Subgroups — #12064941

Order 1280.

772 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
2	#10613780	C₂	1	1	yes	maximal, characteristic
3	C₂×#65214	C₂	1	1	yes	maximal, characteristic
4	#10601536	C₂	1	4	yes	maximal, complemented
5	#10601535	C₂	1	2	yes	maximal, complemented
6	#10601533	C₂	1	2	yes	maximal, complemented
7	#10600519	C₂	1	2	yes	maximal, complemented
8	#10600517	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×#431	C₄	1	2	yes	—
11	C₅×#431	C₄	1	2	yes	—
12	C₅×#431	C₂²	1	1	yes	characteristic
13	C₅×#431	C₂²	1	1	yes	characteristic
14	C₅×#431	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
18	#65496	C₄	1	2	yes	—
19	C₂×C₂²⋊#168	C₄	1	2	yes	—
20	#65215	C₄	1	2	yes	—
21	#65215	C₄	1	2	yes	—
22	#65214	C₄	1	2	yes	—
23	#65214	C₄	1	2	yes	—
24	#65214	C₂²	1	2	yes	—
25	#65214	C₂²	1	1	yes	characteristic
26	#65214	C₂²	1	1	yes	characteristic
27	#65214	C₂²	1	2	yes	—
28	#65214	C₂²	1	2	yes	—
29	#65213	C₄	1	2	yes	—
30	C₂×C₄⋊#168	C₄	1	2	yes	—
31	C₄×#681	C₂²	1	2	yes	—
32	C₂×C₄×#168	C₂²	1	2	yes	—
33	#64675	C₂²	1	4	yes	complemented
34	#64674	C₂²	1	4	yes	complemented
35	#64674	C₂²	1	4	yes	complemented
36	C₈×#168	C₂²	1	4	yes	complemented
37	#17325	—	5	1	no	maximal, Sylow
38	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₂×#681	C₂×C₄	1	4	yes	—
55	C₂²×#168	C₂×C₄	1	4	yes	—
56	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
58	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
59	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
60	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
61	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
62	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
63	C₄×C₅×C₈	C₂³	1	2	yes	—
64	C₄×C₅×C₈	C₂³	1	2	yes	—
65	C₂²⋊#168	C₂×C₄	1	4	yes	—
66	C₂²⋊#168	C₂×C₄	1	2	yes	—
67	C₂²⋊#168	C₂×C₄	1	2	yes	—
68	C₂²⋊#168	C₂×C₄	1	4	yes	—
69	C₂²⋊#168	C₂×C₄	1	4	yes	—
70	C₄⋊#168	C₂×C₄	1	4	yes	—
71	C₄⋊#168	C₂×C₄	1	2	yes	—
72	C₄⋊#168	C₂×C₄	1	2	yes	—
73	C₄⋊#168	C₂×C₄	1	4	yes	—
74	C₄⋊#168	C₂×C₄	1	4	yes	—
75	#3935	C₂×C₄	1	4	yes	—
76	C₄×#168	C₂×C₄	1	4	yes	—
77	C₄×#168	C₂³	1	2	yes	—
78	C₄×#168	C₂³	1	4	yes	—
79	C₄×#168	C₂³	1	2	yes	—
80	#2920	—	5	1	no	—
81	C₂×#431	—	5	1	no	—
82	C₂×#431	D₅	1	1	yes	characteristic
83	#1453	—	5	4	no	—
84	#1452	—	5	2	no	—
85	#1452	—	5	2	no	—
86	#1450	—	5	2	no	—
87	#1450	—	5	2	no	—
88	C₂⁴×C₅	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	2	4	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	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	C₂×C₅×C₈	—	2	8	no	—
111	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
113	C₄²×C₅	C₄²	1	1	yes	characteristic
114	C₄²×C₅	C₄²	1	1	yes	characteristic
115	C₄²×C₅	C₄²	1	1	yes	characteristic
116	C₄²×C₅	C₄²	1	1	yes	characteristic
117	C₄²×C₅	C₄²	1	1	yes	characteristic
118	C₄²×C₅	C₄²	1	1	yes	characteristic
119	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₅	C₂⁴	1	1	yes	characteristic
129	#681	—	4	4	no	—
130	C₂×#168	—	2	8	no	—
131	C₂×#168	C₂²×C₄	1	4	yes	—
132	C₂×#168	C₂²×C₄	1	4	yes	—
133	C₂×#168	C₂²×C₄	1	8	yes	—
134	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
135	#432	—	5	2	no	—
136	#432	—	5	2	no	—
137	#431	—	5	2	no	—
138	#431	—	5	2	no	—
139	#431	—	5	1	no	—
140	#431	—	5	1	no	—
141	#431	—	5	2	no	—
142	#431	—	5	2	no	—
143	#431	—	5	2	no	—
144	#431	Dic₅	1	2	yes	—
145	#431	Dic₅	1	2	yes	—
146	#431	C₂×D₅	1	1	yes	characteristic
147	#431	C₂×D₅	1	1	yes	characteristic
148	#431	C₂×D₅	1	2	yes	—
149	#423	—	5	2	no	—
150	C₂×C₄⋊C₈	—	5	2	no	—
151	C₂×C₄⋊C₈	Dic₅	1	2	yes	—
152	#407	—	5	2	no	—
153	C₂×C₂²⋊C₈	—	5	2	no	—
154	C₂×C₂²⋊C₈	Dic₅	1	2	yes	—
155	C₄×M₁₆	—	5	2	no	—
156	C₂×C₄×C₈	—	5	2	no	—
157	C₂×C₄×C₈	C₂×D₅	1	2	yes	—
158	#322	—	5	4	no	—
159	#322	—	5	4	no	—
160	#322	—	5	4	no	—
161	C₈²	—	5	4	no	—
162	C₂³×C₅	—	2	2	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	4	1	no	—
165	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
166	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
167	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₅	#131	1	4	yes	—
194	C₂×C₄×C₅	#131	1	4	yes	—
195	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
198	C₅×C₈	—	2	4	no	—
199	C₅×C₈	—	2	4	no	—
200	#168	—	2	4	no	—
201	#168	—	2	4	no	—
202	#168	—	2	8	no	—
203	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
204	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
205	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
206	C₂×M₁₆	—	5	4	no	—
207	C₂²×C₈	—	5	4	no	—
208	C₂²×C₈	C₂×Dic₅	1	4	yes	—
209	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
210	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
211	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
212	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
215	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
217	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
218	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
219	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
220	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
221	C₄⋊C₈	—	5	2	no	—
222	C₄⋊C₈	—	5	2	no	—
223	C₄⋊C₈	—	5	4	no	—
224	C₄⋊C₈	—	5	4	no	—
225	C₄⋊C₈	—	5	4	no	—
226	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
227	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
228	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
229	C₂²⋊C₈	—	5	2	no	—
230	C₂²⋊C₈	—	5	2	no	—
231	C₂²⋊C₈	—	5	4	no	—
232	C₂²⋊C₈	—	5	4	no	—
233	C₂²⋊C₈	—	5	4	no	—
234	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
235	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
236	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
237	#97	—	5	4	no	—
238	C₄×C₈	—	5	4	no	—
239	C₄×C₈	—	5	2	no	—
240	C₄×C₈	—	5	4	no	—
241	C₄×C₈	—	5	2	no	—
242	C₄×C₈	C₂×Dic₅	1	4	yes	—
243	C₄×C₈	C₂²×D₅	1	2	yes	—
244	C₄×C₈	C₂²×D₅	1	2	yes	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	#405	1	2	yes	—
254	C₂²×C₅	#405	1	2	yes	—
255	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	2	1	no	—
263	C₄×C₅	#405	1	2	yes	—
264	C₄×C₅	#405	1	2	yes	—
265	C₄×C₅	C₂×#131	1	2	yes	—
266	C₄×C₅	C₂×#131	1	2	yes	—
267	C₄×C₅	#568	1	2	yes	—
268	C₂⁴	C₄×Dic₅	1	1	yes	characteristic
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
273	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
275	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
276	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
277	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
278	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
279	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
290	M₁₆	—	20	4	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	5	4	no	—
293	C₂×C₈	—	5	4	no	—
294	C₂×C₈	—	5	8	no	—
295	C₂×C₈	—	10	8	no	—
296	C₂×C₈	C₂²×Dic₅	1	4	yes	—
297	C₂×C₈	C₂²×Dic₅	1	4	yes	—
298	C₄²	C₄×Dic₅	1	1	yes	characteristic
299	C₄²	C₄×Dic₅	1	1	yes	characteristic
300	C₄²	C₄×Dic₅	1	1	yes	characteristic
301	C₄²	C₄×Dic₅	1	1	yes	characteristic
302	C₄²	C₄×Dic₅	1	1	yes	characteristic
303	C₄²	C₄×Dic₅	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
305	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
306	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
307	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
310	C₄²	C₂²×Dic₅	1	1	yes	characteristic
311	C₄²	C₂²×Dic₅	1	1	yes	characteristic
312	C₄²	C₂²×Dic₅	1	1	yes	characteristic
313	C₄²	C₂³×D₅	1	1	yes	characteristic
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	4	1	no	—
317	C₂×C₅	C₂×#405	1	1	yes	characteristic
318	C₂×C₅	C₂×#405	1	1	yes	characteristic
319	C₂×C₅	#2873	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
324	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
325	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	#4047	1	4	yes	—
343	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
352	C₂×C₄	#4094	1	4	yes	—
353	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
355	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
356	C₈	—	2	4	no	—
357	C₈	—	2	4	no	—
358	C₈	—	10	4	no	—
359	C₈	—	10	4	no	—
360	C₈	—	10	8	no	—
361	C₅	#17325	1	1	yes	characteristic, complemented, Sylow
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#65286	1	2	yes	—
371	C₂²	#65390	1	2	yes	—
372	C₂²	C₂²×C₄×Dic₅	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	#65286	1	2	yes	—
381	C₄	#65390	1	2	yes	—
382	C₄	C₂×#4047	1	2	yes	—
383	C₄	#66079	1	2	yes	—
384	C₄	C₂×#4094	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	C₂×#65286	1	1	yes	characteristic
389	C₂	C₂×#65390	1	1	yes	characteristic
390	C₂	#10615478	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₅
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₂×C₅×#431	C₂
prime radical	C₂⁴×C₅	C₄²
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₂×#431	D₅
hypocenter	C₅	#17325
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
4. #10601536	C₂	semidirect
5. #10601535	C₂	semidirect
6. #10601533	C₂	semidirect
7. #10600519	C₂	semidirect
8. #10600517	C₂	semidirect
33. #64675	C₂²	semidirect
34. #64674	C₂²	semidirect
35. #64674	C₂²	semidirect
36. C₈×#168	C₂²	semidirect
361. C₅	#17325	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#431	2
#10613780	2
C₂×#65214	2
#10601536	2
#10601535	2
#10601533	2
#10600519	2
#10600517	2
#17325	5