Subgroups — #12068198

Order 1280.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617751	C₂	1	1	yes	maximal, characteristic
2	C₅×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	#10614253	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601616	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601614	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601612	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601609	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601569	C₂	1	1	yes	maximal, characteristic, complemented
9	#10601568	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601303	C₂	1	1	yes	maximal, characteristic, complemented
11	#10601296	C₂	1	1	yes	maximal, characteristic, complemented
12	#10601231	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#64702	C₂	1	1	yes	maximal, characteristic, complemented
14	#10601226	C₂	1	1	yes	maximal, characteristic, complemented
15	#10601224	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	#66167	C₄	1	2	yes	—
18	#65918	—	2	1	no	—
19	#65913	—	2	1	no	—
20	#65899	—	2	1	no	—
21	#65899	—	2	1	no	—
22	#65897	—	2	1	no	—
23	#65886	—	2	1	no	—
24	#65886	—	2	1	no	—
25	#65885	—	2	1	no	—
26	#65868	C₄	1	2	yes	—
27	#65868	C₄	1	2	yes	—
28	#65857	C₄	1	2	yes	—
29	#65811	C₂²	1	1	yes	characteristic
30	#65811	C₂²	1	1	yes	characteristic
31	#65811	C₂²	1	1	yes	characteristic
32	#65804	C₂²	1	1	yes	characteristic
33	#65804	C₂²	1	1	yes	characteristic
34	C₂×#4015	C₂²	1	1	yes	characteristic
35	C₅×#446	—	2	1	no	—
36	C₅×#435	—	2	1	no	—
37	C₅×#435	—	2	1	no	—
38	C₅×C₈×D₄	—	2	1	no	—
39	C₅×#432	C₂²	1	1	yes	characteristic
40	C₅×#432	C₂²	1	1	yes	characteristic
41	C₅×#431	C₂²	1	1	yes	characteristic
42	C₅×#423	C₂²	1	1	yes	characteristic
43	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	#65313	—	2	1	no	—
46	#65300	—	2	1	no	—
47	#65300	—	2	1	no	—
48	D₄×#168	—	2	1	no	—
49	#65215	C₂²	1	1	yes	characteristic
50	#65215	C₂²	1	1	yes	characteristic
51	#65214	C₂²	1	1	yes	characteristic
52	#65213	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
55	#64705	C₂²	1	1	yes	characteristic
56	#64705	C₂²	1	1	yes	characteristic
57	#64705	C₂²	1	1	yes	characteristic
58	#64705	C₂²	1	1	yes	characteristic
59	#64702	C₂²	1	1	yes	characteristic
60	#64702	C₂²	1	1	yes	characteristic
61	#64702	C₂²	1	1	yes	characteristic
62	#64702	C₂²	1	1	yes	characteristic
63	#64702	C₂²	1	1	yes	characteristic
64	#64702	C₂²	1	1	yes	characteristic
65	#64702	C₂²	1	1	yes	characteristic
66	#64702	C₂²	1	1	yes	characteristic
67	#64701	C₂²	1	1	yes	characteristic
68	#64701	C₂²	1	1	yes	characteristic
69	#64701	C₂²	1	1	yes	characteristic
70	#64701	C₂²	1	1	yes	characteristic
71	#17775	—	5	1	no	maximal, Sylow
72	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
73	C₂×#709	—	2	1	no	—
74	C₂×#709	—	2	1	no	—
75	C₂×#709	C₂×C₄	1	2	yes	—
76	C₂²×Dic₁₀	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
81	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
82	C₄×C₅×D₄	D₄	1	1	yes	characteristic
83	C₄×C₅×D₄	D₄	1	1	yes	characteristic
84	C₄×C₅×D₄	D₄	1	1	yes	characteristic
85	C₄×C₅×D₄	D₄	1	1	yes	characteristic
86	C₄×C₅×D₄	D₄	1	1	yes	characteristic
87	C₄×C₅×D₄	D₄	1	1	yes	characteristic
88	C₅×#117	C₂×C₄	1	1	yes	characteristic
89	C₅×#117	C₂×C₄	1	1	yes	characteristic
90	C₅×#117	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
94	#4092	—	2	2	no	—
95	#4085	—	2	2	no	—
96	#4085	—	2	2	no	—
97	#4084	—	2	2	no	—
98	#4076	—	2	1	no	—
99	#4076	—	2	1	no	—
100	#4076	—	2	1	no	—
101	#4076	—	2	1	no	—
102	#4076	C₂×C₄	1	2	yes	—
103	#4076	C₂×C₄	1	2	yes	—
104	#4072	—	2	1	no	—
105	#4072	—	2	1	no	—
106	C₂×C₄⋊Dic₅	—	2	1	no	—
107	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
108	#4070	—	2	1	no	—
109	#4070	—	2	1	no	—
110	#4070	C₂×C₄	1	2	yes	—
111	#4070	C₂×C₄	1	2	yes	—
112	C₂×#681	—	2	1	no	—
113	C₂²×#168	—	2	1	no	—
114	C₂²×#168	—	2	1	no	—
115	#4044	—	2	2	no	—
116	#4044	—	2	2	no	—
117	#4042	—	2	2	no	—
118	#4042	—	2	2	no	—
119	#4038	—	2	2	no	—
120	D₅×C₄⋊C₄	—	2	2	no	—
121	#4031	—	2	2	no	—
122	#4031	—	2	2	no	—
123	#4029	—	2	2	no	—
124	#4029	—	2	2	no	—
125	#4027	—	2	2	no	—
126	#4027	—	2	2	no	—
127	#4021	—	2	1	no	—
128	#4021	—	2	1	no	—
129	#4021	C₂×C₄	1	2	yes	—
130	#4020	C₂³	1	1	yes	characteristic
131	C₄×D₂₀	—	2	1	no	—
132	C₄×D₂₀	—	2	1	no	—
133	C₄×D₂₀	—	2	1	no	—
134	C₄×D₂₀	—	2	1	no	—
135	C₄×D₂₀	C₂×C₄	1	2	yes	—
136	C₄×D₂₀	C₂×C₄	1	2	yes	—
137	#4016	—	2	1	no	—
138	#4016	—	2	1	no	—
139	#4015	—	2	1	no	—
140	#4015	—	2	1	no	—
141	#4015	C₂×C₄	1	2	yes	—
142	#4015	C₂³	1	1	yes	characteristic
143	#4015	C₂³	1	1	yes	characteristic
144	#4015	C₂³	1	1	yes	characteristic
145	C₄×Dic₁₀	—	2	1	no	—
146	C₄×Dic₁₀	—	2	1	no	—
147	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
148	C₄×Dic₁₀	C₂×C₄	1	2	yes	—
149	C₅×C₄⋊C₈	—	2	1	no	—
150	C₅×C₄⋊C₈	—	2	1	no	—
151	C₅×C₄⋊C₈	—	2	1	no	—
152	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₅×C₂²⋊C₈	—	2	1	no	—
157	C₅×C₂²⋊C₈	—	2	1	no	—
158	C₅×C₂²⋊C₈	—	2	1	no	—
159	C₅×#97	—	2	1	no	—
160	C₅×#97	—	2	1	no	—
161	C₄×C₅×C₈	—	2	1	no	—
162	C₂²⋊#168	—	2	1	no	—
163	C₂²⋊#168	—	2	1	no	—
164	C₂²⋊#168	—	2	1	no	—
165	C₄⋊#168	—	2	1	no	—
166	C₄⋊#168	—	2	1	no	—
167	C₄⋊#168	—	2	1	no	—
168	C₄⋊#168	C₂³	1	1	yes	characteristic
169	C₄⋊#168	C₂³	1	1	yes	characteristic
170	C₄⋊#168	C₂³	1	1	yes	characteristic
171	C₄⋊#168	C₂³	1	1	yes	characteristic
172	#3935	—	2	1	no	—
173	#3935	—	2	1	no	—
174	C₄×#168	—	2	1	no	—
175	#3511	—	5	1	no	—
176	#2990	—	5	1	no	—
177	#2990	D₅	1	1	yes	characteristic, complemented
178	#1559	—	5	1	no	—
179	#1557	—	5	1	no	—
180	#1556	—	5	1	no	—
181	#1554	—	5	1	no	—
182	#1553	—	5	1	no	—
183	#1551	—	5	1	no	—
184	#1551	—	5	1	no	—
185	#1550	—	5	1	no	—
186	#1547	—	5	1	no	—
187	#1542	—	5	1	no	—
188	#1540	—	5	1	no	—
189	C₂×#332	—	5	1	no	—
190	C₅×#41	—	4	2	no	—
191	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂×C₂²⋊D₅	—	2	2	no	—
205	C₂×C₂²⋊D₅	—	2	2	no	—
206	C₂×C₂²⋊D₅	—	2	2	no	—
207	C₂²×Dic₅	—	2	2	no	—
208	#709	—	4	4	no	—
209	#709	—	8	1	no	—
210	#709	—	8	1	no	—
211	#709	—	8	1	no	—
212	#709	—	8	1	no	—
213	C₂×D₂₀	—	2	1	no	—
214	C₂×D₂₀	—	2	1	no	—
215	C₂×D₂₀	C₂²×C₄	1	2	yes	—
216	C₂×C₄×D₅	—	2	2	no	—
217	C₂×C₄×D₅	—	2	2	no	—
218	C₂×C₄×D₅	—	2	2	no	—
219	C₂×Dic₁₀	—	2	1	no	—
220	C₂×Dic₁₀	—	2	1	no	—
221	C₂×Dic₁₀	—	2	2	no	—
222	C₂×Dic₁₀	—	8	1	no	—
223	C₂×Dic₁₀	—	8	1	no	—
224	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
225	C₅×M₁₆	—	8	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	8	1	no	—
231	C₂×C₅×C₈	—	8	1	no	—
232	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
233	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
234	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
236	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
237	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
238	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
239	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
240	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
244	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
246	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
252	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₅	C₂⁴	1	1	yes	characteristic
254	C₂²⋊Dic₅	—	2	2	no	—
255	C₂²⋊Dic₅	—	2	2	no	—
256	#685	—	2	2	no	—
257	#685	—	2	2	no	—
258	#685	—	2	2	no	—
259	#685	—	2	2	no	—
260	#685	—	2	2	no	—
261	#685	—	2	2	no	—
262	C₄⋊Dic₅	—	2	2	no	—
263	C₄⋊Dic₅	—	2	2	no	—
264	C₄⋊Dic₅	—	2	1	no	—
265	C₄⋊Dic₅	—	2	1	no	—
266	C₄⋊Dic₅	—	2	1	no	—
267	C₄⋊Dic₅	—	2	1	no	—
268	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
269	C₄⋊Dic₅	C₂²×C₄	1	2	yes	—
270	#683	—	2	2	no	—
271	#683	—	2	2	no	—
272	#683	—	2	2	no	—
273	#683	—	2	2	no	—
274	C₄×Dic₅	—	2	2	no	—
275	C₄×Dic₅	—	2	2	no	—
276	#681	—	8	1	no	—
277	C₂×#168	—	2	1	no	—
278	C₂×#168	—	2	1	no	—
279	C₂×#168	—	2	1	no	—
280	C₂×#168	—	2	1	no	—
281	C₂×#168	—	8	1	no	—
282	C₂×#168	—	8	1	no	—
283	#556	—	10	1	no	—
284	#555	—	10	1	no	—
285	#554	—	10	1	no	—
286	#553	—	10	1	no	—
287	#553	—	10	1	no	—
288	#548	—	10	1	no	—
289	#548	—	10	1	no	—
290	#547	—	10	1	no	—
291	#542	—	5	2	no	—
292	#542	—	5	2	no	—
293	#537	—	5	2	no	—
294	#533	—	5	1	no	—
295	#533	—	5	1	no	—
296	#532	—	5	1	no	—
297	#532	—	5	1	no	—
298	#532	—	5	1	no	—
299	C₂×C₄⋊Q₈	—	5	1	no	—
300	#520	—	5	2	no	—
301	C₄×#41	C₂×D₅	1	1	yes	characteristic
302	#446	—	2	1	no	—
303	#446	—	10	1	no	—
304	#435	—	2	1	no	—
305	#435	—	2	1	no	—
306	#435	—	10	1	no	—
307	#435	—	10	1	no	—
308	C₈×D₄	—	2	1	no	—
309	C₈×D₄	—	10	1	no	—
310	#432	—	5	1	no	—
311	#432	—	5	1	no	—
312	#432	C₂×D₅	1	1	yes	characteristic
313	#432	C₂×D₅	1	1	yes	characteristic
314	#431	—	5	1	no	—
315	#431	C₂×D₅	1	1	yes	characteristic
316	#423	—	5	1	no	—
317	#423	C₂×D₅	1	1	yes	characteristic
318	C₂×C₄⋊C₈	—	5	1	no	—
319	C₂×C₄⋊C₈	—	5	1	no	—
320	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
322	#333	—	5	1	no	—
323	#333	—	5	1	no	—
324	#333	—	5	1	no	—
325	#333	—	5	1	no	—
326	#332	—	5	1	no	—
327	#332	—	5	1	no	—
328	#332	—	5	1	no	—
329	#332	—	5	1	no	—
330	#332	—	5	1	no	—
331	#332	—	5	1	no	—
332	#332	—	5	1	no	—
333	#332	—	5	1	no	—
334	#331	—	5	1	no	—
335	#331	—	5	1	no	—
336	#331	—	5	1	no	—
337	#331	—	5	1	no	—
338	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×D₅	—	2	2	no	—
342	C₅×Q₈	—	4	1	no	—
343	C₅×D₄	—	2	2	no	—
344	C₅×D₄	—	2	2	no	—
345	C₅×D₄	—	4	1	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
373	C₂²⋊D₅	—	4	4	no	—
374	C₂²⋊D₅	—	8	2	no	—
375	C₂²⋊D₅	—	8	2	no	—
376	C₂×Dic₅	—	2	2	no	—
377	C₂×Dic₅	—	2	2	no	—
378	C₂×Dic₅	—	2	2	no	—
379	C₂×Dic₅	—	8	2	no	—
380	D₂₀	—	4	2	no	—
381	D₂₀	—	4	1	no	—
382	D₂₀	—	4	1	no	—
383	D₂₀	—	4	1	no	—
384	D₂₀	—	4	1	no	—
385	C₄×D₅	—	4	4	no	—
386	C₄×D₅	—	8	2	no	—
387	C₄×D₅	—	8	2	no	—
388	Dic₁₀	—	4	1	no	—
389	Dic₁₀	—	4	1	no	—
390	Dic₁₀	—	4	1	no	—
391	Dic₁₀	—	4	1	no	—
392	Dic₁₀	—	4	2	no	—
393	Dic₁₀	—	8	2	no	—
394	C₅×C₈	—	4	1	no	—
395	C₅×C₈	—	4	1	no	—
396	C₅×C₈	—	4	1	no	—
397	C₅×C₈	—	4	1	no	—
398	#168	—	4	1	no	—
399	#168	—	4	1	no	—
400	#168	—	4	1	no	—
401	#168	—	4	1	no	—
402	C₂×#41	—	5	2	no	—
403	C₂×#41	—	10	1	no	—
404	C₂×#41	—	10	1	no	—
405	C₂×#41	C₄×D₅	1	1	yes	characteristic
406	C₂²×Q₈	—	10	1	no	—
407	C₂×M₁₆	—	2	1	no	—
408	C₂×M₁₆	—	10	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₂²×C₈	—	2	1	no	—
411	C₂²×C₈	—	10	1	no	—
412	C₂²×C₈	—	10	1	no	—
413	C₄⋊Q₈	—	5	2	no	—
414	C₄⋊Q₈	—	5	1	no	—
415	C₄⋊Q₈	—	5	1	no	—
416	C₄⋊Q₈	—	5	1	no	—
417	C₄⋊Q₈	—	10	1	no	—
418	C₄⋊Q₈	—	10	1	no	—
419	#127	—	5	1	no	—
420	#126	—	10	2	no	—
421	#126	—	10	2	no	—
422	#125	—	10	1	no	—
423	#125	—	10	1	no	—
424	#124	—	5	2	no	—
425	#124	—	10	2	no	—
426	#124	—	10	2	no	—
427	#124	—	10	1	no	—
428	#124	—	10	1	no	—
429	#123	—	10	2	no	—
430	#123	—	10	2	no	—
431	C₂²⋊Q₈	—	5	2	no	—
432	C₂²⋊Q₈	—	5	2	no	—
433	C₂²⋊Q₈	—	10	2	no	—
434	C₂²⋊Q₈	—	10	1	no	—
435	C₂²⋊Q₈	—	10	1	no	—
436	C₂²⋊Q₈	—	10	2	no	—
437	C₂²⋊Q₈	—	10	2	no	—
438	#121	—	5	2	no	—
439	#121	—	5	2	no	—
440	#121	—	10	2	no	—
441	#121	—	10	2	no	—
442	#121	—	10	2	no	—
443	#121	—	10	1	no	—
444	#121	—	10	1	no	—
445	#121	—	10	1	no	—
446	#121	—	10	1	no	—
447	C₄×Q₈	—	5	2	no	—
448	C₄×Q₈	—	5	2	no	—
449	C₄×Q₈	—	10	1	no	—
450	C₄×Q₈	—	10	1	no	—
451	C₄×Q₈	D₂₀	1	1	yes	characteristic
452	C₄×Q₈	C₂²⋊D₅	1	1	yes	characteristic
453	C₄×D₄	—	5	2	no	—
454	C₄×D₄	—	5	2	no	—
455	C₄×D₄	—	10	2	no	—
456	C₄×D₄	—	10	2	no	—
457	C₄×D₄	—	10	1	no	—
458	C₄×D₄	—	10	1	no	—
459	C₄×D₄	—	10	1	no	—
460	C₄×D₄	—	10	1	no	—
461	C₄×D₄	D₂₀	1	1	yes	characteristic
462	C₄×D₄	D₂₀	1	1	yes	characteristic
463	C₄×D₄	D₂₀	1	1	yes	characteristic
464	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
465	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
466	C₄×D₄	C₂²⋊D₅	1	1	yes	characteristic
467	#117	—	10	1	no	—
468	#117	—	10	1	no	—
469	#117	—	10	2	no	—
470	#117	C₄×D₅	1	1	yes	characteristic
471	#117	C₄×D₅	1	1	yes	characteristic
472	#117	C₄×D₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	—	5	2	no	—
474	C₂×C₄⋊C₄	—	10	1	no	—
475	C₂×C₄⋊C₄	—	10	2	no	—
476	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
477	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
478	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
479	C₄⋊C₈	—	2	1	no	—
480	C₄⋊C₈	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	C₄⋊C₈	—	5	1	no	—
483	C₄⋊C₈	—	5	1	no	—
484	C₄⋊C₈	—	5	1	no	—
485	C₄⋊C₈	—	5	1	no	—
486	C₄⋊C₈	—	10	1	no	—
487	C₄⋊C₈	—	10	1	no	—
488	C₄⋊C₈	—	10	1	no	—
489	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
490	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
491	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
492	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
493	C₂²⋊C₈	—	2	1	no	—
494	C₂²⋊C₈	—	2	1	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₂²⋊C₈	—	10	1	no	—
497	C₂²⋊C₈	—	10	1	no	—
498	C₂²⋊C₈	—	10	1	no	—
499	#97	—	2	1	no	—
500	#97	—	2	1	no	—
501	#97	—	10	1	no	—
502	#97	—	10	1	no	—
503	C₄×C₈	—	2	1	no	—
504	C₄×C₈	—	10	1	no	—
505	C₂²×C₅	—	2	1	no	—
506	C₂²×C₅	—	2	1	no	—
507	C₂²×C₅	—	2	1	no	—
508	C₂²×C₅	—	2	1	no	—
509	C₂²×C₅	—	2	1	no	—
510	C₂²×C₅	—	2	1	no	—
511	C₂²×C₅	—	2	1	no	—
512	C₂²×C₅	—	2	1	no	—
513	C₂²×C₅	#413	1	2	yes	—
514	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
515	C₂×D₅	—	4	2	no	—
516	C₂×D₅	—	4	2	no	—
517	C₂×D₅	—	4	2	no	—
518	C₄×C₅	—	2	1	no	—
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	2	1	no	—
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	—	2	1	no	—
523	C₄×C₅	—	2	1	no	—
524	C₄×C₅	—	2	1	no	—
525	C₄×C₅	—	2	1	no	—
526	C₄×C₅	—	2	1	no	—
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	#576	1	1	yes	characteristic
529	C₄×C₅	#577	1	1	yes	characteristic
530	C₄×C₅	#577	1	1	yes	characteristic
531	C₄×C₅	#578	1	1	yes	characteristic
532	Dic₅	—	4	2	no	—
533	Dic₅	—	4	2	no	—
534	Dic₅	—	4	2	no	—
535	#41	—	4	2	no	—
536	#41	—	20	4	no	—
537	#41	—	40	1	no	—
538	#41	—	40	1	no	—
539	#41	—	40	1	no	—
540	#41	—	40	1	no	—
541	C₂×Q₈	—	5	2	no	—
542	C₂×Q₈	—	10	1	no	—
543	C₂×Q₈	—	10	1	no	—
544	C₂×Q₈	—	10	2	no	—
545	C₂×Q₈	—	40	1	no	—
546	C₂×Q₈	—	40	1	no	—
547	C₂×Q₈	#685	1	1	yes	characteristic
548	C₂×D₄	—	5	2	no	—
549	C₂×D₄	—	10	2	no	—
550	C₂×D₄	—	10	2	no	—
551	C₂×D₄	—	10	2	no	—
552	C₂×D₄	—	10	1	no	—
553	C₂×D₄	—	10	1	no	—
554	C₂×D₄	#685	1	1	yes	characteristic
555	C₂×D₄	#685	1	1	yes	characteristic
556	C₂×D₄	#685	1	1	yes	characteristic
557	C₂²×C₄	—	10	2	no	—
558	C₂²×C₄	—	10	2	no	—
559	C₂²×C₄	—	10	2	no	—
560	C₂²×C₄	—	10	2	no	—
561	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
562	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
563	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
567	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
568	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
569	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
570	M₁₆	—	8	1	no	—
571	M₁₆	—	40	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	8	1	no	—
577	C₂×C₈	—	8	1	no	—
578	C₂×C₈	—	10	1	no	—
579	C₂×C₈	—	10	1	no	—
580	C₂×C₈	—	10	1	no	—
581	C₂×C₈	—	10	1	no	—
582	C₂×C₈	—	40	1	no	—
583	C₂×C₈	—	40	1	no	—
584	C₄⋊C₄	—	5	2	no	—
585	C₄⋊C₄	—	5	2	no	—
586	C₄⋊C₄	—	10	1	no	—
587	C₄⋊C₄	—	10	1	no	—
588	C₄⋊C₄	—	10	1	no	—
589	C₄⋊C₄	—	10	1	no	—
590	C₄⋊C₄	—	10	2	no	—
591	C₄⋊C₄	—	10	2	no	—
592	C₄⋊C₄	—	10	2	no	—
593	C₄⋊C₄	—	10	2	no	—
594	C₄⋊C₄	—	10	2	no	—
595	C₄⋊C₄	—	10	2	no	—
596	C₄⋊C₄	#685	1	1	yes	characteristic
597	C₄⋊C₄	#685	1	1	yes	characteristic
598	C₄⋊C₄	#685	1	1	yes	characteristic
599	C₄⋊C₄	#685	1	1	yes	characteristic
600	C₄⋊C₄	#685	1	1	yes	characteristic
601	C₄⋊C₄	#685	1	1	yes	characteristic
602	C₂²⋊C₄	—	10	2	no	—
603	C₂²⋊C₄	—	10	2	no	—
604	C₂²⋊C₄	—	10	2	no	—
605	C₂²⋊C₄	—	10	2	no	—
606	C₂²⋊C₄	—	10	2	no	—
607	C₂²⋊C₄	—	10	2	no	—
608	C₂²⋊C₄	—	10	2	no	—
609	C₂²⋊C₄	—	10	2	no	—
610	C₂²⋊C₄	#685	1	1	yes	characteristic
611	C₂²⋊C₄	#685	1	1	yes	characteristic
612	C₂²⋊C₄	#685	1	1	yes	characteristic
613	C₂²⋊C₄	#685	1	1	yes	characteristic
614	C₂²⋊C₄	#685	1	1	yes	characteristic
615	C₂²⋊C₄	#685	1	1	yes	characteristic
616	C₄²	—	10	2	no	—
617	C₄²	—	10	2	no	—
618	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
619	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
620	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
621	C₄²	C₂×D₂₀	1	1	yes	characteristic
622	C₄²	C₂×D₂₀	1	1	yes	characteristic
623	C₄²	C₂×D₂₀	1	1	yes	characteristic
624	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
625	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
626	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
627	C₄²	C₂³×D₅	1	1	yes	characteristic
628	C₂×C₅	—	2	2	no	—
629	C₂×C₅	—	4	1	no	—
630	C₂×C₅	—	4	1	no	—
631	C₂×C₅	C₂×#413	1	1	yes	characteristic
632	C₂×C₅	#2897	1	1	yes	characteristic
633	C₂×C₅	#2898	1	1	yes	characteristic
634	D₅	—	8	2	no	—
635	C₂³	—	10	2	no	—
636	C₂³	C₂×#685	1	1	yes	characteristic
637	C₂³	C₂×#685	1	1	yes	characteristic
638	C₂³	C₂×#685	1	1	yes	characteristic
639	Q₈	—	4	1	no	—
640	Q₈	—	20	2	no	—
641	Q₈	—	20	1	no	—
642	Q₈	—	20	1	no	—
643	Q₈	—	20	1	no	—
644	Q₈	—	20	1	no	—
645	Q₈	—	40	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	4	1	no	—
649	D₄	—	20	2	no	—
650	D₄	—	20	4	no	—
651	D₄	—	20	1	no	—
652	D₄	—	20	1	no	—
653	D₄	—	20	1	no	—
654	D₄	—	20	1	no	—
655	D₄	—	40	2	no	—
656	D₄	—	40	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	10	2	no	—
673	C₂×C₄	—	10	2	no	—
674	C₂×C₄	—	10	2	no	—
675	C₂×C₄	—	20	4	no	—
676	C₂×C₄	—	40	2	no	—
677	C₂×C₄	—	40	2	no	—
678	C₂×C₄	—	40	2	no	—
679	C₂×C₄	C₂×#685	1	1	yes	characteristic
680	C₂×C₄	C₂×#685	1	1	yes	characteristic
681	C₂×C₄	C₂×#685	1	1	yes	characteristic
682	C₂×C₄	C₂×#685	1	1	yes	characteristic
683	C₂×C₄	C₂×#685	1	1	yes	characteristic
684	C₂×C₄	C₂×#685	1	1	yes	characteristic
685	C₂×C₄	C₂×#685	1	1	yes	characteristic
686	C₂×C₄	C₂×#685	1	1	yes	characteristic
687	C₂×C₄	C₂×#685	1	1	yes	characteristic
688	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
690	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	20	1	no	—
696	C₈	—	20	1	no	—
697	C₈	—	20	1	no	—
698	C₈	—	20	1	no	—
699	C₅	#17775	1	1	yes	characteristic, complemented, Sylow
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	20	2	no	—
709	C₂²	—	20	2	no	—
710	C₂²	—	20	2	no	—
711	C₂²	#65421	1	2	yes	—
712	C₂²	C₂²×#685	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	20	2	no	—
724	C₄	—	20	2	no	—
725	C₄	—	20	2	no	—
726	C₄	#66085	1	1	yes	characteristic
727	C₄	#66087	1	1	yes	characteristic
728	C₄	#66169	1	1	yes	characteristic
729	C₄	#66171	1	1	yes	characteristic
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	40	2	no	—
734	C₂	#10614294	1	1	yes	characteristic
735	C₂	C₂×#65421	1	1	yes	characteristic
736	C₂	#10615537	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#685
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2990	C₂
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	#10617751	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2990	D₅
hypocenter	C₅	#17775
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
2. C₅×#2990	C₂	semidirect
3. #10614253	C₂	semidirect
4. #10601616	C₂	semidirect
5. #10601614	C₂	semidirect
6. #10601612	C₂	semidirect
7. #10601609	C₂	semidirect
8. #10601569	C₂	semidirect
9. #10601568	C₂	semidirect
10. #10601303	C₂	semidirect
11. #10601296	C₂	semidirect
12. #10601231	C₂	semidirect
13. C₂×#64702	C₂	semidirect
14. #10601226	C₂	semidirect
15. #10601224	C₂	semidirect
177. #2990	D₅	semidirect
699. C₅	#17775	semidirect

Maximal subgroups

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

subgroup	index
#10617751	2
C₅×#2990	2
#10614253	2
#10601616	2
#10601614	2
#10601612	2
#10601609	2
#10601569	2
#10601568	2
#10601303	2
#10601296	2
#10601231	2
C₂×#64702	2
#10601226	2
#10601224	2
#17775	5