Subgroups — #12066346

Order 1280.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3482	C₂	1	1	yes	maximal, characteristic
2	#10614253	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614244	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602620	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602617	C₂	1	1	yes	maximal, characteristic, complemented
6	#10602546	C₂	1	1	yes	maximal, characteristic, complemented
7	#10602545	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602544	C₂	1	1	yes	maximal, characteristic, complemented
9	#10602543	C₂	1	1	yes	maximal, characteristic, complemented
10	#10602433	C₂	1	1	yes	maximal, characteristic, complemented
11	#10602432	C₂	1	1	yes	maximal, characteristic, complemented
12	#10602416	C₂	1	1	yes	maximal, characteristic, complemented
13	#10602415	C₂	1	1	yes	maximal, characteristic, complemented
14	#10602414	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#557	C₄	1	1	yes	characteristic
17	C₅×#556	—	2	1	no	—
18	C₅×#556	C₄	1	1	yes	characteristic
19	C₅×#552	—	2	1	no	—
20	C₅×#552	—	2	1	no	—
21	C₅×#552	C₄	1	1	yes	characteristic
22	C₅×#552	C₄	1	1	yes	characteristic
23	C₅×D₄×Q₈	C₄	1	1	yes	characteristic
24	C₅×#548	C₄	1	1	yes	characteristic
25	C₅×#548	C₄	1	1	yes	characteristic
26	C₅×#547	—	2	1	no	—
27	C₅×#547	C₄	1	1	yes	characteristic
28	C₅×#533	—	2	1	no	—
29	C₅×#533	C₂²	1	1	yes	characteristic
30	C₅×#529	—	2	1	no	—
31	C₅×#529	—	2	1	no	—
32	C₅×#529	C₂²	1	1	yes	characteristic
33	C₅×#529	C₂²	1	1	yes	characteristic
34	C₄×C₅×#41	—	2	1	no	—
35	C₄×C₅×#41	C₂²	1	1	yes	characteristic
36	C₄×C₅×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
39	#65523	—	2	1	no	—
40	#65313	—	2	1	no	—
41	#65300	—	2	1	no	—
42	#65300	—	2	1	no	—
43	D₄×#168	—	2	1	no	—
44	#65289	—	2	1	no	—
45	#65289	—	2	1	no	—
46	#65288	—	2	1	no	—
47	#65215	C₂²	1	1	yes	characteristic
48	#65215	C₂²	1	1	yes	characteristic
49	#65214	C₂²	1	1	yes	characteristic
50	#65214	C₂²	1	1	yes	characteristic
51	#65214	C₂²	1	1	yes	characteristic
52	#65214	C₂²	1	1	yes	characteristic
53	#65214	C₂²	1	1	yes	characteristic
54	#65213	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
57	C₄×#681	C₂²	1	1	yes	characteristic
58	C₂×C₄×#168	C₂²	1	1	yes	characteristic
59	Q₈⋊#168	C₂²	1	1	yes	characteristic
60	Q₈⋊#168	C₂²	1	1	yes	characteristic
61	Q₈⋊#168	C₂²	1	1	yes	characteristic
62	Q₈⋊#168	C₂²	1	1	yes	characteristic
63	Q₈⋊#168	C₂²	1	1	yes	characteristic
64	Q₈⋊#168	C₂²	1	1	yes	characteristic
65	Q₈⋊#168	C₂²	1	1	yes	characteristic
66	Q₈⋊#168	C₂²	1	1	yes	characteristic
67	Q₈⋊#168	C₂²	1	1	yes	characteristic
68	Q₈⋊#168	C₂²	1	1	yes	characteristic
69	Q₈⋊#168	C₂²	1	1	yes	characteristic
70	Q₈⋊#168	C₂²	1	1	yes	characteristic
71	D₄⋊#168	C₂²	1	1	yes	characteristic
72	D₄⋊#168	C₂²	1	1	yes	characteristic
73	D₄⋊#168	C₂²	1	1	yes	characteristic
74	D₄⋊#168	C₂²	1	1	yes	characteristic
75	#17524	—	5	1	no	maximal, Sylow
76	C₂×C₅×#41	—	2	1	no	—
77	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₅×#41	D₄	1	1	yes	characteristic
79	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₅×#126	—	2	1	no	—
86	C₅×#126	—	2	1	no	—
87	C₅×#126	—	2	1	no	—
88	C₅×#126	—	2	1	no	—
89	C₅×#126	—	2	1	no	—
90	C₅×#126	—	2	1	no	—
91	C₅×#125	—	2	1	no	—
92	C₅×#125	—	2	1	no	—
93	C₅×#125	—	2	1	no	—
94	C₅×#125	—	2	1	no	—
95	C₅×#125	—	2	1	no	—
96	C₅×#125	C₂×C₄	1	1	yes	characteristic
97	C₅×#125	C₂×C₄	1	1	yes	characteristic
98	C₅×#124	—	2	1	no	—
99	C₅×#124	—	2	1	no	—
100	C₅×#124	C₂×C₄	1	1	yes	characteristic
101	C₅×#124	C₂×C₄	1	1	yes	characteristic
102	C₅×#123	—	2	1	no	—
103	C₅×#123	—	2	1	no	—
104	C₅×#123	—	2	1	no	—
105	C₅×#123	—	2	1	no	—
106	C₅×#123	—	2	1	no	—
107	C₅×#123	—	2	1	no	—
108	C₅×C₂²⋊Q₈	—	2	1	no	—
109	C₅×C₂²⋊Q₈	—	2	1	no	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₅×C₂²⋊Q₈	—	2	1	no	—
113	C₅×C₂²⋊Q₈	—	2	1	no	—
114	C₅×C₂²⋊Q₈	—	2	1	no	—
115	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
117	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
118	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
119	C₅×#121	—	2	1	no	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	C₂×C₄	1	1	yes	characteristic
122	C₅×#121	C₂×C₄	1	1	yes	characteristic
123	C₄×C₅×Q₈	—	2	1	no	—
124	C₄×C₅×Q₈	—	2	1	no	—
125	C₄×C₅×Q₈	—	2	1	no	—
126	C₄×C₅×Q₈	—	2	1	no	—
127	C₄×C₅×Q₈	—	2	1	no	—
128	C₄×C₅×Q₈	—	2	1	no	—
129	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
130	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
131	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
132	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
133	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
134	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
135	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
136	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
137	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
138	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
139	C₄×C₅×D₄	—	2	1	no	—
140	C₄×C₅×D₄	—	2	1	no	—
141	C₄×C₅×D₄	—	2	1	no	—
142	C₄×C₅×D₄	—	2	1	no	—
143	C₄×C₅×D₄	—	2	1	no	—
144	C₄×C₅×D₄	—	2	1	no	—
145	C₄×C₅×D₄	—	2	1	no	—
146	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
147	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
148	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
149	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₅×D₄	D₄	1	1	yes	characteristic
151	C₄×C₅×D₄	D₄	1	1	yes	characteristic
152	C₄×C₅×D₄	D₄	1	1	yes	characteristic
153	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
154	C₅×#117	—	2	1	no	—
155	C₅×#117	—	2	1	no	—
156	C₅×#117	—	2	1	no	—
157	C₅×#117	—	2	1	no	—
158	C₅×#117	—	2	1	no	—
159	C₅×#117	—	2	1	no	—
160	C₅×#117	—	2	1	no	—
161	C₅×#117	C₂×C₄	1	1	yes	characteristic
162	C₅×#117	D₄	1	1	yes	characteristic
163	C₅×#117	D₄	1	1	yes	characteristic
164	C₅×#117	D₄	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	—	2	1	no	—
166	C₂×C₅×C₄⋊C₄	—	2	1	no	—
167	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂×C₄²×C₅	—	2	1	no	—
170	C₂×C₄²×C₅	—	2	1	no	—
171	C₂×C₄²×C₅	—	2	1	no	—
172	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₂×#681	—	2	1	no	—
176	C₂×#681	—	2	1	no	—
177	C₂²×#168	—	2	1	no	—
178	C₂²×#168	—	2	1	no	—
179	C₂²×#168	—	2	1	no	—
180	C₂²⋊#168	—	2	1	no	—
181	C₂²⋊#168	—	2	1	no	—
182	C₂²⋊#168	—	2	1	no	—
183	C₂²⋊#168	—	2	1	no	—
184	C₂²⋊#168	—	2	1	no	—
185	C₂²⋊#168	—	2	1	no	—
186	C₂²⋊#168	—	2	1	no	—
187	C₄⋊#168	—	2	1	no	—
188	C₄⋊#168	—	2	1	no	—
189	C₄⋊#168	—	2	1	no	—
190	C₄⋊#168	—	2	1	no	—
191	C₄⋊#168	—	2	1	no	—
192	C₄⋊#168	—	2	1	no	—
193	C₄⋊#168	—	2	1	no	—
194	C₄⋊#168	C₂³	1	1	yes	characteristic
195	C₄⋊#168	C₂³	1	1	yes	characteristic
196	C₄⋊#168	C₂³	1	1	yes	characteristic
197	C₄⋊#168	C₂³	1	1	yes	characteristic
198	#3935	—	2	1	no	—
199	#3935	—	2	1	no	—
200	#3935	—	2	1	no	—
201	C₄×#168	—	2	1	no	—
202	C₄×#168	—	2	1	no	—
203	C₄×#168	C₂³	1	1	yes	characteristic
204	C₄×#168	C₂³	1	1	yes	characteristic
205	C₄×#168	C₂³	1	1	yes	characteristic
206	C₄×#168	C₂³	1	1	yes	characteristic
207	#3482	D₅	1	1	yes	characteristic
208	#2990	—	5	1	no	—
209	#2922	—	5	1	no	—
210	#1497	—	5	1	no	—
211	#1495	—	5	1	no	—
212	#1494	—	5	1	no	—
213	#1491	—	5	1	no	—
214	#1488	—	5	1	no	—
215	#1487	—	5	1	no	—
216	#1483	—	5	1	no	—
217	#1482	—	5	1	no	—
218	#1481	—	5	1	no	—
219	#1479	—	5	1	no	—
220	#1477	—	5	1	no	—
221	C₂×Q₈⋊C₈	—	5	1	no	—
222	C₅×#41	—	2	2	no	—
223	C₅×#41	—	4	2	no	—
224	C₅×#41	—	4	1	no	—
225	C₅×#41	—	4	4	no	—
226	C₂×C₅×Q₈	—	2	1	no	—
227	C₂×C₅×Q₈	—	2	1	no	—
228	C₂×C₅×Q₈	—	2	1	no	—
229	C₂×C₅×Q₈	—	2	2	no	—
230	C₂×C₅×Q₈	—	2	2	no	—
231	C₂×C₅×Q₈	—	4	1	no	—
232	C₂×C₅×Q₈	—	4	1	no	—
233	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₅×D₄	—	2	1	no	—
238	C₂×C₅×D₄	—	2	1	no	—
239	C₂×C₅×D₄	—	2	1	no	—
240	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×C₅	—	2	1	no	—
245	C₂²×C₄×C₅	—	2	1	no	—
246	C₂²×C₄×C₅	—	2	1	no	—
247	C₂²×C₄×C₅	—	2	1	no	—
248	C₂²×C₄×C₅	—	2	1	no	—
249	C₂²×C₄×C₅	—	2	1	no	—
250	C₂²×C₄×C₅	—	2	1	no	—
251	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
260	C₅×C₄⋊C₄	—	2	1	no	—
261	C₅×C₄⋊C₄	—	2	1	no	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	—	2	1	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	1	no	—
271	C₅×C₄⋊C₄	—	2	1	no	—
272	C₅×C₄⋊C₄	—	2	1	no	—
273	C₅×C₄⋊C₄	—	2	1	no	—
274	C₅×C₄⋊C₄	—	2	1	no	—
275	C₅×C₄⋊C₄	—	2	1	no	—
276	C₅×C₄⋊C₄	—	2	1	no	—
277	C₅×C₄⋊C₄	—	2	1	no	—
278	C₅×C₄⋊C₄	—	2	1	no	—
279	C₅×C₄⋊C₄	—	2	1	no	—
280	C₅×C₄⋊C₄	—	2	1	no	—
281	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
282	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
283	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
284	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
285	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
286	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
287	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
288	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
289	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
290	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
291	C₅×C₂²⋊C₄	—	2	1	no	—
292	C₅×C₂²⋊C₄	—	2	1	no	—
293	C₅×C₂²⋊C₄	—	2	1	no	—
294	C₅×C₂²⋊C₄	—	2	1	no	—
295	C₅×C₂²⋊C₄	—	2	1	no	—
296	C₅×C₂²⋊C₄	—	2	1	no	—
297	C₅×C₂²⋊C₄	—	2	1	no	—
298	C₅×C₂²⋊C₄	—	2	1	no	—
299	C₅×C₂²⋊C₄	—	2	1	no	—
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
304	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
305	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
306	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
307	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
308	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
309	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
310	C₄²×C₅	—	2	1	no	—
311	C₄²×C₅	—	2	1	no	—
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	2	1	no	—
314	C₄²×C₅	—	2	1	no	—
315	C₄²×C₅	—	2	1	no	—
316	C₄²×C₅	—	2	1	no	—
317	C₄²×C₅	—	2	1	no	—
318	C₄²×C₅	—	2	1	no	—
319	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
320	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
321	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
322	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₅	C₂⁴	1	1	yes	characteristic
329	#681	—	4	2	no	—
330	#681	—	8	1	no	—
331	C₂×#168	—	2	1	no	—
332	C₂×#168	—	2	1	no	—
333	C₂×#168	—	2	1	no	—
334	C₂×#168	—	2	1	no	—
335	C₂×#168	—	2	1	no	—
336	C₂×#168	—	2	1	no	—
337	C₂×#168	—	2	1	no	—
338	C₂×#168	—	2	1	no	—
339	C₂×#168	—	4	2	no	—
340	C₂×#168	—	8	1	no	—
341	C₂×#168	—	8	1	no	—
342	#557	Dic₅	1	1	yes	characteristic
343	#556	—	2	1	no	—
344	#556	Dic₅	1	1	yes	characteristic
345	#552	—	2	1	no	—
346	#552	—	2	1	no	—
347	#552	Dic₅	1	1	yes	characteristic
348	#552	Dic₅	1	1	yes	characteristic
349	D₄×Q₈	Dic₅	1	1	yes	characteristic
350	#548	Dic₅	1	1	yes	characteristic
351	#548	Dic₅	1	1	yes	characteristic
352	#547	—	2	1	no	—
353	#547	Dic₅	1	1	yes	characteristic
354	#533	—	2	1	no	—
355	#533	C₂×D₅	1	1	yes	characteristic
356	#529	—	2	1	no	—
357	#529	—	2	1	no	—
358	#529	C₂×D₅	1	1	yes	characteristic
359	#529	C₂×D₅	1	1	yes	characteristic
360	C₄×#41	—	2	1	no	—
361	C₄×#41	C₂×D₅	1	1	yes	characteristic
362	C₄×#41	C₂×D₅	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
364	C₂×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
365	#446	—	10	1	no	—
366	#435	—	10	1	no	—
367	#435	—	10	1	no	—
368	C₈×D₄	—	10	1	no	—
369	#433	—	10	1	no	—
370	#433	—	10	1	no	—
371	#432	—	5	1	no	—
372	#432	—	5	1	no	—
373	#431	—	5	1	no	—
374	#431	—	5	1	no	—
375	#431	—	5	1	no	—
376	#431	—	5	1	no	—
377	#431	—	5	1	no	—
378	#424	—	10	1	no	—
379	#423	—	5	1	no	—
380	C₂×C₄⋊C₈	—	5	1	no	—
381	C₂×C₄⋊C₈	—	5	1	no	—
382	#408	—	10	1	no	—
383	C₄×M₁₆	—	5	1	no	—
384	C₂×C₄×C₈	—	5	1	no	—
385	Q₈⋊C₈	—	5	1	no	—
386	Q₈⋊C₈	—	5	1	no	—
387	Q₈⋊C₈	—	5	1	no	—
388	Q₈⋊C₈	—	5	1	no	—
389	Q₈⋊C₈	—	5	1	no	—
390	Q₈⋊C₈	—	5	1	no	—
391	Q₈⋊C₈	—	5	1	no	—
392	Q₈⋊C₈	—	5	1	no	—
393	Q₈⋊C₈	—	5	1	no	—
394	Q₈⋊C₈	—	5	1	no	—
395	Q₈⋊C₈	—	5	1	no	—
396	Q₈⋊C₈	—	5	1	no	—
397	D₄⋊C₈	—	5	1	no	—
398	D₄⋊C₈	—	5	1	no	—
399	D₄⋊C₈	—	5	1	no	—
400	D₄⋊C₈	—	5	1	no	—
401	C₂³×C₅	—	2	1	no	—
402	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₅×Q₈	—	2	1	no	—
406	C₅×Q₈	—	2	1	no	—
407	C₅×Q₈	—	2	1	no	—
408	C₅×Q₈	—	2	1	no	—
409	C₅×Q₈	—	2	1	no	—
410	C₅×Q₈	—	4	1	no	—
411	C₅×Q₈	—	4	2	no	—
412	C₅×Q₈	—	4	2	no	—
413	C₅×Q₈	—	4	2	no	—
414	C₅×Q₈	#131	1	2	yes	—
415	C₅×D₄	—	2	2	no	—
416	C₅×D₄	—	2	2	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	2	1	no	—
419	C₅×D₄	—	4	1	no	—
420	C₅×D₄	—	4	2	no	—
421	C₅×D₄	—	4	2	no	—
422	C₅×D₄	—	4	2	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	2	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	4	1	no	—
444	C₂×C₄×C₅	—	4	1	no	—
445	C₂×C₄×C₅	—	4	2	no	—
446	C₂×C₄×C₅	—	4	2	no	—
447	C₂×C₄×C₅	—	4	2	no	—
448	C₂×C₄×C₅	—	4	2	no	—
449	C₂×C₄×C₅	—	4	2	no	—
450	C₂×C₄×C₅	—	4	2	no	—
451	C₂×C₄×C₅	—	4	1	no	—
452	C₂×C₄×C₅	—	4	1	no	—
453	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
465	#168	—	4	1	no	—
466	#168	—	4	1	no	—
467	#168	—	4	1	no	—
468	#168	—	4	1	no	—
469	#168	—	4	1	no	—
470	#168	—	4	1	no	—
471	#168	—	4	1	no	—
472	#168	—	4	1	no	—
473	C₂×#41	—	2	1	no	—
474	C₂×#41	C₂×Dic₅	1	1	yes	characteristic
475	C₂×#41	C₂²⋊D₅	1	1	yes	characteristic
476	C₂²×Q₈	C₂×Dic₅	1	1	yes	characteristic
477	C₂²×Q₈	C₂×Dic₅	1	1	yes	characteristic
478	C₂×M₁₆	—	10	1	no	—
479	C₂×M₁₆	—	10	1	no	—
480	C₂²×C₈	—	10	1	no	—
481	C₂²×C₈	—	10	1	no	—
482	C₂²×C₈	—	10	1	no	—
483	C₄⋊Q₈	—	2	1	no	—
484	C₄⋊Q₈	—	2	1	no	—
485	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
486	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
487	#126	—	2	1	no	—
488	#126	—	2	1	no	—
489	#126	—	2	1	no	—
490	#126	—	2	1	no	—
491	#126	—	2	1	no	—
492	#126	—	2	1	no	—
493	#125	—	2	1	no	—
494	#125	—	2	1	no	—
495	#125	—	2	1	no	—
496	#125	—	2	1	no	—
497	#125	—	2	1	no	—
498	#125	C₂×Dic₅	1	1	yes	characteristic
499	#125	C₂×Dic₅	1	1	yes	characteristic
500	#124	—	2	1	no	—
501	#124	—	2	1	no	—
502	#124	C₂×Dic₅	1	1	yes	characteristic
503	#124	C₂×Dic₅	1	1	yes	characteristic
504	#123	—	2	1	no	—
505	#123	—	2	1	no	—
506	#123	—	2	1	no	—
507	#123	—	2	1	no	—
508	#123	—	2	1	no	—
509	#123	—	2	1	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	1	no	—
515	C₂²⋊Q₈	—	2	1	no	—
516	C₂²⋊Q₈	—	2	1	no	—
517	C₂²⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
518	C₂²⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
519	C₂²⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
520	C₂²⋊Q₈	C₂×Dic₅	1	1	yes	characteristic
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	C₂×Dic₅	1	1	yes	characteristic
524	#121	C₂×Dic₅	1	1	yes	characteristic
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
532	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
533	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
534	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
535	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
536	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
537	C₄×Q₈	C₂²⋊D₅	1	1	yes	characteristic
538	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
539	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
540	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
549	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
550	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
551	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
552	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
553	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
554	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
555	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
556	#117	—	2	1	no	—
557	#117	—	2	1	no	—
558	#117	—	2	1	no	—
559	#117	—	2	1	no	—
560	#117	—	2	1	no	—
561	#117	—	2	1	no	—
562	#117	—	2	1	no	—
563	#117	C₂×Dic₅	1	1	yes	characteristic
564	#117	C₂²⋊D₅	1	1	yes	characteristic
565	#117	C₂²⋊D₅	1	1	yes	characteristic
566	#117	C₂²⋊D₅	1	1	yes	characteristic
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	—	2	1	no	—
574	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
575	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
576	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
577	C₄⋊C₈	—	5	1	no	—
578	C₄⋊C₈	—	5	1	no	—
579	C₄⋊C₈	—	5	1	no	—
580	C₄⋊C₈	—	5	1	no	—
581	C₄⋊C₈	—	10	1	no	—
582	C₄⋊C₈	—	10	1	no	—
583	C₄⋊C₈	—	10	1	no	—
584	C₄⋊C₈	—	10	1	no	—
585	C₄⋊C₈	—	10	1	no	—
586	C₄⋊C₈	—	10	1	no	—
587	C₄⋊C₈	—	10	1	no	—
588	C₂²⋊C₈	—	10	1	no	—
589	C₂²⋊C₈	—	10	1	no	—
590	C₂²⋊C₈	—	10	1	no	—
591	C₂²⋊C₈	—	10	1	no	—
592	C₂²⋊C₈	—	10	1	no	—
593	C₂²⋊C₈	—	10	1	no	—
594	C₂²⋊C₈	—	10	1	no	—
595	#97	—	10	1	no	—
596	#97	—	10	1	no	—
597	#97	—	10	1	no	—
598	C₄×C₈	—	5	1	no	—
599	C₄×C₈	—	5	1	no	—
600	C₄×C₈	—	5	1	no	—
601	C₄×C₈	—	5	1	no	—
602	C₄×C₈	—	10	1	no	—
603	C₄×C₈	—	10	1	no	—
604	C₂²×C₅	—	2	1	no	—
605	C₂²×C₅	—	2	1	no	—
606	C₂²×C₅	—	2	1	no	—
607	C₂²×C₅	—	2	1	no	—
608	C₂²×C₅	—	2	1	no	—
609	C₂²×C₅	—	2	1	no	—
610	C₂²×C₅	—	2	1	no	—
611	C₂²×C₅	—	2	1	no	—
612	C₂²×C₅	—	4	1	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	#421	1	2	yes	—
616	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
617	C₄×C₅	—	2	1	no	—
618	C₄×C₅	—	2	1	no	—
619	C₄×C₅	—	2	1	no	—
620	C₄×C₅	—	2	2	no	—
621	C₄×C₅	—	2	1	no	—
622	C₄×C₅	—	2	1	no	—
623	C₄×C₅	—	2	1	no	—
624	C₄×C₅	—	2	1	no	—
625	C₄×C₅	—	2	1	no	—
626	C₄×C₅	—	2	1	no	—
627	C₄×C₅	—	2	1	no	—
628	C₄×C₅	—	4	1	no	—
629	C₄×C₅	—	4	1	no	—
630	C₄×C₅	—	4	1	no	—
631	C₄×C₅	—	4	1	no	—
632	C₄×C₅	—	4	1	no	—
633	C₄×C₅	—	4	1	no	—
634	C₄×C₅	C₂×#131	1	1	yes	characteristic
635	C₄×C₅	#568	1	1	yes	characteristic
636	C₄×C₅	#577	1	1	yes	characteristic
637	C₄×C₅	#578	1	1	yes	characteristic
638	#41	—	2	2	no	—
639	#41	—	4	2	no	—
640	#41	—	4	1	no	—
641	#41	—	4	4	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	1	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	4	1	no	—
648	C₂×Q₈	—	4	1	no	—
649	C₂×Q₈	C₂²⋊Dic₅	1	1	yes	characteristic
650	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
651	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
652	C₂×Q₈	C₂²×Dic₅	1	1	yes	characteristic
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	C₂²⋊Dic₅	1	1	yes	characteristic
657	C₂×D₄	C₂²⋊Dic₅	1	1	yes	characteristic
658	C₂×D₄	C₂²⋊Dic₅	1	1	yes	characteristic
659	C₂×D₄	C₂²×Dic₅	1	1	yes	characteristic
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
668	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
669	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
675	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
676	M₁₆	—	20	2	no	—
677	M₁₆	—	40	1	no	—
678	C₂×C₈	—	10	1	no	—
679	C₂×C₈	—	10	1	no	—
680	C₂×C₈	—	10	1	no	—
681	C₂×C₈	—	10	1	no	—
682	C₂×C₈	—	10	1	no	—
683	C₂×C₈	—	10	1	no	—
684	C₂×C₈	—	10	1	no	—
685	C₂×C₈	—	10	1	no	—
686	C₂×C₈	—	20	2	no	—
687	C₂×C₈	—	40	1	no	—
688	C₂×C₈	—	40	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
711	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
712	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
713	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
714	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
715	C₄⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
716	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
718	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
719	C₄⋊C₄	C₂²×Dic₅	1	1	yes	characteristic
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
734	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
735	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
736	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
737	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
738	C₂²⋊C₄	C₂²⋊Dic₅	1	1	yes	characteristic
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	1	no	—
746	C₄²	—	2	1	no	—
747	C₄²	—	2	1	no	—
748	C₄²	C₂²×Dic₅	1	1	yes	characteristic
749	C₄²	C₂²×Dic₅	1	1	yes	characteristic
750	C₄²	C₂²×Dic₅	1	1	yes	characteristic
751	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
752	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
753	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
754	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
755	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
756	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
757	C₄²	C₂³×D₅	1	1	yes	characteristic
758	C₂×C₅	—	2	2	no	—
759	C₂×C₅	—	4	1	no	—
760	C₂×C₅	—	4	1	no	—
761	C₂×C₅	—	8	1	no	—
762	C₂×C₅	#2880	1	1	yes	characteristic
763	C₂×C₅	#2898	1	1	yes	characteristic
764	C₂×C₅	C₂×#421	1	1	yes	characteristic
765	C₂³	—	2	1	no	—
766	C₂³	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
767	C₂³	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
768	C₂³	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
769	Q₈	—	2	1	no	—
770	Q₈	—	2	1	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	2	1	no	—
773	Q₈	—	2	1	no	—
774	Q₈	—	4	1	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	#4094	1	2	yes	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	1	no	—
782	D₄	—	2	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
818	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
819	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
820	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
821	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
822	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
823	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
824	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
825	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
826	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
827	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
828	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
829	C₈	—	20	1	no	—
830	C₈	—	20	1	no	—
831	C₈	—	20	1	no	—
832	C₈	—	20	1	no	—
833	C₈	—	20	1	no	—
834	C₈	—	20	1	no	—
835	C₈	—	20	1	no	—
836	C₈	—	20	1	no	—
837	C₅	#17524	1	1	yes	characteristic, complemented, Sylow
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	#65525	1	2	yes	—
850	C₂²	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	1	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	C₂×#4094	1	1	yes	characteristic
869	C₄	#66153	1	1	yes	characteristic
870	C₄	#66171	1	1	yes	characteristic
871	C₄	#66172	1	1	yes	characteristic
872	C₂	—	2	2	no	—
873	C₂	—	4	1	no	—
874	C₂	—	4	1	no	—
875	C₂	—	8	1	no	—
876	C₂	#10615806	1	1	yes	characteristic
877	C₂	C₂×#65525	1	1	yes	characteristic
878	C₂	#10615842	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting, prime radical	C₅×#3482	C₂
socle	C₂²×C₅	C₂²×C₂²⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#3482	D₅
hypocenter	C₅	#17524
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3482

Complements

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

N	H ≅ G/N	type
2. #10614253	C₂	semidirect
3. #10614244	C₂	semidirect
4. #10602620	C₂	semidirect
5. #10602617	C₂	semidirect
6. #10602546	C₂	semidirect
7. #10602545	C₂	semidirect
8. #10602544	C₂	semidirect
9. #10602543	C₂	semidirect
10. #10602433	C₂	semidirect
11. #10602432	C₂	semidirect
12. #10602416	C₂	semidirect
13. #10602415	C₂	semidirect
14. #10602414	C₂	semidirect
15. C₂×Q₈⋊#168	C₂	semidirect
837. C₅	#17524	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3482	2
#10614253	2
#10614244	2
#10602620	2
#10602617	2
#10602546	2
#10602545	2
#10602544	2
#10602543	2
#10602433	2
#10602432	2
#10602416	2
#10602415	2
#10602414	2
C₂×Q₈⋊#168	2
#17524	5