Subgroups — C₂×#10598227 #11988735

Order 1280.

974 conjugacy classes of subgroups.

The subgroup lattice has 396 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	C₂×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#65214	C₂	1	1	yes	maximal, characteristic
4	#10598227	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×Dic₅	—	2	1	no	—
7	C₂²×C₄×Dic₅	—	2	1	no	—
8	C₂²×C₄×Dic₅	C₄	1	2	yes	—
9	C₅×#431	—	2	1	no	—
10	C₅×#431	—	2	1	no	—
11	C₅×#431	C₄	1	2	yes	complemented
12	C₅×#431	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
14	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
15	C₂×C₄×C₅×C₈	—	2	1	no	—
16	C₂×C₂²⋊#168	—	2	1	no	—
17	C₄²×Dic₅	—	2	1	no	—
18	C₄²×Dic₅	—	2	1	no	—
19	C₄²×Dic₅	C₄	1	2	yes	—
20	C₄²×Dic₅	C₂²	1	2	yes	—
21	#65214	—	2	1	no	—
22	#65214	—	2	1	no	—
23	#65214	C₄	1	2	yes	complemented
24	#65214	C₂²	1	2	yes	—
25	C₂×C₄⋊#168	C₄	1	2	yes	complemented
26	C₂×C₄×#168	—	2	1	no	—
27	C₂×#1276	—	5	1	no	maximal, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂³×Dic₅	—	2	2	no	—
32	C₂²×C₅×C₈	—	2	2	no	—
33	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₄×Dic₅	—	2	8	no	—
46	C₂×C₄×Dic₅	—	2	8	no	—
47	C₂×C₄×Dic₅	—	2	2	no	—
48	C₂×C₄×Dic₅	—	2	2	no	—
49	C₂×C₄×Dic₅	—	2	2	no	—
50	C₂×C₄×Dic₅	—	2	4	no	—
51	C₂×C₄×Dic₅	—	2	2	no	—
52	C₂×C₄×Dic₅	—	2	2	no	—
53	C₂×C₄×Dic₅	C₈	1	8	yes	complemented
54	C₂×C₄×Dic₅	C₂×C₄	1	4	yes	—
55	C₂²×#168	—	2	2	no	—
56	C₅×C₄⋊C₈	—	2	2	no	—
57	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
58	C₅×C₂²⋊C₈	—	2	2	no	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₄×C₅×C₈	—	2	2	no	—
61	C₄×C₅×C₈	—	2	2	no	—
62	C₂²⋊#168	—	2	2	no	—
63	C₂²⋊#168	—	2	2	no	—
64	C₄⋊#168	—	2	2	no	—
65	C₄⋊#168	C₂×C₄	1	4	yes	complemented
66	C₄×#168	—	2	2	no	—
67	C₄×#168	—	2	2	no	—
68	C₂×#431	—	5	1	no	—
69	C₂×#431	D₅	1	1	yes	characteristic
70	C₂×C₄³	—	5	1	no	—
71	#1276	—	5	4	no	—
72	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅	—	2	4	no	—
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²⋊C₄	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	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₅	—	2	8	no	—
96	C₂²×Dic₅	—	2	8	no	—
97	C₂²×Dic₅	—	2	8	no	—
98	C₂²×Dic₅	—	2	4	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	4	4	no	—
101	C₄²×C₅	C₄²	1	1	yes	characteristic
102	C₄²×C₅	C₄²	1	1	yes	characteristic
103	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₅	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
117	C₄×Dic₅	—	2	8	no	—
118	C₄×Dic₅	—	2	8	no	—
119	C₄×Dic₅	—	2	8	no	—
120	C₄×Dic₅	—	2	8	no	—
121	C₄×Dic₅	—	2	8	no	—
122	C₄×Dic₅	—	2	4	no	—
123	C₄×Dic₅	C₂×C₈	1	8	yes	complemented
124	C₂×#168	—	2	4	no	—
125	C₂×#168	—	4	4	no	—
126	C₂²×C₄²	—	5	2	no	—
127	C₂²×C₄²	—	10	1	no	—
128	C₂²×C₄²	—	10	1	no	—
129	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
130	#431	—	2	1	no	—
131	#431	—	2	1	no	—
132	#431	—	5	2	no	—
133	#431	—	5	2	no	—
134	#431	—	10	1	no	—
135	#431	—	10	1	no	—
136	#431	Dic₅	1	2	yes	complemented
137	#431	C₂×D₅	1	2	yes	—
138	C₂×C₄⋊C₈	—	5	2	no	—
139	C₂×C₄⋊C₈	Dic₅	1	2	yes	complemented
140	C₂×C₂²⋊C₈	—	2	1	no	—
141	C₂×C₂²⋊C₈	—	10	1	no	—
142	C₂×C₄×C₈	—	2	1	no	—
143	C₂×C₄×C₈	—	10	1	no	—
144	C₄³	—	5	2	no	—
145	C₄³	—	5	2	no	—
146	C₄³	—	10	1	no	—
147	C₄³	—	10	1	no	—
148	C₂³×C₅	—	2	2	no	—
149	C₂³×C₅	—	2	2	no	—
150	C₂³×C₅	#95	1	1	yes	characteristic
151	C₂³×C₅	#95	1	1	yes	characteristic
152	C₂³×C₅	C₂²⋊C₈	1	4	yes	—
153	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	2	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	C₄×C₈	1	2	yes	—
172	C₂×C₄×C₅	#97	1	2	yes	—
173	C₂×C₄×C₅	#97	1	2	yes	—
174	C₂×C₄×C₅	C₂²⋊C₈	1	4	yes	—
175	C₂×C₄×C₅	#104	1	4	yes	—
176	C₂×C₄×C₅	#104	1	4	yes	—
177	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
178	C₂×C₄×C₅	C₄⋊C₈	1	4	yes	—
179	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₂²⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
187	C₂×Dic₅	—	2	8	no	—
188	C₂×Dic₅	—	2	8	no	—
189	C₂×Dic₅	—	2	32	no	—
190	C₂×Dic₅	—	2	8	no	—
191	C₅×C₈	—	4	4	no	—
192	#168	—	4	4	no	—
193	C₂³×C₄	—	10	2	no	—
194	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
195	C₂³×C₄	D₂₀	1	1	yes	characteristic
196	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	10	2	no	—
199	C₂×C₄²	—	5	8	no	—
200	C₂×C₄²	—	5	4	no	—
201	C₂×C₄²	—	10	8	no	—
202	C₂×C₄²	—	10	8	no	—
203	C₂×C₄²	—	10	4	no	—
204	C₂×C₄²	—	10	2	no	—
205	C₂×C₄²	—	10	2	no	—
206	C₂×C₄²	—	10	2	no	—
207	C₂×C₄²	—	10	2	no	—
208	C₂×C₄²	—	10	2	no	—
209	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
210	C₂×C₄²	Dic₁₀	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	D₂₀	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	C₂²⋊D₅	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	—	2	2	no	—
222	C₄⋊C₈	—	5	4	no	—
223	C₄⋊C₈	—	10	2	no	—
224	C₄⋊C₈	C₂×Dic₅	1	4	yes	complemented
225	C₂²⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	2	2	no	—
227	C₂²⋊C₈	—	10	2	no	—
228	C₂²⋊C₈	—	10	2	no	—
229	C₄×C₈	—	2	2	no	—
230	C₄×C₈	—	2	2	no	—
231	C₄×C₈	—	10	2	no	—
232	C₄×C₈	—	10	2	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	2	1	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	2	8	no	—
238	C₂²×C₅	#336	1	2	yes	—
239	C₂²×C₅	#336	1	2	yes	—
240	C₂²×C₅	#339	1	2	yes	—
241	C₂²×C₅	#339	1	2	yes	—
242	C₂²×C₅	C₂×#95	1	1	yes	characteristic
243	C₂²×C₅	C₂×C₂²⋊C₈	1	2	yes	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	#336	1	2	yes	—
249	C₄×C₅	#336	1	2	yes	—
250	C₄×C₅	#339	1	2	yes	—
251	C₄×C₅	#339	1	2	yes	—
252	C₄×C₅	C₂×C₄×C₈	1	1	yes	characteristic
253	C₄×C₅	C₂×#97	1	1	yes	characteristic
254	C₄×C₅	C₂×#104	1	2	yes	—
255	C₄×C₅	C₂×#104	1	2	yes	—
256	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
257	Dic₅	—	2	16	no	—
258	C₂⁴	#685	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	10	8	no	—
262	C₂²×C₄	—	10	8	no	—
263	C₂²×C₄	—	10	8	no	—
264	C₂²×C₄	—	10	4	no	—
265	C₂²×C₄	C₈×D₅	1	4	yes	—
266	C₂²×C₄	#676	1	4	yes	—
267	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
268	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
269	C₂²×C₄	#683	1	1	yes	characteristic
270	C₂²×C₄	#683	1	1	yes	characteristic
271	C₂²×C₄	#683	1	1	yes	characteristic
272	C₂²×C₄	#683	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	#685	1	1	yes	characteristic
276	C₂²×C₄	#685	1	1	yes	characteristic
277	C₂²×C₄	#685	1	1	yes	characteristic
278	C₂²×C₄	#685	1	1	yes	characteristic
279	C₂²×C₄	#685	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	10	4	no	—
288	C₂×C₈	—	20	4	no	—
289	C₄²	—	5	8	no	—
290	C₄²	—	10	8	no	—
291	C₄²	—	10	8	no	—
292	C₄²	—	10	8	no	—
293	C₄²	—	10	8	no	—
294	C₄²	—	10	8	no	—
295	C₄²	—	10	4	no	—
296	C₄²	C₄×Dic₅	1	1	yes	characteristic
297	C₄²	C₄×Dic₅	1	1	yes	characteristic
298	C₄²	#683	1	1	yes	characteristic
299	C₄²	#683	1	1	yes	characteristic
300	C₄²	#683	1	1	yes	characteristic
301	C₄²	#683	1	1	yes	characteristic
302	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
303	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
304	C₄²	#685	1	1	yes	characteristic
305	C₄²	#685	1	1	yes	characteristic
306	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
307	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
308	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
309	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
310	C₄²	C₂²×Dic₅	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
312	C₂×C₅	—	2	2	no	—
313	C₂×C₅	—	2	2	no	—
314	C₂×C₅	#1276	1	4	yes	complemented
315	C₂×C₅	C₂×#336	1	1	yes	characteristic
316	C₂×C₅	C₂×#339	1	1	yes	characteristic
317	C₂×C₅	C₂×#339	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	#3952	1	4	yes	—
321	C₂³	#3963	1	1	yes	characteristic
322	C₂³	#3963	1	1	yes	characteristic
323	C₂³	C₂×#685	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
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	—	10	8	no	—
335	C₂×C₄	—	10	8	no	—
336	C₂×C₄	—	10	32	no	—
337	C₂×C₄	—	10	8	no	—
338	C₂×C₄	C₈×Dic₅	1	2	yes	—
339	C₂×C₄	C₈×Dic₅	1	2	yes	—
340	C₂×C₄	#3946	1	4	yes	—
341	C₂×C₄	#3946	1	4	yes	—
342	C₂×C₄	#3947	1	2	yes	—
343	C₂×C₄	#3947	1	2	yes	—
344	C₂×C₄	#3952	1	4	yes	—
345	C₂×C₄	#3957	1	4	yes	—
346	C₂×C₄	#3963	1	1	yes	characteristic
347	C₂×C₄	#3963	1	1	yes	characteristic
348	C₂×C₄	#3963	1	1	yes	characteristic
349	C₂×C₄	#3963	1	1	yes	characteristic
350	C₂×C₄	#3963	1	1	yes	characteristic
351	C₂×C₄	#3963	1	1	yes	characteristic
352	C₂×C₄	#3969	1	4	yes	—
353	C₂×C₄	C₂×C₈×D₅	1	2	yes	—
354	C₂×C₄	C₂×#676	1	2	yes	—
355	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
356	C₂×C₄	C₂×#683	1	1	yes	characteristic
357	C₂×C₄	C₂×#683	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
359	C₂×C₄	C₂×#685	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	20	4	no	—
363	C₅	C₂×#1276	1	1	yes	characteristic, complemented, Sylow
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	#64752	1	2	yes	—
370	C₂²	#64770	1	2	yes	—
371	C₂²	#64770	1	2	yes	—
372	C₂²	#64775	1	2	yes	—
373	C₂²	C₂×#3952	1	2	yes	—
374	C₂²	C₂×#3963	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	10	16	no	—
380	C₄	#64752	1	2	yes	—
381	C₄	#64770	1	2	yes	—
382	C₄	#64770	1	2	yes	—
383	C₄	#64775	1	2	yes	—
384	C₄	C₂×C₈×Dic₅	1	1	yes	characteristic
385	C₄	C₂×#3946	1	2	yes	—
386	C₄	C₂×#3947	1	1	yes	characteristic
387	C₄	C₂×#3957	1	2	yes	—
388	C₄	C₂×#3969	1	2	yes	—
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	#10598227	1	4	yes	direct product factor
392	C₂	C₂×#64752	1	1	yes	characteristic
393	C₂	C₂×#64770	1	1	yes	characteristic
394	C₂	C₂×#64775	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#431	C₂
socle	C₂³×C₅	#95
prime radical	C₂⁴×C₅	C₂²⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#431	D₅
hypocenter	C₅	C₂×#1276
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
4. #10598227	C₂	direct (N × H)
11. C₅×#431	C₄	semidirect
13. C₂×C₅×C₄⋊C₈	C₄	semidirect
23. #65214	C₄	semidirect
25. C₂×C₄⋊#168	C₄	semidirect
53. C₂×C₄×Dic₅	C₈	semidirect
57. C₅×C₄⋊C₈	C₂×C₄	semidirect
65. C₄⋊#168	C₂×C₄	semidirect
123. C₄×Dic₅	C₂×C₈	semidirect
136. #431	Dic₅	semidirect
139. C₂×C₄⋊C₈	Dic₅	semidirect
224. C₄⋊C₈	C₂×Dic₅	semidirect
314. C₂×C₅	#1276	semidirect
363. C₅	C₂×#1276	semidirect
391. C₂	#10598227	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
C₂×C₄²×Dic₅	2
C₂×#65214	2
#10598227	2
C₂×#1276	5

Subgroups — C2×#10598227 #11988735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10598227 #11988735