Subgroups — #12069394

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611032	C₂	1	1	yes	maximal, characteristic
2	#10611022	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611021	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1454	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601556	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601551	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601545	C₂	1	1	yes	maximal, characteristic, complemented
8	#10598881	C₂	1	1	yes	maximal, characteristic, complemented
9	#10598878	C₂	1	1	yes	maximal, characteristic, complemented
10	#10598874	C₂	1	1	yes	maximal, characteristic, complemented
11	#10598871	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598870	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#677	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
16	#65811	C₂²	1	1	yes	characteristic
17	C₄×#709	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₅×#431	C₂²	1	1	yes	characteristic
21	#65215	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
23	#65139	C₄	1	1	yes	characteristic
24	#65137	C₄	1	1	yes	characteristic
25	#65132	C₄	1	1	yes	characteristic
26	#65131	C₄	1	1	yes	characteristic
27	#65125	—	2	1	no	—
28	#65125	—	2	1	no	—
29	#65122	—	2	1	no	—
30	D₅×C₄⋊C₈	—	2	1	no	—
31	#65026	C₄	1	1	yes	characteristic
32	#65026	C₄	1	1	yes	characteristic
33	#65023	C₄	1	1	yes	characteristic
34	#65023	C₄	1	1	yes	characteristic
35	#65016	—	2	1	no	—
36	#65016	—	2	1	no	—
37	#65014	—	2	1	no	—
38	#65014	—	2	1	no	—
39	C₄×D₄₀	C₂²	1	1	yes	characteristic
40	C₄×D₄₀	C₂²	1	1	yes	characteristic
41	C₄×#677	C₂²	1	1	yes	characteristic
42	C₄×#677	C₂²	1	1	yes	characteristic
43	#64977	C₂²	1	1	yes	characteristic
44	#64977	C₂²	1	1	yes	characteristic
45	C₈×D₂₀	C₂²	1	1	yes	characteristic
46	C₈×D₂₀	C₂²	1	1	yes	characteristic
47	C₈×D₂₀	C₂²	1	1	yes	characteristic
48	C₈×D₂₀	C₂²	1	1	yes	characteristic
49	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₀	C₂²	1	1	yes	characteristic
51	C₅×#322	C₂²	1	1	yes	characteristic
52	C₅×#322	C₂²	1	1	yes	characteristic
53	C₅×#322	C₂²	1	1	yes	characteristic
54	C₅×C₈²	C₂²	1	1	yes	characteristic
55	#64679	C₂²	1	1	yes	characteristic
56	#64679	C₂²	1	1	yes	characteristic
57	#64679	C₂²	1	1	yes	characteristic
58	#64679	C₂²	1	1	yes	characteristic
59	#64679	C₂²	1	1	yes	characteristic
60	#64679	C₂²	1	1	yes	characteristic
61	#64678	C₂²	1	1	yes	characteristic
62	#64678	C₂²	1	1	yes	characteristic
63	#64677	C₂²	1	1	yes	characteristic
64	#64677	C₂²	1	1	yes	characteristic
65	#64676	C₂²	1	1	yes	characteristic
66	#64676	C₂²	1	1	yes	characteristic
67	#17920	—	5	1	no	maximal, Sylow
68	C₂×#709	—	2	1	no	—
69	C₂×#709	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	#4076	—	2	1	no	—
72	#4076	C₂×C₄	1	1	yes	characteristic
73	#4076	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₅	—	2	1	no	—
75	C₄×C₂²⋊D₅	—	2	1	no	—
76	#4072	C₂×C₄	1	1	yes	characteristic
77	C₂²×#168	—	2	1	no	—
78	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
79	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
80	C₂×#677	C₂×C₄	1	1	yes	characteristic
81	C₂×#677	C₂×C₄	1	1	yes	characteristic
82	C₂×#676	—	2	1	no	—
83	C₂×#676	—	2	1	no	—
84	C₂×C₈×D₅	—	2	1	no	—
85	C₂×C₈×D₅	—	2	1	no	—
86	C₂×C₈×D₅	—	2	1	no	—
87	C₂×C₈×D₅	—	2	1	no	—
88	#4021	—	2	1	no	—
89	#4020	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₀	—	2	1	no	—
91	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
92	C₄×D₂₀	C₂³	1	1	yes	characteristic
93	C₄×D₂₀	C₂³	1	1	yes	characteristic
94	C₄×D₂₀	C₂³	1	1	yes	characteristic
95	#4018	—	2	1	no	—
96	C₄²×D₅	—	2	1	no	—
97	#4015	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	—	2	1	no	—
101	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
103	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
105	C₅×C₂²⋊C₈	—	2	1	no	—
106	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
108	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
109	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
116	C₂²⋊#168	—	2	1	no	—
117	#3953	C₂×C₄	1	1	yes	characteristic
118	#3953	C₂×C₄	1	1	yes	characteristic
119	#3953	C₂×C₄	1	1	yes	characteristic
120	#3953	C₂×C₄	1	1	yes	characteristic
121	#3953	C₂×C₄	1	1	yes	characteristic
122	#3953	C₂×C₄	1	1	yes	characteristic
123	#3952	—	2	1	no	—
124	#3952	—	2	1	no	—
125	#3952	—	2	1	no	—
126	#3952	—	2	1	no	—
127	#3952	—	2	1	no	—
128	#3952	—	2	1	no	—
129	#3950	C₂×C₄	1	1	yes	characteristic
130	#3950	C₂×C₄	1	1	yes	characteristic
131	#3949	C₂×C₄	1	1	yes	characteristic
132	#3949	C₂×C₄	1	1	yes	characteristic
133	#3948	C₂×C₄	1	1	yes	characteristic
134	#3948	C₂×C₄	1	1	yes	characteristic
135	#3946	—	2	1	no	—
136	#3946	—	2	1	no	—
137	C₈×Dic₅	—	2	1	no	—
138	C₈×Dic₅	—	2	1	no	—
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	C₂³	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄⋊#168	C₂³	1	1	yes	characteristic
143	C₄⋊#168	C₂³	1	1	yes	characteristic
144	#3935	—	2	1	no	—
145	#3106	—	5	1	no	—
146	#2988	—	5	1	no	—
147	#2981	—	5	1	no	—
148	#1588	—	5	1	no	—
149	#1586	—	5	1	no	—
150	#1583	—	5	1	no	—
151	#1581	—	5	1	no	—
152	#1580	—	5	1	no	—
153	SD₁₆⋊C₈	—	5	1	no	—
154	C₈×SD₁₆	—	5	1	no	—
155	C₈×D₈	—	5	1	no	—
156	#1573	—	5	1	no	—
157	#1488	—	5	1	no	—
158	#1480	—	5	1	no	—
159	#1454	D₅	1	1	yes	characteristic, complemented
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	#41	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	—	2	1	no	—
164	C₂×C₂²⋊D₅	—	2	1	no	—
165	C₂×C₂²⋊D₅	—	2	1	no	—
166	#709	—	2	2	no	—
167	#709	—	2	2	no	—
168	#709	—	8	1	no	—
169	#709	—	8	1	no	—
170	C₂×D₂₀	—	2	1	no	—
171	C₂×D₂₀	—	2	1	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
173	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
174	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	2	1	no	—
179	C₂×C₄×D₅	—	2	1	no	—
180	C₂×Dic₁₀	—	2	1	no	—
181	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	#41	1	1	yes	characteristic
195	C₄²×C₅	C₂⁴	1	1	yes	characteristic
196	C₂²⋊Dic₅	—	2	1	no	—
197	#685	—	2	1	no	—
198	#685	—	2	1	no	—
199	#685	—	2	1	no	—
200	#685	—	2	1	no	—
201	#685	—	2	1	no	—
202	#685	—	2	1	no	—
203	C₄⋊Dic₅	—	2	1	no	—
204	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
205	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
208	#683	—	2	1	no	—
209	#683	—	2	1	no	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	—	2	1	no	—
213	C₂×#168	—	2	1	no	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	8	1	no	—
218	D₄₀	—	2	2	no	—
219	D₄₀	—	2	2	no	—
220	#677	—	2	2	no	—
221	#677	—	2	2	no	—
222	#676	—	8	1	no	—
223	#676	—	8	1	no	—
224	C₈×D₅	—	8	1	no	—
225	C₈×D₅	—	8	1	no	—
226	C₈×D₅	—	8	1	no	—
227	C₈×D₅	—	8	1	no	—
228	#532	—	5	1	no	—
229	C₄×#41	—	5	1	no	—
230	#482	—	5	1	no	—
231	#482	—	5	1	no	—
232	#477	—	5	1	no	—
233	#476	—	5	1	no	—
234	#460	—	5	1	no	—
235	#459	—	5	1	no	—
236	#449	—	5	1	no	—
237	#449	—	5	1	no	—
238	C₈×Q₈	—	5	1	no	—
239	C₈×Q₈	—	5	1	no	—
240	C₄×SD₁₆	—	5	1	no	—
241	C₄×SD₁₆	—	5	1	no	—
242	C₄×D₈	—	5	1	no	—
243	C₄×D₈	—	5	1	no	—
244	#436	—	5	1	no	—
245	#436	—	5	1	no	—
246	#435	—	10	1	no	—
247	#435	—	10	1	no	—
248	C₈×D₄	—	5	1	no	—
249	C₈×D₄	—	5	1	no	—
250	C₈×D₄	—	5	1	no	—
251	C₈×D₄	—	5	1	no	—
252	C₈×D₄	—	10	1	no	—
253	C₈×D₄	—	10	1	no	—
254	#432	—	5	1	no	—
255	#431	—	10	1	no	—
256	#431	C₂×D₅	1	1	yes	characteristic
257	#431	C₂×D₅	1	1	yes	characteristic
258	#431	C₂×D₅	1	1	yes	characteristic
259	C₂×C₄⋊C₈	—	5	1	no	—
260	C₂×C₄⋊C₈	—	10	1	no	—
261	#408	—	10	1	no	—
262	#408	—	10	1	no	—
263	#335	—	5	1	no	—
264	#335	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	Q₈⋊C₈	—	5	1	no	—
268	Q₈⋊C₈	—	5	1	no	—
269	D₄⋊C₈	—	5	1	no	—
270	D₄⋊C₈	—	5	1	no	—
271	D₄⋊C₈	—	5	1	no	—
272	D₄⋊C₈	—	5	1	no	—
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	#322	C₂×D₅	1	1	yes	characteristic
276	#322	C₂×D₅	1	1	yes	characteristic
277	#322	C₂×D₅	1	1	yes	characteristic
278	C₈²	C₂×D₅	1	1	yes	characteristic
279	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
280	C₂²×D₅	—	2	1	no	—
281	C₂²×D₅	—	2	1	no	—
282	C₂²×D₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
294	C₂²⋊D₅	—	2	4	no	—
295	C₂²⋊D₅	—	8	1	no	—
296	C₂²⋊D₅	—	8	1	no	—
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	1	no	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	D₂₀	—	2	1	no	—
303	D₂₀	—	2	1	no	—
304	D₂₀	—	2	1	no	—
305	D₂₀	—	2	1	no	—
306	D₂₀	—	2	1	no	—
307	D₂₀	—	8	1	no	—
308	D₂₀	—	8	1	no	—
309	D₂₀	#131	1	2	yes	—
310	C₄×D₅	—	2	4	no	—
311	C₄×D₅	—	4	1	no	—
312	C₄×D₅	—	4	1	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	4	1	no	—
315	C₄×D₅	—	4	1	no	—
316	C₄×D₅	—	4	1	no	—
317	C₄×D₅	—	8	1	no	—
318	Dic₁₀	—	2	1	no	—
319	Dic₁₀	—	8	1	no	—
320	Dic₁₀	#131	1	2	yes	—
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	2	1	no	—
329	C₅×C₈	—	4	1	no	—
330	C₅×C₈	—	4	1	no	—
331	#168	—	4	1	no	—
332	#168	—	4	1	no	—
333	#168	—	4	1	no	—
334	#168	—	4	1	no	—
335	C₂×#41	—	5	1	no	—
336	C₂×#41	—	10	1	no	—
337	C₂×SD₁₆	—	5	1	no	—
338	C₂×SD₁₆	—	5	1	no	—
339	C₂×D₈	—	5	1	no	—
340	C₂×D₈	—	5	1	no	—
341	C₂×M₁₆	—	10	1	no	—
342	C₂×M₁₆	—	10	1	no	—
343	C₂²×C₈	—	10	1	no	—
344	C₂²×C₈	—	10	1	no	—
345	C₂²×C₈	—	10	1	no	—
346	C₂²×C₈	—	10	1	no	—
347	C₂²×C₈	—	10	1	no	—
348	C₄⋊Q₈	—	5	1	no	—
349	#127	—	5	1	no	—
350	#124	—	10	1	no	—
351	#121	—	5	1	no	—
352	#121	—	5	1	no	—
353	#121	—	10	1	no	—
354	C₄×Q₈	—	5	1	no	—
355	C₄×Q₈	—	5	1	no	—
356	C₄×D₄	—	5	1	no	—
357	C₄×D₄	—	5	1	no	—
358	C₄×D₄	—	5	1	no	—
359	C₄×D₄	—	5	1	no	—
360	C₄×D₄	—	10	1	no	—
361	C₄×D₄	—	10	1	no	—
362	C₄×D₄	—	10	1	no	—
363	#117	—	5	1	no	—
364	#117	—	10	1	no	—
365	C₂×C₄²	—	10	1	no	—
366	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
367	#107	—	5	1	no	—
368	#107	—	5	1	no	—
369	#106	—	5	1	no	—
370	#106	—	5	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₄⋊C₈	—	5	1	no	—
375	C₄⋊C₈	—	5	1	no	—
376	C₄⋊C₈	—	10	1	no	—
377	C₄⋊C₈	—	10	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
380	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
381	C₄⋊C₈	D₂₀	1	1	yes	characteristic
382	C₄⋊C₈	D₂₀	1	1	yes	characteristic
383	#103	—	5	1	no	—
384	#103	—	5	1	no	—
385	#102	—	5	1	no	—
386	#102	—	5	1	no	—
387	#102	—	5	1	no	—
388	#102	—	5	1	no	—
389	#102	—	5	1	no	—
390	#102	—	5	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	10	1	no	—
393	C₂²⋊C₈	—	10	1	no	—
394	C₂²⋊C₈	—	10	1	no	—
395	C₂²⋊C₈	—	10	1	no	—
396	C₂²⋊C₈	—	10	1	no	—
397	C₂²⋊C₈	—	10	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
400	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
401	C₂²⋊C₈	D₂₀	1	1	yes	characteristic
402	C₂²⋊C₈	D₂₀	1	1	yes	characteristic
403	#97	—	10	1	no	—
404	C₄×C₈	—	10	1	no	—
405	C₄×C₈	—	10	1	no	—
406	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
407	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
408	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
409	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
410	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
411	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
416	C₂×D₅	—	2	2	no	—
417	C₂×D₅	—	4	1	no	—
418	C₂×D₅	—	4	1	no	—
419	C₂×D₅	—	4	1	no	—
420	C₂×D₅	—	4	1	no	—
421	C₂×D₅	—	4	1	no	—
422	C₂×D₅	—	4	1	no	—
423	C₂×D₅	—	4	1	no	—
424	C₂×D₅	—	4	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	C₂×#131	1	1	yes	characteristic
430	C₄×C₅	C₂×#131	1	1	yes	characteristic
431	C₄×C₅	#576	1	1	yes	characteristic
432	C₄×C₅	#577	1	1	yes	characteristic
433	Dic₅	—	2	2	no	—
434	Dic₅	—	4	1	no	—
435	Dic₅	—	4	1	no	—
436	Dic₅	—	4	1	no	—
437	Dic₅	—	4	1	no	—
438	#41	—	10	2	no	—
439	#41	—	10	2	no	—
440	#41	—	40	1	no	—
441	#41	—	40	1	no	—
442	C₂×Q₈	—	5	1	no	—
443	C₂×Q₈	—	10	1	no	—
444	C₂×D₄	—	5	1	no	—
445	C₂×D₄	—	5	1	no	—
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	10	1	no	—
448	C₂×D₄	—	10	1	no	—
449	C₂×D₄	—	10	1	no	—
450	C₂×D₄	—	10	1	no	—
451	C₂×D₄	—	10	1	no	—
452	C₂²×C₄	—	10	1	no	—
453	C₂²×C₄	—	10	1	no	—
454	C₂²×C₄	—	10	1	no	—
455	C₂²×C₄	—	10	1	no	—
456	C₂²×C₄	—	10	1	no	—
457	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
459	C₂²×C₄	#709	1	1	yes	characteristic
460	SD₁₆	—	10	2	no	—
461	SD₁₆	—	10	2	no	—
462	D₈	—	10	2	no	—
463	D₈	—	10	2	no	—
464	M₁₆	—	40	1	no	—
465	M₁₆	—	40	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	10	1	no	—
469	C₂×C₈	—	10	1	no	—
470	C₂×C₈	—	10	1	no	—
471	C₂×C₈	—	10	1	no	—
472	C₂×C₈	—	40	1	no	—
473	C₂×C₈	—	40	1	no	—
474	C₂×C₈	—	40	1	no	—
475	C₂×C₈	—	40	1	no	—
476	C₂×C₈	—	40	1	no	—
477	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
478	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
479	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
480	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
481	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
482	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
483	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
484	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	1	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	10	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	—	10	1	no	—
492	C₂²⋊C₄	—	10	1	no	—
493	C₂²⋊C₄	—	10	1	no	—
494	C₂²⋊C₄	—	10	1	no	—
495	C₂²⋊C₄	—	10	1	no	—
496	C₂²⋊C₄	—	10	1	no	—
497	C₂²⋊C₄	—	10	1	no	—
498	C₂²⋊C₄	—	10	1	no	—
499	C₄²	—	10	1	no	—
500	C₄²	—	10	1	no	—
501	C₄²	—	10	1	no	—
502	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
503	C₄²	C₂×D₂₀	1	1	yes	characteristic
504	C₄²	#709	1	1	yes	characteristic
505	C₄²	C₂³×D₅	1	1	yes	characteristic
506	C₂×C₅	—	4	1	no	—
507	C₂×C₅	#2929	1	1	yes	characteristic
508	C₂×C₅	#2946	1	1	yes	characteristic
509	C₂×C₅	#2957	1	1	yes	characteristic
510	D₅	—	4	2	no	—
511	D₅	—	8	1	no	—
512	D₅	—	8	1	no	—
513	C₂³	—	10	1	no	—
514	C₂³	—	10	1	no	—
515	C₂³	—	10	1	no	—
516	C₂³	C₄×D₂₀	1	1	yes	characteristic
517	Q₈	—	5	2	no	—
518	Q₈	—	10	1	no	—
519	Q₈	—	40	1	no	—
520	D₄	—	5	2	no	—
521	D₄	—	10	4	no	—
522	D₄	—	10	1	no	—
523	D₄	—	10	1	no	—
524	D₄	—	10	1	no	—
525	D₄	—	10	1	no	—
526	D₄	—	10	1	no	—
527	D₄	—	40	1	no	—
528	D₄	—	40	1	no	—
529	D₄	—	40	1	no	—
530	D₄	—	40	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	10	4	no	—
537	C₂×C₄	—	10	1	no	—
538	C₂×C₄	—	10	1	no	—
539	C₂×C₄	—	10	1	no	—
540	C₂×C₄	—	10	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	20	1	no	—
543	C₂×C₄	—	20	1	no	—
544	C₂×C₄	—	20	1	no	—
545	C₂×C₄	—	20	1	no	—
546	C₂×C₄	—	20	1	no	—
547	C₂×C₄	—	20	1	no	—
548	C₂×C₄	—	40	1	no	—
549	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
550	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
551	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
554	C₂×C₄	C₂×#709	1	1	yes	characteristic
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	20	1	no	—
566	C₈	—	20	1	no	—
567	C₈	—	20	1	no	—
568	C₈	—	20	1	no	—
569	C₅	#17920	1	1	yes	characteristic, complemented, Sylow
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	10	2	no	—
574	C₂²	—	20	1	no	—
575	C₂²	—	20	1	no	—
576	C₂²	—	20	1	no	—
577	C₂²	—	20	1	no	—
578	C₂²	—	20	1	no	—
579	C₂²	—	20	1	no	—
580	C₂²	—	20	1	no	—
581	C₂²	—	20	1	no	—
582	C₂²	C₂×C₄×D₂₀	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	10	2	no	—
588	C₄	—	20	1	no	—
589	C₄	—	20	1	no	—
590	C₄	—	20	1	no	—
591	C₄	—	20	1	no	—
592	C₄	D₅×#131	1	1	yes	characteristic
593	C₄	D₅×#131	1	1	yes	characteristic
594	C₄	#66085	1	1	yes	characteristic
595	C₄	#66086	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	20	2	no	—
598	C₂	—	40	1	no	—
599	C₂	—	40	1	no	—
600	C₂	#10610284	1	1	yes	characteristic
601	C₂	#10610291	1	1	yes	characteristic
602	C₂	#10610311	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₀
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1454	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10611032	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1454	D₅
hypocenter	C₅	#17920
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1454

Complements

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

N	H ≅ G/N	type
2. #10611022	C₂	semidirect
3. #10611021	C₂	semidirect
4. C₅×#1454	C₂	semidirect
5. #10601556	C₂	semidirect
6. #10601551	C₂	semidirect
7. #10601545	C₂	semidirect
8. #10598881	C₂	semidirect
9. #10598878	C₂	semidirect
10. #10598874	C₂	semidirect
11. #10598871	C₂	semidirect
12. #10598870	C₂	semidirect
13. #10598869	C₂	semidirect
14. C₈×#677	C₂	semidirect
15. C₈×D₄₀	C₂	semidirect
159. #1454	D₅	semidirect
569. C₅	#17920	semidirect

Maximal subgroups

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

subgroup	index
#10611032	2
#10611022	2
#10611021	2
C₅×#1454	2
#10601556	2
#10601551	2
#10601545	2
#10598881	2
#10598878	2
#10598874	2
#10598871	2
#10598870	2
#10598869	2
C₈×#677	2
C₈×D₄₀	2
#17920	5