Subgroups — C₂×#10598305 #12014166

Order 1280.

586 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#65390	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3944	C₂	1	1	yes	maximal, characteristic
4	#10598305	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂×#4072	C₄	1	1	yes	characteristic
7	C₂²×#681	C₄	1	1	yes	characteristic
8	C₂×C₅×M₃₂	—	2	1	no	—
9	C₂×C₅×M₃₂	—	2	1	no	—
10	C₂×C₅×M₃₂	—	2	1	no	—
11	C₂×C₅×M₃₂	C₄	1	2	yes	complemented
12	C₂×C₅×M₃₂	C₄	1	2	yes	complemented
13	C₂×C₅×M₃₂	C₂²	1	2	yes	—
14	C₂²×C₅×C₁₆	—	2	1	no	—
15	#65390	—	2	1	no	—
16	#65390	—	2	1	no	—
17	#65390	C₄	1	2	yes	—
18	#65390	C₂²	1	2	yes	—
19	C₂×#3947	—	2	1	no	—
20	C₂×C₈×Dic₅	—	2	1	no	—
21	C₂×#3944	—	2	1	no	—
22	C₂×#3944	—	2	1	no	—
23	C₂×#3944	—	2	1	no	—
24	C₂×#3944	—	2	1	no	—
25	C₂×#3944	C₄	1	2	yes	complemented
26	C₂×#3944	C₂²	1	2	yes	—
27	C₂²×#672	C₄	1	2	yes	complemented
28	C₂×#1378	—	5	1	no	maximal, Sylow
29	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
36	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
37	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
38	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
40	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
41	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
42	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₅	C₈	1	2	yes	—
45	#4072	—	2	1	no	—
46	#4072	—	2	1	no	—
47	#4072	C₈	1	2	yes	—
48	#4072	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₅	—	2	1	no	—
50	C₂×C₄×Dic₅	—	2	1	no	—
51	C₂×#681	—	2	1	no	—
52	C₂×#681	—	2	1	no	—
53	C₂×#681	—	2	1	no	—
54	C₂×#681	C₈	1	2	yes	—
55	C₂×#681	C₈	1	2	yes	—
56	C₂×#681	C₂×C₄	1	2	yes	—
57	C₂²×#168	—	2	1	no	—
58	C₅×M₃₂	—	2	2	no	—
59	C₅×M₃₂	—	2	2	no	—
60	C₅×M₃₂	—	2	2	no	—
61	C₅×M₃₂	C₂×C₄	1	4	yes	complemented
62	C₂×C₅×C₁₆	—	2	2	no	—
63	C₂×C₅×C₁₆	—	2	2	no	—
64	C₂×C₅×C₁₆	—	2	2	no	—
65	#3947	—	2	2	no	—
66	#3947	—	2	2	no	—
67	C₈×Dic₅	—	2	2	no	—
68	C₈×Dic₅	—	2	2	no	—
69	#3944	—	2	2	no	—
70	#3944	—	2	2	no	—
71	#3944	—	2	2	no	—
72	#3944	—	2	2	no	—
73	C₂×#672	—	2	2	no	—
74	C₂×#672	—	2	2	no	—
75	C₂×#672	C₂×C₄	1	4	yes	complemented
76	C₂²×M₃₂	—	5	1	no	—
77	C₂²×M₃₂	D₅	1	1	yes	characteristic
78	C₂×#405	—	5	1	no	—
79	#1378	—	5	4	no	—
80	C₂⁴×C₅	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²⋊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	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
91	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
92	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
93	C₂²×C₄×C₅	M₁₆	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₅	—	2	2	no	—
96	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
97	C₂×C₅×C₈	C₄²	1	1	yes	characteristic
98	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
124	C₂²⋊Dic₅	—	2	2	no	—
125	C₂²⋊Dic₅	C₂×C₈	1	4	yes	—
126	C₄⋊Dic₅	—	2	2	no	—
127	C₄⋊Dic₅	—	2	2	no	—
128	C₄×Dic₅	—	2	2	no	—
129	C₄×Dic₅	—	2	2	no	—
130	#681	—	2	2	no	—
131	#681	—	2	2	no	—
132	#681	—	2	2	no	—
133	#681	C₂×C₈	1	4	yes	—
134	C₂×#168	—	2	2	no	—
135	C₂×#168	—	2	2	no	—
136	C₂×#168	—	2	2	no	—
137	C₅×C₁₆	—	2	4	no	—
138	#672	—	2	4	no	—
139	C₂²×M₁₆	—	5	1	no	—
140	C₂³×C₈	C₂×D₅	1	1	yes	characteristic
141	C₂×#117	—	5	1	no	—
142	C₂×M₃₂	—	2	1	no	—
143	C₂×M₃₂	—	2	1	no	—
144	C₂×M₃₂	—	2	1	no	—
145	C₂×M₃₂	—	5	2	no	—
146	C₂×M₃₂	—	5	2	no	—
147	C₂×M₃₂	—	10	1	no	—
148	C₂×M₃₂	—	10	1	no	—
149	C₂×M₃₂	—	10	1	no	—
150	C₂×M₃₂	—	10	1	no	—
151	C₂×M₃₂	Dic₅	1	2	yes	complemented
152	C₂×M₃₂	Dic₅	1	2	yes	complemented
153	C₂×M₃₂	C₂×D₅	1	2	yes	—
154	C₂²×C₁₆	—	2	1	no	—
155	C₂²×C₁₆	—	5	2	no	—
156	#405	—	5	2	no	—
157	#405	—	5	2	no	—
158	#405	—	10	1	no	—
159	#405	—	10	1	no	—
160	C₂×#97	—	10	1	no	—
161	C₂×C₄×C₈	—	10	1	no	—
162	C₂³×C₅	—	4	2	no	—
163	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
164	C₂³×C₅	C₄×C₈	1	1	yes	characteristic
165	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
166	C₂³×C₅	C₂²⋊C₈	1	1	yes	characteristic
167	C₂³×C₅	C₄⋊C₈	1	1	yes	characteristic
168	C₂³×C₅	C₄⋊C₈	1	1	yes	characteristic
169	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₅	#95	1	1	yes	characteristic
171	C₂×C₄×C₅	#95	1	1	yes	characteristic
172	C₂×C₄×C₅	#95	1	1	yes	characteristic
173	C₂×C₄×C₅	#95	1	1	yes	characteristic
174	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₄×C₈	1	1	yes	characteristic
176	C₂×C₄×C₅	#97	1	1	yes	characteristic
177	C₂×C₄×C₅	#97	1	1	yes	characteristic
178	C₂×C₄×C₅	#97	1	1	yes	characteristic
179	C₂×C₄×C₅	#97	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
187	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
188	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
189	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
190	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
198	C₂×Dic₅	—	2	4	no	—
199	C₂×Dic₅	—	4	4	no	—
200	C₅×C₈	#95	1	1	yes	characteristic
201	C₅×C₈	#95	1	1	yes	characteristic
202	C₅×C₈	#95	1	1	yes	characteristic
203	C₅×C₈	#95	1	1	yes	characteristic
204	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
208	#168	—	2	4	no	—
209	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
210	C₂×M₁₆	—	5	2	no	—
211	C₂×M₁₆	—	5	2	no	—
212	C₂×M₁₆	—	5	2	no	—
213	C₂×M₁₆	—	10	1	no	—
214	C₂×M₁₆	—	10	1	no	—
215	C₂×M₁₆	—	10	1	no	—
216	C₂²×C₈	—	10	1	no	—
217	C₂²×C₈	Dic₁₀	1	1	yes	characteristic
218	C₂²×C₈	Dic₁₀	1	1	yes	characteristic
219	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
220	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
221	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
222	C₂²×C₈	D₂₀	1	1	yes	characteristic
223	C₂²×C₈	D₂₀	1	1	yes	characteristic
224	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
225	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
226	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
227	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
228	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
229	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
230	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
231	#117	—	5	2	no	—
232	#117	—	5	2	no	—
233	#117	—	10	1	no	—
234	#117	—	10	1	no	—
235	C₂×C₄⋊C₄	—	10	1	no	—
236	C₂×C₂²⋊C₄	—	5	2	no	—
237	C₂×C₄²	—	10	1	no	—
238	M₃₂	—	2	2	no	—
239	M₃₂	—	2	2	no	—
240	M₃₂	—	2	2	no	—
241	M₃₂	—	10	2	no	—
242	M₃₂	—	10	2	no	—
243	M₃₂	—	10	2	no	—
244	M₃₂	—	10	2	no	—
245	M₃₂	C₂×Dic₅	1	4	yes	complemented
246	C₂×C₁₆	—	2	2	no	—
247	C₂×C₁₆	—	2	2	no	—
248	C₂×C₁₆	—	2	2	no	—
249	C₂×C₁₆	—	5	4	no	—
250	C₂×C₁₆	—	10	2	no	—
251	C₂×C₁₆	—	10	2	no	—
252	#97	—	10	2	no	—
253	#97	—	10	2	no	—
254	C₄×C₈	—	10	2	no	—
255	C₄×C₈	—	10	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	4	1	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	#336	1	1	yes	characteristic
264	C₂²×C₅	#336	1	1	yes	characteristic
265	C₂²×C₅	#336	1	1	yes	characteristic
266	C₂²×C₅	#336	1	1	yes	characteristic
267	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
268	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
269	C₂²×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
270	C₄×C₅	#336	1	1	yes	characteristic
271	C₄×C₅	#336	1	1	yes	characteristic
272	C₄×C₅	#336	1	1	yes	characteristic
273	C₄×C₅	#336	1	1	yes	characteristic
274	C₄×C₅	C₂×#95	1	1	yes	characteristic
275	C₄×C₅	C₂×#97	1	1	yes	characteristic
276	C₄×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
277	C₄×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
278	Dic₅	—	4	4	no	—
279	C₂⁴	C₈×D₅	1	1	yes	characteristic
280	C₂²×C₄	—	10	2	no	—
281	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
282	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
283	C₂²×C₄	C₈×D₅	1	1	yes	characteristic
284	C₂²×C₄	#676	1	1	yes	characteristic
285	C₂²×C₄	#676	1	1	yes	characteristic
286	C₂²×C₄	#676	1	1	yes	characteristic
287	C₂²×C₄	#676	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
290	C₂²×C₄	#683	1	1	yes	characteristic
291	C₂²×C₄	#683	1	1	yes	characteristic
292	C₂²×C₄	#685	1	1	yes	characteristic
293	C₂²×C₄	#685	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	M₁₆	—	5	4	no	—
296	M₁₆	—	10	2	no	—
297	M₁₆	—	10	2	no	—
298	M₁₆	—	10	2	no	—
299	C₂×C₈	—	10	2	no	—
300	C₂×C₈	—	10	2	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	C₄×Dic₅	1	1	yes	characteristic
303	C₂×C₈	C₄×Dic₅	1	1	yes	characteristic
304	C₂×C₈	#683	1	1	yes	characteristic
305	C₂×C₈	#683	1	1	yes	characteristic
306	C₂×C₈	#683	1	1	yes	characteristic
307	C₂×C₈	#683	1	1	yes	characteristic
308	C₂×C₈	#683	1	1	yes	characteristic
309	C₂×C₈	#683	1	1	yes	characteristic
310	C₂×C₈	C₄⋊Dic₅	1	1	yes	characteristic
311	C₂×C₈	C₄⋊Dic₅	1	1	yes	characteristic
312	C₂×C₈	C₄⋊Dic₅	1	1	yes	characteristic
313	C₂×C₈	C₄⋊Dic₅	1	1	yes	characteristic
314	C₂×C₈	#685	1	1	yes	characteristic
315	C₂×C₈	#685	1	1	yes	characteristic
316	C₂×C₈	#685	1	1	yes	characteristic
317	C₂×C₈	#685	1	1	yes	characteristic
318	C₂×C₈	#685	1	1	yes	characteristic
319	C₂×C₈	#685	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊Dic₅	1	1	yes	characteristic
321	C₂×C₈	C₂²⋊Dic₅	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊Dic₅	1	1	yes	characteristic
323	C₂×C₈	C₂²⋊Dic₅	1	1	yes	characteristic
324	C₂×C₈	C₂×Dic₁₀	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
326	C₂×C₈	C₂×D₂₀	1	1	yes	characteristic
327	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
329	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
330	C₄⋊C₄	—	10	2	no	—
331	C₄⋊C₄	—	10	2	no	—
332	C₂²⋊C₄	—	5	4	no	—
333	C₂²⋊C₄	—	10	2	no	—
334	C₄²	—	10	2	no	—
335	C₄²	—	10	2	no	—
336	C₁₆	—	2	4	no	—
337	C₁₆	—	10	4	no	—
338	C₂×C₅	—	2	1	no	—
339	C₂×C₅	—	2	1	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	2	1	no	—
343	C₂×C₅	—	2	1	no	—
344	C₂×C₅	#1378	1	2	yes	complemented
345	C₂×C₅	C₂×#336	1	1	yes	characteristic
346	C₂³	—	4	2	no	—
347	C₂³	C₈×Dic₅	1	1	yes	characteristic
348	C₂³	C₈×Dic₅	1	1	yes	characteristic
349	C₂³	#3946	1	1	yes	characteristic
350	C₂³	#3946	1	1	yes	characteristic
351	C₂³	#3952	1	1	yes	characteristic
352	C₂³	#3952	1	1	yes	characteristic
353	C₂³	C₂×C₈×D₅	1	1	yes	characteristic
354	C₂×C₄	—	10	4	no	—
355	C₂×C₄	—	20	4	no	—
356	C₂×C₄	C₈×Dic₅	1	1	yes	characteristic
357	C₂×C₄	C₈×Dic₅	1	1	yes	characteristic
358	C₂×C₄	#3946	1	1	yes	characteristic
359	C₂×C₄	#3946	1	1	yes	characteristic
360	C₂×C₄	#3946	1	1	yes	characteristic
361	C₂×C₄	#3946	1	1	yes	characteristic
362	C₂×C₄	#3946	1	1	yes	characteristic
363	C₂×C₄	#3946	1	1	yes	characteristic
364	C₂×C₄	#3947	1	1	yes	characteristic
365	C₂×C₄	#3947	1	1	yes	characteristic
366	C₂×C₄	#3947	1	1	yes	characteristic
367	C₂×C₄	#3947	1	1	yes	characteristic
368	C₂×C₄	#3952	1	1	yes	characteristic
369	C₂×C₄	#3952	1	1	yes	characteristic
370	C₂×C₄	#3952	1	1	yes	characteristic
371	C₂×C₄	#3952	1	1	yes	characteristic
372	C₂×C₄	#3952	1	1	yes	characteristic
373	C₂×C₄	#3952	1	1	yes	characteristic
374	C₂×C₄	#3963	1	1	yes	characteristic
375	C₂×C₄	#3963	1	1	yes	characteristic
376	C₂×C₄	#3963	1	1	yes	characteristic
377	C₂×C₄	#3963	1	1	yes	characteristic
378	C₂×C₄	C₂×C₈×D₅	1	1	yes	characteristic
379	C₂×C₄	C₂×#676	1	1	yes	characteristic
380	C₂×C₄	C₂×#676	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
382	C₂×C₄	C₂×#683	1	1	yes	characteristic
383	C₂×C₄	C₂×#685	1	1	yes	characteristic
384	C₈	—	10	4	no	—
385	C₈	#3963	1	1	yes	characteristic
386	C₈	#3963	1	1	yes	characteristic
387	C₈	#3963	1	1	yes	characteristic
388	C₈	#3963	1	1	yes	characteristic
389	C₈	C₂×#683	1	1	yes	characteristic
390	C₈	C₂×C₄⋊Dic₅	1	1	yes	characteristic
391	C₈	C₂×#685	1	1	yes	characteristic
392	C₈	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
393	C₅	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	#64770	1	1	yes	characteristic
402	C₂²	#64770	1	1	yes	characteristic
403	C₂²	#64770	1	1	yes	characteristic
404	C₂²	#64770	1	1	yes	characteristic
405	C₂²	C₂×C₈×Dic₅	1	1	yes	characteristic
406	C₂²	C₂×#3946	1	1	yes	characteristic
407	C₂²	C₂×#3952	1	1	yes	characteristic
408	C₄	—	20	4	no	—
409	C₄	#64770	1	1	yes	characteristic
410	C₄	#64770	1	1	yes	characteristic
411	C₄	#64770	1	1	yes	characteristic
412	C₄	#64770	1	1	yes	characteristic
413	C₄	C₂×#3946	1	1	yes	characteristic
414	C₄	C₂×#3947	1	1	yes	characteristic
415	C₄	C₂×#3952	1	1	yes	characteristic
416	C₄	C₂×#3963	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	#10598305	1	2	yes	direct product factor
424	C₂	C₂×#64770	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#685
commutator	C₂²×C₅	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₅
Fitting	C₂²×C₅×M₃₂	C₂
socle	C₂²×C₅	#336
prime radical	C₂⁴×C₅	C₂×C₈
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	C₂²×M₃₂	D₅
hypocenter	C₅	C₂×#1378
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
4. #10598305	C₂	direct (N × H)
11. C₂×C₅×M₃₂	C₄	semidirect
12. C₂×C₅×M₃₂	C₄	semidirect
25. C₂×#3944	C₄	semidirect
27. C₂²×#672	C₄	semidirect
61. C₅×M₃₂	C₂×C₄	semidirect
75. C₂×#672	C₂×C₄	semidirect
151. C₂×M₃₂	Dic₅	semidirect
152. C₂×M₃₂	Dic₅	semidirect
245. M₃₂	C₂×Dic₅	semidirect
344. C₂×C₅	#1378	semidirect
393. C₅	C₂×#1378	semidirect
423. C₂	#10598305	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×M₃₂	2
C₂×#65390	2
C₂²×#3944	2
#10598305	2
C₂×#1378	5

Subgroups — C2×#10598305 #12014166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10598305 #12014166