Subgroups — C₂×#10618909 #13006592

Order 1280.

7418 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618909	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66067	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#66068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66045	C₂	1	2	yes	maximal, complemented
6	C₂×#66039	C₂	1	2	yes	maximal, complemented
7	C₂×#66038	C₂	1	2	yes	maximal, complemented
8	C₂×#66044	C₂	1	2	yes	maximal, complemented
9	C₂×#66017	C₂	1	2	yes	maximal, complemented
10	C₂×#66012	C₂	1	2	yes	maximal, complemented
11	C₂×#65967	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65964	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65962	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#65961	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#65910	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#65916	C₂	1	2	yes	maximal, complemented
17	C₂×#65916	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#65919	C₂	1	2	yes	maximal, complemented
19	C₂×#65884	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#65881	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#65867	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#65866	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#65859	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#65858	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#713	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#709	C₂²	1	1	yes	characteristic
28	C₂²×#709	C₂²	1	1	yes	characteristic
29	C₂³×D₂₀	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
31	C₅×#556	C₂²	1	16	yes	complemented
32	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#126	C₂²	1	2	yes	complemented
34	C₂×C₅×#126	C₂²	1	2	yes	complemented
35	C₂×C₅×#124	C₂²	1	2	yes	—
36	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
39	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×#4093	C₂²	1	1	yes	characteristic, complemented
44	C₂×#4093	C₂²	1	2	yes	complemented
45	C₂×#4093	C₂²	1	2	yes	complemented
46	C₂×#4093	C₂²	1	2	yes	complemented
47	C₂×#4092	C₂²	1	1	yes	characteristic, complemented
48	C₂×#4092	C₂²	1	2	yes	complemented
49	C₂×#4085	C₂²	1	1	yes	characteristic
50	C₂×#4083	C₂²	1	1	yes	characteristic
51	C₂×#4083	C₂²	1	2	yes	—
52	C₂×#4076	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
55	C₂×#4070	C₂²	1	1	yes	characteristic, complemented
56	#66068	C₂²	1	16	yes	complemented
57	#66067	C₂²	1	16	yes	complemented
58	#66045	C₂²	1	32	yes	complemented
59	#66044	C₂²	1	32	yes	complemented
60	#66039	C₂²	1	32	yes	complemented
61	#66038	C₂²	1	32	yes	complemented
62	#66017	C₂²	1	32	yes	complemented
63	#66012	C₂²	1	32	yes	complemented
64	#65967	C₂²	1	16	yes	complemented
65	#65964	C₂²	1	16	yes	complemented
66	#65962	C₂²	1	16	yes	complemented
67	#65961	C₂²	1	16	yes	complemented
68	#65919	C₂²	1	32	yes	complemented
69	#65916	C₂²	1	16	yes	complemented
70	#65916	C₂²	1	32	yes	complemented
71	#65910	C₂²	1	16	yes	complemented
72	#65884	C₂²	1	16	yes	complemented
73	#65881	C₂²	1	16	yes	complemented
74	#65867	C₂²	1	16	yes	complemented
75	#65866	C₂²	1	16	yes	complemented
76	#65859	C₂²	1	16	yes	complemented
77	#65858	C₂²	1	16	yes	complemented
78	C₂×#4044	C₂²	1	2	yes	complemented
79	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
80	C₂×#4043	C₂²	1	1	yes	characteristic, complemented
81	C₂×#4043	C₂²	1	2	yes	complemented
82	C₂×#4042	C₂²	1	2	yes	complemented
83	C₂×#4042	C₂²	1	1	yes	characteristic, complemented
84	C₂×#4042	C₂²	1	2	yes	complemented
85	C₂×#4041	C₂²	1	1	yes	characteristic
86	C₂×#4041	C₂²	1	1	yes	characteristic
87	C₂×#4041	C₂²	1	2	yes	—
88	C₂×#4041	C₂²	1	1	yes	characteristic
89	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
90	C₂×#4041	C₂²	1	1	yes	characteristic, complemented
91	C₂×#4041	C₂²	1	2	yes	complemented
92	C₂×#4041	C₂²	1	2	yes	complemented
93	C₂×#4040	C₂²	1	2	yes	complemented
94	C₂×#4040	C₂²	1	2	yes	complemented
95	C₂×#4040	C₂²	1	2	yes	complemented
96	C₂×#4040	C₂²	1	1	yes	characteristic, complemented
97	C₂×#4040	C₂²	1	2	yes	complemented
98	C₂×#4040	C₂²	1	2	yes	complemented
99	C₂×#4040	C₂²	1	2	yes	complemented
100	C₂×#4039	C₂²	1	2	yes	complemented
101	C₂×#4039	C₂²	1	1	yes	characteristic, complemented
102	C₂×#4039	C₂²	1	2	yes	complemented
103	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
104	C₂×#4038	C₂²	1	1	yes	characteristic, complemented
105	C₂×#4038	C₂²	1	2	yes	complemented
106	C₂×#4034	C₂²	1	2	yes	complemented
107	C₂×#4034	C₂²	1	1	yes	characteristic, complemented
108	C₂×#4033	C₂²	1	1	yes	characteristic, complemented
109	C₂×#4032	C₂²	1	2	yes	complemented
110	C₂×#4031	C₂²	1	2	yes	—
111	C₂×#4031	C₂²	1	2	yes	—
112	C₂×#4031	C₂²	1	2	yes	complemented
113	C₂×#4031	C₂²	1	2	yes	complemented
114	C₂×#4030	C₂²	1	1	yes	characteristic
115	C₂×#4030	C₂²	1	2	yes	—
116	C₂×#4030	C₂²	1	2	yes	complemented
117	C₂×#4030	C₂²	1	2	yes	complemented
118	C₂×#4029	C₂²	1	1	yes	characteristic
119	C₂×#4029	C₂²	1	2	yes	complemented
120	C₂×#4028	C₂²	1	2	yes	—
121	C₂×#4028	C₂²	1	2	yes	—
122	C₂×#4028	C₂²	1	2	yes	complemented
123	C₂×#4028	C₂²	1	2	yes	complemented
124	C₂×#4028	C₂²	1	2	yes	complemented
125	C₂×#4028	C₂²	1	1	yes	characteristic, complemented
126	C₂×#4027	C₂²	1	2	yes	complemented
127	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
128	C₂×D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
129	C₂×#4025	C₂²	1	2	yes	complemented
130	C₂×#4024	C₂²	1	1	yes	characteristic, complemented
131	C₂×#4022	C₂²	1	2	yes	complemented
132	C₂×#4022	C₂²	1	2	yes	complemented
133	C₂×#4021	C₂²	1	2	yes	complemented
134	C₂×#4021	C₂²	1	2	yes	complemented
135	C₂×#4021	C₂²	1	1	yes	characteristic, complemented
136	C₂×#4021	C₂²	1	2	yes	complemented
137	C₂×#4021	C₂²	1	2	yes	complemented
138	C₂×#4020	C₂²	1	2	yes	—
139	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
140	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
141	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₂₀	C₂²	1	2	yes	complemented
144	C₂×#4018	C₂²	1	2	yes	complemented
145	C₂×#4018	C₂²	1	1	yes	characteristic, complemented
146	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
147	C₂×#3540	—	5	1	no	maximal, Sylow
148	C₂⁴×D₅	C₂³	1	2	yes	—
149	C₂⁴×D₅	C₂³	1	1	yes	characteristic
150	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₅×Q₈	C₂³	1	2	yes	—
152	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
157	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
158	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
159	C₂²×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂²×C₂²⋊D₅	C₂³	1	1	yes	characteristic
161	C₂³×Dic₅	C₂³	1	1	yes	characteristic
162	C₂×#713	—	4	4	no	—
163	C₂×#713	C₂³	1	8	yes	—
164	C₂×Q₈×D₅	—	4	4	no	—
165	C₂×Q₈×D₅	C₂³	1	8	yes	complemented
166	C₂×#709	—	4	4	no	—
167	C₂×#709	—	4	4	no	—
168	C₂×#709	C₂³	1	8	yes	—
169	C₂×#709	C₂³	1	8	yes	—
170	C₂²×D₂₀	—	4	4	no	—
171	C₂²×D₂₀	C₂³	1	1	yes	characteristic
172	C₂²×D₂₀	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
178	C₂²×D₂₀	C₂³	1	2	yes	—
179	C₂²×D₂₀	C₂³	1	2	yes	—
180	C₂²×D₂₀	C₂³	1	2	yes	—
181	C₂²×D₂₀	C₂³	1	2	yes	—
182	C₂²×D₂₀	C₂³	1	8	yes	complemented
183	C₂²×C₄×D₅	—	4	4	no	—
184	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
185	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
186	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
187	C₂²×C₄×D₅	C₂³	1	2	yes	—
188	C₂²×C₄×D₅	C₂³	1	2	yes	—
189	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅	C₂³	1	2	yes	—
192	C₂²×C₄×D₅	C₂³	1	2	yes	—
193	C₂²×C₄×D₅	C₂³	1	2	yes	—
194	C₂²×C₄×D₅	C₂³	1	8	yes	complemented
195	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
196	C₂²×Dic₁₀	C₂³	1	2	yes	—
197	C₂²×Dic₁₀	C₂³	1	1	yes	characteristic
198	C₂²×Dic₁₀	C₂³	1	2	yes	—
199	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
200	C₅×#126	C₂³	1	16	yes	complemented
201	C₅×#126	C₂³	1	16	yes	complemented
202	C₅×#124	C₂³	1	16	yes	—
203	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
204	C₅×C₂²⋊Q₈	C₂³	1	8	yes	complemented
205	C₄×C₅×Q₈	C₂³	1	8	yes	complemented
206	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
207	C₄×C₅×D₄	C₂³	1	8	yes	—
208	C₅×#117	C₂³	1	8	yes	complemented
209	C₅×#117	C₂³	1	8	yes	complemented
210	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₄²×C₅	C₂³	1	2	yes	—
225	C₂×C₄²×C₅	C₂³	1	2	yes	—
226	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂³	1	2	yes	—
228	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊Dic₅	C₂³	1	2	yes	—
231	#4093	C₂³	1	16	yes	complemented
232	#4093	C₂³	1	16	yes	complemented
233	#4093	C₂³	1	16	yes	complemented
234	#4093	C₂³	1	8	yes	complemented
235	#4092	C₂³	1	16	yes	complemented
236	#4092	C₂³	1	8	yes	complemented
237	#4085	C₂³	1	8	yes	—
238	#4083	C₂³	1	8	yes	—
239	#4083	C₂³	1	16	yes	—
240	#4076	C₂³	1	8	yes	—
241	C₄×C₂²⋊D₅	C₂³	1	8	yes	—
242	C₄×C₂²⋊D₅	C₂³	1	8	yes	complemented
243	C₂×#685	C₂³	1	2	yes	—
244	C₂×#685	C₂³	1	1	yes	characteristic
245	C₂×#685	C₂³	1	2	yes	—
246	C₂×#685	C₂³	1	1	yes	characteristic
247	C₂×#685	C₂³	1	1	yes	characteristic
248	C₂×#685	C₂³	1	2	yes	—
249	C₂×#685	C₂³	1	1	yes	characteristic
250	C₂×#685	C₂³	1	2	yes	—
251	C₂×#685	C₂³	1	2	yes	—
252	C₂×#685	C₂³	1	2	yes	—
253	C₂×#685	C₂³	1	2	yes	—
254	C₂×#685	C₂³	1	2	yes	—
255	C₂×#685	C₂³	1	1	yes	characteristic
256	C₂×#685	C₂³	1	2	yes	—
257	C₂×#685	C₂³	1	2	yes	—
258	C₂×#685	C₂³	1	2	yes	—
259	C₂×#685	C₂³	1	2	yes	—
260	C₂×#685	C₂³	1	2	yes	—
261	C₂×#685	C₂³	1	2	yes	—
262	C₂×#685	C₂³	1	2	yes	—
263	C₂×#685	C₂³	1	1	yes	characteristic
264	C₂×#685	C₂³	1	2	yes	—
265	C₂×#685	C₂³	1	2	yes	—
266	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
267	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
269	C₂×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
270	#4070	C₂³	1	8	yes	complemented
271	C₂×#683	C₂³	1	1	yes	characteristic
272	C₂×#683	C₂³	1	2	yes	—
273	C₂×#683	C₂³	1	1	yes	characteristic
274	C₂×#683	C₂³	1	2	yes	—
275	C₂×#683	C₂³	1	1	yes	characteristic
276	C₂×#683	C₂³	1	1	yes	characteristic
277	C₂×#683	C₂³	1	2	yes	—
278	C₂×#683	C₂³	1	2	yes	—
279	C₂×C₄×Dic₅	C₂³	1	2	yes	—
280	C₂×C₄×Dic₅	C₂³	1	2	yes	—
281	C₂×C₄×Dic₅	C₂³	1	2	yes	—
282	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
283	#4044	C₂³	1	16	yes	complemented
284	#4043	C₂³	1	8	yes	complemented
285	#4043	C₂³	1	8	yes	complemented
286	#4043	C₂³	1	16	yes	complemented
287	#4042	C₂³	1	8	yes	complemented
288	#4042	C₂³	1	16	yes	complemented
289	#4042	C₂³	1	16	yes	complemented
290	#4041	C₂³	1	8	yes	—
291	#4041	C₂³	1	8	yes	—
292	#4041	C₂³	1	8	yes	—
293	#4041	C₂³	1	16	yes	—
294	#4041	C₂³	1	8	yes	complemented
295	#4041	C₂³	1	16	yes	complemented
296	#4041	C₂³	1	8	yes	complemented
297	#4041	C₂³	1	16	yes	complemented
298	#4040	C₂³	1	16	yes	complemented
299	#4040	C₂³	1	8	yes	complemented
300	#4040	C₂³	1	16	yes	complemented
301	#4040	C₂³	1	16	yes	complemented
302	#4040	C₂³	1	16	yes	complemented
303	#4040	C₂³	1	16	yes	complemented
304	#4040	C₂³	1	16	yes	complemented
305	#4039	C₂³	1	8	yes	complemented
306	#4039	C₂³	1	16	yes	complemented
307	#4039	C₂³	1	16	yes	complemented
308	#4038	C₂³	1	8	yes	complemented
309	#4038	C₂³	1	8	yes	complemented
310	#4038	C₂³	1	16	yes	complemented
311	#4034	C₂³	1	8	yes	complemented
312	#4034	C₂³	1	16	yes	complemented
313	#4033	C₂³	1	8	yes	complemented
314	#4032	C₂³	1	16	yes	complemented
315	#4031	C₂³	1	16	yes	—
316	#4031	C₂³	1	16	yes	—
317	#4031	C₂³	1	16	yes	complemented
318	#4031	C₂³	1	16	yes	complemented
319	#4030	C₂³	1	8	yes	—
320	#4030	C₂³	1	16	yes	—
321	#4030	C₂³	1	16	yes	complemented
322	#4030	C₂³	1	16	yes	complemented
323	#4029	C₂³	1	8	yes	—
324	#4029	C₂³	1	16	yes	complemented
325	#4028	C₂³	1	16	yes	—
326	#4028	C₂³	1	16	yes	—
327	#4028	C₂³	1	16	yes	complemented
328	#4028	C₂³	1	16	yes	complemented
329	#4028	C₂³	1	8	yes	complemented
330	#4028	C₂³	1	16	yes	complemented
331	#4027	C₂³	1	16	yes	complemented
332	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
333	D₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
334	#4025	C₂³	1	16	yes	complemented
335	#4024	C₂³	1	8	yes	complemented
336	#4022	C₂³	1	16	yes	complemented
337	#4022	C₂³	1	16	yes	complemented
338	#4021	C₂³	1	8	yes	complemented
339	#4021	C₂³	1	16	yes	complemented
340	#4021	C₂³	1	16	yes	complemented
341	#4021	C₂³	1	16	yes	complemented
342	#4021	C₂³	1	16	yes	complemented
343	#4020	C₂³	1	16	yes	—
344	C₄×D₂₀	C₂³	1	8	yes	complemented
345	C₄×D₂₀	C₂³	1	8	yes	complemented
346	C₄×D₂₀	C₂³	1	16	yes	complemented
347	C₄×D₂₀	C₂³	1	16	yes	complemented
348	C₄×D₂₀	C₂³	1	16	yes	complemented
349	#4018	C₂³	1	8	yes	complemented
350	#4018	C₂³	1	16	yes	complemented
351	C₄×Dic₁₀	C₂³	1	16	yes	complemented
352	#3540	—	5	32	no	—
353	C₂×H(3,𝔽₄)	—	5	2	no	—
354	C₂×#560	—	5	2	no	—
355	C₂×#559	—	5	2	no	—
356	C₂×#556	—	5	1	no	—
357	C₂×#556	D₅	1	1	yes	characteristic, complemented
358	C₂×#555	—	5	1	no	—
359	C₂×#555	—	5	1	no	—
360	C₂×#551	—	5	2	no	—
361	C₂×#548	—	5	1	no	—
362	C₂×#548	—	5	1	no	—
363	C₂×#546	—	5	1	no	—
364	C₂×#546	—	5	1	no	—
365	C₂×#542	—	5	1	no	—
366	C₂×#542	—	5	2	no	—
367	C₂×#542	—	5	1	no	—
368	C₂×#542	—	5	2	no	—
369	C₂×#538	—	5	2	no	—
370	C₂×#538	—	5	2	no	—
371	C₂×#536	—	5	1	no	—
372	C₂×#535	—	5	1	no	—
373	C₂×#525	—	5	1	no	—
374	C₂×#525	—	5	1	no	—
375	C₂×#525	—	5	1	no	—
376	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
378	C₂³×D₅	—	4	2	no	—
379	C₂³×D₅	—	4	2	no	—
380	C₂³×D₅	—	4	2	no	—
381	C₂³×D₅	—	4	4	no	—
382	C₂³×D₅	—	4	4	no	—
383	C₂³×D₅	—	4	4	no	—
384	C₂³×D₅	C₂⁴	1	1	yes	characteristic
385	C₂³×D₅	C₂⁴	1	1	yes	characteristic
386	C₂³×D₅	C₂⁴	1	1	yes	characteristic
387	C₂³×D₅	C₂⁴	1	2	yes	—
388	C₂³×D₅	C₂⁴	1	2	yes	—
389	C₂³×D₅	C₂⁴	1	4	yes	—
390	C₂³×D₅	C₂⁴	1	8	yes	—
391	C₂×C₅×Q₈	—	2	4	no	—
392	C₂×C₅×Q₈	—	4	4	no	—
393	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
394	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
395	C₂×C₅×D₄	—	4	2	no	—
396	C₂×C₅×D₄	C₂⁴	1	4	yes	—
397	C₂²×C₄×C₅	—	2	4	no	—
398	C₂²×C₄×C₅	—	2	4	no	—
399	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
405	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₂²⋊D₅	—	4	4	no	—
411	C₂×C₂²⋊D₅	—	4	2	no	—
412	C₂×C₂²⋊D₅	—	4	2	no	—
413	C₂×C₂²⋊D₅	—	4	2	no	—
414	C₂×C₂²⋊D₅	—	4	4	no	—
415	C₂×C₂²⋊D₅	—	4	2	no	—
416	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
417	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
418	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
419	C₂×C₂²⋊D₅	C₂⁴	1	8	yes	—
420	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
421	C₂×C₂²⋊D₅	C₂⁴	1	4	yes	—
422	C₂²×Dic₅	—	4	2	no	—
423	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅	C₂⁴	1	2	yes	—
425	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅	C₂⁴	1	2	yes	—
427	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅	C₂⁴	1	1	yes	characteristic
430	C₂²×Dic₅	C₂⁴	1	4	yes	—
431	#713	—	4	16	no	—
432	Q₈×D₅	—	4	16	no	—
433	#709	—	4	16	no	—
434	#709	—	4	16	no	—
435	C₂×D₂₀	—	2	4	no	—
436	C₂×D₂₀	—	2	4	no	—
437	C₂×D₂₀	—	4	16	no	—
438	C₂×D₂₀	—	4	4	no	—
439	C₂×D₂₀	—	4	4	no	—
440	C₂×D₂₀	—	4	4	no	—
441	C₂×D₂₀	—	4	2	no	—
442	C₂×D₂₀	—	4	4	no	—
443	C₂×D₂₀	—	4	4	no	—
444	C₂×D₂₀	—	4	4	no	—
445	C₂×D₂₀	—	4	2	no	—
446	C₂×D₂₀	—	4	4	no	—
447	C₂×D₂₀	C₂⁴	1	4	yes	—
448	C₂×D₂₀	C₂⁴	1	4	yes	—
449	C₂×D₂₀	C₂⁴	1	8	yes	—
450	C₂×D₂₀	C₂⁴	1	4	yes	—
451	C₂×D₂₀	C₂⁴	1	8	yes	—
452	C₂×D₂₀	C₂⁴	1	8	yes	—
453	C₂×D₂₀	C₂⁴	1	8	yes	—
454	C₂×D₂₀	C₂⁴	1	8	yes	—
455	C₂×D₂₀	C₂⁴	1	4	yes	—
456	C₂×D₂₀	C₂⁴	1	8	yes	—
457	C₂×D₂₀	C₂⁴	1	8	yes	—
458	C₂×C₄×D₅	—	2	4	no	—
459	C₂×C₄×D₅	—	2	4	no	—
460	C₂×C₄×D₅	—	2	4	no	—
461	C₂×C₄×D₅	—	4	16	no	—
462	C₂×C₄×D₅	—	4	2	no	—
463	C₂×C₄×D₅	—	4	2	no	—
464	C₂×C₄×D₅	—	4	4	no	—
465	C₂×C₄×D₅	—	4	4	no	—
466	C₂×C₄×D₅	—	4	4	no	—
467	C₂×C₄×D₅	—	4	4	no	—
468	C₂×C₄×D₅	—	4	4	no	—
469	C₂×C₄×D₅	C₂⁴	1	4	yes	—
470	C₂×C₄×D₅	C₂⁴	1	4	yes	—
471	C₂×C₄×D₅	C₂⁴	1	4	yes	—
472	C₂×C₄×D₅	C₂⁴	1	4	yes	—
473	C₂×C₄×D₅	C₂⁴	1	4	yes	—
474	C₂×C₄×D₅	C₂⁴	1	8	yes	—
475	C₂×C₄×D₅	C₂⁴	1	8	yes	—
476	C₂×C₄×D₅	C₂⁴	1	8	yes	—
477	C₂×C₄×D₅	C₂⁴	1	8	yes	—
478	C₂×C₄×D₅	C₂⁴	1	8	yes	—
479	C₂×Dic₁₀	—	2	4	no	—
480	C₂×Dic₁₀	—	4	4	no	—
481	C₂×Dic₁₀	—	4	2	no	—
482	C₂×Dic₁₀	—	4	4	no	—
483	C₂×Dic₁₀	C₂⁴	1	4	yes	—
484	C₂×Dic₁₀	C₂⁴	1	4	yes	—
485	C₂×Dic₁₀	C₂⁴	1	8	yes	—
486	C₂×Dic₁₀	C₂⁴	1	8	yes	—
487	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
488	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
489	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
490	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
491	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
492	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
493	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
494	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
495	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
496	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
497	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
498	C₅×C₂²⋊C₄	C₂⁴	1	4	yes	—
499	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
500	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
501	C₄²×C₅	C₂⁴	1	8	yes	—
502	C₄²×C₅	C₂⁴	1	8	yes	—
503	C₄²×C₅	C₂⁴	1	4	yes	—
504	C₄²×C₅	C₂⁴	1	8	yes	—
505	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
506	C₂²⋊Dic₅	C₂⁴	1	4	yes	—
507	C₂²⋊Dic₅	C₂⁴	1	8	yes	—
508	#685	C₂⁴	1	8	yes	—
509	#685	C₂⁴	1	4	yes	—
510	#685	C₂⁴	1	8	yes	—
511	#685	C₂⁴	1	4	yes	—
512	#685	C₂⁴	1	4	yes	—
513	#685	C₂⁴	1	8	yes	—
514	#685	C₂⁴	1	4	yes	—
515	#685	C₂⁴	1	8	yes	—
516	#685	C₂⁴	1	8	yes	—
517	#685	C₂⁴	1	8	yes	—
518	#685	C₂⁴	1	8	yes	—
519	#685	C₂⁴	1	8	yes	—
520	#685	C₂⁴	1	4	yes	—
521	#685	C₂⁴	1	8	yes	—
522	#685	C₂⁴	1	8	yes	—
523	#685	C₂⁴	1	8	yes	—
524	#685	C₂⁴	1	8	yes	—
525	#685	C₂⁴	1	8	yes	—
526	#685	C₂⁴	1	8	yes	—
527	#685	C₂⁴	1	8	yes	—
528	#685	C₂⁴	1	4	yes	—
529	#685	C₂⁴	1	8	yes	—
530	#685	C₂⁴	1	8	yes	—
531	C₄⋊Dic₅	C₂⁴	1	8	yes	—
532	C₄⋊Dic₅	C₂⁴	1	4	yes	—
533	C₄⋊Dic₅	C₂⁴	1	8	yes	—
534	C₄⋊Dic₅	C₂⁴	1	4	yes	—
535	#683	C₂⁴	1	4	yes	—
536	#683	C₂⁴	1	8	yes	—
537	#683	C₂⁴	1	4	yes	—
538	#683	C₂⁴	1	8	yes	—
539	#683	C₂⁴	1	4	yes	—
540	#683	C₂⁴	1	4	yes	—
541	#683	C₂⁴	1	8	yes	—
542	#683	C₂⁴	1	8	yes	—
543	C₄×Dic₅	C₂⁴	1	8	yes	—
544	C₄×Dic₅	C₂⁴	1	8	yes	—
545	C₄×Dic₅	C₂⁴	1	8	yes	—
546	C₄×Dic₅	C₂⁴	1	4	yes	—
547	C₂²×#41	—	5	1	no	—
548	C₂²×#41	—	5	1	no	—
549	C₂²×#41	—	5	1	no	—
550	C₂³×Q₈	—	5	1	no	—
551	C₂³×D₄	—	5	1	no	—
552	C₂⁴×C₄	—	5	1	no	—
553	H(3,𝔽₄)	—	5	32	no	—
554	#560	—	5	32	no	—
555	#559	—	5	32	no	—
556	#556	—	5	16	no	—
557	#556	C₂×D₅	1	16	yes	complemented
558	#555	—	5	16	no	—
559	#555	—	5	16	no	—
560	#551	—	5	32	no	—
561	#548	—	5	16	no	—
562	#548	—	5	16	no	—
563	#546	—	5	16	no	—
564	#546	—	5	16	no	—
565	#542	—	5	16	no	—
566	#542	—	5	32	no	—
567	#542	—	5	16	no	—
568	#542	—	5	32	no	—
569	#538	—	5	32	no	—
570	#538	—	5	32	no	—
571	#536	—	5	16	no	—
572	#535	—	5	16	no	—
573	C₂×C₄⋊Q₈	—	5	2	no	—
574	C₂×C₄⋊Q₈	—	5	1	no	—
575	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
576	C₂×#127	—	5	2	no	—
577	C₂×#126	—	5	2	no	—
578	C₂×#126	—	5	2	no	—
579	C₂×#126	—	5	2	no	—
580	C₂×#126	—	5	2	no	—
581	C₂×#126	C₂×D₅	1	2	yes	complemented
582	C₂×#126	C₂×D₅	1	2	yes	complemented
583	C₂×#124	—	5	2	no	—
584	C₂×#124	—	5	1	no	—
585	C₂×#124	—	5	2	no	—
586	C₂×#124	—	5	2	no	—
587	C₂×#124	—	5	2	no	—
588	C₂×#124	—	5	2	no	—
589	C₂×#124	—	5	2	no	—
590	C₂×#124	—	5	2	no	—
591	C₂×#124	—	5	2	no	—
592	C₂×#124	—	5	2	no	—
593	C₂×#124	—	5	1	no	—
594	C₂×#124	—	5	2	no	—
595	C₂×#124	—	5	2	no	—
596	C₂×#124	C₂×D₅	1	2	yes	—
597	#525	—	5	16	no	—
598	#525	—	5	16	no	—
599	#525	—	5	16	no	—
600	C₂×#123	—	5	2	no	—
601	C₂×#123	—	5	1	no	—
602	C₂×#123	—	5	2	no	—
603	C₂×#123	—	5	2	no	—
604	C₂×#123	—	5	2	no	—
605	C₂×#123	—	5	2	no	—
606	C₂×#123	—	5	2	no	—
607	C₂×#123	—	5	1	no	—
608	C₂×#123	—	5	2	no	—
609	C₂×#123	—	5	2	no	—
610	C₂×C₂²⋊Q₈	—	5	1	no	—
611	C₂×C₂²⋊Q₈	—	5	2	no	—
612	C₂×C₂²⋊Q₈	—	5	1	no	—
613	C₂×C₂²⋊Q₈	—	5	1	no	—
614	C₂×C₂²⋊Q₈	—	5	2	no	—
615	C₂×C₂²⋊Q₈	—	5	2	no	—
616	C₂×C₂²⋊Q₈	—	5	1	no	—
617	C₂×C₂²⋊Q₈	—	5	1	no	—
618	C₂×C₂²⋊Q₈	—	5	2	no	—
619	C₂×C₂²⋊Q₈	—	5	1	no	—
620	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
621	C₂×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
622	C₂×#121	—	5	1	no	—
623	C₂×#121	—	5	1	no	—
624	C₂×#121	—	5	1	no	—
625	C₂×#121	—	5	1	no	—
626	C₂×#121	—	5	1	no	—
627	C₂×#121	—	5	2	no	—
628	C₂×#121	—	5	1	no	—
629	C₂×#121	—	5	1	no	—
630	C₂×#121	—	5	2	no	—
631	C₂×#121	—	5	2	no	—
632	C₂×#121	—	5	1	no	—
633	C₂×#121	—	5	2	no	—
634	C₂×#121	—	5	2	no	—
635	C₂×#121	—	5	2	no	—
636	C₂×#120	—	5	1	no	—
637	C₂×#120	—	5	2	no	—
638	C₂×#120	—	5	2	no	—
639	C₂×#120	—	5	2	no	—
640	C₂×#120	—	5	1	no	—
641	C₂×#120	—	5	2	no	—
642	C₂×#120	—	5	2	no	—
643	C₂×#120	—	5	2	no	—
644	C₂×C₄×Q₈	—	5	1	no	—
645	C₂×C₄×Q₈	—	5	2	no	—
646	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
647	C₂×C₄×Q₈	C₂×D₅	1	2	yes	complemented
648	C₂×C₄×D₄	—	5	1	no	—
649	C₂×C₄×D₄	—	5	1	no	—
650	C₂×C₄×D₄	—	5	2	no	—
651	C₂×C₄×D₄	—	5	2	no	—
652	C₂×C₄×D₄	—	5	1	no	—
653	C₂×C₄×D₄	—	5	2	no	—
654	C₂×C₄×D₄	—	5	2	no	—
655	C₂×C₄×D₄	—	5	1	no	—
656	C₂×C₄×D₄	—	5	2	no	—
657	C₂×C₄×D₄	—	5	2	no	—
658	C₂×C₄×D₄	—	5	1	no	—
659	C₂×C₄×D₄	C₂×D₅	1	1	yes	characteristic
660	C₂×#117	—	5	1	no	—
661	C₂×#117	—	5	1	no	—
662	C₂×#117	—	5	2	no	—
663	C₂×#117	—	5	1	no	—
664	C₂×#117	—	5	2	no	—
665	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
666	C₂×#117	C₂×D₅	1	1	yes	characteristic, complemented
667	C₂²×C₂²⋊C₄	—	5	2	no	—
668	C₂²×C₂²⋊C₄	—	5	2	no	—
669	C₂³×C₅	—	2	2	no	—
670	C₂³×C₅	—	2	2	no	—
671	C₂³×C₅	—	2	2	no	—
672	C₂³×C₅	—	2	2	no	—
673	C₂³×C₅	—	2	2	no	—
674	C₂³×C₅	—	2	2	no	—
675	C₂³×C₅	C₂⁵	1	2	yes	—
676	C₂³×C₅	C₂⁵	1	2	yes	—
677	C₂³×C₅	C₂⁵	1	1	yes	characteristic
678	C₂²×D₅	—	2	2	no	—
679	C₂²×D₅	—	2	2	no	—
680	C₂²×D₅	—	2	2	no	—
681	C₂²×D₅	—	2	4	no	—
682	C₂²×D₅	—	2	4	no	—
683	C₂²×D₅	—	2	4	no	—
684	C₂²×D₅	—	2	4	no	—
685	C₂²×D₅	—	2	2	no	—
686	C₂²×D₅	—	2	2	no	—
687	C₂²×D₅	—	2	2	no	—
688	C₂²×D₅	—	2	2	no	—
689	C₂²×D₅	—	2	4	no	—
690	C₂²×D₅	—	2	2	no	—
691	C₂²×D₅	—	2	2	no	—
692	C₂²×D₅	—	2	4	no	—
693	C₂²×D₅	—	4	4	no	—
694	C₂²×D₅	—	4	4	no	—
695	C₂²×D₅	—	4	4	no	—
696	C₂²×D₅	—	4	8	no	—
697	C₂²×D₅	—	4	8	no	—
698	C₂²×D₅	—	4	8	no	—
699	C₂²×D₅	—	4	16	no	—
700	C₂²×D₅	—	8	16	no	—
701	C₂²×D₅	C₂⁵	1	2	yes	—
702	C₂²×D₅	C₂⁵	1	2	yes	—
703	C₂²×D₅	C₂⁵	1	4	yes	—
704	C₂²×D₅	C₂⁵	1	4	yes	—
705	C₂²×D₅	C₂⁵	1	2	yes	—
706	C₅×Q₈	—	2	8	no	—
707	C₅×Q₈	—	4	8	no	—
708	C₅×D₄	—	4	4	no	—
709	C₂×C₄×C₅	—	2	4	no	—
710	C₂×C₄×C₅	—	2	2	no	—
711	C₂×C₄×C₅	—	2	2	no	—
712	C₂×C₄×C₅	—	2	4	no	—
713	C₂×C₄×C₅	—	2	2	no	—
714	C₂×C₄×C₅	—	2	4	no	—
715	C₂×C₄×C₅	—	2	4	no	—
716	C₂×C₄×C₅	—	2	2	no	—
717	C₂×C₄×C₅	—	2	8	no	—
718	C₂×C₄×C₅	—	2	8	no	—
719	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
720	C₂×C₄×C₅	C₂⁵	1	4	yes	—
721	C₂×C₄×C₅	C₂⁵	1	4	yes	—
722	C₂×C₄×C₅	C₂⁵	1	2	yes	—
723	C₂×C₄×C₅	C₂⁵	1	4	yes	—
724	C₂×C₄×C₅	C₂⁵	1	2	yes	—
725	C₂×C₄×C₅	C₂⁵	1	2	yes	—
726	C₂×C₄×C₅	C₂⁵	1	2	yes	—
727	C₂×C₄×C₅	C₂⁵	1	4	yes	—
728	C₂×C₄×C₅	C₂⁵	1	2	yes	—
729	C₂²⋊D₅	—	4	8	no	—
730	C₂²⋊D₅	—	4	4	no	—
731	C₂²⋊D₅	—	4	4	no	—
732	C₂²⋊D₅	—	4	4	no	—
733	C₂²⋊D₅	—	4	8	no	—
734	C₂²⋊D₅	—	4	4	no	—
735	C₂×Dic₅	—	2	4	no	—
736	C₂×Dic₅	—	2	2	no	—
737	C₂×Dic₅	—	2	2	no	—
738	C₂×Dic₅	—	2	2	no	—
739	C₂×Dic₅	—	2	2	no	—
740	C₂×Dic₅	—	2	4	no	—
741	C₂×Dic₅	—	2	2	no	—
742	C₂×Dic₅	—	4	4	no	—
743	C₂×Dic₅	C₂⁵	1	2	yes	—
744	C₂×Dic₅	C₂⁵	1	4	yes	—
745	C₂×Dic₅	C₂⁵	1	2	yes	—
746	C₂×Dic₅	C₂⁵	1	2	yes	—
747	C₂×Dic₅	C₂⁵	1	2	yes	—
748	C₂×Dic₅	C₂⁵	1	4	yes	—
749	C₂×Dic₅	C₂⁵	1	2	yes	—
750	D₂₀	—	2	8	no	—
751	D₂₀	—	2	8	no	—
752	D₂₀	—	4	8	no	—
753	D₂₀	—	4	8	no	—
754	D₂₀	—	4	8	no	—
755	D₂₀	—	4	4	no	—
756	D₂₀	—	4	8	no	—
757	D₂₀	—	4	8	no	—
758	D₂₀	—	4	8	no	—
759	D₂₀	—	4	4	no	—
760	D₂₀	—	4	8	no	—
761	C₄×D₅	—	2	8	no	—
762	C₄×D₅	—	2	8	no	—
763	C₄×D₅	—	2	8	no	—
764	C₄×D₅	—	4	4	no	—
765	C₄×D₅	—	4	4	no	—
766	C₄×D₅	—	4	8	no	—
767	C₄×D₅	—	4	8	no	—
768	C₄×D₅	—	4	8	no	—
769	C₄×D₅	—	4	8	no	—
770	C₄×D₅	—	4	8	no	—
771	Dic₁₀	—	2	8	no	—
772	Dic₁₀	—	4	8	no	—
773	Dic₁₀	—	4	4	no	—
774	Dic₁₀	—	4	8	no	—
775	C₂⁵	—	5	2	no	—
776	C₂⁵	—	5	1	no	—
777	C₂×#41	—	5	8	no	—
778	C₂×#41	—	5	8	no	—
779	C₂×#41	—	5	8	no	—
780	C₂×#41	—	20	4	no	—
781	C₂×#41	—	20	4	no	—
782	C₂×#41	—	20	4	no	—
783	C₂²×Q₈	—	5	8	no	—
784	C₂²×Q₈	—	5	1	no	—
785	C₂²×Q₈	—	5	2	no	—
786	C₂²×Q₈	—	5	2	no	—
787	C₂²×Q₈	—	5	1	no	—
788	C₂²×Q₈	—	20	4	no	—
789	C₂²×Q₈	C₂²×D₅	1	1	yes	characteristic
790	C₂²×Q₈	C₂²×D₅	1	2	yes	—
791	C₂²×D₄	—	5	1	no	—
792	C₂²×D₄	—	5	2	no	—
793	C₂²×D₄	—	5	1	no	—
794	C₂²×D₄	—	5	1	no	—
795	C₂²×D₄	—	5	1	no	—
796	C₂²×D₄	—	5	2	no	—
797	C₂²×D₄	—	5	1	no	—
798	C₂²×D₄	—	5	1	no	—
799	C₂²×D₄	—	5	2	no	—
800	C₂²×D₄	—	5	2	no	—
801	C₂²×D₄	—	5	2	no	—
802	C₂²×D₄	—	5	1	no	—
803	C₂²×D₄	—	5	2	no	—
804	C₂²×D₄	—	5	2	no	—
805	C₂²×D₄	—	5	2	no	—
806	C₂²×D₄	—	5	1	no	—
807	C₂²×D₄	—	5	2	no	—
808	C₂²×D₄	—	5	8	no	—
809	C₂²×D₄	—	20	4	no	—
810	C₂²×D₄	C₂²×D₅	1	1	yes	characteristic
811	C₂³×C₄	—	5	1	no	—
812	C₂³×C₄	—	5	1	no	—
813	C₂³×C₄	—	5	1	no	—
814	C₂³×C₄	—	5	1	no	—
815	C₂³×C₄	—	5	2	no	—
816	C₂³×C₄	—	5	2	no	—
817	C₂³×C₄	—	5	2	no	—
818	C₂³×C₄	—	5	2	no	—
819	C₂³×C₄	—	5	1	no	—
820	C₂³×C₄	—	5	2	no	—
821	C₂³×C₄	—	5	1	no	—
822	C₂³×C₄	—	5	8	no	—
823	C₂³×C₄	—	20	4	no	—
824	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
825	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
826	C₄⋊Q₈	—	5	16	no	—
827	C₄⋊Q₈	—	5	8	no	—
828	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
829	#127	—	5	16	no	—
830	#126	—	5	16	no	—
831	#126	—	5	16	no	—
832	#126	—	5	16	no	—
833	#126	—	5	16	no	—
834	#126	C₂²×D₅	1	16	yes	complemented
835	#126	C₂²×D₅	1	16	yes	complemented
836	#124	—	5	16	no	—
837	#124	—	5	8	no	—
838	#124	—	5	16	no	—
839	#124	—	5	16	no	—
840	#124	—	5	16	no	—
841	#124	—	5	16	no	—
842	#124	—	5	16	no	—
843	#124	—	5	16	no	—
844	#124	—	5	16	no	—
845	#124	—	5	16	no	—
846	#124	—	5	8	no	—
847	#124	—	5	16	no	—
848	#124	—	5	16	no	—
849	#124	C₂²×D₅	1	16	yes	—
850	#123	—	5	16	no	—
851	#123	—	5	8	no	—
852	#123	—	5	16	no	—
853	#123	—	5	16	no	—
854	#123	—	5	16	no	—
855	#123	—	5	16	no	—
856	#123	—	5	16	no	—
857	#123	—	5	16	no	—
858	#123	—	5	8	no	—
859	#123	—	5	16	no	—
860	C₂²⋊Q₈	—	5	8	no	—
861	C₂²⋊Q₈	—	5	16	no	—
862	C₂²⋊Q₈	—	5	8	no	—
863	C₂²⋊Q₈	—	5	8	no	—
864	C₂²⋊Q₈	—	5	8	no	—
865	C₂²⋊Q₈	—	5	8	no	—
866	C₂²⋊Q₈	—	5	16	no	—
867	C₂²⋊Q₈	—	5	16	no	—
868	C₂²⋊Q₈	—	5	16	no	—
869	C₂²⋊Q₈	—	5	8	no	—
870	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
871	C₂²⋊Q₈	C₂²×D₅	1	8	yes	complemented
872	#121	—	5	8	no	—
873	#121	—	5	8	no	—
874	#121	—	5	8	no	—
875	#121	—	5	8	no	—
876	#121	—	5	8	no	—
877	#121	—	5	8	no	—
878	#121	—	5	8	no	—
879	#121	—	5	16	no	—
880	#121	—	5	16	no	—
881	#121	—	5	16	no	—
882	#121	—	5	8	no	—
883	#121	—	5	16	no	—
884	#121	—	5	16	no	—
885	#121	—	5	16	no	—
886	#120	—	5	8	no	—
887	#120	—	5	16	no	—
888	#120	—	5	8	no	—
889	#120	—	5	16	no	—
890	#120	—	5	16	no	—
891	#120	—	5	16	no	—
892	#120	—	5	16	no	—
893	#120	—	5	16	no	—
894	C₄×Q₈	—	5	8	no	—
895	C₄×Q₈	—	5	16	no	—
896	C₄×Q₈	C₂²×D₅	1	8	yes	complemented
897	C₄×Q₈	C₂²×D₅	1	16	yes	complemented
898	C₄×D₄	—	5	8	no	—
899	C₄×D₄	—	5	8	no	—
900	C₄×D₄	—	5	16	no	—
901	C₄×D₄	—	5	16	no	—
902	C₄×D₄	—	5	8	no	—
903	C₄×D₄	—	5	16	no	—
904	C₄×D₄	—	5	16	no	—
905	C₄×D₄	—	5	8	no	—
906	C₄×D₄	—	5	16	no	—
907	C₄×D₄	—	5	16	no	—
908	C₄×D₄	—	5	8	no	—
909	C₄×D₄	C₂²×D₅	1	8	yes	—
910	#117	—	5	8	no	—
911	#117	—	5	8	no	—
912	#117	—	5	16	no	—
913	#117	—	5	8	no	—
914	#117	—	5	16	no	—
915	#117	C₂²×D₅	1	8	yes	complemented
916	#117	C₂²×D₅	1	8	yes	complemented
917	C₂×C₄⋊C₄	—	5	1	no	—
918	C₂×C₄⋊C₄	—	5	1	no	—
919	C₂×C₄⋊C₄	—	5	1	no	—
920	C₂×C₄⋊C₄	—	5	1	no	—
921	C₂×C₄⋊C₄	—	5	1	no	—
922	C₂×C₄⋊C₄	—	5	2	no	—
923	C₂×C₄⋊C₄	—	5	2	no	—
924	C₂×C₄⋊C₄	—	5	1	no	—
925	C₂×C₄⋊C₄	—	5	2	no	—
926	C₂×C₄⋊C₄	—	5	2	no	—
927	C₂×C₄⋊C₄	—	5	2	no	—
928	C₂×C₄⋊C₄	—	5	2	no	—
929	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
932	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
934	C₂×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
935	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
936	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
937	C₂×C₂²⋊C₄	—	5	1	no	—
938	C₂×C₂²⋊C₄	—	5	2	no	—
939	C₂×C₂²⋊C₄	—	5	1	no	—
940	C₂×C₂²⋊C₄	—	5	2	no	—
941	C₂×C₂²⋊C₄	—	5	2	no	—
942	C₂×C₂²⋊C₄	—	5	2	no	—
943	C₂×C₂²⋊C₄	—	5	2	no	—
944	C₂×C₂²⋊C₄	—	5	2	no	—
945	C₂×C₂²⋊C₄	—	5	2	no	—
946	C₂×C₂²⋊C₄	—	5	2	no	—
947	C₂×C₂²⋊C₄	—	5	1	no	—
948	C₂×C₂²⋊C₄	—	5	1	no	—
949	C₂×C₂²⋊C₄	—	5	2	no	—
950	C₂×C₂²⋊C₄	—	5	1	no	—
951	C₂×C₂²⋊C₄	—	5	1	no	—
952	C₂×C₂²⋊C₄	—	5	1	no	—
953	C₂×C₂²⋊C₄	—	5	2	no	—
954	C₂×C₂²⋊C₄	—	5	2	no	—
955	C₂×C₂²⋊C₄	—	5	2	no	—
956	C₂×C₂²⋊C₄	—	5	2	no	—
957	C₂×C₂²⋊C₄	—	5	2	no	—
958	C₂×C₂²⋊C₄	—	5	2	no	—
959	C₂×C₂²⋊C₄	—	5	2	no	—
960	C₂×C₂²⋊C₄	—	5	1	no	—
961	C₂×C₂²⋊C₄	—	5	2	no	—
962	C₂×C₂²⋊C₄	—	5	2	no	—
963	C₂×C₂²⋊C₄	—	5	16	no	—
964	C₂×C₂²⋊C₄	—	5	16	no	—
965	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
967	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
968	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
969	C₂×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
970	C₂×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
971	C₂×C₄²	—	5	2	no	—
972	C₂×C₄²	—	5	2	no	—
973	C₂×C₄²	—	5	1	no	—
974	C₂×C₄²	—	5	2	no	—
975	C₂×C₄²	C₂²×D₅	1	2	yes	—
976	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
977	C₂×C₄²	C₂²×D₅	1	2	yes	—
978	C₂×C₄²	C₂²×D₅	1	2	yes	—
979	C₂²×C₅	—	2	2	no	—
980	C₂²×C₅	—	2	2	no	—
981	C₂²×C₅	—	2	2	no	—
982	C₂²×C₅	—	2	2	no	—
983	C₂²×C₅	—	2	2	no	—
984	C₂²×C₅	—	2	2	no	—
985	C₂²×C₅	—	4	4	no	—
986	C₂²×C₅	—	4	4	no	—
987	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
988	C₂²×C₅	#585	1	2	yes	—
989	C₂²×C₅	#585	1	2	yes	—
990	C₂²×C₅	C₂⁶	1	1	yes	characteristic
991	C₂×D₅	—	2	2	no	—
992	C₂×D₅	—	2	2	no	—
993	C₂×D₅	—	2	2	no	—
994	C₂×D₅	—	2	4	no	—
995	C₂×D₅	—	2	4	no	—
996	C₂×D₅	—	2	4	no	—
997	C₂×D₅	—	2	4	no	—
998	C₂×D₅	—	2	2	no	—
999	C₂×D₅	—	2	2	no	—
1000	C₂×D₅	—	2	2	no	—
1001	C₂×D₅	—	2	2	no	—
1002	C₂×D₅	—	2	4	no	—
1003	C₂×D₅	—	2	2	no	—
1004	C₂×D₅	—	2	2	no	—
1005	C₂×D₅	—	2	4	no	—
1006	C₂×D₅	—	4	16	no	—
1007	C₂×D₅	—	4	4	no	—
1008	C₂×D₅	—	4	4	no	—
1009	C₂×D₅	—	4	4	no	—
1010	C₂×D₅	—	4	8	no	—
1011	C₂×D₅	—	4	8	no	—
1012	C₂×D₅	—	8	16	no	—
1013	C₄×C₅	—	2	4	no	—
1014	C₄×C₅	—	2	2	no	—
1015	C₄×C₅	—	2	2	no	—
1016	C₄×C₅	—	2	4	no	—
1017	C₄×C₅	—	2	2	no	—
1018	C₄×C₅	—	2	4	no	—
1019	C₄×C₅	—	2	4	no	—
1020	C₄×C₅	—	2	2	no	—
1021	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
1022	Dic₅	—	2	4	no	—
1023	Dic₅	—	2	2	no	—
1024	Dic₅	—	2	2	no	—
1025	Dic₅	—	2	2	no	—
1026	Dic₅	—	2	2	no	—
1027	Dic₅	—	2	4	no	—
1028	Dic₅	—	2	2	no	—
1029	C₂⁴	—	5	1	no	—
1030	C₂⁴	—	5	1	no	—
1031	C₂⁴	—	5	2	no	—
1032	C₂⁴	—	5	2	no	—
1033	C₂⁴	—	5	1	no	—
1034	C₂⁴	—	5	8	no	—
1035	C₂⁴	—	5	4	no	—
1036	C₂⁴	—	20	2	no	—
1037	C₂⁴	—	20	2	no	—
1038	C₂⁴	—	20	2	no	—
1039	C₂⁴	—	20	4	no	—
1040	C₂⁴	—	20	4	no	—
1041	C₂⁴	—	20	4	no	—
1042	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1043	C₂⁴	C₂³×D₅	1	1	yes	characteristic
1044	#41	—	20	16	no	—
1045	#41	—	20	16	no	—
1046	#41	—	20	16	no	—
1047	C₂×Q₈	—	2	4	no	—
1048	C₂×Q₈	—	4	4	no	—
1049	C₂×Q₈	—	5	4	no	—
1050	C₂×Q₈	—	5	8	no	—
1051	C₂×Q₈	—	5	8	no	—
1052	C₂×Q₈	—	5	4	no	—
1053	C₂×Q₈	—	10	4	no	—
1054	C₂×Q₈	—	20	4	no	—
1055	C₂×Q₈	—	20	2	no	—
1056	C₂×Q₈	—	20	4	no	—
1057	C₂×Q₈	—	20	16	no	—
1058	C₂×Q₈	C₂³×D₅	1	4	yes	—
1059	C₂×Q₈	C₂³×D₅	1	8	yes	—
1060	C₂×D₄	—	4	2	no	—
1061	C₂×D₄	—	5	4	no	—
1062	C₂×D₄	—	5	8	no	—
1063	C₂×D₄	—	5	4	no	—
1064	C₂×D₄	—	5	4	no	—
1065	C₂×D₄	—	5	4	no	—
1066	C₂×D₄	—	5	8	no	—
1067	C₂×D₄	—	5	4	no	—
1068	C₂×D₄	—	5	4	no	—
1069	C₂×D₄	—	5	8	no	—
1070	C₂×D₄	—	5	8	no	—
1071	C₂×D₄	—	5	8	no	—
1072	C₂×D₄	—	5	4	no	—
1073	C₂×D₄	—	5	8	no	—
1074	C₂×D₄	—	5	8	no	—
1075	C₂×D₄	—	5	8	no	—
1076	C₂×D₄	—	5	4	no	—
1077	C₂×D₄	—	5	8	no	—
1078	C₂×D₄	—	10	4	no	—
1079	C₂×D₄	—	10	4	no	—
1080	C₂×D₄	—	20	16	no	—
1081	C₂×D₄	—	20	4	no	—
1082	C₂×D₄	—	20	2	no	—
1083	C₂×D₄	—	20	4	no	—
1084	C₂×D₄	—	20	4	no	—
1085	C₂×D₄	—	20	4	no	—
1086	C₂×D₄	—	20	4	no	—
1087	C₂×D₄	—	20	2	no	—
1088	C₂×D₄	—	20	4	no	—
1089	C₂×D₄	—	20	4	no	—
1090	C₂×D₄	—	20	2	no	—
1091	C₂×D₄	—	20	2	no	—
1092	C₂×D₄	—	20	4	no	—
1093	C₂×D₄	—	20	2	no	—
1094	C₂×D₄	—	20	4	no	—
1095	C₂×D₄	—	20	2	no	—
1096	C₂×D₄	C₂³×D₅	1	4	yes	—
1097	C₂²×C₄	—	2	4	no	—
1098	C₂²×C₄	—	2	4	no	—
1099	C₂²×C₄	—	5	1	no	—
1100	C₂²×C₄	—	5	2	no	—
1101	C₂²×C₄	—	5	1	no	—
1102	C₂²×C₄	—	5	1	no	—
1103	C₂²×C₄	—	5	1	no	—
1104	C₂²×C₄	—	5	2	no	—
1105	C₂²×C₄	—	5	1	no	—
1106	C₂²×C₄	—	5	4	no	—
1107	C₂²×C₄	—	5	4	no	—
1108	C₂²×C₄	—	5	4	no	—
1109	C₂²×C₄	—	5	4	no	—
1110	C₂²×C₄	—	5	8	no	—
1111	C₂²×C₄	—	5	8	no	—
1112	C₂²×C₄	—	5	8	no	—
1113	C₂²×C₄	—	5	8	no	—
1114	C₂²×C₄	—	5	4	no	—
1115	C₂²×C₄	—	5	8	no	—
1116	C₂²×C₄	—	5	4	no	—
1117	C₂²×C₄	—	10	4	no	—
1118	C₂²×C₄	—	10	4	no	—
1119	C₂²×C₄	—	10	4	no	—
1120	C₂²×C₄	—	20	16	no	—
1121	C₂²×C₄	—	20	2	no	—
1122	C₂²×C₄	—	20	2	no	—
1123	C₂²×C₄	—	20	4	no	—
1124	C₂²×C₄	—	20	4	no	—
1125	C₂²×C₄	—	20	4	no	—
1126	C₂²×C₄	—	20	4	no	—
1127	C₂²×C₄	—	20	4	no	—
1128	C₂²×C₄	—	20	2	no	—
1129	C₂²×C₄	C₂³×D₅	1	4	yes	—
1130	C₂²×C₄	C₂³×D₅	1	4	yes	—
1131	C₂²×C₄	C₂³×D₅	1	2	yes	—
1132	C₂²×C₄	C₂³×D₅	1	2	yes	—
1133	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1134	C₂²×C₄	C₂³×D₅	1	2	yes	—
1135	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1136	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1137	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1138	C₂²×C₄	C₂³×D₅	1	2	yes	—
1139	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
1140	C₄⋊C₄	—	5	4	no	—
1141	C₄⋊C₄	—	5	4	no	—
1142	C₄⋊C₄	—	5	4	no	—
1143	C₄⋊C₄	—	5	4	no	—
1144	C₄⋊C₄	—	5	4	no	—
1145	C₄⋊C₄	—	5	8	no	—
1146	C₄⋊C₄	—	5	8	no	—
1147	C₄⋊C₄	—	5	4	no	—
1148	C₄⋊C₄	—	5	8	no	—
1149	C₄⋊C₄	—	5	8	no	—
1150	C₄⋊C₄	—	5	8	no	—
1151	C₄⋊C₄	—	5	8	no	—
1152	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1153	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1154	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1155	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1156	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1157	C₄⋊C₄	C₂³×D₅	1	4	yes	—
1158	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1159	C₄⋊C₄	C₂³×D₅	1	8	yes	—
1160	C₂²⋊C₄	—	5	4	no	—
1161	C₂²⋊C₄	—	5	8	no	—
1162	C₂²⋊C₄	—	5	4	no	—
1163	C₂²⋊C₄	—	5	8	no	—
1164	C₂²⋊C₄	—	5	8	no	—
1165	C₂²⋊C₄	—	5	8	no	—
1166	C₂²⋊C₄	—	5	8	no	—
1167	C₂²⋊C₄	—	5	8	no	—
1168	C₂²⋊C₄	—	5	8	no	—
1169	C₂²⋊C₄	—	5	8	no	—
1170	C₂²⋊C₄	—	5	4	no	—
1171	C₂²⋊C₄	—	5	4	no	—
1172	C₂²⋊C₄	—	5	8	no	—
1173	C₂²⋊C₄	—	5	4	no	—
1174	C₂²⋊C₄	—	5	4	no	—
1175	C₂²⋊C₄	—	5	4	no	—
1176	C₂²⋊C₄	—	5	8	no	—
1177	C₂²⋊C₄	—	5	8	no	—
1178	C₂²⋊C₄	—	5	8	no	—
1179	C₂²⋊C₄	—	5	8	no	—
1180	C₂²⋊C₄	—	5	8	no	—
1181	C₂²⋊C₄	—	5	8	no	—
1182	C₂²⋊C₄	—	5	8	no	—
1183	C₂²⋊C₄	—	5	4	no	—
1184	C₂²⋊C₄	—	5	8	no	—
1185	C₂²⋊C₄	—	5	8	no	—
1186	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1187	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1188	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1189	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1190	C₂²⋊C₄	C₂³×D₅	1	8	yes	—
1191	C₂²⋊C₄	C₂³×D₅	1	4	yes	—
1192	C₄²	—	5	8	no	—
1193	C₄²	—	5	8	no	—
1194	C₄²	—	5	4	no	—
1195	C₄²	—	5	8	no	—
1196	C₄²	C₂³×D₅	1	8	yes	—
1197	C₄²	C₂³×D₅	1	4	yes	—
1198	C₄²	C₂³×D₅	1	8	yes	—
1199	C₄²	C₂³×D₅	1	8	yes	—
1200	C₂×C₅	—	4	2	no	—
1201	C₂×C₅	—	4	2	no	—
1202	C₂×C₅	#3540	1	4	yes	complemented
1203	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1204	C₂×C₅	C₂×#585	1	1	yes	characteristic
1205	C₂×C₅	C₂×#585	1	1	yes	characteristic
1206	D₅	—	4	2	no	—
1207	D₅	—	4	2	no	—
1208	D₅	—	4	2	no	—
1209	D₅	—	4	4	no	—
1210	D₅	—	4	4	no	—
1211	C₂³	—	2	2	no	—
1212	C₂³	—	2	2	no	—
1213	C₂³	—	2	2	no	—
1214	C₂³	—	2	2	no	—
1215	C₂³	—	2	2	no	—
1216	C₂³	—	2	2	no	—
1217	C₂³	—	5	2	no	—
1218	C₂³	—	5	2	no	—
1219	C₂³	—	5	4	no	—
1220	C₂³	—	5	4	no	—
1221	C₂³	—	5	2	no	—
1222	C₂³	—	10	2	no	—
1223	C₂³	—	10	2	no	—
1224	C₂³	—	10	2	no	—
1225	C₂³	—	10	4	no	—
1226	C₂³	—	10	4	no	—
1227	C₂³	—	10	4	no	—
1228	C₂³	—	10	2	no	—
1229	C₂³	—	10	2	no	—
1230	C₂³	—	10	2	no	—
1231	C₂³	—	10	4	no	—
1232	C₂³	—	10	4	no	—
1233	C₂³	—	10	2	no	—
1234	C₂³	—	10	2	no	—
1235	C₂³	—	10	2	no	—
1236	C₂³	—	10	4	no	—
1237	C₂³	—	20	4	no	—
1238	C₂³	—	20	4	no	—
1239	C₂³	—	20	4	no	—
1240	C₂³	—	20	8	no	—
1241	C₂³	—	20	8	no	—
1242	C₂³	—	20	8	no	—
1243	C₂³	—	20	16	no	—
1244	C₂³	—	40	16	no	—
1245	C₂³	C₂⁴×D₅	1	2	yes	—
1246	C₂³	C₂⁴×D₅	1	2	yes	—
1247	C₂³	C₂⁴×D₅	1	1	yes	characteristic
1248	Q₈	—	2	8	no	—
1249	Q₈	—	4	8	no	—
1250	Q₈	—	10	8	no	—
1251	Q₈	—	20	8	no	—
1252	Q₈	—	20	4	no	—
1253	Q₈	—	20	8	no	—
1254	D₄	—	4	4	no	—
1255	D₄	—	10	8	no	—
1256	D₄	—	10	8	no	—
1257	D₄	—	20	8	no	—
1258	D₄	—	20	4	no	—
1259	D₄	—	20	8	no	—
1260	D₄	—	20	8	no	—
1261	D₄	—	20	8	no	—
1262	D₄	—	20	8	no	—
1263	D₄	—	20	4	no	—
1264	D₄	—	20	8	no	—
1265	D₄	—	20	8	no	—
1266	D₄	—	20	4	no	—
1267	D₄	—	20	4	no	—
1268	D₄	—	20	8	no	—
1269	D₄	—	20	4	no	—
1270	D₄	—	20	8	no	—
1271	D₄	—	20	4	no	—
1272	C₂×C₄	—	2	2	no	—
1273	C₂×C₄	—	2	2	no	—
1274	C₂×C₄	—	2	4	no	—
1275	C₂×C₄	—	2	4	no	—
1276	C₂×C₄	—	2	2	no	—
1277	C₂×C₄	—	2	4	no	—
1278	C₂×C₄	—	2	2	no	—
1279	C₂×C₄	—	2	4	no	—
1280	C₂×C₄	—	2	8	no	—
1281	C₂×C₄	—	2	8	no	—
1282	C₂×C₄	—	5	2	no	—
1283	C₂×C₄	—	5	4	no	—
1284	C₂×C₄	—	5	2	no	—
1285	C₂×C₄	—	5	2	no	—
1286	C₂×C₄	—	5	2	no	—
1287	C₂×C₄	—	5	4	no	—
1288	C₂×C₄	—	5	2	no	—
1289	C₂×C₄	—	10	2	no	—
1290	C₂×C₄	—	10	2	no	—
1291	C₂×C₄	—	10	2	no	—
1292	C₂×C₄	—	10	4	no	—
1293	C₂×C₄	—	10	2	no	—
1294	C₂×C₄	—	10	4	no	—
1295	C₂×C₄	—	10	2	no	—
1296	C₂×C₄	—	10	8	no	—
1297	C₂×C₄	—	10	8	no	—
1298	C₂×C₄	—	10	8	no	—
1299	C₂×C₄	—	20	4	no	—
1300	C₂×C₄	—	20	4	no	—
1301	C₂×C₄	—	20	8	no	—
1302	C₂×C₄	—	20	8	no	—
1303	C₂×C₄	—	20	8	no	—
1304	C₂×C₄	—	20	8	no	—
1305	C₂×C₄	—	20	8	no	—
1306	C₂×C₄	—	20	4	no	—
1307	C₂×C₄	#4149	1	4	yes	—
1308	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1309	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1310	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1311	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1312	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1313	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1314	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1315	C₂×C₄	C₂⁴×D₅	1	4	yes	—
1316	C₂×C₄	C₂⁴×D₅	1	2	yes	—
1317	C₅	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
1318	C₂²	—	2	2	no	—
1319	C₂²	—	2	2	no	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	2	2	no	—
1324	C₂²	—	4	4	no	—
1325	C₂²	—	4	4	no	—
1326	C₂²	—	10	2	no	—
1327	C₂²	—	10	2	no	—
1328	C₂²	—	10	2	no	—
1329	C₂²	—	10	4	no	—
1330	C₂²	—	10	4	no	—
1331	C₂²	—	10	4	no	—
1332	C₂²	—	10	2	no	—
1333	C₂²	—	10	2	no	—
1334	C₂²	—	10	2	no	—
1335	C₂²	—	10	4	no	—
1336	C₂²	—	10	4	no	—
1337	C₂²	—	10	2	no	—
1338	C₂²	—	10	2	no	—
1339	C₂²	—	10	2	no	—
1340	C₂²	—	10	4	no	—
1341	C₂²	—	20	16	no	—
1342	C₂²	—	20	4	no	—
1343	C₂²	—	20	4	no	—
1344	C₂²	—	20	8	no	—
1345	C₂²	—	20	8	no	—
1346	C₂²	—	20	4	no	—
1347	C₂²	—	40	16	no	—
1348	C₂²	C₂×#4149	1	2	yes	—
1349	C₂²	#66283	1	2	yes	—
1350	C₂²	#66287	1	2	yes	—
1351	C₂²	C₂⁵×D₅	1	1	yes	characteristic
1352	C₄	—	2	2	no	—
1353	C₄	—	2	2	no	—
1354	C₄	—	2	4	no	—
1355	C₄	—	2	4	no	—
1356	C₄	—	2	2	no	—
1357	C₄	—	2	4	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	2	4	no	—
1360	C₄	—	10	2	no	—
1361	C₄	—	10	2	no	—
1362	C₄	—	10	2	no	—
1363	C₄	—	10	4	no	—
1364	C₄	—	10	2	no	—
1365	C₄	—	10	4	no	—
1366	C₄	—	10	2	no	—
1367	C₄	C₂×#4149	1	4	yes	—
1368	C₂	—	4	2	no	—
1369	C₂	—	4	2	no	—
1370	C₂	—	20	2	no	—
1371	C₂	—	20	2	no	—
1372	C₂	—	20	4	no	—
1373	C₂	—	20	4	no	—
1374	C₂	—	20	2	no	—
1375	C₂	#10618909	1	4	yes	direct product factor
1376	C₂	C₂²×#4149	1	1	yes	characteristic
1377	C₂	C₂×#66283	1	1	yes	characteristic
1378	C₂	C₂×#66287	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#556	C₂
socle	C₂³×C₅	C₂⁵
hypercenter	C₂×#556	D₅
hypocenter	C₅	C₂×#3540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#556

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#556	C₂	semidirect
2. #10618909	C₂	direct (N × H)
3. C₂×#66067	C₂	semidirect
4. C₂×#66068	C₂	semidirect
5. C₂×#66045	C₂	semidirect
6. C₂×#66039	C₂	semidirect
7. C₂×#66038	C₂	semidirect
8. C₂×#66044	C₂	semidirect
9. C₂×#66017	C₂	semidirect
10. C₂×#66012	C₂	semidirect
11. C₂×#65967	C₂	semidirect
12. C₂×#65964	C₂	semidirect
13. C₂×#65962	C₂	semidirect
14. C₂×#65961	C₂	semidirect
15. C₂×#65910	C₂	semidirect
16. C₂×#65916	C₂	semidirect
17. C₂×#65916	C₂	semidirect
18. C₂×#65919	C₂	semidirect
19. C₂×#65884	C₂	semidirect
20. C₂×#65881	C₂	semidirect
21. C₂×#65867	C₂	semidirect
22. C₂×#65866	C₂	semidirect
23. C₂×#65859	C₂	semidirect
24. C₂×#65858	C₂	semidirect
26. C₂²×Q₈×D₅	C₂²	semidirect
29. C₂³×D₂₀	C₂²	semidirect
30. C₂³×C₄×D₅	C₂²	semidirect
31. C₅×#556	C₂²	semidirect
32. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₅×#126	C₂²	semidirect
34. C₂×C₅×#126	C₂²	semidirect
36. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₄×C₅×Q₈	C₂²	semidirect
39. C₂×C₄×C₅×Q₈	C₂²	semidirect
41. C₂×C₅×#117	C₂²	semidirect
42. C₂×C₅×#117	C₂²	semidirect
43. C₂×#4093	C₂²	semidirect
44. C₂×#4093	C₂²	semidirect
45. C₂×#4093	C₂²	semidirect
46. C₂×#4093	C₂²	semidirect
47. C₂×#4092	C₂²	semidirect
48. C₂×#4092	C₂²	semidirect
54. C₂×C₄×C₂²⋊D₅	C₂²	semidirect
55. C₂×#4070	C₂²	semidirect
56. #66068	C₂²	semidirect
57. #66067	C₂²	semidirect
58. #66045	C₂²	semidirect
59. #66044	C₂²	semidirect
60. #66039	C₂²	semidirect
61. #66038	C₂²	semidirect
62. #66017	C₂²	semidirect
63. #66012	C₂²	semidirect
64. #65967	C₂²	semidirect
65. #65964	C₂²	semidirect
66. #65962	C₂²	semidirect
67. #65961	C₂²	semidirect
68. #65919	C₂²	semidirect
69. #65916	C₂²	semidirect
70. #65916	C₂²	semidirect
71. #65910	C₂²	semidirect
72. #65884	C₂²	semidirect
73. #65881	C₂²	semidirect
74. #65867	C₂²	semidirect
75. #65866	C₂²	semidirect
76. #65859	C₂²	semidirect
77. #65858	C₂²	semidirect
78. C₂×#4044	C₂²	semidirect
79. C₂×#4043	C₂²	semidirect
80. C₂×#4043	C₂²	semidirect
81. C₂×#4043	C₂²	semidirect
82. C₂×#4042	C₂²	semidirect
83. C₂×#4042	C₂²	semidirect
84. C₂×#4042	C₂²	semidirect
89. C₂×#4041	C₂²	semidirect
90. C₂×#4041	C₂²	semidirect
91. C₂×#4041	C₂²	semidirect
92. C₂×#4041	C₂²	semidirect
93. C₂×#4040	C₂²	semidirect
94. C₂×#4040	C₂²	semidirect
95. C₂×#4040	C₂²	semidirect
96. C₂×#4040	C₂²	semidirect
97. C₂×#4040	C₂²	semidirect
98. C₂×#4040	C₂²	semidirect
99. C₂×#4040	C₂²	semidirect
100. C₂×#4039	C₂²	semidirect
101. C₂×#4039	C₂²	semidirect
102. C₂×#4039	C₂²	semidirect
103. C₂×#4038	C₂²	semidirect
104. C₂×#4038	C₂²	semidirect
105. C₂×#4038	C₂²	semidirect
106. C₂×#4034	C₂²	semidirect
107. C₂×#4034	C₂²	semidirect
108. C₂×#4033	C₂²	semidirect
109. C₂×#4032	C₂²	semidirect
112. C₂×#4031	C₂²	semidirect
113. C₂×#4031	C₂²	semidirect
116. C₂×#4030	C₂²	semidirect
117. C₂×#4030	C₂²	semidirect
119. C₂×#4029	C₂²	semidirect
122. C₂×#4028	C₂²	semidirect
123. C₂×#4028	C₂²	semidirect
124. C₂×#4028	C₂²	semidirect
125. C₂×#4028	C₂²	semidirect
126. C₂×#4027	C₂²	semidirect
127. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
128. C₂×D₅×C₂²⋊C₄	C₂²	semidirect
129. C₂×#4025	C₂²	semidirect
130. C₂×#4024	C₂²	semidirect
131. C₂×#4022	C₂²	semidirect
132. C₂×#4022	C₂²	semidirect
133. C₂×#4021	C₂²	semidirect
134. C₂×#4021	C₂²	semidirect
135. C₂×#4021	C₂²	semidirect
136. C₂×#4021	C₂²	semidirect
137. C₂×#4021	C₂²	semidirect
139. C₂×C₄×D₂₀	C₂²	semidirect
140. C₂×C₄×D₂₀	C₂²	semidirect
141. C₂×C₄×D₂₀	C₂²	semidirect
142. C₂×C₄×D₂₀	C₂²	semidirect
143. C₂×C₄×D₂₀	C₂²	semidirect
144. C₂×#4018	C₂²	semidirect
145. C₂×#4018	C₂²	semidirect
146. C₂×C₄×Dic₁₀	C₂²	semidirect
165. C₂×Q₈×D₅	C₂³	semidirect
182. C₂²×D₂₀	C₂³	semidirect
194. C₂²×C₄×D₅	C₂³	semidirect
199. C₅×C₄⋊Q₈	C₂³	semidirect
200. C₅×#126	C₂³	semidirect
201. C₅×#126	C₂³	semidirect
203. C₅×C₂²⋊Q₈	C₂³	semidirect
204. C₅×C₂²⋊Q₈	C₂³	semidirect
205. C₄×C₅×Q₈	C₂³	semidirect
206. C₄×C₅×Q₈	C₂³	semidirect
208. C₅×#117	C₂³	semidirect
209. C₅×#117	C₂³	semidirect
231. #4093	C₂³	semidirect
232. #4093	C₂³	semidirect
233. #4093	C₂³	semidirect
234. #4093	C₂³	semidirect
235. #4092	C₂³	semidirect
236. #4092	C₂³	semidirect
242. C₄×C₂²⋊D₅	C₂³	semidirect
270. #4070	C₂³	semidirect
283. #4044	C₂³	semidirect
284. #4043	C₂³	semidirect
285. #4043	C₂³	semidirect
286. #4043	C₂³	semidirect
287. #4042	C₂³	semidirect
288. #4042	C₂³	semidirect
289. #4042	C₂³	semidirect
294. #4041	C₂³	semidirect
295. #4041	C₂³	semidirect
296. #4041	C₂³	semidirect
297. #4041	C₂³	semidirect
298. #4040	C₂³	semidirect
299. #4040	C₂³	semidirect
300. #4040	C₂³	semidirect
301. #4040	C₂³	semidirect
302. #4040	C₂³	semidirect
303. #4040	C₂³	semidirect
304. #4040	C₂³	semidirect
305. #4039	C₂³	semidirect
306. #4039	C₂³	semidirect
307. #4039	C₂³	semidirect
308. #4038	C₂³	semidirect
309. #4038	C₂³	semidirect
310. #4038	C₂³	semidirect
311. #4034	C₂³	semidirect
312. #4034	C₂³	semidirect
313. #4033	C₂³	semidirect
314. #4032	C₂³	semidirect
317. #4031	C₂³	semidirect
318. #4031	C₂³	semidirect
321. #4030	C₂³	semidirect
322. #4030	C₂³	semidirect
324. #4029	C₂³	semidirect
327. #4028	C₂³	semidirect
328. #4028	C₂³	semidirect
329. #4028	C₂³	semidirect
330. #4028	C₂³	semidirect
331. #4027	C₂³	semidirect
332. D₅×C₂²⋊C₄	C₂³	semidirect
333. D₅×C₂²⋊C₄	C₂³	semidirect
334. #4025	C₂³	semidirect
335. #4024	C₂³	semidirect
336. #4022	C₂³	semidirect
337. #4022	C₂³	semidirect
338. #4021	C₂³	semidirect
339. #4021	C₂³	semidirect
340. #4021	C₂³	semidirect
341. #4021	C₂³	semidirect
342. #4021	C₂³	semidirect
344. C₄×D₂₀	C₂³	semidirect
345. C₄×D₂₀	C₂³	semidirect
346. C₄×D₂₀	C₂³	semidirect
347. C₄×D₂₀	C₂³	semidirect
348. C₄×D₂₀	C₂³	semidirect
349. #4018	C₂³	semidirect
350. #4018	C₂³	semidirect
351. C₄×Dic₁₀	C₂³	semidirect
357. C₂×#556	D₅	semidirect
557. #556	C₂×D₅	semidirect
575. C₂×C₄⋊Q₈	C₂×D₅	semidirect
581. C₂×#126	C₂×D₅	semidirect
582. C₂×#126	C₂×D₅	semidirect
620. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
621. C₂×C₂²⋊Q₈	C₂×D₅	semidirect
646. C₂×C₄×Q₈	C₂×D₅	semidirect
647. C₂×C₄×Q₈	C₂×D₅	semidirect
665. C₂×#117	C₂×D₅	semidirect
666. C₂×#117	C₂×D₅	semidirect
828. C₄⋊Q₈	C₂²×D₅	semidirect
834. #126	C₂²×D₅	semidirect
835. #126	C₂²×D₅	semidirect
870. C₂²⋊Q₈	C₂²×D₅	semidirect
871. C₂²⋊Q₈	C₂²×D₅	semidirect
896. C₄×Q₈	C₂²×D₅	semidirect
897. C₄×Q₈	C₂²×D₅	semidirect
915. #117	C₂²×D₅	semidirect
916. #117	C₂²×D₅	semidirect
1202. C₂×C₅	#3540	semidirect
1317. C₅	C₂×#3540	semidirect
1375. C₂	#10618909	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×#556	2
#10618909	2
C₂×#66067	2
C₂×#66068	2
C₂×#66045	2
C₂×#66039	2
C₂×#66038	2
C₂×#66044	2
C₂×#66017	2
C₂×#66012	2
C₂×#65967	2
C₂×#65964	2
C₂×#65962	2
C₂×#65961	2
C₂×#65910	2
C₂×#65916	2
C₂×#65919	2
C₂×#65884	2
C₂×#65881	2
C₂×#65867	2
C₂×#65866	2
C₂×#65859	2
C₂×#65858	2
C₂×#3540	5

Subgroups — C2×#10618909 #13006592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618909 #13006592