Subgroups — #11994987

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10615000	C₂	1	1	yes	maximal, characteristic
2	C₂×#65124	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#64767	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601268	C₂	1	1	yes	maximal, characteristic
6	#10598193	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598193	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×#4092	—	2	1	no	—
10	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	#65519	—	2	1	no	—
14	C₂×#3952	—	2	1	no	—
15	C₂×#3952	—	2	1	no	—
16	C₂×#3947	—	2	1	no	—
17	#65276	—	2	1	no	—
18	#65276	C₄	1	2	yes	—
19	#65262	—	2	1	no	—
20	#65262	C₄	1	2	yes	—
21	#65224	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
24	#65124	—	2	2	no	—
25	#65124	—	2	2	no	—
26	C₅×#332	—	2	2	no	—
27	#64770	—	2	1	no	—
28	#64767	—	2	2	no	—
29	#9138	—	5	1	no	maximal, Sylow
30	C₂²×C₅×Q₈	—	2	1	no	—
31	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	—	2	1	no	—
35	C₂²×C₅×C₈	—	2	1	no	—
36	C₅×C₄⋊Q₈	—	2	1	no	—
37	C₅×C₄⋊Q₈	—	2	1	no	—
38	C₅×C₄⋊Q₈	—	2	1	no	—
39	C₅×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₅×C₄⋊C₄	—	2	1	no	—
41	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
43	#4092	—	4	2	no	—
44	#4092	—	4	2	no	—
45	C₂×#685	—	2	2	no	—
46	C₂×C₄⋊Dic₅	—	2	1	no	—
47	C₂×C₄⋊Dic₅	—	2	1	no	—
48	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
49	C₂×#683	—	2	2	no	—
50	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
53	C₂²×#168	—	2	1	no	—
54	C₂²×#168	—	2	1	no	—
55	C₄²×D₅	—	2	1	no	—
56	C₄²×D₅	—	2	1	no	—
57	C₄²×D₅	—	2	1	no	—
58	C₄²×D₅	—	2	1	no	—
59	C₅×C₄⋊C₈	—	2	1	no	—
60	C₅×C₄⋊C₈	—	2	1	no	—
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	D₄	1	2	yes	—
63	#3963	—	2	2	no	—
64	#3963	—	2	2	no	—
65	#3952	—	2	4	no	—
66	#3952	—	4	2	no	—
67	#3947	—	2	4	no	—
68	C₄⋊#168	—	2	1	no	—
69	C₄⋊#168	—	2	1	no	—
70	C₄⋊#168	—	2	1	no	—
71	C₄⋊#168	D₄	1	2	yes	—
72	C₂×#432	—	5	1	no	—
73	#2857	—	5	1	no	—
74	#1797	—	5	1	no	—
75	C₂×#332	—	5	1	no	—
76	C₂×#332	D₅	1	1	yes	characteristic, complemented
77	#1296	—	5	1	no	—
78	#1296	—	5	1	no	—
79	C₂³×D₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₅×Q₈	—	4	1	no	—
81	C₂×C₅×Q₈	—	4	1	no	—
82	C₂×C₅×Q₈	—	4	1	no	—
83	C₂×C₅×Q₈	—	4	1	no	—
84	C₂×C₅×Q₈	—	4	1	no	—
85	C₂×C₅×Q₈	—	4	1	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₅	—	2	2	no	—
91	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₅	—	2	2	no	—
95	C₂×C₄×D₅	—	2	1	no	—
96	C₂×C₄×D₅	—	2	1	no	—
97	C₂×C₄×D₅	—	2	1	no	—
98	C₂×C₄×D₅	—	2	1	no	—
99	C₂×C₄×D₅	—	2	1	no	—
100	C₂×C₄×D₅	—	2	1	no	—
101	C₂×C₄×D₅	—	2	1	no	—
102	C₂×C₄×D₅	—	2	1	no	—
103	C₂×C₄×D₅	—	2	1	no	—
104	C₂×C₄×D₅	—	2	1	no	—
105	C₂×C₄×D₅	—	2	1	no	—
106	C₂×C₄×D₅	—	2	1	no	—
107	C₂×C₄×D₅	—	2	1	no	—
108	C₂×C₄×D₅	—	2	1	no	—
109	C₂×C₄×D₅	—	4	1	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	4	1	no	—
112	C₂×C₅×C₈	—	4	1	no	—
113	C₂×C₅×C₈	—	4	1	no	—
114	C₂×C₅×C₈	—	4	1	no	—
115	C₂×C₅×C₈	—	4	1	no	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	4	1	no	—
119	C₅×C₄⋊C₄	—	4	1	no	—
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅	#41	1	1	yes	characteristic
123	C₄²×C₅	#41	1	1	yes	characteristic
124	#685	—	4	4	no	—
125	C₄⋊Dic₅	—	4	1	no	—
126	C₄⋊Dic₅	—	4	1	no	—
127	C₄⋊Dic₅	—	4	1	no	—
128	C₄⋊Dic₅	—	4	1	no	—
129	C₄⋊Dic₅	—	4	2	no	—
130	#683	—	4	4	no	—
131	C₄×Dic₅	—	2	1	no	—
132	C₄×Dic₅	—	2	1	no	—
133	C₄×Dic₅	—	2	1	no	—
134	C₄×Dic₅	—	2	1	no	—
135	C₄×Dic₅	—	2	1	no	—
136	C₄×Dic₅	—	2	1	no	—
137	C₂×#168	—	2	2	no	—
138	C₂×#168	—	4	1	no	—
139	C₂×#168	—	4	1	no	—
140	C₂×#168	—	4	1	no	—
141	C₂×#168	—	4	1	no	—
142	C₂×#168	—	4	1	no	—
143	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
144	C₂×C₂²⋊Q₈	—	10	1	no	—
145	C₂²×C₄²	—	5	1	no	—
146	#432	—	10	2	no	—
147	#432	—	10	2	no	—
148	C₂×C₄⋊C₈	—	5	1	no	—
149	C₂×C₄⋊C₈	—	5	1	no	—
150	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
151	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
152	C₂×C₂²⋊C₈	—	10	1	no	—
153	C₂×C₂²⋊C₈	—	10	1	no	—
154	C₂×#97	—	10	1	no	—
155	#391	—	10	1	no	—
156	#389	—	5	2	no	—
157	#389	—	10	1	no	—
158	#384	—	5	1	no	—
159	#380	—	5	2	no	—
160	#380	—	10	1	no	—
161	#336	—	10	1	no	—
162	#332	—	2	2	no	—
163	#332	—	10	2	no	—
164	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×D₅	—	2	1	no	—
166	C₂²×D₅	—	2	1	no	—
167	C₂²×D₅	—	2	1	no	—
168	C₂²×D₅	—	2	1	no	—
169	C₂²×D₅	—	2	1	no	—
170	C₂²×D₅	—	2	1	no	—
171	C₂²×D₅	#101	1	2	yes	—
172	C₅×Q₈	—	8	1	no	—
173	C₅×Q₈	—	8	1	no	—
174	C₅×Q₈	—	8	1	no	—
175	C₅×Q₈	—	8	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	—	4	2	no	—
180	C₂×C₄×C₅	—	4	2	no	—
181	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅	#120	1	1	yes	characteristic
184	C₂×C₄×C₅	#121	1	1	yes	characteristic
185	C₂×C₄×C₅	#121	1	1	yes	characteristic
186	C₂×C₄×C₅	#123	1	1	yes	characteristic
187	C₂×C₄×C₅	#135	1	1	yes	characteristic
188	C₂×C₄×C₅	#135	1	1	yes	characteristic
189	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂×C₄×C₅	#137	1	1	yes	characteristic
193	C₂×C₄×C₅	#137	1	1	yes	characteristic
194	C₂×C₄×C₅	#137	1	1	yes	characteristic
195	C₂×Dic₅	—	2	1	no	—
196	C₂×Dic₅	—	2	1	no	—
197	C₂×Dic₅	—	2	1	no	—
198	C₂×Dic₅	—	2	1	no	—
199	C₂×Dic₅	—	2	1	no	—
200	C₂×Dic₅	—	2	1	no	—
201	C₂×Dic₅	—	2	1	no	—
202	C₂×Dic₅	—	2	1	no	—
203	C₂×Dic₅	—	2	1	no	—
204	C₂×Dic₅	—	4	2	no	—
205	C₂×Dic₅	—	4	2	no	—
206	C₂×Dic₅	—	4	2	no	—
207	C₄×D₅	—	4	2	no	—
208	C₄×D₅	—	4	2	no	—
209	C₄×D₅	—	4	1	no	—
210	C₄×D₅	—	4	1	no	—
211	C₄×D₅	—	4	1	no	—
212	C₄×D₅	—	4	1	no	—
213	C₄×D₅	—	4	1	no	—
214	C₄×D₅	—	4	1	no	—
215	C₄×D₅	—	4	1	no	—
216	C₄×D₅	—	4	1	no	—
217	C₅×C₈	—	4	2	no	—
218	C₅×C₈	—	8	1	no	—
219	#168	—	4	2	no	—
220	#168	—	8	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂³×C₄	—	5	1	no	—
223	C₂³×C₄	—	5	1	no	—
224	C₂³×C₄	—	5	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	10	1	no	—
228	C₂²×C₈	—	10	1	no	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	—	2	1	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	—	20	2	no	—
234	C₂²⋊Q₈	—	20	2	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	5	2	no	—
237	C₂×C₄⋊C₄	—	10	2	no	—
238	C₂×C₄⋊C₄	—	10	1	no	—
239	C₂×C₄⋊C₄	—	10	1	no	—
240	C₂×C₄⋊C₄	C₄×D₅	1	2	yes	—
241	C₂×C₂²⋊C₄	—	10	2	no	—
242	C₂×C₄²	—	5	1	no	—
243	C₂×C₄²	—	5	1	no	—
244	C₂×C₄²	—	5	1	no	—
245	C₂×C₄²	—	10	1	no	—
246	C₂×C₄²	—	10	1	no	—
247	C₂×C₄²	—	10	1	no	—
248	C₂×C₄²	—	10	1	no	—
249	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	5	2	no	—
254	C₄⋊C₈	—	10	1	no	—
255	C₄⋊C₈	—	10	1	no	—
256	C₄⋊C₈	—	10	1	no	—
257	C₄⋊C₈	C₂²⋊D₅	1	2	yes	—
258	C₂²⋊C₈	—	10	4	no	—
259	C₂²⋊C₈	—	20	2	no	—
260	#97	—	10	4	no	—
261	#95	—	10	2	no	—
262	#95	—	10	2	no	—
263	C₂²×C₅	#386	1	1	yes	characteristic
264	C₂²×C₅	C₂×#101	1	1	yes	characteristic
265	C₂²×C₅	#413	1	1	yes	characteristic
266	C₂²×C₅	#416	1	1	yes	characteristic
267	C₂²×C₅	#417	1	1	yes	characteristic
268	C₂²×C₅	#418	1	1	yes	characteristic
269	C₂²×C₅	#419	1	1	yes	characteristic
270	C₂×D₅	—	2	2	no	—
271	C₂×D₅	—	2	2	no	—
272	C₂×D₅	—	2	2	no	—
273	C₂×D₅	—	4	1	no	—
274	C₂×D₅	—	4	1	no	—
275	C₂×D₅	—	4	1	no	—
276	C₂×D₅	—	4	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	8	2	no	—
280	C₄×C₅	#452	1	1	yes	characteristic
281	C₄×C₅	#452	1	1	yes	characteristic
282	C₄×C₅	#468	1	1	yes	characteristic
283	C₄×C₅	#468	1	1	yes	characteristic
284	C₄×C₅	#469	1	1	yes	characteristic
285	C₄×C₅	#469	1	1	yes	characteristic
286	C₄×C₅	#485	1	1	yes	characteristic
287	C₄×C₅	#485	1	1	yes	characteristic
288	Dic₅	—	4	1	no	—
289	Dic₅	—	4	1	no	—
290	Dic₅	—	4	1	no	—
291	Dic₅	—	8	2	no	—
292	C₂⁴	—	5	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	10	2	no	—
304	C₂²×C₄	—	10	1	no	—
305	C₂²×C₄	—	10	1	no	—
306	C₂²×C₄	—	10	1	no	—
307	C₂²×C₄	—	10	1	no	—
308	C₂²×C₄	—	10	1	no	—
309	C₂²×C₄	—	10	1	no	—
310	C₂²×C₄	—	10	1	no	—
311	C₂²×C₄	—	10	1	no	—
312	C₂²×C₄	—	10	1	no	—
313	C₂²×C₄	—	10	1	no	—
314	C₂²×C₄	—	10	1	no	—
315	C₂²×C₄	—	10	1	no	—
316	C₂²×C₄	—	10	1	no	—
317	C₂²×C₄	—	10	1	no	—
318	C₂²×C₄	—	10	2	no	—
319	C₂²×C₄	—	20	1	no	—
320	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	10	2	no	—
330	C₂×C₈	—	20	1	no	—
331	C₂×C₈	—	20	1	no	—
332	C₂×C₈	—	20	1	no	—
333	C₂×C₈	—	20	1	no	—
334	C₂×C₈	—	20	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	20	2	no	—
340	C₄⋊C₄	—	20	4	no	—
341	C₄⋊C₄	—	20	1	no	—
342	C₄⋊C₄	—	20	1	no	—
343	C₄⋊C₄	—	20	1	no	—
344	C₄⋊C₄	—	20	1	no	—
345	C₂²⋊C₄	—	20	4	no	—
346	C₄²	—	10	1	no	—
347	C₄²	—	10	1	no	—
348	C₄²	—	10	1	no	—
349	C₄²	—	10	1	no	—
350	C₄²	—	10	1	no	—
351	C₄²	—	10	1	no	—
352	C₄²	#709	1	1	yes	characteristic
353	C₄²	D₄×D₅	1	1	yes	characteristic
354	C₄²	#711	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
356	C₂×C₅	#1552	1	1	yes	characteristic
357	C₂×C₅	#1553	1	1	yes	characteristic
358	C₂×C₅	#1556	1	1	yes	characteristic
359	C₂×C₅	#1559	1	1	yes	characteristic
360	C₂×C₅	#1873	1	1	yes	characteristic
361	C₂×C₅	#1895	1	1	yes	characteristic
362	C₂×C₅	#1901	1	1	yes	characteristic
363	D₅	—	4	2	no	—
364	C₂³	—	5	2	no	—
365	C₂³	—	10	1	no	—
366	C₂³	—	10	1	no	—
367	C₂³	—	10	1	no	—
368	C₂³	—	10	1	no	—
369	C₂³	—	10	1	no	—
370	C₂³	—	10	1	no	—
371	C₂³	D₅×C₂²⋊C₄	1	1	yes	characteristic
372	Q₈	—	8	1	no	—
373	Q₈	—	8	1	no	—
374	Q₈	—	8	1	no	—
375	Q₈	—	8	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	10	1	no	—
382	C₂×C₄	—	10	1	no	—
383	C₂×C₄	—	10	1	no	—
384	C₂×C₄	—	10	1	no	—
385	C₂×C₄	—	10	1	no	—
386	C₂×C₄	—	10	1	no	—
387	C₂×C₄	—	10	1	no	—
388	C₂×C₄	—	10	1	no	—
389	C₂×C₄	—	10	1	no	—
390	C₂×C₄	—	20	2	no	—
391	C₂×C₄	—	20	2	no	—
392	C₂×C₄	—	20	1	no	—
393	C₂×C₄	—	20	1	no	—
394	C₂×C₄	—	20	1	no	—
395	C₂×C₄	—	20	1	no	—
396	C₂×C₄	—	20	1	no	—
397	C₂×C₄	—	20	1	no	—
398	C₂×C₄	—	20	1	no	—
399	C₂×C₄	—	20	1	no	—
400	C₂×C₄	—	20	2	no	—
401	C₂×C₄	—	20	2	no	—
402	C₂×C₄	—	20	2	no	—
403	C₂×C₄	#4027	1	1	yes	characteristic
404	C₂×C₄	#4029	1	1	yes	characteristic
405	C₂×C₄	#4030	1	1	yes	characteristic
406	C₂×C₄	#4057	1	1	yes	characteristic
407	C₂×C₄	#4057	1	1	yes	characteristic
408	C₂×C₄	#4060	1	1	yes	characteristic
409	C₂×C₄	#4061	1	1	yes	characteristic
410	C₂×C₄	#4061	1	1	yes	characteristic
411	C₂×C₄	#4062	1	1	yes	characteristic
412	C₂×C₄	#4064	1	1	yes	characteristic
413	C₂×C₄	#4065	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
415	C₂×C₄	#4083	1	1	yes	characteristic
416	C₂×C₄	#4084	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	8	1	no	—
419	C₈	—	20	2	no	—
420	C₈	—	40	1	no	—
421	C₅	#9138	1	1	yes	characteristic, complemented, Sylow
422	C₂²	—	10	2	no	—
423	C₂²	—	10	2	no	—
424	C₂²	—	10	2	no	—
425	C₂²	—	20	1	no	—
426	C₂²	—	20	1	no	—
427	C₂²	—	20	1	no	—
428	C₂²	—	20	1	no	—
429	C₂²	D₅×#101	1	1	yes	characteristic
430	C₂²	#65040	1	1	yes	characteristic
431	C₂²	#65059	1	1	yes	characteristic
432	C₂²	#65060	1	1	yes	characteristic
433	C₂²	#65091	1	1	yes	characteristic
434	C₂²	#65093	1	1	yes	characteristic
435	C₂²	#65245	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	20	1	no	—
440	C₄	—	20	1	no	—
441	C₄	—	20	1	no	—
442	C₄	—	40	2	no	—
443	C₄	#65069	1	1	yes	characteristic
444	C₄	#65071	1	1	yes	characteristic
445	C₄	#65103	1	1	yes	characteristic
446	C₄	#65104	1	1	yes	characteristic
447	C₄	#65448	1	1	yes	characteristic
448	C₄	#65462	1	1	yes	characteristic
449	C₄	#65463	1	1	yes	characteristic
450	C₄	#65476	1	1	yes	characteristic
451	C₂	—	20	2	no	—
452	C₂	#10599218	1	1	yes	characteristic
453	C₂	#10599219	1	1	yes	characteristic
454	C₂	#10599221	1	1	yes	characteristic
455	C₂	#10599223	1	1	yes	characteristic
456	C₂	#10600908	1	1	yes	characteristic
457	C₂	#10600996	1	1	yes	characteristic
458	C₂	#10601062	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₅×C₂²⋊C₄
commutator	C₂²×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#332	C₂
socle	C₂³×C₅	C₂×C₂²⋊C₄
prime radical	C₂³×D₅	C₂²⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#332	D₅
hypocenter	C₅	#9138
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#332	C₂	semidirect
4. C₂×#64767	C₂	semidirect
6. #10598193	C₂	semidirect
7. #10598193	C₂	semidirect
76. C₂×#332	D₅	semidirect
421. C₅	#9138	semidirect

Maximal subgroups

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

subgroup	index
#10615000	2
C₂×#65124	2
C₂×C₅×#332	2
C₂×#64767	2
#10601268	2
#10598193	2
#9138	5