Subgroups — #12107145

Order 1280.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10614242	C₂	1	1	yes	maximal, characteristic
2	#10614238	C₂	1	1	yes	maximal, characteristic
3	#10610776	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1806	C₂	1	1	yes	maximal, characteristic
5	#10601313	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601169	C₂	1	1	yes	maximal, characteristic
7	#10601169	C₂	1	1	yes	maximal, characteristic
8	#10601163	C₂	1	1	yes	maximal, characteristic
9	#10601162	C₂	1	1	yes	maximal, characteristic
10	#10600286	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600271	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599536	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599536	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599535	C₂	1	1	yes	maximal, characteristic, complemented
15	#10599534	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×#4094	C₂²	1	1	yes	characteristic
18	C₂×#4094	C₂²	1	1	yes	characteristic
19	#65804	C₂²	1	1	yes	characteristic
20	C₅×#423	C₂²	1	1	yes	characteristic
21	C₂×C₅×#104	C₂²	1	1	yes	characteristic
22	C₂×C₅×#104	C₂²	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	#65522	C₂²	1	1	yes	characteristic
25	#65522	C₂²	1	1	yes	characteristic
26	C₂×#3954	C₂²	1	1	yes	characteristic
27	C₂×#3954	C₂²	1	1	yes	characteristic
28	#65411	C₂²	1	1	yes	characteristic
29	#65411	C₂²	1	1	yes	characteristic
30	#65408	C₂²	1	1	yes	characteristic
31	#65408	C₂²	1	1	yes	characteristic
32	#65311	C₄	1	1	yes	characteristic, complemented
33	#65311	C₄	1	1	yes	characteristic, complemented
34	#65310	C₄	1	1	yes	characteristic, complemented
35	#65309	C₄	1	1	yes	characteristic, complemented
36	#65298	C₄	1	1	yes	characteristic, complemented
37	#65298	C₄	1	1	yes	characteristic, complemented
38	#65297	C₄	1	1	yes	characteristic, complemented
39	#65296	C₄	1	1	yes	characteristic, complemented
40	#65287	C₂²	1	1	yes	characteristic
41	#65287	C₂²	1	1	yes	characteristic
42	#65286	—	2	1	no	—
43	#65286	—	2	1	no	—
44	#65286	C₂²	1	1	yes	characteristic
45	#65286	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
47	C₄×#681	—	2	1	no	—
48	C₄×#681	C₂²	1	1	yes	characteristic
49	C₂×#3935	—	2	1	no	—
50	C₂×#3935	C₂²	1	1	yes	characteristic
51	C₂×#3935	C₂²	1	1	yes	characteristic
52	C₂×C₄×#168	C₂²	1	1	yes	characteristic
53	#65117	—	2	1	no	—
54	#65117	—	2	1	no	—
55	#65117	—	2	1	no	—
56	#65117	—	2	1	no	—
57	C₅×#339	C₂²	1	1	yes	characteristic
58	C₅×#339	C₂²	1	1	yes	characteristic
59	#64778	C₂²	1	1	yes	characteristic
60	#64778	C₂²	1	1	yes	characteristic
61	#64744	C₂²	1	1	yes	characteristic
62	#64744	C₂²	1	1	yes	characteristic
63	#64743	C₂²	1	1	yes	characteristic
64	#64743	C₂²	1	1	yes	characteristic
65	#64743	C₂²	1	1	yes	characteristic
66	#64743	C₂²	1	1	yes	characteristic
67	#21629	—	5	1	no	maximal, Sylow
68	C₂×C₅×#41	C₂³	1	1	yes	characteristic
69	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
71	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₅×#117	—	2	1	no	—
78	C₅×#117	C₂³	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	#4094	—	2	2	no	—
85	#4094	—	2	2	no	—
86	#4094	—	2	2	no	—
87	#4094	Q₈	1	4	yes	complemented
88	#4072	C₂³	1	1	yes	characteristic
89	#4072	C₂³	1	1	yes	characteristic
90	#4070	—	2	1	no	—
91	#4070	—	2	1	no	—
92	C₂×#681	—	2	1	no	—
93	C₂×#681	—	2	1	no	—
94	C₂×#681	C₂³	1	1	yes	characteristic
95	C₂×#681	C₂³	1	1	yes	characteristic
96	C₂²×#168	—	2	1	no	—
97	C₂²×#168	—	2	1	no	—
98	C₂²×#168	C₂³	1	1	yes	characteristic
99	C₂²×#168	C₂³	1	1	yes	characteristic
100	C₂²×#168	C₂³	1	1	yes	characteristic
101	C₂²×#168	C₂³	1	1	yes	characteristic
102	#4016	C₂×C₄	1	1	yes	characteristic
103	#4016	C₂×C₄	1	1	yes	characteristic
104	#4015	C₂×C₄	1	1	yes	characteristic
105	#4015	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₀	—	2	1	no	—
107	C₄×Dic₁₀	—	2	1	no	—
108	C₅×C₄⋊C₈	—	2	1	no	—
109	C₅×C₄⋊C₈	—	2	1	no	—
110	C₅×#104	—	2	2	no	—
111	C₅×#104	—	2	2	no	—
112	C₅×#95	—	2	1	no	—
113	#3967	C₂×C₄	1	1	yes	characteristic
114	#3967	C₂×C₄	1	1	yes	characteristic
115	#3967	C₂×C₄	1	1	yes	characteristic
116	#3967	C₂×C₄	1	1	yes	characteristic
117	#3964	C₂×C₄	1	1	yes	characteristic
118	#3964	C₂×C₄	1	1	yes	characteristic
119	#3964	C₂×C₄	1	1	yes	characteristic
120	#3964	C₂×C₄	1	1	yes	characteristic
121	#3954	—	2	2	no	—
122	#3954	—	2	2	no	—
123	#3947	—	2	1	no	—
124	#3947	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	—	2	1	no	—
127	#3946	—	2	1	no	—
128	#3946	—	2	1	no	—
129	C₈×Dic₅	—	2	1	no	—
130	C₈×Dic₅	—	2	1	no	—
131	#3940	C₂×C₄	1	1	yes	characteristic
132	#3940	C₂×C₄	1	1	yes	characteristic
133	#3940	C₂×C₄	1	1	yes	characteristic
134	#3940	C₂×C₄	1	1	yes	characteristic
135	#3939	C₂×C₄	1	1	yes	characteristic
136	#3939	C₂×C₄	1	1	yes	characteristic
137	#3939	C₂×C₄	1	1	yes	characteristic
138	#3939	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
140	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
141	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
142	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
143	#3935	—	2	1	no	—
144	#3935	—	2	1	no	—
145	#3935	—	2	1	no	—
146	#3935	—	2	2	no	—
147	#3935	D₄	1	1	yes	characteristic
148	#3935	D₄	1	1	yes	characteristic
149	#3935	D₄	1	1	yes	characteristic
150	#3935	D₄	1	1	yes	characteristic
151	C₄×#168	—	2	1	no	—
152	C₄×#168	—	2	1	no	—
153	C₄×#168	—	2	1	no	—
154	C₄×#168	—	2	2	no	—
155	#3076	—	5	1	no	—
156	#2961	—	5	1	no	—
157	#2875	—	5	1	no	—
158	#1986	—	5	1	no	—
159	#1950	—	5	1	no	—
160	#1922	—	5	1	no	—
161	#1922	—	5	1	no	—
162	#1866	—	5	1	no	—
163	#1866	—	5	1	no	—
164	#1806	D₅	1	1	yes	characteristic
165	#1773	—	5	1	no	—
166	#1772	—	5	1	no	—
167	#1771	—	5	1	no	—
168	#1765	—	5	1	no	—
169	#1764	—	5	1	no	—
170	C₅×#41	—	2	1	no	—
171	C₅×#41	—	2	1	no	—
172	C₅×#41	C₂×Q₈	1	2	yes	—
173	C₅×#41	#41	1	2	yes	—
174	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	#41	1	1	yes	characteristic
183	C₂²×C₄×C₅	#41	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₁₀	—	2	1	no	—
186	C₂×Dic₁₀	—	2	1	no	—
187	C₅×M₁₆	—	2	1	no	—
188	C₅×M₁₆	—	2	1	no	—
189	C₅×M₁₆	—	2	1	no	—
190	C₅×M₁₆	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	4	2	no	—
196	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	1	no	—
200	C₅×C₂²⋊C₄	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	—	2	1	no	—
205	C₄²×C₅	—	2	1	no	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂²⋊Dic₅	—	2	1	no	—
213	C₂²⋊Dic₅	—	2	1	no	—
214	C₄⋊Dic₅	—	2	1	no	—
215	C₄⋊Dic₅	—	2	1	no	—
216	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
220	#683	—	2	1	no	—
221	#683	—	2	1	no	—
222	#683	—	2	1	no	—
223	#683	—	2	1	no	—
224	C₄×Dic₅	—	2	1	no	—
225	C₄×Dic₅	—	2	1	no	—
226	#681	—	2	4	no	—
227	#681	—	2	1	no	—
228	#681	—	2	1	no	—
229	#681	—	2	4	no	—
230	#681	C₂×Q₈	1	2	yes	—
231	#681	#41	1	2	yes	—
232	C₂×#168	—	2	4	no	—
233	C₂×#168	—	2	1	no	—
234	C₂×#168	—	2	1	no	—
235	C₂×#168	—	2	1	no	—
236	C₂×#168	—	2	1	no	—
237	C₂×#168	—	2	1	no	—
238	C₂×#168	—	2	1	no	—
239	C₂×#168	—	2	1	no	—
240	C₂×#168	—	2	1	no	—
241	C₂×#168	—	2	4	no	—
242	C₂×#168	C₂²×C₄	1	1	yes	characteristic
243	C₂×#168	C₂²×C₄	1	1	yes	characteristic
244	C₂×#168	C₂²×C₄	1	1	yes	characteristic
245	C₂×#168	C₂²×C₄	1	1	yes	characteristic
246	C₂×#168	C₂×D₄	1	1	yes	characteristic
247	C₂×#168	C₂×D₄	1	1	yes	characteristic
248	C₂×#168	C₂×D₄	1	1	yes	characteristic
249	C₂×#168	C₂×D₄	1	1	yes	characteristic
250	C₂×#168	C₂×Q₈	1	2	yes	—
251	C₂×#168	#41	1	2	yes	—
252	C₂×#131	—	5	1	no	—
253	C₂×#131	—	5	1	no	—
254	#533	—	5	1	no	—
255	C₄×#41	C₂×D₅	1	1	yes	characteristic
256	#479	—	5	1	no	—
257	#479	—	5	1	no	—
258	#478	—	5	1	no	—
259	#478	—	5	1	no	—
260	#477	—	5	1	no	—
261	#476	—	5	1	no	—
262	#475	—	5	1	no	—
263	#474	—	5	1	no	—
264	#446	—	10	1	no	—
265	#446	—	10	1	no	—
266	#446	—	10	1	no	—
267	#446	—	10	1	no	—
268	C₂×#108	—	5	1	no	—
269	C₂×#108	—	5	1	no	—
270	#427	—	5	1	no	—
271	#427	—	5	1	no	—
272	#424	—	5	1	no	—
273	#424	—	5	1	no	—
274	#423	C₂×D₅	1	1	yes	characteristic
275	C₂×C₄⋊C₈	—	5	1	no	—
276	C₂×#104	C₂×D₅	1	1	yes	characteristic
277	C₂×#104	C₂×D₅	1	1	yes	characteristic
278	#416	—	5	1	no	—
279	#416	—	5	1	no	—
280	#405	—	5	1	no	—
281	#405	—	5	1	no	—
282	#405	—	5	1	no	—
283	#405	—	5	1	no	—
284	#405	—	10	1	no	—
285	#405	—	10	1	no	—
286	C₄×M₁₆	—	5	1	no	—
287	C₄×M₁₆	—	10	1	no	—
288	C₂×#97	—	5	1	no	—
289	C₂×#97	—	5	1	no	—
290	C₂×#97	—	10	1	no	—
291	C₂×C₄×C₈	—	5	1	no	—
292	C₄×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
293	#341	—	5	1	no	—
294	#341	—	5	1	no	—
295	#339	—	5	1	no	—
296	#339	—	5	1	no	—
297	#339	—	5	1	no	—
298	#339	—	5	1	no	—
299	#339	C₂×D₅	1	1	yes	characteristic
300	#339	C₂×D₅	1	1	yes	characteristic
301	#336	—	5	1	no	—
302	#336	—	5	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	C₂×#41	1	1	yes	characteristic
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	C₄×Q₈	1	2	yes	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	2	1	no	—
310	C₅×D₄	C₄×Q₈	1	2	yes	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	8	1	no	—
325	C₂×C₄×C₅	—	8	1	no	—
326	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
336	C₂×Dic₅	—	2	1	no	—
337	C₂×Dic₅	—	2	1	no	—
338	C₂×Dic₅	—	2	1	no	—
339	C₂×Dic₅	—	2	1	no	—
340	Dic₁₀	—	8	1	no	—
341	Dic₁₀	—	8	1	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	#168	—	2	1	no	—
345	#168	—	2	1	no	—
346	#168	—	2	1	no	—
347	#168	—	2	1	no	—
348	#168	—	2	2	no	—
349	#168	—	2	1	no	—
350	#168	—	2	2	no	—
351	#168	—	2	1	no	—
352	#168	C₂²⋊Q₈	1	2	yes	—
353	#168	C₂²⋊Q₈	1	2	yes	—
354	C₂×#41	C₂²×D₅	1	1	yes	characteristic
355	#131	—	5	4	no	—
356	#131	—	10	2	no	—
357	#131	—	10	2	no	—
358	#131	—	10	2	no	—
359	C₂×M₁₆	—	5	1	no	—
360	C₂×M₁₆	—	5	1	no	—
361	C₂×M₁₆	—	10	1	no	—
362	C₂×M₁₆	—	10	1	no	—
363	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
364	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
365	C₂²×C₈	—	5	1	no	—
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	5	1	no	—
369	C₂²×C₈	—	10	1	no	—
370	C₂²×C₈	—	10	1	no	—
371	C₄⋊Q₈	—	5	1	no	—
372	C₄⋊Q₈	—	5	1	no	—
373	#125	—	5	1	no	—
374	#125	—	5	1	no	—
375	C₂²⋊Q₈	—	10	1	no	—
376	C₂²⋊Q₈	—	10	1	no	—
377	C₄×Q₈	—	10	1	no	—
378	C₄×Q₈	—	10	1	no	—
379	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
380	C₄×Q₈	C₄×D₅	1	1	yes	characteristic
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₄×D₅	1	1	yes	characteristic
384	C₄×D₄	C₄×D₅	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	5	1	no	—
387	#117	—	5	1	no	—
388	#117	C₂²×D₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
393	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
394	#108	—	10	2	no	—
395	#108	—	10	2	no	—
396	#107	—	5	1	no	—
397	#107	—	5	1	no	—
398	#107	—	5	1	no	—
399	#107	—	5	1	no	—
400	#106	—	5	1	no	—
401	#106	—	5	1	no	—
402	#106	—	5	1	no	—
403	#106	—	5	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	5	1	no	—
407	C₄⋊C₈	—	5	1	no	—
408	C₄⋊C₈	—	5	1	no	—
409	C₄⋊C₈	—	5	1	no	—
410	C₄⋊C₈	—	10	1	no	—
411	C₄⋊C₈	—	10	1	no	—
412	C₄⋊C₈	—	10	1	no	—
413	C₄⋊C₈	—	10	1	no	—
414	#104	—	2	2	no	—
415	#104	—	2	2	no	—
416	#103	—	5	1	no	—
417	#103	—	5	1	no	—
418	#103	—	5	1	no	—
419	#103	—	5	1	no	—
420	#102	—	5	1	no	—
421	#102	—	5	1	no	—
422	#102	—	5	1	no	—
423	#102	—	5	1	no	—
424	#97	—	5	1	no	—
425	#97	—	5	1	no	—
426	#97	—	5	1	no	—
427	#97	—	5	1	no	—
428	#97	—	10	2	no	—
429	#97	—	10	1	no	—
430	#97	—	10	1	no	—
431	#97	—	10	1	no	—
432	#97	—	10	1	no	—
433	#97	—	10	1	no	—
434	C₄×C₈	—	10	2	no	—
435	C₄×C₈	—	10	1	no	—
436	C₄×C₈	—	10	1	no	—
437	C₄×C₈	—	10	1	no	—
438	C₄×C₈	—	10	1	no	—
439	C₄×C₈	—	10	1	no	—
440	#95	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	1	no	—
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	—	4	1	no	—
446	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
447	C₂²×C₅	#529	1	1	yes	characteristic
448	C₂²×C₅	#533	1	1	yes	characteristic
449	C₄×C₅	—	2	1	no	—
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	8	1	no	—
458	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
459	C₄×C₅	C₄×#41	1	1	yes	characteristic
460	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
461	C₄×C₅	#525	1	1	yes	characteristic
462	Dic₅	—	4	1	no	—
463	Dic₅	—	4	1	no	—
464	Dic₅	—	4	1	no	—
465	Dic₅	—	4	1	no	—
466	#41	—	2	1	no	—
467	#41	—	2	1	no	—
468	#41	#711	1	2	yes	—
469	#41	Q₈×D₅	1	2	yes	—
470	C₂×Q₈	—	10	1	no	—
471	C₂×Q₈	—	10	1	no	—
472	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	#711	1	1	yes	characteristic
481	C₂²×C₄	#711	1	1	yes	characteristic
482	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
483	M₁₆	—	2	1	no	—
484	M₁₆	—	2	1	no	—
485	M₁₆	—	2	1	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	5	2	no	—
488	M₁₆	—	5	2	no	—
489	M₁₆	—	10	4	no	—
490	M₁₆	—	10	4	no	—
491	M₁₆	—	10	1	no	—
492	M₁₆	—	10	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	5	1	no	—
496	C₂×C₈	—	5	1	no	—
497	C₂×C₈	—	5	2	no	—
498	C₂×C₈	—	5	2	no	—
499	C₂×C₈	—	5	1	no	—
500	C₂×C₈	—	5	1	no	—
501	C₂×C₈	—	5	1	no	—
502	C₂×C₈	—	5	1	no	—
503	C₂×C₈	—	5	1	no	—
504	C₂×C₈	—	5	1	no	—
505	C₂×C₈	—	10	4	no	—
506	C₂×C₈	—	10	4	no	—
507	C₂×C₈	—	10	1	no	—
508	C₂×C₈	—	10	1	no	—
509	C₂×C₈	—	10	1	no	—
510	C₂×C₈	—	10	1	no	—
511	C₂×C₈	—	10	1	no	—
512	C₂×C₈	—	10	1	no	—
513	C₂×C₈	—	10	1	no	—
514	C₂×C₈	—	10	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	5	1	no	—
519	C₄⋊C₄	—	5	1	no	—
520	C₄⋊C₄	—	5	1	no	—
521	C₄⋊C₄	—	5	1	no	—
522	C₄⋊C₄	—	10	1	no	—
523	C₄⋊C₄	—	10	1	no	—
524	C₄⋊C₄	—	10	1	no	—
525	C₄⋊C₄	—	10	1	no	—
526	C₄⋊C₄	—	10	1	no	—
527	C₄⋊C₄	—	10	1	no	—
528	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
529	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	10	1	no	—
534	C₂²⋊C₄	—	10	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	10	1	no	—
543	C₄²	—	10	1	no	—
544	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
545	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
546	C₄²	D₄×D₅	1	1	yes	characteristic
547	C₄²	D₄×D₅	1	1	yes	characteristic
548	C₂×C₅	—	2	1	no	—
549	C₂×C₅	—	2	1	no	—
550	C₂×C₅	—	4	2	no	—
551	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
552	C₂×C₅	#2956	1	1	yes	characteristic
553	C₂×C₅	#2957	1	1	yes	characteristic
554	C₂³	—	2	1	no	—
555	C₂³	C₂×#711	1	1	yes	characteristic
556	Q₈	—	2	1	no	—
557	Q₈	—	40	1	no	—
558	Q₈	—	40	1	no	—
559	Q₈	#4033	1	2	yes	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	1	no	—
563	D₄	#4033	1	2	yes	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	8	1	no	—
578	C₂×C₄	—	8	1	no	—
579	C₂×C₄	—	10	1	no	—
580	C₂×C₄	—	10	1	no	—
581	C₂×C₄	—	10	1	no	—
582	C₂×C₄	—	10	1	no	—
583	C₂×C₄	#4027	1	1	yes	characteristic
584	C₂×C₄	#4027	1	1	yes	characteristic
585	C₂×C₄	#4027	1	1	yes	characteristic
586	C₂×C₄	#4027	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
589	C₂×C₄	C₂×#711	1	1	yes	characteristic
590	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
591	C₂×C₄	D₅×#41	1	1	yes	characteristic
592	C₂×C₄	D₅×#41	1	1	yes	characteristic
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	5	2	no	—
596	C₈	—	5	2	no	—
597	C₈	—	10	1	no	—
598	C₈	—	10	1	no	—
599	C₈	—	10	1	no	—
600	C₈	—	10	1	no	—
601	C₈	—	10	1	no	—
602	C₈	—	10	1	no	—
603	C₈	—	10	2	no	—
604	C₈	—	10	2	no	—
605	C₅	#21629	1	1	yes	characteristic, complemented, Sylow
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₂×#4027	1	1	yes	characteristic
612	C₂²	#65934	1	1	yes	characteristic
613	C₂²	#65956	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	20	1	no	—
624	C₄	—	20	1	no	—
625	C₄	—	20	1	no	—
626	C₄	—	20	1	no	—
627	C₄	C₂×#4033	1	1	yes	characteristic
628	C₄	#65856	1	1	yes	characteristic
629	C₄	#65940	1	1	yes	characteristic
630	C₄	D₅×C₂²⋊Q₈	1	1	yes	characteristic
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	2	no	—
634	C₂	#10605597	1	1	yes	characteristic
635	C₂	#10610711	1	1	yes	characteristic
636	C₂	#10610721	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1806	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#41	C₂³
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1806	D₅
hypocenter	C₅	#21629
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
3. #10610776	C₂	semidirect
5. #10601313	C₂	semidirect
10. #10600286	C₂	semidirect
11. #10600271	C₂	semidirect
12. #10599536	C₂	semidirect
13. #10599536	C₂	semidirect
14. #10599535	C₂	semidirect
15. #10599534	C₂	semidirect
32. #65311	C₄	semidirect
33. #65311	C₄	semidirect
34. #65310	C₄	semidirect
35. #65309	C₄	semidirect
36. #65298	C₄	semidirect
37. #65298	C₄	semidirect
38. #65297	C₄	semidirect
39. #65296	C₄	semidirect
87. #4094	Q₈	semidirect
605. C₅	#21629	semidirect

Maximal subgroups

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

subgroup	index
#10614242	2
#10614238	2
#10610776	2
C₅×#1806	2
#10601313	2
#10601169	2
#10601163	2
#10601162	2
#10600286	2
#10600271	2
#10599536	2
#10599535	2
#10599534	2
#21629	5