Subgroups — C₂×#10598202 #11989243

Order 1280.

690 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×#65213	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
4	#10598202	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×M₁₆	—	2	1	no	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂²×#681	—	2	1	no	—
8	C₂³×#168	C₄	1	2	yes	—
9	C₅×#423	—	2	1	no	—
10	C₅×#423	—	2	1	no	—
11	C₅×#423	C₄	1	2	yes	—
12	C₅×#423	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	—	2	1	no	—
14	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	—
15	#65213	—	2	1	no	—
16	#65213	—	2	1	no	—
17	#65213	C₄	1	2	yes	—
18	#65213	C₂²	1	2	yes	—
19	C₂×C₄⋊#168	—	2	1	no	—
20	C₂×C₄⋊#168	—	2	1	no	—
21	C₂×C₄⋊#168	—	2	1	no	—
22	C₂×C₄⋊#168	—	2	1	no	—
23	C₂×C₄⋊#168	—	2	1	no	—
24	C₂×C₄⋊#168	C₄	1	2	yes	—
25	C₂×C₄⋊#168	C₄	1	2	yes	—
26	C₂×C₄⋊#168	C₂²	1	2	yes	—
27	C₂×#1292	—	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	Q₈	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	4	2	no	—
34	C₂×C₅×M₁₆	—	4	2	no	—
35	C₂²×C₅×C₈	—	2	2	no	—
36	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₂×#681	—	2	2	no	—
49	C₂×#681	—	2	2	no	—
50	C₂×#681	—	4	2	no	—
51	C₂×#681	—	4	2	no	—
52	C₂²×#168	—	2	2	no	—
53	C₂²×#168	—	2	2	no	—
54	C₂²×#168	—	2	2	no	—
55	C₂²×#168	—	4	4	no	—
56	C₂²×#168	C₂×C₄	1	4	yes	—
57	C₅×C₄⋊C₈	—	2	2	no	—
58	C₅×C₄⋊C₈	—	2	2	no	—
59	C₅×C₄⋊C₈	—	2	2	no	—
60	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₄⋊#168	—	2	2	no	—
62	C₄⋊#168	—	2	2	no	—
63	C₄⋊#168	—	2	2	no	—
64	C₄⋊#168	—	2	2	no	—
65	C₄⋊#168	—	2	2	no	—
66	C₄⋊#168	—	2	2	no	—
67	C₄⋊#168	—	2	2	no	—
68	C₄⋊#168	C₂×C₄	1	4	yes	—
69	C₂×#423	—	5	1	no	—
70	C₂×#423	D₅	1	1	yes	characteristic
71	C₂²×C₄⋊C₈	—	5	1	no	—
72	#1292	—	5	4	no	—
73	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅	—	2	2	no	—
75	C₂²×C₄×C₅	—	2	2	no	—
76	C₂²×C₄×C₅	—	4	2	no	—
77	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₄²	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	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	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	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	D₈	1	2	yes	—
93	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₅	Q₁₆	1	2	yes	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
99	C₅×M₁₆	—	4	4	no	—
100	C₅×M₁₆	—	4	2	no	—
101	C₅×M₁₆	—	4	2	no	—
102	C₂×C₅×C₈	—	2	4	no	—
103	C₂×C₅×C₈	—	4	4	no	—
104	C₄²×C₅	C₄²	1	1	yes	characteristic
105	C₄²×C₅	C₄²	1	1	yes	characteristic
106	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	#681	—	4	4	no	—
121	#681	—	4	2	no	—
122	#681	—	4	2	no	—
123	C₂×#168	—	2	4	no	—
124	C₂×#168	—	2	4	no	—
125	C₂×#168	—	4	4	no	—
126	C₂×#168	—	4	4	no	—
127	C₂×#168	—	4	4	no	—
128	C₂×#168	—	4	4	no	—
129	C₂²×M₁₆	—	2	1	no	—
130	C₂²×M₁₆	—	10	1	no	—
131	C₂³×C₈	—	5	2	no	—
132	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
133	#423	—	2	1	no	—
134	#423	—	2	1	no	—
135	#423	—	5	2	no	—
136	#423	—	5	2	no	—
137	#423	—	10	1	no	—
138	#423	—	10	1	no	—
139	#423	Dic₅	1	2	yes	—
140	#423	C₂×D₅	1	2	yes	—
141	C₂×C₄⋊C₈	—	2	1	no	—
142	C₂×C₄⋊C₈	—	5	2	no	—
143	C₂×C₄⋊C₈	—	5	2	no	—
144	C₂×C₄⋊C₈	—	5	2	no	—
145	C₂×C₄⋊C₈	—	10	1	no	—
146	C₂×C₄⋊C₈	—	10	1	no	—
147	C₂×C₄⋊C₈	—	10	1	no	—
148	C₂×C₄⋊C₈	—	10	1	no	—
149	C₂×C₄⋊C₈	—	10	1	no	—
150	C₂×C₄⋊C₈	Dic₅	1	2	yes	—
151	C₂³×C₅	—	2	2	no	—
152	C₂³×C₅	—	2	2	no	—
153	C₂³×C₅	#95	1	1	yes	characteristic
154	C₂³×C₅	#95	1	1	yes	characteristic
155	C₂³×C₅	#106	1	2	yes	—
156	C₂³×C₅	#107	1	2	yes	—
157	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
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	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	4	1	no	—
168	C₂×C₄×C₅	—	4	1	no	—
169	C₂×C₄×C₅	—	4	1	no	—
170	C₂×C₄×C₅	—	4	1	no	—
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	#95	1	1	yes	characteristic
175	C₂×C₄×C₅	#95	1	1	yes	characteristic
176	C₂×C₄×C₅	#95	1	1	yes	characteristic
177	C₂×C₄×C₅	#100	1	2	yes	—
178	C₂×C₄×C₅	#101	1	2	yes	—
179	C₂×C₄×C₅	#102	1	2	yes	—
180	C₂×C₄×C₅	#102	1	2	yes	—
181	C₂×C₄×C₅	#102	1	2	yes	—
182	C₂×C₄×C₅	#102	1	2	yes	—
183	C₂×C₄×C₅	#103	1	2	yes	—
184	C₂×C₄×C₅	#103	1	2	yes	—
185	C₂×C₄×C₅	#103	1	2	yes	—
186	C₂×C₄×C₅	#103	1	2	yes	—
187	C₂×C₄×C₅	#106	1	2	yes	—
188	C₂×C₄×C₅	#107	1	2	yes	—
189	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
199	C₅×C₈	—	4	4	no	—
200	#168	—	4	4	no	—
201	#168	—	4	4	no	—
202	C₂³×C₄	Dic₁₀	1	1	yes	characteristic
203	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
204	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
205	C₂×M₁₆	—	2	2	no	—
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	4	2	no	—
208	C₂×M₁₆	—	4	2	no	—
209	C₂×M₁₆	—	10	2	no	—
210	C₂×M₁₆	—	10	2	no	—
211	C₂×M₁₆	—	20	2	no	—
212	C₂×M₁₆	—	20	2	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	5	4	no	—
215	C₂²×C₈	—	10	2	no	—
216	C₂²×C₈	—	10	2	no	—
217	C₂²×C₈	—	10	2	no	—
218	C₂²×C₈	—	20	4	no	—
219	C₂×C₄²	Dic₁₀	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
221	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
223	C₂×C₄²	D₂₀	1	1	yes	characteristic
224	C₂×C₄²	D₂₀	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
227	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
228	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	5	4	no	—
235	C₄⋊C₈	—	10	2	no	—
236	C₄⋊C₈	—	10	2	no	—
237	C₄⋊C₈	—	10	2	no	—
238	C₄⋊C₈	—	10	2	no	—
239	C₄⋊C₈	—	10	2	no	—
240	C₄⋊C₈	—	10	2	no	—
241	C₄⋊C₈	—	10	2	no	—
242	C₄⋊C₈	C₂×Dic₅	1	4	yes	—
243	C₂²×C₅	—	2	4	no	—
244	C₂²×C₅	—	2	4	no	—
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	#338	1	2	yes	—
250	C₂²×C₅	#340	1	2	yes	—
251	C₂²×C₅	#340	1	2	yes	—
252	C₂²×C₅	#343	1	2	yes	—
253	C₂²×C₅	C₂×#95	1	1	yes	characteristic
254	C₂²×C₅	C₂×#106	1	1	yes	characteristic
255	C₂²×C₅	C₂×#107	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	#340	1	2	yes	—
263	C₄×C₅	#340	1	2	yes	—
264	C₄×C₅	#343	1	2	yes	—
265	C₄×C₅	C₂×#100	1	1	yes	characteristic
266	C₄×C₅	C₂×#101	1	1	yes	characteristic
267	C₄×C₅	C₂×#102	1	1	yes	characteristic
268	C₄×C₅	C₂×#102	1	1	yes	characteristic
269	C₄×C₅	C₂×#103	1	1	yes	characteristic
270	C₄×C₅	C₂×#103	1	1	yes	characteristic
271	C₂⁴	#683	1	1	yes	characteristic
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
276	C₂²×C₄	C₄×Dic₅	1	1	yes	characteristic
277	C₂²×C₄	#683	1	1	yes	characteristic
278	C₂²×C₄	#683	1	1	yes	characteristic
279	C₂²×C₄	#683	1	1	yes	characteristic
280	C₂²×C₄	#683	1	1	yes	characteristic
281	C₂²×C₄	#683	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊Dic₅	1	1	yes	characteristic
284	C₂²×C₄	#685	1	1	yes	characteristic
285	C₂²×C₄	#685	1	1	yes	characteristic
286	C₂²×C₄	#685	1	1	yes	characteristic
287	C₂²×C₄	#685	1	1	yes	characteristic
288	C₂²×C₄	#686	1	2	yes	—
289	C₂²×C₄	#687	1	2	yes	—
290	C₂²×C₄	#688	1	2	yes	—
291	C₂²×C₄	#689	1	2	yes	—
292	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
297	M₁₆	—	4	4	no	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	M₁₆	—	20	4	no	—
301	M₁₆	—	20	2	no	—
302	M₁₆	—	20	2	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	10	4	no	—
306	C₂×C₈	—	10	4	no	—
307	C₂×C₈	—	20	4	no	—
308	C₂×C₈	—	20	4	no	—
309	C₂×C₈	—	20	4	no	—
310	C₂×C₈	—	20	4	no	—
311	C₄²	C₄×Dic₅	1	1	yes	characteristic
312	C₄²	C₄×Dic₅	1	1	yes	characteristic
313	C₄²	#683	1	1	yes	characteristic
314	C₄²	#683	1	1	yes	characteristic
315	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
316	C₄²	C₄⋊Dic₅	1	1	yes	characteristic
317	C₄²	#685	1	1	yes	characteristic
318	C₄²	#685	1	1	yes	characteristic
319	C₄²	#685	1	1	yes	characteristic
320	C₄²	#685	1	1	yes	characteristic
321	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
322	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
324	C₄²	C₂×D₂₀	1	1	yes	characteristic
325	C₄²	C₂²×Dic₅	1	1	yes	characteristic
326	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
327	C₂×C₅	—	2	2	no	—
328	C₂×C₅	—	2	1	no	—
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	#1292	1	4	yes	complemented
331	C₂×C₅	C₂×#338	1	1	yes	characteristic
332	C₂×C₅	C₂×#340	1	1	yes	characteristic
333	C₂×C₅	C₂×#343	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	#3939	1	2	yes	—
337	C₂³	#3940	1	2	yes	—
338	C₂³	#3963	1	1	yes	characteristic
339	C₂³	#3963	1	1	yes	characteristic
340	C₂³	C₂×#683	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	#3939	1	2	yes	—
355	C₂×C₄	#3940	1	2	yes	—
356	C₂×C₄	#3941	1	2	yes	—
357	C₂×C₄	#3941	1	2	yes	—
358	C₂×C₄	#3942	1	2	yes	—
359	C₂×C₄	#3942	1	2	yes	—
360	C₂×C₄	#3955	1	2	yes	—
361	C₂×C₄	#3956	1	2	yes	—
362	C₂×C₄	#3963	1	1	yes	characteristic
363	C₂×C₄	#3963	1	1	yes	characteristic
364	C₂×C₄	#3963	1	1	yes	characteristic
365	C₂×C₄	#3963	1	1	yes	characteristic
366	C₂×C₄	#3963	1	1	yes	characteristic
367	C₂×C₄	#3963	1	1	yes	characteristic
368	C₂×C₄	#3964	1	2	yes	—
369	C₂×C₄	#3964	1	2	yes	—
370	C₂×C₄	#3967	1	2	yes	—
371	C₂×C₄	#3967	1	2	yes	—
372	C₂×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
373	C₂×C₄	C₂×#683	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
375	C₂×C₄	C₂×#685	1	1	yes	characteristic
376	C₂×C₄	C₂×#685	1	1	yes	characteristic
377	C₂×C₄	C₂×#686	1	1	yes	characteristic
378	C₂×C₄	C₂×#687	1	1	yes	characteristic
379	C₂×C₄	C₂×#688	1	1	yes	characteristic
380	C₂×C₄	C₂×#689	1	1	yes	characteristic
381	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
382	C₈	—	4	4	no	—
383	C₈	—	20	4	no	—
384	C₈	—	20	4	no	—
385	C₅	C₂×#1292	1	1	yes	characteristic, complemented, Sylow
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	#64749	1	2	yes	—
393	C₂²	#64749	1	2	yes	—
394	C₂²	#64774	1	2	yes	—
395	C₂²	#64780	1	2	yes	—
396	C₂²	C₂×#3939	1	1	yes	characteristic
397	C₂²	C₂×#3940	1	1	yes	characteristic
398	C₂²	C₂×#3963	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	#64749	1	2	yes	—
406	C₄	#64749	1	2	yes	—
407	C₄	#64774	1	2	yes	—
408	C₄	C₂×#3941	1	1	yes	characteristic
409	C₄	C₂×#3942	1	1	yes	characteristic
410	C₄	C₂×#3955	1	1	yes	characteristic
411	C₄	C₂×#3956	1	1	yes	characteristic
412	C₄	C₂×#3964	1	1	yes	characteristic
413	C₄	C₂×#3967	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	#10598202	1	4	yes	direct product factor
418	C₂	C₂×#64749	1	1	yes	characteristic
419	C₂	C₂×#64774	1	1	yes	characteristic
420	C₂	C₂×#64780	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#3963
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅
Fitting	C₂×C₅×#423	C₂
socle	C₂³×C₅	#95
prime radical	C₂⁴×C₅	C₄⋊C₄
cosocle	C₂×C₄²×C₅	C₂³
hypercenter	C₂×#423	D₅
hypocenter	C₅	C₂×#1292
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
4. #10598202	C₂	direct (N × H)
330. C₂×C₅	#1292	semidirect
385. C₅	C₂×#1292	semidirect
417. C₂	#10598202	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×#423	2
C₂×#65213	2
C₂²×C₄⋊#168	2
#10598202	2
C₂×#1292	5

Subgroups — C2×#10598202 #11989243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10598202 #11989243