Subgroups — #12005235

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3951	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3950	C₂	1	1	yes	maximal, characteristic
4	C₂×#64774	C₂	1	2	yes	maximal
5	#10602374	C₂	1	2	yes	maximal
6	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
7	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₅×#117	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₅	C₂²	1	2	yes	—
10	C₂²×#681	C₂²	1	2	yes	—
11	C₅×#405	—	2	2	no	—
12	C₅×#405	C₄	1	4	yes	complemented
13	C₂×C₅×#97	—	2	1	no	—
14	C₂×C₄×C₅×C₈	—	2	1	no	—
15	C₂×#3951	—	2	2	no	—
16	C₂×#3951	—	2	2	no	—
17	C₂×#3951	C₄	1	4	yes	complemented
18	C₂×#3950	—	2	2	no	—
19	C₂×#3950	—	2	1	no	—
20	C₂×#3950	—	2	1	no	—
21	C₂×#3950	C₄	1	4	yes	complemented
22	#64774	—	2	4	no	—
23	#64749	—	2	4	no	—
24	#10870	—	5	1	no	maximal, Sylow
25	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂³×Dic₅	—	2	2	no	—
27	C₂×C₅×M₁₆	—	2	1	no	—
28	C₂×C₅×M₁₆	—	2	1	no	—
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₅×M₁₆	D₄	1	2	yes	—
32	C₂×C₅×M₁₆	Q₈	1	2	yes	—
33	C₂²×C₅×C₈	—	2	1	no	—
34	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₂²×C₅×C₈	D₄	1	2	yes	—
38	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	D₄	1	2	yes	—
41	C₂²×C₅×C₈	Q₈	1	2	yes	—
42	C₅×#117	—	2	1	no	—
43	C₅×#117	—	2	1	no	—
44	C₅×#117	C₂×C₄	1	2	yes	—
45	C₅×#117	Q₈	1	2	yes	—
46	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
47	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₄²×C₅	—	2	1	no	—
49	C₂×C₄⋊Dic₅	—	2	2	no	—
50	C₂×C₄⋊Dic₅	—	2	2	no	—
51	C₂×C₄⋊Dic₅	—	2	2	no	—
52	C₂×C₄⋊Dic₅	—	2	2	no	—
53	C₂×C₄⋊Dic₅	—	2	2	no	—
54	C₂×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
55	C₂×#681	—	2	2	no	—
56	C₂×#681	—	2	2	no	—
57	C₂×#681	—	2	2	no	—
58	C₂×#681	—	2	2	no	—
59	C₂×#681	—	2	2	no	—
60	C₂×#681	C₂×C₄	1	4	yes	—
61	C₂²×#168	—	2	2	no	—
62	C₅×#97	—	2	4	no	—
63	C₄×C₅×C₈	—	2	4	no	—
64	#3951	—	2	8	no	—
65	#3950	—	2	4	no	—
66	#3950	—	2	4	no	—
67	C₂²×#108	—	5	1	no	—
68	C₂²×#107	—	5	1	no	—
69	C₂×#405	D₅	1	1	yes	characteristic
70	C₂×#343	—	5	2	no	—
71	#1736	—	5	2	no	—
72	C₂⁴×C₅	#41	1	1	yes	characteristic
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₅	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅	#41	1	1	yes	characteristic
87	C₂²×C₄×C₅	#41	1	1	yes	characteristic
88	C₂²×Dic₅	—	2	4	no	—
89	C₂²×Dic₅	—	4	2	no	—
90	C₂²×Dic₅	—	4	2	no	—
91	C₂²×Dic₅	—	8	4	no	—
92	C₅×M₁₆	—	2	2	no	—
93	C₅×M₁₆	—	2	2	no	—
94	C₅×M₁₆	—	2	2	no	—
95	C₅×M₁₆	C₄⋊C₄	1	4	yes	—
96	C₂×C₅×C₈	—	2	2	no	—
97	C₂×C₅×C₈	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	C₄²	1	4	yes	—
100	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
101	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
102	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
103	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
105	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
106	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
107	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
108	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
109	C₅×C₄⋊C₄	—	2	2	no	—
110	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
111	C₅×C₂²⋊C₄	—	2	2	no	—
112	C₅×C₂²⋊C₄	—	2	2	no	—
113	C₄²×C₅	—	2	2	no	—
114	C₄²×C₅	—	2	2	no	—
115	C₄⋊Dic₅	—	2	4	no	—
116	C₄⋊Dic₅	—	2	4	no	—
117	C₄⋊Dic₅	—	4	2	no	—
118	C₄⋊Dic₅	—	4	2	no	—
119	#681	—	2	4	no	—
120	#681	—	2	4	no	—
121	#681	—	4	2	no	—
122	#681	—	4	2	no	—
123	C₂×#168	—	2	4	no	—
124	C₂×#168	—	4	2	no	—
125	C₂×#168	—	4	2	no	—
126	C₂²×M₁₆	—	5	2	no	—
127	C₂²×M₁₆	C₂×D₅	1	1	yes	characteristic
128	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
129	C₂×#117	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	—	5	2	no	—
131	C₂×#108	—	5	4	no	—
132	C₂×#108	—	10	2	no	—
133	C₂×#108	—	10	2	no	—
134	C₂×#107	—	5	4	no	—
135	C₂×#107	—	10	2	no	—
136	C₂×#107	—	10	1	no	—
137	C₂×#107	—	10	1	no	—
138	#405	—	2	2	no	—
139	#405	Dic₅	1	4	yes	complemented
140	C₂×#97	—	2	1	no	—
141	C₂×C₄×C₈	—	2	1	no	—
142	#343	—	10	4	no	—
143	#340	—	10	4	no	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	#117	1	1	yes	characteristic
147	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
149	C₂³×C₅	#121	1	1	yes	characteristic
150	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂³×C₅	#124	1	1	yes	characteristic
152	C₂³×C₅	#125	1	1	yes	characteristic
153	C₂×C₄×C₅	—	2	4	no	—
154	C₂×C₄×C₅	—	4	2	no	—
155	C₂×C₄×C₅	—	4	2	no	—
156	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅	#117	1	1	yes	characteristic
166	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅	#121	1	1	yes	characteristic
173	C₂×C₄×C₅	#121	1	1	yes	characteristic
174	C₂×C₄×C₅	#121	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅	#124	1	1	yes	characteristic
179	C₂×C₄×C₅	#125	1	1	yes	characteristic
180	C₂×C₄×C₅	#127	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
184	C₂×Dic₅	—	4	4	no	—
185	C₂×Dic₅	—	8	4	no	—
186	C₂×Dic₅	—	8	4	no	—
187	C₂×Dic₅	—	8	4	no	—
188	C₅×C₈	—	2	4	no	—
189	C₅×C₈	#95	1	4	yes	—
190	C₅×C₈	#95	1	4	yes	—
191	#168	—	4	4	no	—
192	C₂³×C₄	—	10	2	no	—
193	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
194	C₂×M₁₆	—	2	1	no	—
195	C₂×M₁₆	—	2	1	no	—
196	C₂×M₁₆	—	2	1	no	—
197	C₂×M₁₆	—	5	4	no	—
198	C₂×M₁₆	—	10	2	no	—
199	C₂×M₁₆	—	10	2	no	—
200	C₂×M₁₆	—	10	2	no	—
201	C₂×M₁₆	—	10	2	no	—
202	C₂×M₁₆	—	10	2	no	—
203	C₂×M₁₆	Dic₁₀	1	2	yes	—
204	C₂×M₁₆	D₂₀	1	2	yes	—
205	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
206	C₂²×C₈	—	2	1	no	—
207	C₂²×C₈	—	10	2	no	—
208	C₂²×C₈	Dic₁₀	1	2	yes	—
209	C₂²×C₈	C₄×D₅	1	2	yes	—
210	C₂²×C₈	C₄×D₅	1	2	yes	—
211	C₂²×C₈	D₂₀	1	2	yes	—
212	C₂²×C₈	C₂×Dic₅	1	2	yes	—
213	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
214	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
215	C₂²×C₈	C₂²⋊D₅	1	2	yes	—
216	#117	—	2	1	no	—
217	#117	—	2	1	no	—
218	#117	Dic₁₀	1	2	yes	—
219	#117	C₂×Dic₅	1	2	yes	—
220	C₂×C₄⋊C₄	—	5	4	no	—
221	C₂×C₄⋊C₄	—	10	2	no	—
222	C₂×C₄⋊C₄	—	10	2	no	—
223	C₂×C₄⋊C₄	—	10	2	no	—
224	C₂×C₄⋊C₄	—	10	2	no	—
225	C₂×C₄⋊C₄	—	10	2	no	—
226	C₂×C₄⋊C₄	D₂₀	1	2	yes	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₄²	—	2	1	no	—
229	#108	—	10	8	no	—
230	#107	—	10	4	no	—
231	#107	—	10	4	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	1	no	—
242	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
243	C₂²×C₅	#380	1	1	yes	characteristic
244	C₂²×C₅	#382	1	1	yes	characteristic
245	C₂²×C₅	#389	1	1	yes	characteristic
246	C₂²×C₅	#389	1	1	yes	characteristic
247	C₂²×C₅	#390	1	1	yes	characteristic
248	C₂²×C₅	#391	1	1	yes	characteristic
249	C₂²×C₅	#472	1	2	yes	—
250	C₂²×C₅	#473	1	2	yes	—
251	C₄×C₅	—	4	4	no	—
252	C₄×C₅	C₂×#95	1	1	yes	characteristic
253	C₄×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
254	C₄×C₅	#380	1	1	yes	characteristic
255	C₄×C₅	#384	1	1	yes	characteristic
256	C₄×C₅	#389	1	1	yes	characteristic
257	C₄×C₅	#389	1	1	yes	characteristic
258	C₄×C₅	#390	1	1	yes	characteristic
259	C₄×C₅	#391	1	1	yes	characteristic
260	Dic₅	—	8	4	no	—
261	C₂⁴	#709	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	10	4	no	—
264	C₂²×C₄	—	20	2	no	—
265	C₂²×C₄	—	20	2	no	—
266	C₂²×C₄	—	40	4	no	—
267	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
269	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
275	C₂²×C₄	#709	1	1	yes	characteristic
276	C₂²×C₄	#709	1	1	yes	characteristic
277	C₂²×C₄	#709	1	1	yes	characteristic
278	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
281	M₁₆	—	2	2	no	—
282	M₁₆	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	10	4	no	—
285	M₁₆	—	10	4	no	—
286	M₁₆	—	20	2	no	—
287	M₁₆	—	20	2	no	—
288	M₁₆	C₄⋊Dic₅	1	4	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	10	4	no	—
293	C₂×C₈	—	20	2	no	—
294	C₂×C₈	—	20	2	no	—
295	C₂×C₈	C₄×Dic₅	1	4	yes	—
296	C₂×C₈	#683	1	4	yes	—
297	C₂×C₈	#683	1	2	yes	—
298	C₂×C₈	#683	1	2	yes	—
299	C₂×C₈	C₄⋊Dic₅	1	4	yes	—
300	C₂×C₈	#685	1	2	yes	—
301	C₂×C₈	#685	1	2	yes	—
302	C₂×C₈	#685	1	4	yes	—
303	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
304	C₂×C₈	C₂²⋊Dic₅	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	10	4	no	—
307	C₄⋊C₄	—	10	4	no	—
308	C₄⋊C₄	—	20	2	no	—
309	C₄⋊C₄	—	20	2	no	—
310	C₄⋊C₄	C₄⋊Dic₅	1	4	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	2	1	no	—
318	C₂×C₅	—	2	1	no	—
319	C₂×C₅	C₄⋊#95	1	1	yes	characteristic
320	C₂×C₅	#1816	1	2	yes	—
321	C₂×C₅	#1952	1	2	yes	—
322	C₂×C₅	#1978	1	1	yes	characteristic
323	C₂×C₅	#1979	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	C₄×Dic₁₀	1	1	yes	characteristic
327	C₂³	#4016	1	1	yes	characteristic
328	C₂³	C₄×D₂₀	1	1	yes	characteristic
329	C₂³	#4021	1	1	yes	characteristic
330	C₂³	#4070	1	1	yes	characteristic
331	C₂³	#4072	1	1	yes	characteristic
332	C₂³	#4076	1	1	yes	characteristic
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	20	4	no	—
337	C₂×C₄	—	40	4	no	—
338	C₂×C₄	—	40	4	no	—
339	C₂×C₄	—	40	4	no	—
340	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
341	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
342	C₂×C₄	C₄×Dic₁₀	1	1	yes	characteristic
343	C₂×C₄	#4015	1	1	yes	characteristic
344	C₂×C₄	#4015	1	1	yes	characteristic
345	C₂×C₄	#4015	1	1	yes	characteristic
346	C₂×C₄	#4016	1	1	yes	characteristic
347	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
348	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
349	C₂×C₄	C₄×D₂₀	1	1	yes	characteristic
350	C₂×C₄	#4020	1	1	yes	characteristic
351	C₂×C₄	#4021	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
353	C₂×C₄	C₂×#683	1	1	yes	characteristic
354	C₂×C₄	C₂×#683	1	1	yes	characteristic
355	C₂×C₄	#4070	1	1	yes	characteristic
356	C₂×C₄	#4070	1	1	yes	characteristic
357	C₂×C₄	#4070	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
361	C₂×C₄	#4072	1	1	yes	characteristic
362	C₂×C₄	C₂×#685	1	1	yes	characteristic
363	C₂×C₄	C₂×#685	1	1	yes	characteristic
364	C₂×C₄	#4076	1	1	yes	characteristic
365	C₂×C₄	#4076	1	1	yes	characteristic
366	C₂×C₄	#4076	1	1	yes	characteristic
367	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
368	C₈	—	2	4	no	—
369	C₈	—	20	4	no	—
370	C₈	#3963	1	4	yes	—
371	C₈	#3963	1	4	yes	—
372	C₅	#10870	1	1	yes	characteristic, complemented, Sylow
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	#65217	1	1	yes	characteristic
382	C₂²	#65217	1	1	yes	characteristic
383	C₂²	#65218	1	1	yes	characteristic
384	C₂²	C₄×C₄⋊Dic₅	1	1	yes	characteristic
385	C₂²	#65225	1	1	yes	characteristic
386	C₂²	#65228	1	1	yes	characteristic
387	C₂²	#65431	1	2	yes	—
388	C₂²	#65432	1	2	yes	—
389	C₂²	#65501	1	1	yes	characteristic
390	C₄	—	4	4	no	—
391	C₄	—	40	4	no	—
392	C₄	#65217	1	1	yes	characteristic
393	C₄	#65217	1	1	yes	characteristic
394	C₄	#65218	1	1	yes	characteristic
395	C₄	C₄×C₄⋊Dic₅	1	1	yes	characteristic
396	C₄	#65224	1	1	yes	characteristic
397	C₄	#65228	1	1	yes	characteristic
398	C₄	C₂×#3963	1	1	yes	characteristic
399	C₄	#65501	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#10600687	1	2	yes	—
405	C₂	#10600696	1	1	yes	characteristic
406	C₂	#10600697	1	1	yes	characteristic
407	C₂	#10602328	1	1	yes	characteristic
408	C₂	#10602809	1	2	yes	—

	subgroup	G/H
center	C₂³	#4076
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅
Fitting	C₂×C₅×#405	C₂
socle	C₂³×C₅	#121
prime radical	C₂⁴×C₅	#41
cosocle	C₂³×C₄×C₅	C₂³
hypercenter	C₂×#405	D₅
hypocenter	C₅	#10870
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
12. C₅×#405	C₄	semidirect
17. C₂×#3951	C₄	semidirect
21. C₂×#3950	C₄	semidirect
139. #405	Dic₅	semidirect
372. C₅	#10870	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#405	2
C₂²×#3951	2
C₂²×#3950	2
C₂×#64774	2
#10602374	2
#10870	5