Subgroups — C₂×#10598235 #11988979

Order 1280.

722 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	C₂²×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#681	C₂	1	1	yes	maximal, characteristic
4	#10598235	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₂²×#681	C₄	1	2	yes	—
7	C₂³×#168	C₄	1	2	yes	—
8	C₅×#431	—	2	1	no	—
9	C₅×#431	—	2	1	no	—
10	C₅×#431	C₄	1	2	yes	—
11	C₅×#431	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	—	2	1	no	—
13	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
14	C₂×C₄×C₅×C₈	—	2	1	no	—
15	C₂×C₄⋊#168	—	2	1	no	—
16	C₂×C₄⋊#168	—	2	1	no	—
17	C₂×C₄⋊#168	—	2	1	no	—
18	C₂×C₄⋊#168	—	2	1	no	—
19	C₂×C₄⋊#168	C₄	1	2	yes	—
20	C₂×C₄⋊#168	C₂²	1	2	yes	—
21	C₄×#681	—	2	1	no	—
22	C₄×#681	—	2	1	no	—
23	C₄×#681	C₄	1	2	yes	—
24	C₄×#681	C₂²	1	2	yes	—
25	C₂×#3935	—	2	1	no	—
26	C₂×C₄×#168	—	2	1	no	—
27	C₂×#1283	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	—	2	2	no	—
32	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
44	C₂×#681	—	2	2	no	—
45	C₂×#681	—	2	4	no	—
46	C₂×#681	C₈	1	8	yes	complemented
47	C₂×#681	C₂×C₄	1	4	yes	—
48	C₂²×#168	—	2	2	no	—
49	C₂²×#168	—	2	2	no	—
50	C₂²×#168	—	2	2	no	—
51	C₂²×#168	—	4	4	no	—
52	C₂²×#168	C₂×C₄	1	4	yes	—
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	—	2	2	no	—
55	C₅×C₂²⋊C₈	—	2	2	no	—
56	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
57	C₄×C₅×C₈	—	2	2	no	—
58	C₄×C₅×C₈	—	2	2	no	—
59	C₄⋊#168	—	2	2	no	—
60	C₄⋊#168	—	2	2	no	—
61	C₄⋊#168	—	2	2	no	—
62	C₄⋊#168	—	2	2	no	—
63	#3935	—	2	2	no	—
64	#3935	—	2	2	no	—
65	C₄×#168	—	2	2	no	—
66	C₄×#168	—	2	2	no	—
67	C₂×#431	D₅	1	1	yes	characteristic
68	C₂²×C₄⋊C₈	—	5	1	no	—
69	C₂×C₄×M₁₆	—	5	1	no	—
70	#1283	—	5	4	no	—
71	C₂⁴×C₅	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₅	—	2	2	no	—
73	C₂²×C₄×C₅	—	2	2	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₅	M₁₆	1	4	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₅×C₈	—	2	4	no	—
96	C₂×C₅×C₈	—	4	4	no	—
97	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
113	#681	—	2	8	no	—
114	#681	—	2	4	no	—
115	#681	C₂×C₈	1	8	yes	complemented
116	C₂×#168	—	2	8	no	—
117	C₂×#168	—	2	4	no	—
118	C₂×#168	—	2	4	no	—
119	C₂×#168	—	4	4	no	—
120	C₂×#168	—	4	4	no	—
121	C₂×#168	—	4	4	no	—
122	C₂²×M₁₆	—	5	2	no	—
123	C₂³×C₈	—	5	2	no	—
124	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
125	#431	—	2	1	no	—
126	#431	—	2	1	no	—
127	#431	Dic₅	1	2	yes	—
128	#431	C₂×D₅	1	2	yes	—
129	C₂×C₄⋊C₈	—	2	1	no	—
130	C₂×C₄⋊C₈	—	5	2	no	—
131	C₂×C₄⋊C₈	—	5	2	no	—
132	C₂×C₄⋊C₈	—	10	1	no	—
133	C₂×C₄⋊C₈	—	10	1	no	—
134	C₂×C₄⋊C₈	—	10	1	no	—
135	C₂×C₄⋊C₈	—	10	1	no	—
136	C₂×C₂²⋊C₈	Dic₅	1	2	yes	—
137	C₄×M₁₆	—	5	2	no	—
138	C₄×M₁₆	—	5	2	no	—
139	C₄×M₁₆	—	10	1	no	—
140	C₄×M₁₆	—	10	1	no	—
141	C₂×#97	—	10	1	no	—
142	C₂×C₄×C₈	—	2	1	no	—
143	C₂×C₄×C₈	—	10	1	no	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	#95	1	1	yes	characteristic
147	C₂³×C₅	#95	1	1	yes	characteristic
148	C₂³×C₅	C₄×C₈	1	2	yes	—
149	C₂³×C₅	#97	1	2	yes	—
150	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	4	1	no	—
161	C₂×C₄×C₅	—	4	1	no	—
162	C₂×C₄×C₅	—	4	1	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	#95	1	1	yes	characteristic
165	C₂×C₄×C₅	#95	1	1	yes	characteristic
166	C₂×C₄×C₅	#95	1	1	yes	characteristic
167	C₂×C₄×C₅	#95	1	1	yes	characteristic
168	C₂×C₄×C₅	#95	1	1	yes	characteristic
169	C₂×C₄×C₅	#95	1	1	yes	characteristic
170	C₂×C₄×C₅	C₄×C₈	1	2	yes	—
171	C₂×C₄×C₅	#97	1	2	yes	—
172	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
173	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
174	C₂×C₄×C₅	#100	1	2	yes	—
175	C₂×C₄×C₅	#101	1	2	yes	—
176	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
177	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
178	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
186	C₅×C₈	—	4	4	no	—
187	#168	—	2	8	no	—
188	#168	—	4	4	no	—
189	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
190	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
191	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
192	C₂×M₁₆	—	5	8	no	—
193	C₂×M₁₆	—	5	4	no	—
194	C₂×M₁₆	—	10	4	no	—
195	C₂×M₁₆	—	10	2	no	—
196	C₂²×C₈	—	2	2	no	—
197	C₂²×C₈	—	5	4	no	—
198	C₂²×C₈	—	10	2	no	—
199	C₂²×C₈	—	10	2	no	—
200	C₂²×C₈	—	10	2	no	—
201	C₂²×C₈	—	20	4	no	—
202	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
203	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
204	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
205	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
206	C₂×C₄²	D₂₀	1	1	yes	characteristic
207	C₂×C₄²	D₂₀	1	1	yes	characteristic
208	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
209	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
210	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
211	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
212	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
213	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
214	C₄⋊C₈	—	2	2	no	—
215	C₄⋊C₈	—	2	2	no	—
216	C₄⋊C₈	—	10	2	no	—
217	C₄⋊C₈	—	10	2	no	—
218	C₄⋊C₈	—	10	2	no	—
219	C₄⋊C₈	—	10	2	no	—
220	C₂²⋊C₈	—	2	2	no	—
221	C₂²⋊C₈	C₂×Dic₅	1	4	yes	—
222	#97	—	10	2	no	—
223	#97	—	10	2	no	—
224	C₄×C₈	—	2	2	no	—
225	C₄×C₈	—	2	2	no	—
226	C₄×C₈	—	10	2	no	—
227	C₄×C₈	—	10	2	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	—	2	4	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	#336	1	2	yes	—
235	C₂²×C₅	#336	1	2	yes	—
236	C₂²×C₅	#343	1	2	yes	—
237	C₂²×C₅	#344	1	2	yes	—
238	C₂²×C₅	C₂×#95	1	1	yes	characteristic
239	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
240	C₂²×C₅	C₂×#97	1	1	yes	characteristic
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	#336	1	2	yes	—
248	C₄×C₅	#336	1	2	yes	—
249	C₄×C₅	#343	1	2	yes	—
250	C₄×C₅	C₂×C₂²⋊C₈	1	2	yes	—
251	C₄×C₅	C₂×#100	1	1	yes	characteristic
252	C₄×C₅	C₂×#101	1	1	yes	characteristic
253	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
254	C₂⁴	C₄×Dic₅	1	1	yes	characteristic
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	C₈×D₅	1	4	yes	—
259	C₂²×C₄	#676	1	4	yes	—
260	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
261	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
263	C₂²×C₄	#683	1	1	yes	characteristic
264	C₂²×C₄	#683	1	1	yes	characteristic
265	C₂²×C₄	#683	1	1	yes	characteristic
266	C₂²×C₄	#683	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
269	C₂²×C₄	#685	1	1	yes	characteristic
270	C₂²×C₄	#685	1	1	yes	characteristic
271	C₂²×C₄	#685	1	1	yes	characteristic
272	C₂²×C₄	#685	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
278	M₁₆	—	5	8	no	—
279	M₁₆	—	10	8	no	—
280	M₁₆	—	10	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	—	10	8	no	—
284	C₂×C₈	—	10	4	no	—
285	C₂×C₈	—	10	4	no	—
286	C₂×C₈	—	20	4	no	—
287	C₂×C₈	—	20	4	no	—
288	C₂×C₈	—	20	4	no	—
289	C₄²	#683	1	1	yes	characteristic
290	C₄²	#683	1	1	yes	characteristic
291	C₄²	#683	1	1	yes	characteristic
292	C₄²	#683	1	1	yes	characteristic
293	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
294	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
295	C₄²	#685	1	1	yes	characteristic
296	C₄²	#685	1	1	yes	characteristic
297	C₄²	#685	1	1	yes	characteristic
298	C₄²	#685	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
300	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
301	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
302	C₄²	C₂×D₂₀	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
305	C₂×C₅	—	2	2	no	—
306	C₂×C₅	—	2	1	no	—
307	C₂×C₅	—	2	1	no	—
308	C₂×C₅	#1283	1	4	yes	complemented
309	C₂×C₅	C₂×#336	1	1	yes	characteristic
310	C₂×C₅	C₂×#343	1	1	yes	characteristic
311	C₂×C₅	C₂×#344	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	C₈×Dic₅	1	2	yes	—
315	C₂³	#3947	1	2	yes	—
316	C₂³	#3963	1	1	yes	characteristic
317	C₂³	#3963	1	1	yes	characteristic
318	C₂³	C₂×C₄×Dic₅	1	1	yes	characteristic
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₈×Dic₅	1	2	yes	—
333	C₂×C₄	#3946	1	4	yes	—
334	C₂×C₄	#3946	1	4	yes	—
335	C₂×C₄	#3947	1	2	yes	—
336	C₂×C₄	#3952	1	4	yes	—
337	C₂×C₄	#3952	1	4	yes	—
338	C₂×C₄	#3955	1	2	yes	—
339	C₂×C₄	#3956	1	2	yes	—
340	C₂×C₄	#3963	1	1	yes	characteristic
341	C₂×C₄	#3963	1	1	yes	characteristic
342	C₂×C₄	#3963	1	1	yes	characteristic
343	C₂×C₄	#3963	1	1	yes	characteristic
344	C₂×C₄	#3963	1	1	yes	characteristic
345	C₂×C₄	#3963	1	1	yes	characteristic
346	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
347	C₂×C₄	C₂×#676	1	2	yes	—
348	C₂×C₄	C₂×#683	1	1	yes	characteristic
349	C₂×C₄	C₂×#683	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
351	C₂×C₄	C₂×#685	1	1	yes	characteristic
352	C₂×C₄	C₂×#685	1	1	yes	characteristic
353	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
354	C₈	—	4	4	no	—
355	C₈	—	10	8	no	—
356	C₈	—	20	4	no	—
357	C₅	C₂×#1283	1	1	yes	characteristic, complemented, Sylow
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	#64753	1	2	yes	—
365	C₂²	#64770	1	2	yes	—
366	C₂²	#64770	1	2	yes	—
367	C₂²	#64774	1	2	yes	—
368	C₂²	C₂×C₈×Dic₅	1	1	yes	characteristic
369	C₂²	C₂×#3947	1	1	yes	characteristic
370	C₂²	C₂×#3963	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	#64770	1	2	yes	—
378	C₄	#64770	1	2	yes	—
379	C₄	#64774	1	2	yes	—
380	C₄	C₂×#3946	1	2	yes	—
381	C₄	C₂×#3952	1	2	yes	—
382	C₄	C₂×#3955	1	1	yes	characteristic
383	C₄	C₂×#3956	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	#10598235	1	4	yes	direct product factor
388	C₂	C₂×#64753	1	1	yes	characteristic
389	C₂	C₂×#64770	1	1	yes	characteristic
390	C₂	C₂×#64774	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#685
commutator	C₂²×C₅	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#431	C₂
socle	C₂³×C₅	#95
prime radical	C₂⁴×C₅	C₄²
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#431	D₅
hypocenter	C₅	C₂×#1283
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
4. #10598235	C₂	direct (N × H)
46. C₂×#681	C₈	semidirect
115. #681	C₂×C₈	semidirect
308. C₂×C₅	#1283	semidirect
357. C₅	C₂×#1283	semidirect
387. C₂	#10598235	direct (N × H)

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
C₂²×C₄⋊#168	2
C₂×C₄×#681	2
#10598235	2
C₂×#1283	5

Subgroups — C2×#10598235 #11988979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10598235 #11988979