Subgroups — #12068552

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic
2	#10614246	C₂	1	1	yes	maximal, characteristic
3	#10614243	C₂	1	1	yes	maximal, characteristic
4	#10601546	C₂	1	2	yes	maximal, complemented
5	#10601545	C₂	1	2	yes	maximal, complemented
6	#10601543	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601542	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600644	C₂	1	2	yes	maximal, complemented
9	#10600643	C₂	1	2	yes	maximal, complemented
10	#10600524	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#64677	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₂×#4094	—	2	1	no	—
14	C₅×#446	C₄	1	1	yes	characteristic
15	C₅×#446	C₄	1	1	yes	characteristic
16	C₅×#436	C₄	1	1	yes	characteristic
17	C₅×#436	C₄	1	1	yes	characteristic
18	C₅×#435	C₄	1	2	yes	—
19	C₅×#435	C₄	1	2	yes	—
20	C₅×#431	C₂²	1	1	yes	characteristic
21	C₅×#431	C₂²	1	2	yes	—
22	C₄×C₅×M₁₆	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	#65523	—	2	1	no	—
25	#65289	—	2	2	no	—
26	#65288	—	2	1	no	—
27	#65288	—	2	2	no	—
28	#65286	—	2	1	no	—
29	#65215	C₂²	1	2	yes	—
30	#65214	C₂²	1	2	yes	—
31	#65213	C₂²	1	1	yes	characteristic
32	#65213	C₂²	1	1	yes	characteristic
33	#65213	C₂²	1	2	yes	—
34	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#168	C₂²	1	2	yes	—
37	#64678	C₂²	1	2	yes	—
38	#64678	C₂²	1	2	yes	—
39	#64678	C₂²	1	2	yes	—
40	#64678	C₂²	1	2	yes	—
41	#64677	C₂²	1	2	yes	—
42	#64677	C₂²	1	2	yes	—
43	#64677	C₂²	1	1	yes	characteristic
44	#64677	C₂²	1	1	yes	characteristic
45	#64677	C₂²	1	1	yes	characteristic
46	#64677	C₂²	1	1	yes	characteristic
47	#17830	—	5	1	no	maximal, Sylow
48	C₂×C₅×#41	D₄	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×Q₈	Q₈	1	1	yes	characteristic
55	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
56	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₄	Q₈	1	2	yes	—
58	C₄×C₅×D₄	Q₈	1	1	yes	characteristic
59	C₅×#117	D₄	1	1	yes	characteristic
60	C₅×#117	D₄	1	2	yes	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	#4094	—	4	4	no	—
64	C₂×#681	—	2	1	no	—
65	C₂×#681	—	2	2	no	—
66	C₂×#681	—	2	1	no	—
67	C₂²×#168	—	2	1	no	—
68	C₂²×#168	—	2	2	no	—
69	C₂²×#168	—	2	1	no	—
70	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
75	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
76	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₅×#97	C₂×C₄	1	2	yes	—
78	C₅×#97	C₂×C₄	1	2	yes	—
79	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₄×C₅×C₈	C₂³	1	2	yes	—
84	C₂²⋊#168	—	2	2	no	—
85	C₂²⋊#168	—	2	2	no	—
86	C₄⋊#168	—	2	2	no	—
87	C₄⋊#168	—	2	1	no	—
88	C₄⋊#168	—	2	2	no	—
89	C₄⋊#168	—	2	1	no	—
90	C₄⋊#168	—	2	1	no	—
91	C₄⋊#168	—	2	1	no	—
92	C₄⋊#168	C₂³	1	1	yes	characteristic
93	C₄⋊#168	C₂³	1	1	yes	characteristic
94	C₄⋊#168	C₂³	1	1	yes	characteristic
95	C₄⋊#168	C₂³	1	2	yes	—
96	C₄⋊#168	C₂³	1	1	yes	characteristic
97	C₄⋊#168	C₂³	1	2	yes	—
98	#3935	—	2	2	no	—
99	C₄×#168	—	2	2	no	—
100	#2965	D₅	1	1	yes	characteristic
101	#2925	—	5	1	no	—
102	#2906	—	5	1	no	—
103	#1574	—	5	2	no	—
104	#1573	—	5	2	no	—
105	#1571	—	5	1	no	—
106	#1570	—	5	1	no	—
107	#1569	—	5	2	no	—
108	#1567	—	5	1	no	—
109	#1565	—	5	2	no	—
110	C₂×#334	—	5	1	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
115	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
121	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₅×M₁₆	—	2	4	no	—
123	C₅×M₁₆	—	4	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	4	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	C₂²×C₄	1	2	yes	—
130	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
132	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
133	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
135	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
137	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
138	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
139	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₅	C₂²×C₄	1	2	yes	—
141	C₄²×C₅	C₂×D₄	1	2	yes	—
142	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×Q₈	1	2	yes	—
144	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₅	C₂⁴	1	1	yes	characteristic
146	#681	—	4	4	no	—
147	#681	—	4	2	no	—
148	#681	—	4	2	no	—
149	C₂×#168	—	2	1	no	—
150	C₂×#168	—	2	2	no	—
151	C₂×#168	—	2	1	no	—
152	C₂×#168	—	2	1	no	—
153	C₂×#168	—	2	2	no	—
154	C₂×#168	—	2	1	no	—
155	C₂×#168	—	4	4	no	—
156	C₂×#168	—	4	2	no	—
157	C₂×#168	—	4	2	no	—
158	C₂×#131	—	10	1	no	—
159	C₄×#41	C₂×D₅	1	1	yes	characteristic
160	#446	Dic₅	1	1	yes	characteristic
161	#446	Dic₅	1	1	yes	characteristic
162	#436	Dic₅	1	1	yes	characteristic
163	#436	Dic₅	1	1	yes	characteristic
164	#435	Dic₅	1	2	yes	—
165	#435	Dic₅	1	2	yes	—
166	#433	—	10	2	no	—
167	#432	—	5	2	no	—
168	#431	—	5	2	no	—
169	#431	C₂×D₅	1	1	yes	characteristic
170	#431	C₂×D₅	1	2	yes	—
171	#424	—	10	1	no	—
172	#424	—	10	2	no	—
173	#423	—	5	1	no	—
174	#423	—	5	1	no	—
175	#423	—	5	2	no	—
176	C₂×C₄⋊C₈	—	5	1	no	—
177	C₂×C₄⋊C₈	—	5	1	no	—
178	C₂×C₄⋊C₈	—	5	2	no	—
179	#408	—	10	1	no	—
180	#405	—	10	1	no	—
181	C₄×M₁₆	C₂×D₅	1	2	yes	—
182	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
183	#335	—	5	2	no	—
184	#335	—	5	2	no	—
185	#335	—	5	2	no	—
186	#335	—	5	2	no	—
187	#334	—	5	1	no	—
188	#334	—	5	1	no	—
189	#334	—	5	1	no	—
190	#334	—	5	1	no	—
191	#334	—	5	2	no	—
192	#334	—	5	2	no	—
193	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
194	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₅×Q₈	—	2	2	no	—
196	C₅×D₄	—	2	4	no	—
197	C₅×D₄	—	2	2	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
210	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₅	#137	1	2	yes	—
214	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
217	C₅×C₈	—	2	1	no	—
218	C₅×C₈	—	2	2	no	—
219	C₅×C₈	—	2	1	no	—
220	C₅×C₈	—	2	1	no	—
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	#131	1	2	yes	complemented
223	#168	—	4	1	no	—
224	#168	—	4	2	no	—
225	#168	—	4	1	no	—
226	#168	—	4	2	no	—
227	#168	—	4	1	no	—
228	#168	—	4	1	no	—
229	C₂×#41	D₂₀	1	1	yes	characteristic
230	#131	—	20	4	no	—
231	C₂×M₁₆	—	10	2	no	—
232	C₂×M₁₆	—	10	1	no	—
233	C₂×M₁₆	—	10	1	no	—
234	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
235	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
236	C₂²×C₈	—	10	2	no	—
237	C₂²×C₈	—	10	1	no	—
238	C₂²×C₈	—	10	1	no	—
239	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
240	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
241	C₄×Q₈	Dic₁₀	1	1	yes	characteristic
242	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
243	C₄×D₄	Dic₁₀	1	2	yes	—
244	C₄×D₄	Dic₁₀	1	1	yes	characteristic
245	C₄×D₄	C₂×Dic₅	1	2	yes	—
246	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
247	#117	D₂₀	1	1	yes	characteristic
248	#117	D₂₀	1	2	yes	—
249	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₅	1	2	yes	—
251	C₄⋊C₈	—	5	1	no	—
252	C₄⋊C₈	—	5	1	no	—
253	C₄⋊C₈	—	5	1	no	—
254	C₄⋊C₈	—	5	1	no	—
255	C₄⋊C₈	—	5	2	no	—
256	C₄⋊C₈	—	5	2	no	—
257	C₄⋊C₈	—	10	2	no	—
258	C₄⋊C₈	—	10	1	no	—
259	C₄⋊C₈	—	10	1	no	—
260	C₄⋊C₈	—	10	2	no	—
261	C₄⋊C₈	—	10	1	no	—
262	C₄⋊C₈	—	10	1	no	—
263	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
264	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
265	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
266	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
267	C₂²⋊C₈	—	10	2	no	—
268	C₂²⋊C₈	—	10	2	no	—
269	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
270	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
271	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
272	#97	—	10	2	no	—
273	#97	C₂×Dic₅	1	2	yes	—
274	#97	C₂×Dic₅	1	2	yes	—
275	C₄×C₈	—	10	2	no	—
276	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
277	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
279	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
280	C₄×C₈	C₂²×D₅	1	2	yes	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	#428	1	2	yes	—
287	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	#428	1	2	yes	—
295	C₄×C₅	C₂×#131	1	1	yes	characteristic
296	C₄×C₅	#568	1	1	yes	characteristic
297	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₄×C₅	C₂×#137	1	1	yes	characteristic
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	C₂×Q₈	C₄⋊Dic₅	1	1	yes	characteristic
302	C₂×D₄	C₄⋊Dic₅	1	2	yes	—
303	C₂×D₄	C₄⋊Dic₅	1	1	yes	characteristic
304	C₂²×C₄	C₂×Dic₁₀	1	2	yes	—
305	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₂₀	1	2	yes	—
307	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
308	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₅	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	4	2	no	—
312	M₁₆	—	20	4	no	—
313	M₁₆	—	20	2	no	—
314	M₁₆	—	20	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	10	1	no	—
318	C₂×C₈	—	10	2	no	—
319	C₂×C₈	—	10	1	no	—
320	C₂×C₈	—	10	1	no	—
321	C₂×C₈	—	10	2	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	20	4	no	—
324	C₂×C₈	—	20	2	no	—
325	C₂×C₈	—	20	2	no	—
326	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
327	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
328	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
329	C₂×C₈	C₂²×Dic₅	1	2	yes	—
330	C₂×C₈	C₂²×Dic₅	1	2	yes	—
331	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
332	C₄⋊C₄	C₄⋊Dic₅	1	2	yes	—
333	C₄⋊C₄	C₄⋊Dic₅	1	1	yes	characteristic
334	C₄⋊C₄	C₄⋊Dic₅	1	2	yes	—
335	C₄⋊C₄	C₄⋊Dic₅	1	1	yes	characteristic
336	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
337	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
338	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
339	C₄²	C₂×Dic₁₀	1	2	yes	—
340	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
341	C₄²	C₂×D₂₀	1	2	yes	—
342	C₄²	C₂×D₂₀	1	1	yes	characteristic
343	C₄²	C₂²×Dic₅	1	1	yes	characteristic
344	C₄²	C₂²×Dic₅	1	2	yes	—
345	C₄²	C₂³×D₅	1	1	yes	characteristic
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	4	2	no	—
348	C₂×C₅	#2906	1	1	yes	characteristic
349	C₂×C₅	C₂×#428	1	1	yes	characteristic
350	C₂×C₅	#2916	1	1	yes	characteristic
351	C₂³	C₂×C₄⋊Dic₅	1	2	yes	—
352	C₂³	C₂×C₄⋊Dic₅	1	1	yes	characteristic
353	Q₈	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	#4054	1	2	yes	—
365	C₂×C₄	#4055	1	2	yes	—
366	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
367	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
369	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
370	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
372	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
374	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	2	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	2	no	—
380	C₈	—	20	1	no	—
381	C₈	—	20	2	no	—
382	C₈	—	20	1	no	—
383	C₈	—	20	2	no	—
384	C₈	—	20	1	no	—
385	C₈	—	20	1	no	—
386	C₈	#4094	1	2	yes	complemented
387	C₅	#17830	1	1	yes	characteristic, complemented, Sylow
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#65410	1	2	yes	—
394	C₂²	C₂²×C₄⋊Dic₅	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#65410	1	2	yes	—
402	C₄	C₂×#4054	1	1	yes	characteristic
403	C₄	C₂×#4055	1	1	yes	characteristic
404	C₄	C₂×#4094	1	1	yes	characteristic
405	C₄	#66153	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#10614243	1	1	yes	characteristic
409	C₂	C₂×#65410	1	1	yes	characteristic
410	C₂	#10615520	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₀
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2965	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	D₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2965	D₅
hypocenter	C₅	#17830
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
4. #10601546	C₂	semidirect
5. #10601545	C₂	semidirect
6. #10601543	C₂	semidirect
7. #10601542	C₂	semidirect
8. #10600644	C₂	semidirect
9. #10600643	C₂	semidirect
10. #10600524	C₂	semidirect
11. C₂×#64677	C₂	semidirect
222. C₅×C₈	#131	semidirect
386. C₈	#4094	semidirect
387. C₅	#17830	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2965	2
#10614246	2
#10614243	2
#10601546	2
#10601545	2
#10601543	2
#10601542	2
#10600644	2
#10600643	2
#10600524	2
C₂×#64677	2
#17830	5