Subgroups — C₅×#35350 #11958070

Order 1280.

4142 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2482	C₂	1	4	yes	maximal, complemented
4	C₅×#2418	C₂	1	16	yes	maximal, complemented
5	C₅×#2405	C₂	1	4	yes	maximal, complemented
6	C₅×#2315	C₂	1	2	yes	maximal, complemented
7	C₅×#2308	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#379	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₅×D₄	C₂²	1	2	yes	—
12	C₂×C₅×#123	C₂²	1	8	yes	complemented
13	C₂×C₅×#120	—	2	8	no	—
14	C₂×C₅×#120	C₂²	1	8	yes	—
15	C₅×#518	—	2	8	no	—
16	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
17	C₂×C₅×#117	C₂²	1	2	yes	complemented
18	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
24	C₅×#399	C₂²	1	8	yes	complemented
25	C₅×#397	C₂²	1	8	yes	complemented
26	C₅×#394	C₂²	1	16	yes	complemented
27	C₅×#388	C₂²	1	16	yes	complemented
28	C₅×#386	C₂²	1	8	yes	complemented
29	C₅×#386	C₂²	1	8	yes	complemented
30	C₅×#385	C₂²	1	8	yes	complemented
31	C₅×#385	C₂²	1	8	yes	complemented
32	C₅×#381	C₂²	1	2	yes	complemented
33	C₅×#380	C₂²	1	8	yes	complemented
34	C₅×#379	C₂²	1	8	yes	—
35	C₅×#379	C₂²	1	8	yes	complemented
36	C₅×#379	C₂²	1	2	yes	complemented
37	#35350	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂⁵×C₅	—	2	4	no	—
39	C₂⁵×C₅	—	2	8	no	—
40	C₂⁵×C₅	—	4	8	no	—
41	C₂⁵×C₅	C₂³	1	2	yes	—
42	C₂⁵×C₅	C₂³	1	4	yes	—
43	C₂⁵×C₅	C₂³	1	1	yes	characteristic
44	C₂⁵×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×D₄	—	2	8	no	—
46	C₂²×C₅×D₄	—	2	8	no	—
47	C₂²×C₅×D₄	—	4	8	no	—
48	C₂²×C₅×D₄	D₄	1	8	yes	—
49	C₂²×C₅×D₄	C₂³	1	8	yes	—
50	C₂²×C₅×D₄	C₂³	1	4	yes	—
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂³	1	4	yes	—
53	C₂³×C₄×C₅	C₂³	1	2	yes	—
54	C₂³×C₄×C₅	C₂³	1	4	yes	—
55	C₂³×C₄×C₅	C₂³	1	4	yes	complemented
56	C₅×#123	—	4	16	no	—
57	C₅×#120	—	2	32	no	—
58	C₄×C₅×D₄	—	2	32	no	—
59	C₅×#117	—	2	8	no	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
61	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	complemented
62	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₅×C₂²⋊C₄	—	4	16	no	—
68	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
73	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
77	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
78	C₂×C₄²×C₅	C₂³	1	4	yes	complemented
79	C₅×#95	C₂³	1	16	yes	complemented
80	C₅×#95	C₂³	1	8	yes	complemented
81	C₂²×#120	C₂×C₅	1	1	yes	characteristic
82	C₂×#518	C₂×C₅	1	1	yes	characteristic, complemented
83	#2482	C₂×C₅	1	4	yes	complemented
84	#2418	C₂×C₅	1	16	yes	complemented
85	#2405	C₂×C₅	1	4	yes	complemented
86	#2315	C₂×C₅	1	2	yes	complemented
87	#2308	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#379	C₂×C₅	1	2	yes	complemented
89	C₂⁴×C₅	—	2	4	no	—
90	C₂⁴×C₅	—	2	8	no	—
91	C₂⁴×C₅	—	2	16	no	—
92	C₂⁴×C₅	—	2	8	no	—
93	C₂⁴×C₅	—	2	4	no	—
94	C₂⁴×C₅	—	2	8	no	—
95	C₂⁴×C₅	—	2	8	no	—
96	C₂⁴×C₅	—	2	8	no	—
97	C₂⁴×C₅	—	4	4	no	—
98	C₂⁴×C₅	—	4	8	no	—
99	C₂⁴×C₅	—	4	4	no	—
100	C₂⁴×C₅	—	4	4	no	—
101	C₂⁴×C₅	—	4	32	no	—
102	C₂⁴×C₅	—	4	64	no	—
103	C₂⁴×C₅	—	4	16	no	—
104	C₂⁴×C₅	C₂×D₄	1	4	yes	—
105	C₂⁴×C₅	C₂×D₄	1	4	yes	—
106	C₂⁴×C₅	#41	1	8	yes	—
107	C₂⁴×C₅	C₂⁴	1	2	yes	—
108	C₂⁴×C₅	C₂⁴	1	4	yes	—
109	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
110	C₂⁴×C₅	C₂⁴	1	2	yes	—
111	C₂×C₅×D₄	—	2	32	no	—
112	C₂×C₅×D₄	—	2	8	no	—
113	C₂×C₅×D₄	—	2	8	no	—
114	C₂×C₅×D₄	—	2	16	no	—
115	C₂×C₅×D₄	—	2	16	no	—
116	C₂×C₅×D₄	—	4	8	no	—
117	C₂×C₅×D₄	—	4	32	no	—
118	C₂×C₅×D₄	C₂×D₄	1	16	yes	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	2	4	no	—
121	C₂²×C₄×C₅	—	2	8	no	—
122	C₂²×C₄×C₅	—	2	8	no	—
123	C₂²×C₄×C₅	—	2	8	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	—	4	8	no	—
126	C₂²×C₄×C₅	—	4	8	no	—
127	C₂²×C₄×C₅	—	4	8	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
131	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
133	C₅×C₄⋊C₄	—	2	8	no	—
134	C₅×C₄⋊C₄	—	4	16	no	—
135	C₅×C₂²⋊C₄	—	2	8	no	—
136	C₅×C₂²⋊C₄	—	2	8	no	—
137	C₅×C₂²⋊C₄	—	2	8	no	—
138	C₅×C₂²⋊C₄	—	2	8	no	—
139	C₅×C₂²⋊C₄	—	2	8	no	—
140	C₅×C₂²⋊C₄	—	2	8	no	—
141	C₅×C₂²⋊C₄	—	2	32	no	—
142	C₅×C₂²⋊C₄	—	2	16	no	—
143	C₅×C₂²⋊C₄	—	4	16	no	—
144	C₅×C₂²⋊C₄	—	4	8	no	—
145	C₄²×C₅	—	2	8	no	—
146	C₂⁶	C₂²×C₅	1	1	yes	characteristic
147	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
148	C₂³×D₄	C₂²×C₅	1	2	yes	—
149	C₂×#123	C₂²×C₅	1	8	yes	complemented
150	C₂×#120	—	2	8	no	—
151	C₂×#120	C₂²×C₅	1	8	yes	—
152	#518	—	2	8	no	—
153	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
154	C₂×#117	C₂²×C₅	1	2	yes	complemented
155	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
156	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
160	C₂²×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
161	#399	C₂²×C₅	1	8	yes	complemented
162	#397	C₂²×C₅	1	8	yes	complemented
163	#394	C₂²×C₅	1	16	yes	complemented
164	#388	C₂²×C₅	1	16	yes	complemented
165	#386	C₂²×C₅	1	8	yes	complemented
166	#386	C₂²×C₅	1	8	yes	complemented
167	#385	C₂²×C₅	1	8	yes	complemented
168	#385	C₂²×C₅	1	8	yes	complemented
169	#381	C₂²×C₅	1	2	yes	complemented
170	#380	C₂²×C₅	1	8	yes	complemented
171	#379	C₂²×C₅	1	8	yes	—
172	#379	C₂²×C₅	1	8	yes	complemented
173	#379	C₂²×C₅	1	2	yes	complemented
174	C₂³×C₅	—	2	8	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	16	no	—
177	C₂³×C₅	—	2	32	no	—
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	4	no	—
180	C₂³×C₅	—	2	8	no	—
181	C₂³×C₅	—	2	8	no	—
182	C₂³×C₅	—	2	8	no	—
183	C₂³×C₅	—	2	4	no	—
184	C₂³×C₅	—	2	8	no	—
185	C₂³×C₅	—	4	8	no	—
186	C₂³×C₅	—	4	16	no	—
187	C₂³×C₅	—	4	8	no	—
188	C₂³×C₅	—	4	32	no	—
189	C₂³×C₅	—	4	32	no	—
190	C₂³×C₅	—	4	32	no	—
191	C₂³×C₅	—	4	8	no	—
192	C₂³×C₅	—	4	16	no	—
193	C₂³×C₅	—	4	128	no	—
194	C₂³×C₅	—	4	8	no	—
195	C₂³×C₅	—	4	16	no	—
196	C₂³×C₅	—	8	8	no	—
197	C₂³×C₅	#123	1	16	yes	complemented
198	C₂³×C₅	C₂²×D₄	1	4	yes	—
199	C₂³×C₅	C₂²×D₄	1	2	yes	—
200	C₂³×C₅	C₂²×D₄	1	4	yes	—
201	C₂³×C₅	C₂×#41	1	4	yes	—
202	C₂³×C₅	C₂×#41	1	4	yes	—
203	C₂³×C₅	C₂×#41	1	4	yes	—
204	C₂³×C₅	H(5,𝔽₂)	1	8	yes	—
205	C₂³×C₅	C₂⁵	1	1	yes	characteristic
206	C₅×D₄	—	2	32	no	—
207	C₅×D₄	—	4	32	no	—
208	C₂×C₄×C₅	—	2	8	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	8	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	8	no	—
213	C₂×C₄×C₅	—	2	16	no	—
214	C₂×C₄×C₅	—	2	16	no	—
215	C₂×C₄×C₅	—	2	8	no	—
216	C₂×C₄×C₅	—	4	8	no	—
217	C₂×C₄×C₅	—	8	8	no	—
218	C₂×C₄×C₅	—	8	8	no	—
219	C₂×C₄×C₅	—	8	8	no	—
220	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
221	C₂⁵	—	2	4	no	—
222	C₂⁵	—	2	8	no	—
223	C₂⁵	—	4	8	no	—
224	C₂⁵	C₂³×C₅	1	2	yes	—
225	C₂⁵	C₂³×C₅	1	4	yes	—
226	C₂⁵	C₂³×C₅	1	1	yes	characteristic
227	C₂⁵	C₂³×C₅	1	1	yes	characteristic
228	C₂²×D₄	—	2	8	no	—
229	C₂²×D₄	—	2	8	no	—
230	C₂²×D₄	—	4	8	no	—
231	C₂²×D₄	C₅×D₄	1	8	yes	—
232	C₂²×D₄	C₂³×C₅	1	8	yes	—
233	C₂²×D₄	C₂³×C₅	1	4	yes	—
234	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₅	1	2	yes	—
236	C₂³×C₄	C₂³×C₅	1	4	yes	—
237	C₂³×C₄	C₂³×C₅	1	4	yes	—
238	C₂³×C₄	C₂³×C₅	1	4	yes	complemented
239	#123	—	4	16	no	—
240	#120	—	2	32	no	—
241	C₄×D₄	—	2	32	no	—
242	#117	—	2	8	no	—
243	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
244	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	complemented
245	C₂×C₂²⋊C₄	—	2	8	no	—
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₂²⋊C₄	—	2	8	no	—
248	C₂×C₂²⋊C₄	—	2	8	no	—
249	C₂×C₂²⋊C₄	—	2	8	no	—
250	C₂×C₂²⋊C₄	—	4	16	no	—
251	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
252	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
253	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
254	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
260	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
261	C₂×C₄²	C₂³×C₅	1	4	yes	complemented
262	#95	C₂³×C₅	1	16	yes	complemented
263	#95	C₂³×C₅	1	8	yes	complemented
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	8	no	—
266	C₂²×C₅	—	2	8	no	—
267	C₂²×C₅	—	2	8	no	—
268	C₂²×C₅	—	2	8	no	—
269	C₂²×C₅	—	2	4	no	—
270	C₂²×C₅	—	2	8	no	—
271	C₂²×C₅	—	2	8	no	—
272	C₂²×C₅	—	2	16	no	—
273	C₂²×C₅	—	4	16	no	—
274	C₂²×C₅	—	4	32	no	—
275	C₂²×C₅	—	4	64	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	4	4	no	—
278	C₂²×C₅	—	4	8	no	—
279	C₂²×C₅	—	4	8	no	—
280	C₂²×C₅	—	8	8	no	—
281	C₂²×C₅	C₂×#123	1	4	yes	—
282	C₂²×C₅	C₂×#123	1	8	yes	—
283	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
284	C₂²×C₅	C₂²×#41	1	2	yes	—
285	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
286	C₄×C₅	—	2	4	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	—	4	8	no	—
289	C₄×C₅	—	4	8	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	16	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	8	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	4	4	no	—
299	C₂⁴	—	4	8	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	32	no	—
303	C₂⁴	—	4	64	no	—
304	C₂⁴	—	4	16	no	—
305	C₂⁴	C₂×C₅×D₄	1	4	yes	—
306	C₂⁴	C₂×C₅×D₄	1	4	yes	—
307	C₂⁴	C₅×#41	1	8	yes	—
308	C₂⁴	C₂⁴×C₅	1	2	yes	—
309	C₂⁴	C₂⁴×C₅	1	4	yes	—
310	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
311	C₂⁴	C₂⁴×C₅	1	2	yes	—
312	C₂×D₄	—	2	32	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	16	no	—
316	C₂×D₄	—	2	16	no	—
317	C₂×D₄	—	4	8	no	—
318	C₂×D₄	—	4	32	no	—
319	C₂×D₄	C₂×C₅×D₄	1	16	yes	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	—	4	8	no	—
329	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
333	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	4	16	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	32	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	—	4	16	no	—
345	C₂²⋊C₄	—	4	8	no	—
346	C₄²	—	2	8	no	—
347	C₂×C₅	—	2	4	no	—
348	C₂×C₅	—	2	8	no	—
349	C₂×C₅	—	4	8	no	—
350	C₂×C₅	—	4	4	no	—
351	C₂×C₅	C₂²×#123	1	1	yes	characteristic
352	C₂×C₅	#3484	1	2	yes	—
353	C₂×C₅	#3490	1	4	yes	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	16	no	—
357	C₂³	—	2	32	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	16	no	—
367	C₂³	—	4	8	no	—
368	C₂³	—	4	32	no	—
369	C₂³	—	4	32	no	—
370	C₂³	—	4	32	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	16	no	—
373	C₂³	—	4	128	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	16	no	—
376	C₂³	—	8	8	no	—
377	C₂³	C₅×#123	1	16	yes	complemented
378	C₂³	C₂²×C₅×D₄	1	4	yes	—
379	C₂³	C₂²×C₅×D₄	1	2	yes	—
380	C₂³	C₂²×C₅×D₄	1	4	yes	—
381	C₂³	C₂×C₅×#41	1	4	yes	—
382	C₂³	C₂×C₅×#41	1	4	yes	—
383	C₂³	C₂×C₅×#41	1	4	yes	—
384	C₂³	C₅×H(5,𝔽₂)	1	8	yes	—
385	C₂³	C₂⁵×C₅	1	1	yes	characteristic
386	D₄	—	2	32	no	—
387	D₄	—	4	32	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	8	8	no	—
398	C₂×C₄	—	8	8	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
401	C₅	#35350	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	2	16	no	—
411	C₂²	—	4	16	no	—
412	C₂²	—	4	32	no	—
413	C₂²	—	4	64	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₂×C₅×#123	1	4	yes	—
420	C₂²	C₂×C₅×#123	1	8	yes	—
421	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
422	C₂²	C₂²×C₅×#41	1	2	yes	—
423	C₂²	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	—	4	8	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	8	no	—
430	C₂	—	4	8	no	—
431	C₂	—	4	4	no	—
432	C₂	C₂²×C₅×#123	1	1	yes	characteristic
433	C₂	C₅×#3484	1	2	yes	—
434	C₂	C₅×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×#120	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#518	C₂	semidirect
3. C₅×#2482	C₂	semidirect
4. C₅×#2418	C₂	semidirect
5. C₅×#2405	C₂	semidirect
6. C₅×#2315	C₂	semidirect
7. C₅×#2308	C₂	semidirect
8. C₂×C₅×#379	C₂	semidirect
12. C₂×C₅×#123	C₂²	semidirect
16. C₂×C₄×C₅×D₄	C₂²	semidirect
17. C₂×C₅×#117	C₂²	semidirect
22. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
23. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₅×#399	C₂²	semidirect
25. C₅×#397	C₂²	semidirect
26. C₅×#394	C₂²	semidirect
27. C₅×#388	C₂²	semidirect
28. C₅×#386	C₂²	semidirect
29. C₅×#386	C₂²	semidirect
30. C₅×#385	C₂²	semidirect
31. C₅×#385	C₂²	semidirect
32. C₅×#381	C₂²	semidirect
33. C₅×#380	C₂²	semidirect
35. C₅×#379	C₂²	semidirect
36. C₅×#379	C₂²	semidirect
37. #35350	C₅	direct (N × H)
55. C₂³×C₄×C₅	C₂³	semidirect
60. C₂×C₅×C₄⋊C₄	C₂³	semidirect
61. C₂×C₅×C₄⋊C₄	C₂³	semidirect
76. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
77. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
78. C₂×C₄²×C₅	C₂³	semidirect
79. C₅×#95	C₂³	semidirect
80. C₅×#95	C₂³	semidirect
82. C₂×#518	C₂×C₅	semidirect
83. #2482	C₂×C₅	semidirect
84. #2418	C₂×C₅	semidirect
85. #2405	C₂×C₅	semidirect
86. #2315	C₂×C₅	semidirect
87. #2308	C₂×C₅	semidirect
88. C₂×#379	C₂×C₅	semidirect
149. C₂×#123	C₂²×C₅	semidirect
153. C₂×C₄×D₄	C₂²×C₅	semidirect
154. C₂×#117	C₂²×C₅	semidirect
159. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
160. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
161. #399	C₂²×C₅	semidirect
162. #397	C₂²×C₅	semidirect
163. #394	C₂²×C₅	semidirect
164. #388	C₂²×C₅	semidirect
165. #386	C₂²×C₅	semidirect
166. #386	C₂²×C₅	semidirect
167. #385	C₂²×C₅	semidirect
168. #385	C₂²×C₅	semidirect
169. #381	C₂²×C₅	semidirect
170. #380	C₂²×C₅	semidirect
172. #379	C₂²×C₅	semidirect
173. #379	C₂²×C₅	semidirect
197. C₂³×C₅	#123	semidirect
238. C₂³×C₄	C₂³×C₅	semidirect
243. C₂×C₄⋊C₄	C₂³×C₅	semidirect
244. C₂×C₄⋊C₄	C₂³×C₅	semidirect
259. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
260. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
261. C₂×C₄²	C₂³×C₅	semidirect
262. #95	C₂³×C₅	semidirect
263. #95	C₂³×C₅	semidirect
377. C₂³	C₅×#123	semidirect
401. C₅	#35350	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×#120	2
C₂×C₅×#518	2
C₅×#2482	2
C₅×#2418	2
C₅×#2405	2
C₅×#2315	2
C₅×#2308	2
C₂×C₅×#379	2
#35350	5

Subgroups — C5×#35350 #11958070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35350 #11958070