²×D₅	1	8	yes	complemented
605	#124	—	5	16	no	—
606	#124	—	5	8	no	—
607	#124	—	5	16	no	—
608	#124	C₂²×D₅	1	8	yes	complemented
609	#123	—	5	16	no	—
610	#123	—	5	32	no	—
611	#123	—	5	32	no	—
612	#123	—	5	32	no	—
613	#123	—	5	32	no	—
614	#123	C₂²×D₅	1	16	yes	complemented
615	C₂²⋊Q₈	—	5	8	no	—
616	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
617	#121	—	5	8	no	—
618	#121	—	5	16	no	—
619	#121	—	5	16	no	—
620	#121	—	5	32	no	—
621	#121	—	5	32	no	—
622	#121	—	5	32	no	—
623	#121	—	5	16	no	—
624	#121	—	5	16	no	—
625	#121	—	5	32	no	—
626	#121	—	5	32	no	—
627	#121	—	5	32	no	—
628	#121	—	5	32	no	—
629	#121	—	5	32	no	—
630	#121	C₂²×D₅	1	8	yes	—
631	#120	—	5	32	no	—
632	#120	—	5	32	no	—
633	#120	—	5	32	no	—
634	#120	—	5	32	no	—
635	#120	—	5	32	no	—
636	#120	—	5	32	no	—
637	C₄×Q₈	—	5	8	no	—
638	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
639	C₄×D₄	—	5	16	no	—
640	C₄×D₄	—	5	16	no	—
641	C₄×D₄	—	5	16	no	—
642	C₄×D₄	—	5	8	no	—
643	C₄×D₄	—	5	16	no	—
644	C₄×D₄	—	5	16	no	—
645	C₄×D₄	C₂²×D₅	1	16	yes	complemented
646	C₄×D₄	C₂²×D₅	1	8	yes	complemented
647	#117	—	5	16	no	—
648	#117	C₂²×D₅	1	16	yes	complemented
649	C₂×C₄⋊C₄	—	5	2	no	—
650	C₂×C₄⋊C₄	—	5	2	no	—
651	C₂×C₄⋊C₄	—	5	1	no	—
652	C₂×C₄⋊C₄	—	5	1	no	—
653	C₂×C₄⋊C₄	—	5	2	no	—
654	C₂×C₄⋊C₄	—	5	2	no	—
655	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
656	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
657	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
660	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
661	C₂×C₂²⋊C₄	—	5	2	no	—
662	C₂×C₂²⋊C₄	—	5	4	no	—
663	C₂×C₂²⋊C₄	—	5	4	no	—
664	C₂×C₂²⋊C₄	—	5	2	no	—
665	C₂×C₂²⋊C₄	—	5	2	no	—
666	C₂×C₂²⋊C₄	—	5	2	no	—
667	C₂×C₂²⋊C₄	—	5	2	no	—
668	C₂×C₂²⋊C₄	—	5	4	no	—
669	C₂×C₂²⋊C₄	—	5	4	no	—
670	C₂×C₂²⋊C₄	—	5	4	no	—
671	C₂×C₂²⋊C₄	—	5	4	no	—
672	C₂×C₂²⋊C₄	—	5	32	no	—
673	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
678	C₂×C₄²	—	5	2	no	—
679	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
680	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
681	C₂×C₄²	C₂²×D₅	1	2	yes	—
682	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
683	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
684	C₂×C₄²	C₂²×D₅	1	8	yes	complemented
685	C₂²×C₅	—	2	2	no	—
686	C₂²×C₅	—	2	2	no	—
687	C₂²×C₅	—	2	8	no	—
688	C₂²×C₅	—	2	4	no	—
689	C₂²×C₅	—	2	4	no	—
690	C₂²×C₅	—	2	4	no	—
691	C₂²×C₅	—	4	8	no	—
692	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
693	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
694	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
695	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
696	C₂²×C₅	C₂⁶	1	1	yes	characteristic
697	C₂×D₅	—	2	4	no	—
698	C₂×D₅	—	2	8	no	—
699	C₂×D₅	—	2	8	no	—
700	C₂×D₅	—	2	8	no	—
701	C₂×D₅	—	2	4	no	—
702	C₂×D₅	—	2	8	no	—
703	C₂×D₅	—	2	8	no	—
704	C₂×D₅	—	2	8	no	—
705	C₂×D₅	—	2	4	no	—
706	C₂×D₅	—	4	16	no	—
707	C₂×D₅	—	4	8	no	—
708	C₂×D₅	—	4	16	no	—
709	C₂×D₅	—	8	32	no	—
710	C₂×D₅	—	8	32	no	—
711	C₄×C₅	—	2	4	no	—
712	C₄×C₅	—	2	4	no	—
713	C₄×C₅	—	2	4	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	2	2	no	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
719	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
720	Dic₅	—	2	4	no	—
721	Dic₅	—	2	4	no	—
722	Dic₅	—	2	4	no	—
723	C₂⁴	—	5	2	no	—
724	C₂⁴	—	5	4	no	—
725	C₂⁴	—	5	4	no	—
726	C₂⁴	—	5	16	no	—
727	C₂⁴	—	5	16	no	—
728	C₂⁴	—	10	16	no	—
729	C₂⁴	—	20	8	no	—
730	C₂⁴	—	20	8	no	—
731	C₂⁴	—	20	8	no	—
732	C₂⁴	—	20	8	no	—
733	C₂⁴	—	20	8	no	—
734	C₂⁴	C₂³×D₅	1	2	yes	—
735	C₂⁴	C₂³×D₅	1	1	yes	characteristic
736	#41	—	20	32	no	—
737	#41	—	20	32	no	—
738	C₂×Q₈	—	2	4	no	—
739	C₂×Q₈	—	5	4	no	—
740	C₂×Q₈	—	10	4	no	—
741	C₂×Q₈	C₂³×D₅	1	4	yes	—
742	C₂×D₄	—	2	8	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	5	8	no	—
745	C₂×D₄	—	5	16	no	—
746	C₂×D₄	—	5	16	no	—
747	C₂×D₄	—	5	16	no	—
748	C₂×D₄	—	5	8	no	—
749	C₂×D₄	—	5	4	no	—
750	C₂×D₄	—	5	8	no	—
751	C₂×D₄	—	5	8	no	—
752	C₂×D₄	—	5	8	no	—
753	C₂×D₄	—	5	16	no	—
754	C₂×D₄	—	5	16	no	—
755	C₂×D₄	—	5	8	no	—
756	C₂×D₄	—	5	16	no	—
757	C₂×D₄	—	5	16	no	—
758	C₂×D₄	—	5	16	no	—
759	C₂×D₄	—	5	16	no	—
760	C₂×D₄	—	5	8	no	—
761	C₂×D₄	—	10	8	no	—
762	C₂×D₄	—	10	4	no	—
763	C₂×D₄	—	10	8	no	—
764	C₂×D₄	—	10	8	no	—
765	C₂×D₄	—	10	8	no	—
766	C₂×D₄	—	10	8	no	—
767	C₂×D₄	—	20	32	no	—
768	C₂×D₄	—	20	32	no	—
769	C₂×D₄	—	20	32	no	—
770	C₂×D₄	—	20	8	no	—
771	C₂×D₄	—	20	8	no	—
772	C₂×D₄	—	20	8	no	—
773	C₂×D₄	—	20	4	no	—
774	C₂×D₄	—	20	8	no	—
775	C₂×D₄	—	20	4	no	—
776	C₂×D₄	—	20	32	no	—
777	C₂×D₄	—	20	8	no	—
778	C₂×D₄	—	20	8	no	—
779	C₂×D₄	—	20	32	no	—
780	C₂×D₄	—	20	8	no	—
781	C₂×D₄	—	20	8	no	—
782	C₂×D₄	—	20	8	no	—
783	C₂×D₄	—	20	64	no	—
784	C₂×D₄	C₂³×D₅	1	8	yes	—
785	C₂×D₄	C₂³×D₅	1	4	yes	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	8	no	—
790	C₂²×C₄	—	5	2	no	—
791	C₂²×C₄	—	5	2	no	—
792	C₂²×C₄	—	5	2	no	—
793	C₂²×C₄	—	5	8	no	—
794	C₂²×C₄	—	5	16	no	—
795	C₂²×C₄	—	5	16	no	—
796	C₂²×C₄	—	5	16	no	—
797	C₂²×C₄	—	10	8	no	—
798	C₂²×C₄	—	20	8	no	—
799	C₂²×C₄	—	20	8	no	—
800	C₂²×C₄	—	20	8	no	—
801	C₂²×C₄	C₂³×D₅	1	4	yes	—
802	C₂²×C₄	C₂³×D₅	1	4	yes	—
803	C₂²×C₄	C₂³×D₅	1	4	yes	—
804	C₂²×C₄	C₂³×D₅	1	8	yes	—
805	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
806	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
807	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
808	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
809	C₂²×C₄	C₂³×D₅	1	2	yes	—
810	C₂²×C₄	C₂³×D₅	1	2	yes	—
811	C₂²×C₄	C₂³×D₅	1	2	yes	—
812	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
813	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
814	C₄⋊C₄	—	5	8	no	—
815	C₄⋊C₄	—	5	8	no	—
816	C₄⋊C₄	—	5	4	no	—
817	C₄⋊C₄	—	5	4	no	—
818	C₄⋊C₄	—	5	8	no	—
819	C₄⋊C₄	—	5	8	no	—
820	C₄⋊C₄	C₂³×D₅	1	8	yes	—
821	C₄⋊C₄	C₂³×D₅	1	8	yes	—
822	C₄⋊C₄	C₂³×D₅	1	4	yes	—
823	C₄⋊C₄	C₂³×D₅	1	4	yes	—
824	C₄⋊C₄	C₂³×D₅	1	8	yes	—
825	C₄⋊C₄	C₂³×D₅	1	8	yes	—
826	C₂²⋊C₄	—	5	8	no	—
827	C₂²⋊C₄	—	5	16	no	—
828	C₂²⋊C₄	—	5	16	no	—
829	C₂²⋊C₄	—	5	8	no	—
830	C₂²⋊C₄	—	5	8	no	—
831	C₂²⋊C₄	—	5	8	no	—
832	C₂²⋊C₄	—	5	8	no	—
833	C₂²⋊C₄	—	5	16	no	—
834	C₂²⋊C₄	—	5	16	no	—
835	C₂²⋊C₄	—	5	16	no	—
836	C₂²⋊C₄	—	5	16	no	—
837	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
838	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
839	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
840	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
841	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
842	C₄²	—	5	8	no	—
843	C₄²	C₂³×D₅	1	4	yes	—
844	C₄²	C₂³×D₅	1	4	yes	—
845	C₄²	C₂³×D₅	1	4	yes	—
846	C₄²	C₂³×D₅	1	4	yes	—
847	C₄²	C₂³×D₅	1	8	yes	—
848	C₂×C₅	—	2	4	no	—
849	C₂×C₅	—	4	4	no	—
850	C₂×C₅	#3543	1	4	yes	complemented
851	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
853	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
854	D₅	—	4	8	no	—
855	D₅	—	4	4	no	—
856	D₅	—	4	8	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	4	no	—
862	C₂³	—	5	4	no	—
863	C₂³	—	5	8	no	—
864	C₂³	—	5	8	no	—
865	C₂³	—	10	4	no	—
866	C₂³	—	10	8	no	—
867	C₂³	—	10	8	no	—
868	C₂³	—	10	8	no	—
869	C₂³	—	10	4	no	—
870	C₂³	—	10	4	no	—
871	C₂³	—	10	8	no	—
872	C₂³	—	10	8	no	—
873	C₂³	—	10	8	no	—
874	C₂³	—	10	32	no	—
875	C₂³	—	20	16	no	—
876	C₂³	—	20	16	no	—
877	C₂³	—	20	16	no	—
878	C₂³	—	20	16	no	—
879	C₂³	—	20	16	no	—
880	C₂³	—	40	32	no	—
881	C₂³	—	40	32	no	—
882	C₂³	#4149	1	4	yes	—
883	C₂³	C₂⁴×D₅	1	4	yes	—
884	C₂³	C₂⁴×D₅	1	2	yes	—
885	C₂³	C₂⁴×D₅	1	1	yes	characteristic
886	Q₈	—	2	8	no	—
887	Q₈	—	10	8	no	—
888	D₄	—	2	16	no	—
889	D₄	—	2	8	no	—
890	D₄	—	10	16	no	—
891	D₄	—	10	8	no	—
892	D₄	—	10	16	no	—
893	D₄	—	10	16	no	—
894	D₄	—	10	16	no	—
895	D₄	—	10	16	no	—
896	D₄	—	20	16	no	—
897	D₄	—	20	16	no	—
898	D₄	—	20	16	no	—
899	D₄	—	20	8	no	—
900	D₄	—	20	16	no	—
901	D₄	—	20	8	no	—
902	D₄	—	20	16	no	—
903	D₄	—	20	16	no	—
904	D₄	—	20	16	no	—
905	D₄	—	20	16	no	—
906	D₄	—	20	16	no	—
907	C₂×C₄	—	2	4	no	—
908	C₂×C₄	—	2	8	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	4	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	8	no	—
916	C₂×C₄	—	2	8	no	—
917	C₂×C₄	—	2	16	no	—
918	C₂×C₄	—	5	4	no	—
919	C₂×C₄	—	5	4	no	—
920	C₂×C₄	—	5	4	no	—
921	C₂×C₄	—	10	4	no	—
922	C₂×C₄	—	10	4	no	—
923	C₂×C₄	—	10	4	no	—
924	C₂×C₄	—	10	16	no	—
925	C₂×C₄	—	20	16	no	—
926	C₂×C₄	—	20	16	no	—
927	C₂×C₄	—	20	16	no	—
928	C₂×C₄	#4149	1	4	yes	—
929	C₂×C₄	#4149	1	4	yes	—
930	C₂×C₄	C₂⁴×D₅	1	2	yes	—
931	C₂×C₄	C₂⁴×D₅	1	2	yes	—
932	C₂×C₄	C₂⁴×D₅	1	2	yes	—
933	C₂×C₄	C₂⁴×D₅	1	2	yes	—
934	C₂×C₄	C₂⁴×D₅	1	4	yes	—
935	C₂×C₄	C₂⁴×D₅	1	4	yes	—
936	C₂×C₄	C₂⁴×D₅	1	4	yes	—
937	C₂×C₄	C₂⁴×D₅	1	2	yes	—
938	C₂×C₄	C₂⁴×D₅	1	2	yes	—
939	C₅	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	8	no	—
943	C₂²	—	2	4	no	—
944	C₂²	—	2	4	no	—
945	C₂²	—	2	4	no	—
946	C₂²	—	4	8	no	—
947	C₂²	—	10	4	no	—
948	C₂²	—	10	8	no	—
949	C₂²	—	10	8	no	—
950	C₂²	—	10	8	no	—
951	C₂²	—	10	4	no	—
952	C₂²	—	10	4	no	—
953	C₂²	—	10	8	no	—
954	C₂²	—	10	8	no	—
955	C₂²	—	10	8	no	—
956	C₂²	—	20	8	no	—
957	C₂²	—	20	16	no	—
958	C₂²	—	20	16	no	—
959	C₂²	—	40	32	no	—
960	C₂²	—	40	32	no	—
961	C₂²	C₂×#4149	1	4	yes	—
962	C₂²	C₂×#4149	1	2	yes	—
963	C₂²	C₂×#4149	1	2	yes	—
964	C₂²	C₂×#4149	1	2	yes	—
965	C₂²	C₂⁵×D₅	1	1	yes	characteristic
966	C₄	—	2	4	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	4	no	—
972	C₄	—	2	4	no	—
973	C₄	—	10	4	no	—
974	C₄	—	10	4	no	—
975	C₄	—	10	4	no	—
976	C₄	C₂×#4149	1	4	yes	—
977	C₄	C₂×#4149	1	4	yes	—
978	C₂	—	2	4	no	—
979	C₂	—	4	4	no	—
980	C₂	—	20	4	no	—
981	C₂	—	20	8	no	—
982	C₂	—	20	8	no	—
983	C₂	#10618073	1	4	yes	direct product factor
984	C₂	C₂²×#4149	1	1	yes	characteristic
985	C₂	C₂²×#4149	1	1	yes	characteristic
986	C₂	C₂²×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#529	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#529	D₅
hypocenter	C₅	C₂×#3543
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#529	C₂	semidirect
2. #10618073	C₂	direct (N × H)
3. C₂×#66045	C₂	semidirect
4. C₂×#66032	C₂	semidirect
5. C₂×#66008	C₂	semidirect
6. C₂×#65987	C₂	semidirect
7. C₂×#65964	C₂	semidirect
8. C₂×#65943	C₂	semidirect
9. C₂×#65919	C₂	semidirect
10. C₂×#65911	C₂	semidirect
11. C₂×#65884	C₂	semidirect
12. C₂×D₄×D₂₀	C₂	semidirect
13. C₂×D₄×D₂₀	C₂	semidirect
14. C₂×#65887	C₂	semidirect
15. C₂×#65869	C₂	semidirect
16. C₂×#65859	C₂	semidirect
17. C₂²×#4020	C₂	semidirect
18. C₂×#65813	C₂	semidirect
19. C₂²×#713	C₂²	semidirect
20. C₂²×D₄×D₅	C₂²	semidirect
21. C₂²×D₄×D₅	C₂²	semidirect
22. C₂²×#709	C₂²	semidirect
23. C₂³×D₂₀	C₂²	semidirect
24. C₂³×D₂₀	C₂²	semidirect
25. C₂³×D₂₀	C₂²	semidirect
26. C₂³×D₂₀	C₂²	semidirect
27. C₅×#529	C₂²	semidirect
28. C₂×C₅×#126	C₂²	semidirect
29. C₂×C₅×#125	C₂²	semidirect
30. C₂×C₅×#124	C₂²	semidirect
31. C₂×C₅×#123	C₂²	semidirect
32. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₂×C₄×C₅×Q₈	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₄×C₅×D₄	C₂²	semidirect
37. C₂×C₅×#117	C₂²	semidirect
38. C₂²×C₄²×C₅	C₂²	semidirect
39. C₂×#4093	C₂²	semidirect
40. C₂×#4086	C₂²	semidirect
41. C₂×#4083	C₂²	semidirect
43. C₂×#4076	C₂²	semidirect
44. C₂×#4076	C₂²	semidirect
45. C₂×#4075	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
47. C₂×#4070	C₂²	semidirect
48. #66045	C₂²	semidirect
49. #66032	C₂²	semidirect
50. #66008	C₂²	semidirect
51. #65987	C₂²	semidirect
52. #65964	C₂²	semidirect
53. #65943	C₂²	semidirect
54. #65919	C₂²	semidirect
55. #65911	C₂²	semidirect
56. #65887	C₂²	semidirect
57. #65884	C₂²	semidirect
58. D₄×D₂₀	C₂²	semidirect
59. D₄×D₂₀	C₂²	semidirect
60. #65869	C₂²	semidirect
61. #65859	C₂²	semidirect
62. C₂×#4041	C₂²	semidirect
63. C₂×#4041	C₂²	semidirect
64. C₂×#4041	C₂²	semidirect
65. C₂×#4041	C₂²	semidirect
66. C₂×#4041	C₂²	semidirect
67. C₂×#4041	C₂²	semidirect
68. C₂×#4040	C₂²	semidirect
69. C₂×#4040	C₂²	semidirect
70. C₂×#4040	C₂²	semidirect
71. C₂×#4040	C₂²	semidirect
72. C₂×#4039	C₂²	semidirect
73. C₂×#4039	C₂²	semidirect
74. C₂×#4030	C₂²	semidirect
75. C₂×#4030	C₂²	semidirect
76. C₂×#4030	C₂²	semidirect
77. C₂×#4030	C₂²	semidirect
78. C₂×#4028	C₂²	semidirect
79. C₂×#4028	C₂²	semidirect
80. C₂×#4028	C₂²	semidirect
81. C₂×#4028	C₂²	semidirect
82. C₂×#4028	C₂²	semidirect
83. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
84. #65813	C₂²	semidirect
85. C₂×#4022	C₂²	semidirect
86. C₂×#4021	C₂²	semidirect
87. C₂×#4021	C₂²	semidirect
89. C₂×#4020	C₂²	semidirect
90. C₂×#4020	C₂²	semidirect
91. C₂×#4020	C₂²	semidirect
92. C₂×#4020	C₂²	semidirect
93. C₂×#4020	C₂²	semidirect
94. C₂×#4020	C₂²	semidirect
95. C₂×C₄×D₂₀	C₂²	semidirect
96. C₂×C₄×D₂₀	C₂²	semidirect
97. C₂×C₄×D₂₀	C₂²	semidirect
98. C₂×#4018	C₂²	semidirect
99. C₂×#4016	C₂²	semidirect
100. C₂×C₄×Dic₁₀	C₂²	semidirect
116. C₂×#713	C₂³	semidirect
119. C₂×D₄×D₅	C₂³	semidirect
120. C₂×D₄×D₅	C₂³	semidirect
122. C₂×#709	C₂³	semidirect
140. C₂²×D₂₀	C₂³	semidirect
141. C₂²×D₂₀	C₂³	semidirect
142. C₂²×D₂₀	C₂³	semidirect
143. C₂²×D₂₀	C₂³	semidirect
149. C₅×#126	C₂³	semidirect
150. C₅×#125	C₂³	semidirect
151. C₅×#124	C₂³	semidirect
152. C₅×#123	C₂³	semidirect
153. C₅×C₂²⋊Q₈	C₂³	semidirect
155. C₄×C₅×Q₈	C₂³	semidirect
156. C₄×C₅×D₄	C₂³	semidirect
157. C₄×C₅×D₄	C₂³	semidirect
158. C₅×#117	C₂³	semidirect
175. C₂×C₄²×C₅	C₂³	semidirect
177. #4093	C₂³	semidirect
178. #4086	C₂³	semidirect
179. #4083	C₂³	semidirect
181. #4076	C₂³	semidirect
182. #4076	C₂³	semidirect
183. #4075	C₂³	semidirect
184. C₄×C₂²⋊D₅	C₂³	semidirect
197. #4070	C₂³	semidirect
203. #4041	C₂³	semidirect
204. #4041	C₂³	semidirect
205. #4041	C₂³	semidirect
206. #4041	C₂³	semidirect
207. #4041	C₂³	semidirect
208. #4041	C₂³	semidirect
209. #4040	C₂³	semidirect
210. #4040	C₂³	semidirect
211. #4040	C₂³	semidirect
212. #4040	C₂³	semidirect
213. #4039	C₂³	semidirect
214. #4039	C₂³	semidirect
215. #4030	C₂³	semidirect
216. #4030	C₂³	semidirect
217. #4030	C₂³	semidirect
218. #4030	C₂³	semidirect
219. #4028	C₂³	semidirect
220. #4028	C₂³	semidirect
221. #4028	C₂³	semidirect
222. #4028	C₂³	semidirect
223. #4028	C₂³	semidirect
224. D₅×C₂²⋊C₄	C₂³	semidirect
225. #4022	C₂³	semidirect
226. #4021	C₂³	semidirect
227. #4021	C₂³	semidirect
229. #4020	C₂³	semidirect
230. #4020	C₂³	semidirect
231. #4020	C₂³	semidirect
232. #4020	C₂³	semidirect
233. #4020	C₂³	semidirect
234. C₄×D₂₀	C₂³	semidirect
235. C₄×D₂₀	C₂³	semidirect
236. C₄×D₂₀	C₂³	semidirect
237. #4018	C₂³	semidirect
238. #4016	C₂³	semidirect
239. C₄×Dic₁₀	C₂³	semidirect
257. C₂×#529	D₅	semidirect
414. #529	C₂×D₅	semidirect
416. C₂×#126	C₂×D₅	semidirect
418. C₂×#125	C₂×D₅	semidirect
422. C₂×#124	C₂×D₅	semidirect
428. C₂×#123	C₂×D₅	semidirect
430. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
452. C₂×C₄×Q₈	C₂×D₅	semidirect
459. C₂×C₄×D₄	C₂×D₅	semidirect
460. C₂×C₄×D₄	C₂×D₅	semidirect
462. C₂×#117	C₂×D₅	semidirect
464. C₂²×C₄²	C₂×D₅	semidirect
602. #126	C₂²×D₅	semidirect
604. #125	C₂²×D₅	semidirect
608. #124	C₂²×D₅	semidirect
614. #123	C₂²×D₅	semidirect
616. C₂²⋊Q₈	C₂²×D₅	semidirect
638. C₄×Q₈	C₂²×D₅	semidirect
645. C₄×D₄	C₂²×D₅	semidirect
646. C₄×D₄	C₂²×D₅	semidirect
648. #117	C₂²×D₅	semidirect
684. C₂×C₄²	C₂²×D₅	semidirect
850. C₂×C₅	#3543	semidirect
939. C₅	C₂×#3543	semidirect
983. C₂	#10618073	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×#529	2
#10618073	2
C₂×#66045	2
C₂×#66032	2
C₂×#66008	2
C₂×#65987	2
C₂×#65964	2
C₂×#65943	2
C₂×#65919	2
C₂×#65911	2
C₂×#65884	2
C₂×D₄×D₂₀	2
C₂×#65887	2
C₂×#65869	2
C₂×#65859	2
C₂²×#4020	2
C₂×#65813	2
C₂×#3543	5

Subgroups — C2×#10618073 #13006890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618073 #13006890