Subgroups — C₅×#22434 #11945154

Order 1280.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1963	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1871	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1806	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1789	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1789	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1759	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₅×#550	C₄	1	1	yes	characteristic, complemented
21	C₅×D₄×Q₈	C₄	1	1	yes	characteristic, complemented
22	C₅×#548	C₄	1	1	yes	characteristic, complemented
23	C₅×#548	C₄	1	1	yes	characteristic, complemented
24	C₅×#547	—	2	1	no	—
25	C₅×#547	C₄	1	1	yes	characteristic, complemented
26	C₅×#546	—	2	1	no	—
27	C₅×#546	—	2	1	no	—
28	C₅×#546	C₄	1	1	yes	characteristic, complemented
29	C₅×#546	C₄	1	1	yes	characteristic, complemented
30	C₅×D₄²	—	2	1	no	—
31	C₅×D₄²	C₄	1	1	yes	characteristic, complemented
32	C₅×#532	—	2	1	no	—
33	C₅×#532	C₂²	1	1	yes	characteristic
34	C₅×#525	—	2	1	no	—
35	C₅×#525	—	2	1	no	—
36	C₅×#525	C₂²	1	1	yes	characteristic
37	C₅×#525	C₂²	1	1	yes	characteristic
38	C₄×C₅×#41	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	—	2	1	no	—
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
43	C₅×#436	—	2	1	no	—
44	C₅×#435	—	2	1	no	—
45	C₅×#435	—	2	1	no	—
46	C₅×C₈×D₄	—	2	1	no	—
47	C₅×#423	C₂²	1	1	yes	characteristic, complemented
48	C₅×#421	—	2	4	no	—
49	C₂×C₅×#104	—	2	4	no	—
50	C₂×C₅×#104	C₂²	1	1	yes	characteristic
51	C₂×C₅×#104	C₂²	1	1	yes	characteristic
52	C₂×C₅×#104	C₂²	1	1	yes	characteristic
53	C₂×C₅×#104	C₂²	1	1	yes	characteristic
54	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₅×#104	C₂²	1	1	yes	characteristic, complemented
62	C₅×#407	C₂²	1	1	yes	characteristic, complemented
63	C₅×#407	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
65	C₅×#388	—	2	1	no	—
66	C₅×#387	—	2	1	no	—
67	C₅×#386	—	2	1	no	—
68	C₅×#385	—	2	1	no	—
69	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
70	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₅×#376	C₂²	1	1	yes	characteristic, complemented
73	C₅×#339	C₂²	1	1	yes	characteristic, complemented
74	C₅×#339	C₂²	1	1	yes	characteristic, complemented
75	C₅×#339	C₂²	1	1	yes	characteristic, complemented
76	C₅×#339	C₂²	1	1	yes	characteristic, complemented
77	#22434	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₅×#41	—	2	1	no	—
79	C₂×C₅×#41	—	2	1	no	—
80	C₂×C₅×#41	—	2	1	no	—
81	C₂×C₅×#41	—	2	1	no	—
82	C₂×C₅×#41	—	2	2	no	—
83	C₂×C₅×#41	—	2	2	no	—
84	C₂×C₅×#41	—	2	2	no	—
85	C₂×C₅×#41	—	2	2	no	—
86	C₂×C₅×#41	—	4	1	no	—
87	C₂×C₅×#41	—	4	1	no	—
88	C₂×C₅×#41	—	4	1	no	—
89	C₂×C₅×#41	—	4	1	no	—
90	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂×C₅×#41	C₂³	1	1	yes	characteristic
95	C₂×C₅×#41	C₂³	1	1	yes	characteristic
96	C₂×C₅×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂²×C₅×D₄	—	2	1	no	—
100	C₂²×C₅×D₄	—	2	1	no	—
101	C₂²×C₅×D₄	—	2	1	no	—
102	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
105	C₂³×C₄×C₅	—	2	1	no	—
106	C₂³×C₄×C₅	—	2	1	no	—
107	C₂³×C₄×C₅	—	2	1	no	—
108	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂×C₅×M₁₆	—	2	1	no	—
111	C₂×C₅×M₁₆	—	2	1	no	—
112	C₂×C₅×M₁₆	—	2	2	no	—
113	C₂×C₅×M₁₆	—	2	2	no	—
114	C₂×C₅×M₁₆	—	4	1	no	—
115	C₂×C₅×M₁₆	—	4	1	no	—
116	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
120	C₂²×C₅×C₈	—	2	1	no	—
121	C₂²×C₅×C₈	—	2	1	no	—
122	C₅×C₄⋊Q₈	—	2	1	no	—
123	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
124	C₅×#127	—	2	1	no	—
125	C₅×#127	C₂×C₄	1	1	yes	characteristic, complemented
126	C₅×#124	—	2	1	no	—
127	C₅×#124	—	2	1	no	—
128	C₅×#124	C₂×C₄	1	1	yes	characteristic, complemented
129	C₅×#124	C₂×C₄	1	1	yes	characteristic, complemented
130	C₅×#123	—	2	1	no	—
131	C₅×#123	—	2	1	no	—
132	C₅×#123	—	2	1	no	—
133	C₅×#123	—	2	1	no	—
134	C₅×#123	—	2	1	no	—
135	C₅×#123	—	2	1	no	—
136	C₅×C₂²⋊Q₈	—	2	1	no	—
137	C₅×C₂²⋊Q₈	—	2	1	no	—
138	C₅×C₂²⋊Q₈	—	2	1	no	—
139	C₅×C₂²⋊Q₈	—	2	1	no	—
140	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
141	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
142	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
143	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
144	C₅×#121	—	2	1	no	—
145	C₅×#121	—	2	1	no	—
146	C₅×#121	—	2	1	no	—
147	C₅×#121	—	2	1	no	—
148	C₅×#121	—	2	1	no	—
149	C₅×#121	—	2	1	no	—
150	C₅×#121	—	2	1	no	—
151	C₅×#121	—	2	1	no	—
152	C₅×#121	—	2	1	no	—
153	C₅×#121	—	2	1	no	—
154	C₅×#121	C₂×C₄	1	1	yes	characteristic
155	C₅×#121	C₂×C₄	1	1	yes	characteristic
156	C₅×#121	C₂×C₄	1	1	yes	characteristic, complemented
157	C₅×#121	C₂×C₄	1	1	yes	characteristic, complemented
158	C₅×#120	—	2	1	no	—
159	C₅×#120	—	2	1	no	—
160	C₅×#120	—	2	1	no	—
161	C₅×#120	—	2	1	no	—
162	C₅×#120	—	2	1	no	—
163	C₅×#120	—	2	1	no	—
164	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
165	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
166	C₄×C₅×D₄	—	2	1	no	—
167	C₄×C₅×D₄	—	2	1	no	—
168	C₄×C₅×D₄	—	2	1	no	—
169	C₄×C₅×D₄	—	2	1	no	—
170	C₄×C₅×D₄	—	2	1	no	—
171	C₄×C₅×D₄	—	2	1	no	—
172	C₄×C₅×D₄	—	2	1	no	—
173	C₄×C₅×D₄	—	2	1	no	—
174	C₄×C₅×D₄	—	2	1	no	—
175	C₄×C₅×D₄	—	2	1	no	—
176	C₄×C₅×D₄	—	2	1	no	—
177	C₄×C₅×D₄	—	2	1	no	—
178	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
179	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
180	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
181	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
182	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
183	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
184	C₄×C₅×D₄	D₄	1	1	yes	characteristic
185	C₄×C₅×D₄	D₄	1	1	yes	characteristic
186	C₄×C₅×D₄	D₄	1	1	yes	characteristic
187	C₄×C₅×D₄	D₄	1	1	yes	characteristic
188	C₅×#117	—	2	1	no	—
189	C₅×#117	—	2	2	no	—
190	C₅×#117	—	4	1	no	—
191	C₅×#117	C₂³	1	1	yes	characteristic
192	C₂×C₅×C₄⋊C₄	—	2	1	no	—
193	C₂×C₅×C₄⋊C₄	—	2	1	no	—
194	C₂×C₅×C₄⋊C₄	—	2	1	no	—
195	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
197	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
198	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
202	C₂×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
203	C₂×C₄²×C₅	—	2	1	no	—
204	C₂×C₄²×C₅	—	2	2	no	—
205	C₂×C₄²×C₅	—	2	1	no	—
206	C₂×C₄²×C₅	—	4	1	no	—
207	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
212	C₅×C₄⋊C₈	—	2	1	no	—
213	C₅×C₄⋊C₈	—	2	1	no	—
214	C₅×#104	—	2	2	no	—
215	C₅×#104	—	2	2	no	—
216	C₅×#104	—	2	2	no	—
217	C₅×#104	—	2	2	no	—
218	C₅×#104	—	2	2	no	—
219	C₅×#104	—	2	2	no	—
220	C₅×#104	—	2	2	no	—
221	C₅×#104	—	4	1	no	—
222	C₅×#104	—	4	1	no	—
223	C₅×#104	—	4	1	no	—
224	C₅×#104	—	4	1	no	—
225	C₅×#104	D₄	1	4	yes	complemented
226	C₅×C₂²⋊C₈	—	2	1	no	—
227	C₅×C₂²⋊C₈	—	2	1	no	—
228	C₅×C₂²⋊C₈	—	2	1	no	—
229	C₅×C₂²⋊C₈	—	2	1	no	—
230	C₅×#97	—	2	1	no	—
231	C₄×C₅×C₈	—	2	1	no	—
232	C₅×#95	—	2	1	no	—
233	C₅×#95	—	2	1	no	—
234	C₅×#95	—	2	1	no	—
235	C₅×#95	—	2	1	no	—
236	C₅×#95	—	2	1	no	—
237	D₄×#41	C₂×C₅	1	1	yes	characteristic
238	D₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
239	C₂×#421	C₂×C₅	1	1	yes	characteristic, complemented
240	C₂²×#104	C₂×C₅	1	1	yes	characteristic, complemented
241	#2290	C₂×C₅	1	1	yes	characteristic, complemented
242	#1980	C₂×C₅	1	1	yes	characteristic, complemented
243	#1963	C₂×C₅	1	1	yes	characteristic, complemented
244	#1897	C₂×C₅	1	1	yes	characteristic, complemented
245	#1896	C₂×C₅	1	1	yes	characteristic, complemented
246	#1871	C₂×C₅	1	1	yes	characteristic, complemented
247	#1871	C₂×C₅	1	1	yes	characteristic, complemented
248	#1806	C₂×C₅	1	1	yes	characteristic, complemented
249	#1789	C₂×C₅	1	1	yes	characteristic, complemented
250	#1789	C₂×C₅	1	1	yes	characteristic, complemented
251	#1759	C₂×C₅	1	1	yes	characteristic, complemented
252	C₂⁴×C₅	—	2	1	no	—
253	C₂⁴×C₅	—	2	1	no	—
254	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
255	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
256	C₅×#41	—	2	1	no	—
257	C₅×#41	—	2	1	no	—
258	C₅×#41	—	2	2	no	—
259	C₅×#41	—	2	2	no	—
260	C₅×#41	—	2	2	no	—
261	C₅×#41	—	2	2	no	—
262	C₅×#41	—	2	1	no	—
263	C₅×#41	—	2	1	no	—
264	C₅×#41	—	2	1	no	—
265	C₅×#41	—	2	1	no	—
266	C₅×#41	—	2	1	no	—
267	C₅×#41	—	2	1	no	—
268	C₅×#41	—	2	1	no	—
269	C₅×#41	—	2	1	no	—
270	C₅×#41	—	4	2	no	—
271	C₅×#41	—	4	2	no	—
272	C₅×#41	—	4	2	no	—
273	C₅×#41	—	4	2	no	—
274	C₅×#41	—	4	1	no	—
275	C₅×#41	—	4	1	no	—
276	C₅×#41	—	4	1	no	—
277	C₅×#41	—	4	1	no	—
278	C₅×#41	—	4	2	no	—
279	C₅×#41	—	4	2	no	—
280	C₅×#41	—	4	2	no	—
281	C₅×#41	—	4	2	no	—
282	C₅×#41	C₂×D₄	1	2	yes	—
283	C₅×#41	#41	1	2	yes	—
284	C₂×C₅×Q₈	—	2	1	no	—
285	C₂×C₅×Q₈	—	2	1	no	—
286	C₂×C₅×Q₈	—	2	2	no	—
287	C₂×C₅×Q₈	—	2	2	no	—
288	C₂×C₅×Q₈	—	4	1	no	—
289	C₂×C₅×Q₈	—	4	1	no	—
290	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₅×D₄	—	2	1	no	—
294	C₂×C₅×D₄	—	2	2	no	—
295	C₂×C₅×D₄	—	2	2	no	—
296	C₂×C₅×D₄	—	2	1	no	—
297	C₂×C₅×D₄	—	2	1	no	—
298	C₂×C₅×D₄	—	2	1	no	—
299	C₂×C₅×D₄	—	2	1	no	—
300	C₂×C₅×D₄	—	2	1	no	—
301	C₂×C₅×D₄	—	2	1	no	—
302	C₂×C₅×D₄	—	2	1	no	—
303	C₂×C₅×D₄	—	2	1	no	—
304	C₂×C₅×D₄	—	2	1	no	—
305	C₂×C₅×D₄	—	2	1	no	—
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	—	2	1	no	—
310	C₂×C₅×D₄	—	4	1	no	—
311	C₂×C₅×D₄	—	4	1	no	—
312	C₂×C₅×D₄	—	4	2	no	—
313	C₂×C₅×D₄	—	4	2	no	—
314	C₂×C₅×D₄	—	4	2	no	—
315	C₂×C₅×D₄	—	4	2	no	—
316	C₂×C₅×D₄	—	4	2	no	—
317	C₂×C₅×D₄	—	4	4	no	—
318	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
323	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
325	C₂²×C₄×C₅	—	2	1	no	—
326	C₂²×C₄×C₅	—	2	1	no	—
327	C₂²×C₄×C₅	—	2	1	no	—
328	C₂²×C₄×C₅	—	2	1	no	—
329	C₂²×C₄×C₅	—	2	1	no	—
330	C₂²×C₄×C₅	—	2	1	no	—
331	C₂²×C₄×C₅	—	2	1	no	—
332	C₂²×C₄×C₅	—	2	1	no	—
333	C₂²×C₄×C₅	—	2	1	no	—
334	C₂²×C₄×C₅	—	2	1	no	—
335	C₂²×C₄×C₅	—	2	1	no	—
336	C₂²×C₄×C₅	—	2	1	no	—
337	C₂²×C₄×C₅	—	2	1	no	—
338	C₂²×C₄×C₅	—	2	1	no	—
339	C₂²×C₄×C₅	—	2	1	no	—
340	C₂²×C₄×C₅	—	2	1	no	—
341	C₂²×C₄×C₅	—	2	1	no	—
342	C₂²×C₄×C₅	—	2	1	no	—
343	C₂²×C₄×C₅	—	2	1	no	—
344	C₂²×C₄×C₅	—	2	1	no	—
345	C₂²×C₄×C₅	—	2	1	no	—
346	C₂²×C₄×C₅	—	2	1	no	—
347	C₂²×C₄×C₅	—	2	1	no	—
348	C₂²×C₄×C₅	—	4	2	no	—
349	C₂²×C₄×C₅	—	4	2	no	—
350	C₂²×C₄×C₅	—	4	2	no	—
351	C₂²×C₄×C₅	—	4	2	no	—
352	C₂²×C₄×C₅	—	4	2	no	—
353	C₂²×C₄×C₅	—	4	2	no	—
354	C₂²×C₄×C₅	—	4	2	no	—
355	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
356	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
358	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
368	C₅×M₁₆	—	2	1	no	—
369	C₅×M₁₆	—	2	1	no	—
370	C₅×M₁₆	—	2	1	no	—
371	C₅×M₁₆	—	2	1	no	—
372	C₅×M₁₆	—	2	1	no	—
373	C₅×M₁₆	—	2	1	no	—
374	C₅×M₁₆	—	2	1	no	—
375	C₅×M₁₆	—	4	2	no	—
376	C₅×M₁₆	—	4	2	no	—
377	C₅×M₁₆	C₂×D₄	1	2	yes	complemented
378	C₂×C₅×C₈	—	2	1	no	—
379	C₂×C₅×C₈	—	2	1	no	—
380	C₂×C₅×C₈	—	2	1	no	—
381	C₂×C₅×C₈	—	2	1	no	—
382	C₂×C₅×C₈	—	4	2	no	—
383	C₂×C₅×C₈	—	4	2	no	—
384	C₅×C₄⋊C₄	—	2	1	no	—
385	C₅×C₄⋊C₄	—	2	1	no	—
386	C₅×C₄⋊C₄	—	2	1	no	—
387	C₅×C₄⋊C₄	—	2	1	no	—
388	C₅×C₄⋊C₄	—	2	1	no	—
389	C₅×C₄⋊C₄	—	2	1	no	—
390	C₅×C₄⋊C₄	—	2	1	no	—
391	C₅×C₄⋊C₄	—	2	1	no	—
392	C₅×C₄⋊C₄	—	4	2	no	—
393	C₅×C₄⋊C₄	—	4	2	no	—
394	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
395	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
396	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
397	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
398	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
400	C₅×C₂²⋊C₄	—	2	1	no	—
401	C₅×C₂²⋊C₄	—	2	1	no	—
402	C₅×C₂²⋊C₄	—	2	1	no	—
403	C₅×C₂²⋊C₄	—	2	1	no	—
404	C₅×C₂²⋊C₄	—	2	1	no	—
405	C₅×C₂²⋊C₄	—	2	1	no	—
406	C₅×C₂²⋊C₄	—	2	1	no	—
407	C₅×C₂²⋊C₄	—	2	1	no	—
408	C₅×C₂²⋊C₄	—	2	1	no	—
409	C₅×C₂²⋊C₄	—	2	1	no	—
410	C₅×C₂²⋊C₄	—	2	1	no	—
411	C₅×C₂²⋊C₄	—	2	1	no	—
412	C₅×C₂²⋊C₄	—	2	1	no	—
413	C₅×C₂²⋊C₄	—	2	1	no	—
414	C₅×C₂²⋊C₄	—	2	1	no	—
415	C₅×C₂²⋊C₄	—	4	2	no	—
416	C₅×C₂²⋊C₄	—	4	2	no	—
417	C₅×C₂²⋊C₄	—	4	2	no	—
418	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
419	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
420	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
421	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
422	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
423	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
424	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
425	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
426	C₄²×C₅	—	2	1	no	—
427	C₄²×C₅	—	2	1	no	—
428	C₄²×C₅	—	2	1	no	—
429	C₄²×C₅	—	2	1	no	—
430	C₄²×C₅	—	2	1	no	—
431	C₄²×C₅	—	2	1	no	—
432	C₄²×C₅	—	2	1	no	—
433	C₄²×C₅	—	2	1	no	—
434	C₄²×C₅	—	2	1	no	—
435	C₄²×C₅	—	2	1	no	—
436	C₄²×C₅	—	4	2	no	—
437	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
438	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
439	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₅	C₂×D₄	1	2	yes	complemented
442	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
443	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
444	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
445	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
446	#550	C₄×C₅	1	1	yes	characteristic, complemented
447	D₄×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
448	#548	C₄×C₅	1	1	yes	characteristic, complemented
449	#548	C₄×C₅	1	1	yes	characteristic, complemented
450	#547	—	2	1	no	—
451	#547	C₄×C₅	1	1	yes	characteristic, complemented
452	#546	—	2	1	no	—
453	#546	—	2	1	no	—
454	#546	C₄×C₅	1	1	yes	characteristic, complemented
455	#546	C₄×C₅	1	1	yes	characteristic, complemented
456	D₄²	—	2	1	no	—
457	D₄²	C₄×C₅	1	1	yes	characteristic, complemented
458	#532	—	2	1	no	—
459	#532	C₂²×C₅	1	1	yes	characteristic
460	#525	—	2	1	no	—
461	#525	—	2	1	no	—
462	#525	C₂²×C₅	1	1	yes	characteristic
463	#525	C₂²×C₅	1	1	yes	characteristic
464	C₄×#41	C₂²×C₅	1	1	yes	characteristic
465	C₂×C₄×D₄	—	2	1	no	—
466	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
467	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
468	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
469	#436	—	2	1	no	—
470	#435	—	2	1	no	—
471	#435	—	2	1	no	—
472	C₈×D₄	—	2	1	no	—
473	#423	C₂²×C₅	1	1	yes	characteristic, complemented
474	#421	—	2	4	no	—
475	C₂×#104	—	2	4	no	—
476	C₂×#104	C₂²×C₅	1	1	yes	characteristic
477	C₂×#104	C₂²×C₅	1	1	yes	characteristic
478	C₂×#104	C₂²×C₅	1	1	yes	characteristic
479	C₂×#104	C₂²×C₅	1	1	yes	characteristic
480	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
481	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
482	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
483	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
484	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
485	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
486	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
487	C₂×#104	C₂²×C₅	1	1	yes	characteristic, complemented
488	#407	C₂²×C₅	1	1	yes	characteristic, complemented
489	#407	C₂²×C₅	1	1	yes	characteristic, complemented
490	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
491	#388	—	2	1	no	—
492	#387	—	2	1	no	—
493	#386	—	2	1	no	—
494	#385	—	2	1	no	—
495	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
496	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
497	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
498	#376	C₂²×C₅	1	1	yes	characteristic, complemented
499	#339	C₂²×C₅	1	1	yes	characteristic, complemented
500	#339	C₂²×C₅	1	1	yes	characteristic, complemented
501	#339	C₂²×C₅	1	1	yes	characteristic, complemented
502	#339	C₂²×C₅	1	1	yes	characteristic, complemented
503	C₂³×C₅	—	2	1	no	—
504	C₂³×C₅	—	2	1	no	—
505	C₂³×C₅	—	2	1	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	1	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	4	1	no	—
512	C₂³×C₅	—	4	1	no	—
513	C₂³×C₅	—	4	1	no	—
514	C₂³×C₅	—	4	2	no	—
515	C₂³×C₅	—	4	2	no	—
516	C₂³×C₅	—	4	2	no	—
517	C₂³×C₅	—	4	2	no	—
518	C₂³×C₅	—	8	1	no	—
519	C₂³×C₅	—	8	1	no	—
520	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
521	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
523	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
524	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
525	C₅×Q₈	—	2	1	no	—
526	C₅×Q₈	—	2	1	no	—
527	C₅×Q₈	—	2	1	no	—
528	C₅×Q₈	—	2	1	no	—
529	C₅×Q₈	—	2	1	no	—
530	C₅×Q₈	—	4	2	no	—
531	C₅×Q₈	—	4	2	no	—
532	C₅×Q₈	C₄×D₄	1	2	yes	—
533	C₅×D₄	—	2	2	no	—
534	C₅×D₄	—	2	2	no	—
535	C₅×D₄	—	2	2	no	—
536	C₅×D₄	—	2	2	no	—
537	C₅×D₄	—	2	1	no	—
538	C₅×D₄	—	2	1	no	—
539	C₅×D₄	—	2	1	no	—
540	C₅×D₄	—	2	1	no	—
541	C₅×D₄	—	2	1	no	—
542	C₅×D₄	—	4	1	no	—
543	C₅×D₄	—	4	1	no	—
544	C₅×D₄	—	4	2	no	—
545	C₅×D₄	—	4	2	no	—
546	C₅×D₄	—	4	2	no	—
547	C₅×D₄	—	4	2	no	—
548	C₅×D₄	—	4	2	no	—
549	C₅×D₄	—	4	2	no	—
550	C₅×D₄	—	4	2	no	—
551	C₅×D₄	—	4	2	no	—
552	C₅×D₄	—	4	1	no	—
553	C₅×D₄	—	4	1	no	—
554	C₅×D₄	—	4	1	no	—
555	C₅×D₄	—	4	1	no	—
556	C₅×D₄	—	4	2	no	—
557	C₅×D₄	—	8	1	no	—
558	C₅×D₄	—	8	1	no	—
559	C₅×D₄	—	8	1	no	—
560	C₅×D₄	C₄×D₄	1	2	yes	—
561	C₂×C₄×C₅	—	2	1	no	—
562	C₂×C₄×C₅	—	2	1	no	—
563	C₂×C₄×C₅	—	2	1	no	—
564	C₂×C₄×C₅	—	2	1	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	1	no	—
567	C₂×C₄×C₅	—	2	1	no	—
568	C₂×C₄×C₅	—	2	1	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	1	no	—
576	C₂×C₄×C₅	—	2	1	no	—
577	C₂×C₄×C₅	—	2	1	no	—
578	C₂×C₄×C₅	—	2	2	no	—
579	C₂×C₄×C₅	—	2	1	no	—
580	C₂×C₄×C₅	—	2	1	no	—
581	C₂×C₄×C₅	—	2	1	no	—
582	C₂×C₄×C₅	—	2	1	no	—
583	C₂×C₄×C₅	—	2	2	no	—
584	C₂×C₄×C₅	—	2	2	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	2	1	no	—
587	C₂×C₄×C₅	—	2	1	no	—
588	C₂×C₄×C₅	—	2	1	no	—
589	C₂×C₄×C₅	—	2	2	no	—
590	C₂×C₄×C₅	—	4	1	no	—
591	C₂×C₄×C₅	—	4	1	no	—
592	C₂×C₄×C₅	—	4	2	no	—
593	C₂×C₄×C₅	—	4	2	no	—
594	C₂×C₄×C₅	—	4	2	no	—
595	C₂×C₄×C₅	—	4	2	no	—
596	C₂×C₄×C₅	—	4	2	no	—
597	C₂×C₄×C₅	—	4	2	no	—
598	C₂×C₄×C₅	—	4	2	no	—
599	C₂×C₄×C₅	—	4	1	no	—
600	C₂×C₄×C₅	—	4	1	no	—
601	C₂×C₄×C₅	—	4	1	no	—
602	C₂×C₄×C₅	—	4	8	no	—
603	C₂×C₄×C₅	—	4	1	no	—
604	C₂×C₄×C₅	—	4	1	no	—
605	C₂×C₄×C₅	—	4	1	no	—
606	C₂×C₄×C₅	—	4	1	no	—
607	C₂×C₄×C₅	—	4	1	no	—
608	C₂×C₄×C₅	—	4	1	no	—
609	C₂×C₄×C₅	—	4	1	no	—
610	C₂×C₄×C₅	—	4	1	no	—
611	C₂×C₄×C₅	—	4	1	no	—
612	C₂×C₄×C₅	—	4	1	no	—
613	C₂×C₄×C₅	—	4	1	no	—
614	C₂×C₄×C₅	—	8	1	no	—
615	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
616	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
617	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
619	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
620	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
621	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
622	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
623	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
624	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
625	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
626	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
627	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
629	C₅×C₈	—	2	2	no	—
630	C₅×C₈	—	4	1	no	—
631	C₅×C₈	—	4	1	no	—
632	C₅×C₈	—	4	1	no	—
633	C₂×#41	—	2	1	no	—
634	C₂×#41	—	2	1	no	—
635	C₂×#41	—	2	1	no	—
636	C₂×#41	—	2	1	no	—
637	C₂×#41	—	2	2	no	—
638	C₂×#41	—	2	2	no	—
639	C₂×#41	—	2	2	no	—
640	C₂×#41	—	2	2	no	—
641	C₂×#41	—	4	1	no	—
642	C₂×#41	—	4	1	no	—
643	C₂×#41	—	4	1	no	—
644	C₂×#41	—	4	1	no	—
645	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
646	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
647	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic, complemented
648	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic, complemented
649	C₂×#41	C₂³×C₅	1	1	yes	characteristic
650	C₂×#41	C₂³×C₅	1	1	yes	characteristic
651	C₂×#41	C₂³×C₅	1	1	yes	characteristic
652	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
653	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
654	C₂²×D₄	—	2	1	no	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	—	2	1	no	—
657	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
658	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
659	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
660	C₂³×C₄	—	2	1	no	—
661	C₂³×C₄	—	2	1	no	—
662	C₂³×C₄	—	2	1	no	—
663	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
665	C₂×M₁₆	—	2	1	no	—
666	C₂×M₁₆	—	2	1	no	—
667	C₂×M₁₆	—	2	2	no	—
668	C₂×M₁₆	—	2	2	no	—
669	C₂×M₁₆	—	4	1	no	—
670	C₂×M₁₆	—	4	1	no	—
671	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
672	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
673	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
674	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
675	C₂²×C₈	—	2	1	no	—
676	C₂²×C₈	—	2	1	no	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
679	#127	—	2	1	no	—
680	#127	C₂×C₄×C₅	1	1	yes	characteristic, complemented
681	#124	—	2	1	no	—
682	#124	—	2	1	no	—
683	#124	C₂×C₄×C₅	1	1	yes	characteristic, complemented
684	#124	C₂×C₄×C₅	1	1	yes	characteristic, complemented
685	#123	—	2	1	no	—
686	#123	—	2	1	no	—
687	#123	—	2	1	no	—
688	#123	—	2	1	no	—
689	#123	—	2	1	no	—
690	#123	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	1	no	—
694	C₂²⋊Q₈	—	2	1	no	—
695	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
698	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
699	#121	—	2	1	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	2	1	no	—
706	#121	—	2	1	no	—
707	#121	—	2	1	no	—
708	#121	—	2	1	no	—
709	#121	C₂×C₄×C₅	1	1	yes	characteristic
710	#121	C₂×C₄×C₅	1	1	yes	characteristic
711	#121	C₂×C₄×C₅	1	1	yes	characteristic, complemented
712	#121	C₂×C₄×C₅	1	1	yes	characteristic, complemented
713	#120	—	2	1	no	—
714	#120	—	2	1	no	—
715	#120	—	2	1	no	—
716	#120	—	2	1	no	—
717	#120	—	2	1	no	—
718	#120	—	2	1	no	—
719	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
720	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	1	no	—
733	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
734	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
735	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
736	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
737	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
738	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
739	C₄×D₄	C₅×D₄	1	1	yes	characteristic
740	C₄×D₄	C₅×D₄	1	1	yes	characteristic
741	C₄×D₄	C₅×D₄	1	1	yes	characteristic
742	C₄×D₄	C₅×D₄	1	1	yes	characteristic
743	#117	—	2	1	no	—
744	#117	—	2	2	no	—
745	#117	—	4	1	no	—
746	#117	C₂³×C₅	1	1	yes	characteristic
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	—	2	1	no	—
749	C₂×C₄⋊C₄	—	2	1	no	—
750	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₂²⋊C₄	—	2	1	no	—
754	C₂×C₂²⋊C₄	—	2	1	no	—
755	C₂×C₂²⋊C₄	—	2	1	no	—
756	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
758	C₂×C₄²	—	2	1	no	—
759	C₂×C₄²	—	2	2	no	—
760	C₂×C₄²	—	2	1	no	—
761	C₂×C₄²	—	4	1	no	—
762	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
767	C₄⋊C₈	—	2	1	no	—
768	C₄⋊C₈	—	2	1	no	—
769	#104	—	2	2	no	—
770	#104	—	2	2	no	—
771	#104	—	2	2	no	—
772	#104	—	2	2	no	—
773	#104	—	2	2	no	—
774	#104	—	2	2	no	—
775	#104	—	2	2	no	—
776	#104	—	4	1	no	—
777	#104	—	4	1	no	—
778	#104	—	4	1	no	—
779	#104	—	4	1	no	—
780	#104	C₅×D₄	1	4	yes	complemented
781	C₂²⋊C₈	—	2	1	no	—
782	C₂²⋊C₈	—	2	1	no	—
783	C₂²⋊C₈	—	2	1	no	—
784	C₂²⋊C₈	—	2	1	no	—
785	#97	—	2	1	no	—
786	C₄×C₈	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	C₂²×C₅	—	2	1	no	—
793	C₂²×C₅	—	2	1	no	—
794	C₂²×C₅	—	2	1	no	—
795	C₂²×C₅	—	2	1	no	—
796	C₂²×C₅	—	2	1	no	—
797	C₂²×C₅	—	2	1	no	—
798	C₂²×C₅	—	2	1	no	—
799	C₂²×C₅	—	2	2	no	—
800	C₂²×C₅	—	2	1	no	—
801	C₂²×C₅	—	2	1	no	—
802	C₂²×C₅	—	2	1	no	—
803	C₂²×C₅	—	2	1	no	—
804	C₂²×C₅	—	2	1	no	—
805	C₂²×C₅	—	2	1	no	—
806	C₂²×C₅	—	4	2	no	—
807	C₂²×C₅	—	4	2	no	—
808	C₂²×C₅	—	4	1	no	—
809	C₂²×C₅	—	4	1	no	—
810	C₂²×C₅	—	4	1	no	—
811	C₂²×C₅	—	4	1	no	—
812	C₂²×C₅	—	4	1	no	—
813	C₂²×C₅	—	4	1	no	—
814	C₂²×C₅	—	4	1	no	—
815	C₂²×C₅	—	4	1	no	—
816	C₂²×C₅	—	8	1	no	—
817	C₂²×C₅	—	8	1	no	—
818	C₂²×C₅	—	8	4	no	—
819	C₂²×C₅	—	8	4	no	—
820	C₂²×C₅	#421	1	2	yes	complemented
821	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
822	C₂²×C₅	D₄²	1	1	yes	characteristic
823	C₂²×C₅	#546	1	1	yes	characteristic
824	C₄×C₅	—	2	1	no	—
825	C₄×C₅	—	2	1	no	—
826	C₄×C₅	—	2	1	no	—
827	C₄×C₅	—	2	1	no	—
828	C₄×C₅	—	2	2	no	—
829	C₄×C₅	—	2	1	no	—
830	C₄×C₅	—	2	1	no	—
831	C₄×C₅	—	2	1	no	—
832	C₄×C₅	—	2	1	no	—
833	C₄×C₅	—	4	2	no	—
834	C₄×C₅	—	4	2	no	—
835	C₄×C₅	—	4	1	no	—
836	C₄×C₅	—	4	1	no	—
837	C₄×C₅	—	4	1	no	—
838	C₄×C₅	—	4	1	no	—
839	C₄×C₅	—	8	1	no	—
840	C₄×C₅	—	8	1	no	—
841	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
842	C₄×C₅	#518	1	1	yes	characteristic
843	C₄×C₅	D₄²	1	1	yes	characteristic
844	C₄×C₅	#546	1	1	yes	characteristic
845	C₂⁴	—	2	1	no	—
846	C₂⁴	—	2	1	no	—
847	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
848	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
849	#41	—	2	1	no	—
850	#41	—	2	1	no	—
851	#41	—	2	2	no	—
852	#41	—	2	2	no	—
853	#41	—	2	2	no	—
854	#41	—	2	2	no	—
855	#41	—	2	1	no	—
856	#41	—	2	1	no	—
857	#41	—	2	1	no	—
858	#41	—	2	1	no	—
859	#41	—	2	1	no	—
860	#41	—	2	1	no	—
861	#41	—	2	1	no	—
862	#41	—	2	1	no	—
863	#41	—	4	2	no	—
864	#41	—	4	2	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	1	no	—
868	#41	—	4	1	no	—
869	#41	—	4	1	no	—
870	#41	—	4	1	no	—
871	#41	—	4	2	no	—
872	#41	—	4	2	no	—
873	#41	—	4	2	no	—
874	#41	—	4	2	no	—
875	#41	C₂×C₅×D₄	1	2	yes	—
876	#41	C₅×#41	1	2	yes	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	4	1	no	—
882	C₂×Q₈	—	4	1	no	—
883	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
884	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
885	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	—	4	1	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	4	no	—
911	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
912	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
913	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
914	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
915	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
916	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
917	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	2	no	—
946	C₂²×C₄	—	4	2	no	—
947	C₂²×C₄	—	4	2	no	—
948	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
949	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
950	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
951	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
952	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
953	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
954	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
955	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
956	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
957	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
958	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
959	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
961	M₁₆	—	2	1	no	—
962	M₁₆	—	2	1	no	—
963	M₁₆	—	2	1	no	—
964	M₁₆	—	2	1	no	—
965	M₁₆	—	2	1	no	—
966	M₁₆	—	2	1	no	—
967	M₁₆	—	2	1	no	—
968	M₁₆	—	4	2	no	—
969	M₁₆	—	4	2	no	—
970	M₁₆	C₂×C₅×D₄	1	2	yes	complemented
971	C₂×C₈	—	2	1	no	—
972	C₂×C₈	—	2	1	no	—
973	C₂×C₈	—	2	1	no	—
974	C₂×C₈	—	2	1	no	—
975	C₂×C₈	—	4	2	no	—
976	C₂×C₈	—	4	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
988	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
989	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
990	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1012	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1013	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1014	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1015	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1016	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1017	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1018	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	4	2	no	—
1030	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
1031	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
1032	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1033	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
1034	C₄²	C₂×C₅×D₄	1	2	yes	complemented
1035	C₂×C₅	—	2	1	no	—
1036	C₂×C₅	—	2	1	no	—
1037	C₂×C₅	—	2	2	no	—
1038	C₂×C₅	—	4	1	no	—
1039	C₂×C₅	—	4	1	no	—
1040	C₂×C₅	—	4	1	no	—
1041	C₂×C₅	—	4	2	no	—
1042	C₂×C₅	—	8	1	no	—
1043	C₂×C₅	—	8	1	no	—
1044	C₂×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic
1045	C₂×C₅	C₂×#421	1	1	yes	characteristic
1046	C₂×C₅	#2901	1	1	yes	characteristic
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	4	2	no	—
1060	C₂³	—	4	2	no	—
1061	C₂³	—	4	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1065	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1066	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1067	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1068	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	4	2	no	—
1075	Q₈	—	4	2	no	—
1076	Q₈	C₄×C₅×D₄	1	2	yes	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	4	1	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	1	no	—
1098	D₄	—	4	1	no	—
1099	D₄	—	4	1	no	—
1100	D₄	—	4	1	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	C₄×C₅×D₄	1	2	yes	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	8	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1160	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1161	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1162	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1163	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1164	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1165	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1166	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
1167	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
1168	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1169	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
1170	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
1171	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
1172	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₈	—	2	2	no	—
1174	C₈	—	4	1	no	—
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₅	#22434	1	1	yes	characteristic, direct product factor, Sylow
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	1	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	8	1	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	4	no	—
1205	C₂²	—	8	4	no	—
1206	C₂²	C₅×#421	1	2	yes	complemented
1207	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
1208	C₂²	C₅×D₄²	1	1	yes	characteristic
1209	C₂²	C₅×#546	1	1	yes	characteristic
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	2	1	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	1	no	—
1217	C₄	—	2	1	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	4	2	no	—
1220	C₄	—	4	2	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	1	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
1228	C₄	C₅×#518	1	1	yes	characteristic
1229	C₄	C₅×D₄²	1	1	yes	characteristic
1230	C₄	C₅×#546	1	1	yes	characteristic
1231	C₂	—	2	1	no	—
1232	C₂	—	2	1	no	—
1233	C₂	—	2	2	no	—
1234	C₂	—	4	1	no	—
1235	C₂	—	4	1	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	2	no	—
1238	C₂	—	8	1	no	—
1239	C₂	—	8	1	no	—
1240	C₂	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic
1241	C₂	C₂×C₅×#421	1	1	yes	characteristic
1242	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₅×D₄×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×D₄×M₁₆	C₂	semidirect
3. C₂×C₅×#421	C₂	semidirect
4. C₂²×C₅×#104	C₂	semidirect
5. C₅×#2290	C₂	semidirect
6. C₅×#1980	C₂	semidirect
7. C₅×#1963	C₂	semidirect
8. C₅×#1897	C₂	semidirect
9. C₅×#1896	C₂	semidirect
10. C₅×#1871	C₂	semidirect
11. C₅×#1871	C₂	semidirect
12. C₅×#1806	C₂	semidirect
13. C₅×#1789	C₂	semidirect
14. C₅×#1789	C₂	semidirect
15. C₅×#1759	C₂	semidirect
18. C₂²×C₅×M₁₆	C₂²	semidirect
19. C₂²×C₅×M₁₆	C₂²	semidirect
20. C₅×#550	C₄	semidirect
21. C₅×D₄×Q₈	C₄	semidirect
22. C₅×#548	C₄	semidirect
23. C₅×#548	C₄	semidirect
25. C₅×#547	C₄	semidirect
28. C₅×#546	C₄	semidirect
29. C₅×#546	C₄	semidirect
31. C₅×D₄²	C₄	semidirect
41. C₂×C₅×#117	C₂²	semidirect
42. C₂²×C₄²×C₅	C₂²	semidirect
47. C₅×#423	C₂²	semidirect
54. C₂×C₅×#104	C₂²	semidirect
55. C₂×C₅×#104	C₂²	semidirect
56. C₂×C₅×#104	C₂²	semidirect
57. C₂×C₅×#104	C₂²	semidirect
58. C₂×C₅×#104	C₂²	semidirect
59. C₂×C₅×#104	C₂²	semidirect
60. C₂×C₅×#104	C₂²	semidirect
61. C₂×C₅×#104	C₂²	semidirect
62. C₅×#407	C₂²	semidirect
63. C₅×#407	C₂²	semidirect
64. C₄×C₅×M₁₆	C₂²	semidirect
69. C₄×C₅×C₄⋊C₄	C₂²	semidirect
70. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
71. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
72. C₅×#376	C₂²	semidirect
73. C₅×#339	C₂²	semidirect
74. C₅×#339	C₂²	semidirect
75. C₅×#339	C₂²	semidirect
76. C₅×#339	C₂²	semidirect
77. #22434	C₅	direct (N × H)
92. C₂×C₅×#41	C₂×C₄	semidirect
93. C₂×C₅×#41	C₂×C₄	semidirect
98. C₂²×C₅×Q₈	C₂×C₄	semidirect
103. C₂²×C₅×D₄	C₂×C₄	semidirect
123. C₅×C₄⋊Q₈	C₂×C₄	semidirect
125. C₅×#127	C₂×C₄	semidirect
128. C₅×#124	C₂×C₄	semidirect
129. C₅×#124	C₂×C₄	semidirect
142. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
143. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
156. C₅×#121	C₂×C₄	semidirect
157. C₅×#121	C₂×C₄	semidirect
164. C₄×C₅×Q₈	C₂×C₄	semidirect
165. C₄×C₅×Q₈	C₂×C₄	semidirect
182. C₄×C₅×D₄	C₂×C₄	semidirect
183. C₄×C₅×D₄	C₂×C₄	semidirect
225. C₅×#104	D₄	semidirect
238. D₄×M₁₆	C₂×C₅	semidirect
239. C₂×#421	C₂×C₅	semidirect
240. C₂²×#104	C₂×C₅	semidirect
241. #2290	C₂×C₅	semidirect
242. #1980	C₂×C₅	semidirect
243. #1963	C₂×C₅	semidirect
244. #1897	C₂×C₅	semidirect
245. #1896	C₂×C₅	semidirect
246. #1871	C₂×C₅	semidirect
247. #1871	C₂×C₅	semidirect
248. #1806	C₂×C₅	semidirect
249. #1789	C₂×C₅	semidirect
250. #1789	C₂×C₅	semidirect
251. #1759	C₂×C₅	semidirect
377. C₅×M₁₆	C₂×D₄	semidirect
441. C₄²×C₅	C₂×D₄	semidirect
444. C₂²×M₁₆	C₂²×C₅	semidirect
445. C₂²×M₁₆	C₂²×C₅	semidirect
446. #550	C₄×C₅	semidirect
447. D₄×Q₈	C₄×C₅	semidirect
448. #548	C₄×C₅	semidirect
449. #548	C₄×C₅	semidirect
451. #547	C₄×C₅	semidirect
454. #546	C₄×C₅	semidirect
455. #546	C₄×C₅	semidirect
457. D₄²	C₄×C₅	semidirect
467. C₂×#117	C₂²×C₅	semidirect
468. C₂²×C₄²	C₂²×C₅	semidirect
473. #423	C₂²×C₅	semidirect
480. C₂×#104	C₂²×C₅	semidirect
481. C₂×#104	C₂²×C₅	semidirect
482. C₂×#104	C₂²×C₅	semidirect
483. C₂×#104	C₂²×C₅	semidirect
484. C₂×#104	C₂²×C₅	semidirect
485. C₂×#104	C₂²×C₅	semidirect
486. C₂×#104	C₂²×C₅	semidirect
487. C₂×#104	C₂²×C₅	semidirect
488. #407	C₂²×C₅	semidirect
489. #407	C₂²×C₅	semidirect
490. C₄×M₁₆	C₂²×C₅	semidirect
495. C₄×C₄⋊C₄	C₂²×C₅	semidirect
496. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
497. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
498. #376	C₂²×C₅	semidirect
499. #339	C₂²×C₅	semidirect
500. #339	C₂²×C₅	semidirect
501. #339	C₂²×C₅	semidirect
502. #339	C₂²×C₅	semidirect
647. C₂×#41	C₂×C₄×C₅	semidirect
648. C₂×#41	C₂×C₄×C₅	semidirect
653. C₂²×Q₈	C₂×C₄×C₅	semidirect
658. C₂²×D₄	C₂×C₄×C₅	semidirect
678. C₄⋊Q₈	C₂×C₄×C₅	semidirect
680. #127	C₂×C₄×C₅	semidirect
683. #124	C₂×C₄×C₅	semidirect
684. #124	C₂×C₄×C₅	semidirect
697. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
698. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
711. #121	C₂×C₄×C₅	semidirect
712. #121	C₂×C₄×C₅	semidirect
719. C₄×Q₈	C₂×C₄×C₅	semidirect
720. C₄×Q₈	C₂×C₄×C₅	semidirect
737. C₄×D₄	C₂×C₄×C₅	semidirect
738. C₄×D₄	C₂×C₄×C₅	semidirect
780. #104	C₅×D₄	semidirect
820. C₂²×C₅	#421	semidirect
970. M₁₆	C₂×C₅×D₄	semidirect
1034. C₄²	C₂×C₅×D₄	semidirect
1177. C₅	#22434	direct (N × H)
1206. C₂²	C₅×#421	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×#41	2
C₅×D₄×M₁₆	2
C₂×C₅×#421	2
C₂²×C₅×#104	2
C₅×#2290	2
C₅×#1980	2
C₅×#1963	2
C₅×#1897	2
C₅×#1896	2
C₅×#1871	2
C₅×#1806	2
C₅×#1789	2
C₅×#1759	2
#22434	5

Subgroups — C5×#22434 #11945154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22434 #11945154