Subgroups — #12252502

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#10615465	C₂	1	1	yes	maximal, characteristic
3	C₂×#65196	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
5	#10602226	C₂	1	2	yes	maximal, complemented
6	#10602225	C₂	1	1	yes	maximal, characteristic, complemented
7	#10602223	C₂	1	2	yes	maximal, complemented
8	#10602214	C₂	1	1	yes	maximal, characteristic, complemented
9	#10602212	C₂	1	1	yes	maximal, characteristic, complemented
10	#10602200	C₂	1	2	yes	maximal, complemented
11	C₁₆×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	#66125	C₄	1	1	yes	characteristic
14	C₂×#4047	C₂²	1	1	yes	characteristic
15	C₂×C₅×M₃₂	—	2	4	no	—
16	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₅×M₃₂	C₂²	1	2	yes	—
18	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
20	#65496	C₄	1	1	yes	characteristic
21	#65400	C₄	1	2	yes	—
22	#65400	C₄	1	2	yes	—
23	#65399	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₅	C₂²	1	2	yes	—
25	C₈×C₂²⋊D₅	C₂²	1	2	yes	—
26	#65391	C₄	1	1	yes	characteristic
27	#65390	C₂²	1	1	yes	characteristic
28	C₂²×#672	C₂²	1	1	yes	characteristic
29	C₂²×#672	C₂²	1	1	yes	characteristic
30	#65196	—	2	4	no	—
31	C₂×#3930	C₂²	1	2	yes	complemented
32	C₂×D₅×C₁₆	C₂²	1	2	yes	complemented
33	C₂²⋊#672	C₂²	1	1	yes	characteristic
34	C₂²⋊#672	C₂²	1	1	yes	characteristic
35	C₂²⋊#672	C₂²	1	1	yes	characteristic
36	C₂²⋊#672	C₂²	1	1	yes	characteristic
37	#64727	C₂²	1	2	yes	complemented
38	#64727	C₂²	1	2	yes	complemented
39	#64722	C₂²	1	2	yes	complemented
40	#64721	C₂²	1	2	yes	complemented
41	#64721	C₂²	1	2	yes	complemented
42	C₁₆×Dic₅	C₂²	1	2	yes	complemented
43	#33436	—	5	1	no	maximal, Sylow
44	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×#709	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	#4099	C₈	1	2	yes	—
55	#4076	C₈	1	1	yes	characteristic
56	#4076	C₈	1	1	yes	characteristic
57	#4075	C₈	1	2	yes	—
58	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	#4072	C₂×C₄	1	1	yes	characteristic
61	#4070	C₈	1	1	yes	characteristic
62	#4070	C₈	1	1	yes	characteristic
63	C₂×#681	C₂×C₄	1	1	yes	characteristic
64	C₂×#681	C₂×C₄	1	1	yes	characteristic
65	#4047	—	2	2	no	—
66	#4047	—	2	2	no	—
67	C₂×#676	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₅	C₂³	1	2	yes	—
69	C₅×M₃₂	—	2	2	no	—
70	C₅×M₃₂	—	2	4	no	—
71	C₅×M₃₂	D₄	1	4	yes	complemented
72	C₂×C₅×C₁₆	—	2	4	no	—
73	C₂×C₅×C₁₆	C₂³	1	2	yes	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₂²⋊#168	C₂×C₄	1	2	yes	—
76	C₂²⋊#168	C₂×C₄	1	2	yes	—
77	#3952	C₂×C₄	1	2	yes	—
78	#3952	C₂×C₄	1	2	yes	—
79	#3947	C₂×C₄	1	2	yes	—
80	#3946	C₂×C₄	1	2	yes	—
81	#3946	C₂×C₄	1	2	yes	—
82	C₈×Dic₅	C₂³	1	2	yes	—
83	C₂×#672	—	2	2	no	—
84	C₂×#672	—	2	2	no	—
85	C₂×#672	C₂³	1	1	yes	characteristic
86	C₂×#672	C₂³	1	1	yes	characteristic
87	C₂×#672	C₂³	1	1	yes	characteristic
88	C₂×#672	C₂³	1	1	yes	characteristic
89	#3930	—	2	4	no	—
90	D₅×C₁₆	—	2	4	no	—
91	C₂×#504	—	5	1	no	—
92	C₂²×M₃₂	D₅	1	1	yes	characteristic, complemented
93	#2929	—	5	1	no	—
94	#2169	—	5	2	no	—
95	#2168	—	5	2	no	—
96	#2168	—	5	2	no	—
97	D₄×C₁₆	—	5	2	no	—
98	#2151	—	5	1	no	—
99	#2113	—	5	1	no	—
100	C₂×C₂²⋊C₁₆	—	5	1	no	—
101	#2108	—	5	1	no	—
102	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
112	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
113	C₂×C₂²⋊D₅	C₂×C₈	1	2	yes	—
114	#709	—	2	2	no	—
115	#709	—	2	2	no	—
116	C₂×D₂₀	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
118	C₂×Dic₁₀	C₂×C₈	1	1	yes	characteristic
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
130	C₂×C₅×C₈	#41	1	2	yes	—
131	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
133	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
134	C₂²⋊Dic₅	C₂×C₈	1	2	yes	—
135	#685	C₂×C₈	1	2	yes	—
136	#685	C₂×C₈	1	2	yes	—
137	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
138	C₄⋊Dic₅	C₂×C₈	1	1	yes	characteristic
139	#683	C₂×C₈	1	2	yes	—
140	#683	C₂×C₈	1	2	yes	—
141	C₄×Dic₅	C₂²×C₄	1	2	yes	—
142	#681	—	2	2	no	—
143	#681	—	2	2	no	—
144	C₂×#168	C₂²×C₄	1	2	yes	—
145	C₂×#168	C₂²×C₄	1	2	yes	—
146	#676	—	2	4	no	—
147	C₈×D₅	—	2	2	no	—
148	C₈×D₅	—	2	2	no	—
149	C₅×C₁₆	—	2	2	no	—
150	C₅×C₁₆	C₂×D₄	1	4	yes	—
151	#672	—	2	1	no	—
152	#672	—	2	1	no	—
153	#672	—	2	1	no	—
154	#672	—	2	1	no	—
155	C₂×#131	—	5	1	no	—
156	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
157	#525	—	5	1	no	—
158	#504	—	10	4	no	—
159	C₂×M₃₂	—	2	4	no	—
160	C₂×M₃₂	—	5	2	no	—
161	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
162	C₂×M₃₂	C₂×D₅	1	2	yes	—
163	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
164	C₂²×C₁₆	—	5	1	no	—
165	C₂²×C₁₆	—	5	1	no	—
166	C₂²×C₁₆	—	5	2	no	—
167	C₂²×C₁₆	C₂×D₅	1	2	yes	—
168	#435	—	5	2	no	—
169	#435	—	5	2	no	—
170	C₈×D₄	—	5	2	no	—
171	C₈×D₄	—	5	2	no	—
172	#424	—	5	1	no	—
173	#408	—	5	1	no	—
174	#407	—	5	1	no	—
175	#405	—	5	1	no	—
176	C₄⋊C₁₆	—	5	2	no	—
177	C₄⋊C₁₆	—	5	2	no	—
178	C₂²⋊C₁₆	—	5	1	no	—
179	C₂²⋊C₁₆	—	5	1	no	—
180	C₂²⋊C₁₆	—	5	1	no	—
181	C₂²⋊C₁₆	—	5	1	no	—
182	C₂²⋊C₁₆	—	5	2	no	—
183	C₂²⋊C₁₆	—	5	2	no	—
184	#346	—	5	2	no	—
185	C₄×C₁₆	—	5	2	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
190	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
191	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
192	C₂²×D₅	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
204	C₂×C₄×C₅	#131	1	2	yes	—
205	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂²⋊D₅	—	2	4	no	—
207	C₂²⋊D₅	—	2	4	no	—
208	C₂²⋊D₅	—	4	2	no	—
209	C₂×Dic₅	C₂²×C₈	1	2	yes	—
210	C₂×Dic₅	C₂²×C₈	1	2	yes	—
211	C₂×Dic₅	C₂²×C₈	1	2	yes	—
212	D₂₀	—	2	2	no	—
213	C₄×D₅	—	2	2	no	—
214	C₄×D₅	—	2	2	no	—
215	Dic₁₀	—	2	2	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	—	2	1	no	—
218	C₅×C₈	C₄×D₄	1	2	yes	—
219	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
220	C₅×C₈	C₂×#41	1	1	yes	characteristic
221	#168	—	2	2	no	—
222	#168	—	2	2	no	—
223	C₂×#41	—	5	1	no	—
224	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
225	#131	—	10	2	no	—
226	#131	—	10	2	no	—
227	C₂×M₁₆	—	5	1	no	—
228	C₂×M₁₆	—	5	1	no	—
229	C₂×M₁₆	—	5	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	5	2	no	—
233	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
234	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
235	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
236	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
237	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
238	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
239	#123	—	5	2	no	—
240	C₂²⋊Q₈	—	5	1	no	—
241	C₂²⋊Q₈	—	5	1	no	—
242	#121	—	5	1	no	—
243	#121	—	5	1	no	—
244	#120	—	5	2	no	—
245	C₄×D₄	—	5	2	no	—
246	C₄×D₄	—	5	2	no	—
247	#117	—	5	1	no	—
248	M₃₂	—	2	2	no	—
249	M₃₂	—	2	4	no	—
250	M₃₂	—	10	4	no	—
251	M₃₂	C₂²⋊D₅	1	4	yes	complemented
252	C₂×C₁₆	—	2	4	no	—
253	C₂×C₁₆	—	5	1	no	—
254	C₂×C₁₆	—	5	1	no	—
255	C₂×C₁₆	—	5	1	no	—
256	C₂×C₁₆	—	5	1	no	—
257	C₂×C₁₆	—	10	2	no	—
258	C₂×C₁₆	—	10	2	no	—
259	C₂×C₁₆	—	10	4	no	—
260	C₂×C₁₆	C₂²×D₅	1	2	yes	—
261	C₂×C₁₆	C₂²×D₅	1	2	yes	—
262	C₄⋊C₈	—	5	2	no	—
263	C₄⋊C₈	—	5	2	no	—
264	C₂²⋊C₈	—	5	2	no	—
265	C₂²⋊C₈	—	5	2	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	5	2	no	—
268	#97	—	5	2	no	—
269	C₄×C₈	—	5	2	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	4	4	no	—
278	C₂²×C₅	C₈×D₄	1	2	yes	—
279	C₂²×C₅	#504	1	2	yes	complemented
280	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
281	C₂×D₅	—	2	2	no	—
282	C₂×D₅	—	2	2	no	—
283	C₂×D₅	—	2	2	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	C₈×D₄	1	2	yes	—
287	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
288	C₄×C₅	C₂×#131	1	1	yes	characteristic
289	Dic₅	—	2	2	no	—
290	Dic₅	—	2	2	no	—
291	Dic₅	—	2	2	no	—
292	C₂⁴	C₈×D₅	1	1	yes	characteristic
293	#41	—	10	2	no	—
294	#41	—	10	2	no	—
295	C₂×Q₈	—	5	1	no	—
296	C₂×D₄	—	5	2	no	—
297	C₂×D₄	—	5	2	no	—
298	C₂×D₄	—	5	2	no	—
299	C₂×D₄	—	5	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	5	2	no	—
303	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
305	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
309	M₁₆	—	10	2	no	—
310	M₁₆	—	10	2	no	—
311	M₁₆	—	10	4	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	—	5	2	no	—
321	C₂×C₈	—	10	2	no	—
322	C₂×C₈	—	10	2	no	—
323	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
326	C₂×C₈	#709	1	2	yes	—
327	C₂×C₈	C₂×C₂²⋊D₅	1	2	yes	—
328	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
329	C₄⋊C₄	—	5	1	no	—
330	C₄⋊C₄	—	5	1	no	—
331	C₄⋊C₄	—	5	2	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₂²⋊C₄	—	5	2	no	—
334	C₂²⋊C₄	—	5	2	no	—
335	C₂²⋊C₄	—	5	2	no	—
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	2	no	—
338	C₄²	—	5	2	no	—
339	C₁₆	—	2	2	no	—
340	C₁₆	—	10	1	no	—
341	C₁₆	—	10	1	no	—
342	C₁₆	—	10	1	no	—
343	C₁₆	—	10	1	no	—
344	C₁₆	C₂×C₂²⋊D₅	1	4	yes	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	4	1	no	—
348	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
349	C₂×C₅	C₂×#504	1	1	yes	characteristic
350	C₂×C₅	#3407	1	1	yes	characteristic
351	D₅	—	4	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	—	5	2	no	—
356	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
357	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
359	Q₈	—	10	2	no	—
360	D₄	—	10	4	no	—
361	D₄	—	10	4	no	—
362	D₄	—	10	2	no	—
363	D₄	—	20	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	5	2	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	10	2	no	—
376	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
378	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
379	C₂×C₄	#4047	1	2	yes	—
380	C₂×C₄	C₄×C₂²⋊D₅	1	2	yes	—
381	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	10	2	no	—
385	C₈	—	10	2	no	—
386	C₈	C₄×C₂²⋊D₅	1	2	yes	—
387	C₈	C₂×#709	1	1	yes	characteristic
388	C₈	C₂²×C₂²⋊D₅	1	1	yes	characteristic
389	C₅	#33436	1	1	yes	characteristic, complemented, Sylow
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	10	2	no	—
399	C₂²	—	10	2	no	—
400	C₂²	—	10	2	no	—
401	C₂²	#65196	1	2	yes	complemented
402	C₂²	C₈×C₂²⋊D₅	1	2	yes	—
403	C₂²	C₂²×C₈×D₅	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	10	2	no	—
407	C₄	—	10	2	no	—
408	C₄	—	10	2	no	—
409	C₄	C₈×C₂²⋊D₅	1	2	yes	—
410	C₄	C₂×#4047	1	1	yes	characteristic
411	C₄	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	20	2	no	—
416	C₂	C₂×#65196	1	1	yes	characteristic
417	C₂	#10613738	1	1	yes	characteristic
418	C₂	C₂×C₈×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅
commutator, socle	C₂²×C₅	C₂³×C₈
Fitting	C₂²×C₅×M₃₂	C₂
prime radical	#66125	C₄
cosocle	C₂×C₅×C₈	C₂⁴
hypercenter	C₂²×M₃₂	D₅
hypocenter	C₅	#33436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×M₃₂	C₂	semidirect
3. C₂×#65196	C₂	semidirect
4. C₂×C₂²⋊#672	C₂	semidirect
5. #10602226	C₂	semidirect
6. #10602225	C₂	semidirect
7. #10602223	C₂	semidirect
8. #10602214	C₂	semidirect
9. #10602212	C₂	semidirect
10. #10602200	C₂	semidirect
11. C₁₆×C₂²⋊D₅	C₂	semidirect
31. C₂×#3930	C₂²	semidirect
32. C₂×D₅×C₁₆	C₂²	semidirect
37. #64727	C₂²	semidirect
38. #64727	C₂²	semidirect
39. #64722	C₂²	semidirect
40. #64721	C₂²	semidirect
41. #64721	C₂²	semidirect
42. C₁₆×Dic₅	C₂²	semidirect
71. C₅×M₃₂	D₄	semidirect
92. C₂²×M₃₂	D₅	semidirect
251. M₃₂	C₂²⋊D₅	semidirect
279. C₂²×C₅	#504	semidirect
389. C₅	#33436	semidirect
401. C₂²	#65196	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×M₃₂	2
#10615465	2
C₂×#65196	2
C₂×C₂²⋊#672	2
#10602226	2
#10602225	2
#10602223	2
#10602214	2
#10602212	2
#10602200	2
C₁₆×C₂²⋊D₅	2
#33436	5