Subgroups — C₅×#34356 #11957076

Order 1280.

4134 conjugacy classes of subgroups.

The subgroup lattice has 562 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	C₅×#2375	C₂	1	4	yes	maximal, complemented
3	C₅×#2358	C₂	1	4	yes	maximal, complemented
4	C₅×#2342	C₂	1	4	yes	maximal, complemented
5	C₅×D₄×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₅×#2321	C₂	1	8	yes	maximal, complemented
7	C₅×#2312	C₂	1	2	yes	maximal, complemented
8	C₅×#2309	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2308	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#379	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₅×D₄	C₂²	1	2	yes	—
14	C₂×C₅×#120	C₄	1	16	yes	complemented
15	C₂×C₅×#120	C₂²	1	4	yes	—
16	C₂×C₅×#120	C₂²	1	2	yes	—
17	C₂×C₅×#120	C₂²	1	2	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
19	C₂×C₅×#117	C₂²	1	2	yes	complemented
20	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
26	C₅×#390	C₂²	1	4	yes	complemented
27	C₅×#390	C₂²	1	4	yes	complemented
28	C₅×#390	C₂²	1	8	yes	complemented
29	C₅×#388	C₂²	1	8	yes	complemented
30	C₅×#388	C₂²	1	8	yes	complemented
31	C₅×#388	C₂²	1	8	yes	complemented
32	C₅×#388	C₂²	1	8	yes	complemented
33	C₅×#386	C₂²	1	4	yes	complemented
34	C₅×#386	C₂²	1	4	yes	complemented
35	C₅×#386	C₂²	1	8	yes	complemented
36	C₅×#386	C₂²	1	8	yes	complemented
37	C₅×#385	C₂²	1	8	yes	complemented
38	C₅×#381	C₂²	1	2	yes	complemented
39	C₅×#380	C₂²	1	4	yes	complemented
40	C₅×#379	C₂²	1	2	yes	—
41	C₅×#379	C₂²	1	2	yes	—
42	C₅×#379	C₂²	1	4	yes	—
43	C₅×#379	C₂²	1	4	yes	complemented
44	C₅×#379	C₂²	1	4	yes	complemented
45	C₅×#379	C₂²	1	2	yes	complemented
46	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
47	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
48	#34356	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁵×C₅	—	4	4	no	—
50	C₂⁵×C₅	—	4	8	no	—
51	C₂⁵×C₅	C₂×C₄	1	8	yes	complemented
52	C₂⁵×C₅	C₂³	1	2	yes	—
53	C₂⁵×C₅	C₂³	1	1	yes	characteristic
54	C₂⁵×C₅	C₂³	1	1	yes	characteristic
55	C₂⁵×C₅	C₂³	1	2	yes	—
56	C₂⁵×C₅	C₂³	1	1	yes	characteristic
57	C₂⁵×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₅×D₄	—	4	4	no	—
59	C₂²×C₅×D₄	—	4	8	no	—
60	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
61	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
62	C₂²×C₅×D₄	C₂³	1	4	yes	—
63	C₂²×C₅×D₄	C₂³	1	2	yes	—
64	C₂²×C₅×D₄	C₂³	1	2	yes	—
65	C₂²×C₅×D₄	C₂³	1	4	yes	—
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	8	yes	—
68	C₂³×C₄×C₅	C₂³	1	2	yes	—
69	C₂³×C₄×C₅	C₂³	1	4	yes	complemented
70	C₅×#120	C₂×C₄	1	16	yes	complemented
71	C₅×#120	C₂×C₄	1	32	yes	complemented
72	C₅×#120	C₂×C₄	1	16	yes	complemented
73	C₄×C₅×D₄	—	4	16	no	—
74	C₅×#117	—	4	4	no	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
76	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
77	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
78	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
79	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
80	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
81	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
82	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
83	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
97	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
98	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
99	C₂×C₄²×C₅	C₂³	1	4	yes	complemented
100	C₅×#95	C₂³	1	8	yes	complemented
101	C₅×#95	C₂³	1	8	yes	complemented
102	C₅×#95	C₂³	1	8	yes	complemented
103	C₂²×#120	C₂×C₅	1	1	yes	characteristic
104	#2375	C₂×C₅	1	4	yes	complemented
105	#2358	C₂×C₅	1	4	yes	complemented
106	#2342	C₂×C₅	1	4	yes	complemented
107	D₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
108	#2321	C₂×C₅	1	8	yes	complemented
109	#2312	C₂×C₅	1	2	yes	complemented
110	#2309	C₂×C₅	1	1	yes	characteristic, complemented
111	#2308	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#379	C₂×C₅	1	2	yes	complemented
113	C₂⁴×C₅	—	2	8	no	—
114	C₂⁴×C₅	—	2	8	no	—
115	C₂⁴×C₅	—	2	8	no	—
116	C₂⁴×C₅	—	2	8	no	—
117	C₂⁴×C₅	—	2	4	no	—
118	C₂⁴×C₅	—	2	4	no	—
119	C₂⁴×C₅	—	4	32	no	—
120	C₂⁴×C₅	—	4	16	no	—
121	C₂⁴×C₅	—	4	2	no	—
122	C₂⁴×C₅	—	4	4	no	—
123	C₂⁴×C₅	—	4	4	no	—
124	C₂⁴×C₅	—	4	4	no	—
125	C₂⁴×C₅	—	4	4	no	—
126	C₂⁴×C₅	—	4	2	no	—
127	C₂⁴×C₅	—	4	4	no	—
128	C₂⁴×C₅	—	4	4	no	—
129	C₂⁴×C₅	—	4	64	no	—
130	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
131	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
132	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
133	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
134	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
135	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
136	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
137	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
138	C₂⁴×C₅	C₂⁴	1	2	yes	—
139	C₂⁴×C₅	C₂⁴	1	2	yes	—
140	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
141	C₂⁴×C₅	C₂⁴	1	2	yes	—
142	C₂×C₅×D₄	—	2	16	no	—
143	C₂×C₅×D₄	—	4	16	no	—
144	C₂×C₅×D₄	—	4	2	no	—
145	C₂×C₅×D₄	—	4	2	no	—
146	C₂×C₅×D₄	—	4	8	no	—
147	C₂×C₅×D₄	—	4	2	no	—
148	C₂×C₅×D₄	—	4	2	no	—
149	C₂×C₅×D₄	—	4	32	no	—
150	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
151	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
152	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
153	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
154	C₂²×C₄×C₅	—	2	4	no	—
155	C₂²×C₄×C₅	—	2	16	no	—
156	C₂²×C₄×C₅	—	4	4	no	—
157	C₂²×C₄×C₅	—	4	8	no	—
158	C₂²×C₄×C₅	—	4	8	no	—
159	C₂²×C₄×C₅	—	4	4	no	—
160	C₂²×C₄×C₅	—	4	8	no	—
161	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
162	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
163	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
164	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
165	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
167	C₅×C₄⋊C₄	—	4	4	no	—
168	C₅×C₄⋊C₄	—	4	8	no	—
169	C₅×C₂²⋊C₄	—	2	8	no	—
170	C₅×C₂²⋊C₄	—	2	8	no	—
171	C₅×C₂²⋊C₄	—	2	16	no	—
172	C₅×C₂²⋊C₄	—	4	4	no	—
173	C₅×C₂²⋊C₄	—	4	8	no	—
174	C₅×C₂²⋊C₄	—	4	4	no	—
175	C₅×C₂²⋊C₄	—	4	8	no	—
176	C₅×C₂²⋊C₄	—	4	4	no	—
177	C₅×C₂²⋊C₄	—	4	4	no	—
178	C₅×C₂²⋊C₄	—	4	4	no	—
179	C₅×C₂²⋊C₄	—	4	8	no	—
180	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
181	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
182	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
183	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
184	C₄²×C₅	—	4	4	no	—
185	C₄²×C₅	—	4	8	no	—
186	C₂⁶	C₂²×C₅	1	1	yes	characteristic
187	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂³×D₄	C₂²×C₅	1	2	yes	—
189	C₂×#120	C₄×C₅	1	16	yes	complemented
190	C₂×#120	C₂²×C₅	1	4	yes	—
191	C₂×#120	C₂²×C₅	1	2	yes	—
192	C₂×#120	C₂²×C₅	1	2	yes	—
193	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
194	C₂×#117	C₂²×C₅	1	2	yes	complemented
195	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
196	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
199	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
200	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
201	#390	C₂²×C₅	1	4	yes	complemented
202	#390	C₂²×C₅	1	4	yes	complemented
203	#390	C₂²×C₅	1	8	yes	complemented
204	#388	C₂²×C₅	1	8	yes	complemented
205	#388	C₂²×C₅	1	8	yes	complemented
206	#388	C₂²×C₅	1	8	yes	complemented
207	#388	C₂²×C₅	1	8	yes	complemented
208	#386	C₂²×C₅	1	4	yes	complemented
209	#386	C₂²×C₅	1	4	yes	complemented
210	#386	C₂²×C₅	1	8	yes	complemented
211	#386	C₂²×C₅	1	8	yes	complemented
212	#385	C₂²×C₅	1	8	yes	complemented
213	#381	C₂²×C₅	1	2	yes	complemented
214	#380	C₂²×C₅	1	4	yes	complemented
215	#379	C₂²×C₅	1	2	yes	—
216	#379	C₂²×C₅	1	2	yes	—
217	#379	C₂²×C₅	1	4	yes	—
218	#379	C₂²×C₅	1	4	yes	complemented
219	#379	C₂²×C₅	1	4	yes	complemented
220	#379	C₂²×C₅	1	2	yes	complemented
221	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
222	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	4	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	2	16	no	—
227	C₂³×C₅	—	2	8	no	—
228	C₂³×C₅	—	2	16	no	—
229	C₂³×C₅	—	2	16	no	—
230	C₂³×C₅	—	2	16	no	—
231	C₂³×C₅	—	2	2	no	—
232	C₂³×C₅	—	2	4	no	—
233	C₂³×C₅	—	2	4	no	—
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	2	8	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	4	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	2	8	no	—
242	C₂³×C₅	—	4	8	no	—
243	C₂³×C₅	—	4	8	no	—
244	C₂³×C₅	—	4	4	no	—
245	C₂³×C₅	—	4	8	no	—
246	C₂³×C₅	—	4	8	no	—
247	C₂³×C₅	—	4	4	no	—
248	C₂³×C₅	—	4	8	no	—
249	C₂³×C₅	—	4	8	no	—
250	C₂³×C₅	—	4	16	no	—
251	C₂³×C₅	—	4	32	no	—
252	C₂³×C₅	—	4	32	no	—
253	C₂³×C₅	—	4	16	no	—
254	C₂³×C₅	—	4	128	no	—
255	C₂³×C₅	—	4	16	no	—
256	C₂³×C₅	—	8	8	no	—
257	C₂³×C₅	C₂³×C₄	1	4	yes	—
258	C₂³×C₅	C₂³×C₄	1	2	yes	—
259	C₂³×C₅	C₂³×C₄	1	2	yes	—
260	C₂³×C₅	C₂³×C₄	1	4	yes	—
261	C₂³×C₅	C₂³×C₄	1	4	yes	—
262	C₂³×C₅	C₂³×C₄	1	2	yes	—
263	C₂³×C₅	H(5,𝔽₂)	1	4	yes	—
264	C₂³×C₅	H(5,𝔽₂)	1	8	yes	—
265	C₂³×C₅	C₂⁵	1	1	yes	characteristic
266	C₅×D₄	—	2	32	no	—
267	C₅×D₄	—	4	8	no	—
268	C₅×D₄	—	4	8	no	—
269	C₅×D₄	—	4	16	no	—
270	C₂×C₄×C₅	—	2	8	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	8	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	8	no	—
275	C₂×C₄×C₅	—	2	8	no	—
276	C₂×C₄×C₅	—	2	8	no	—
277	C₂×C₄×C₅	—	2	8	no	—
278	C₂×C₄×C₅	—	2	8	no	—
279	C₂×C₄×C₅	—	2	8	no	—
280	C₂×C₄×C₅	—	4	8	no	—
281	C₂×C₄×C₅	—	8	16	no	—
282	C₂×C₄×C₅	—	8	8	no	—
283	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
284	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
285	C₂⁵	—	4	4	no	—
286	C₂⁵	—	4	8	no	—
287	C₂⁵	C₂×C₄×C₅	1	8	yes	complemented
288	C₂⁵	C₂³×C₅	1	2	yes	—
289	C₂⁵	C₂³×C₅	1	1	yes	characteristic
290	C₂⁵	C₂³×C₅	1	1	yes	characteristic
291	C₂⁵	C₂³×C₅	1	2	yes	—
292	C₂⁵	C₂³×C₅	1	1	yes	characteristic
293	C₂⁵	C₂³×C₅	1	1	yes	characteristic
294	C₂²×D₄	—	4	4	no	—
295	C₂²×D₄	—	4	8	no	—
296	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
297	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
298	C₂²×D₄	C₂³×C₅	1	4	yes	—
299	C₂²×D₄	C₂³×C₅	1	2	yes	—
300	C₂²×D₄	C₂³×C₅	1	4	yes	—
301	C₂²×D₄	C₂³×C₅	1	2	yes	—
302	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₅	1	8	yes	—
304	C₂³×C₄	C₂³×C₅	1	2	yes	—
305	C₂³×C₄	C₂³×C₅	1	4	yes	complemented
306	#120	C₂×C₄×C₅	1	16	yes	complemented
307	#120	C₂×C₄×C₅	1	32	yes	complemented
308	#120	C₂×C₄×C₅	1	16	yes	complemented
309	C₄×D₄	—	4	16	no	—
310	#117	—	4	4	no	—
311	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
312	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
313	C₂×C₂²⋊C₄	—	4	8	no	—
314	C₂×C₂²⋊C₄	—	4	4	no	—
315	C₂×C₂²⋊C₄	—	4	8	no	—
316	C₂×C₂²⋊C₄	—	4	8	no	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
318	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
319	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
333	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
334	C₂×C₄²	C₂³×C₅	1	4	yes	complemented
335	C₂×C₄²	C₂³×C₅	1	8	yes	complemented
336	#95	C₂³×C₅	1	8	yes	complemented
337	#95	C₂³×C₅	1	8	yes	complemented
338	#95	C₂³×C₅	1	8	yes	complemented
339	C₂²×C₅	—	2	4	no	—
340	C₂²×C₅	—	2	4	no	—
341	C₂²×C₅	—	2	4	no	—
342	C₂²×C₅	—	2	16	no	—
343	C₂²×C₅	—	2	8	no	—
344	C₂²×C₅	—	2	8	no	—
345	C₂²×C₅	—	2	2	no	—
346	C₂²×C₅	—	2	4	no	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	4	no	—
349	C₂²×C₅	—	2	4	no	—
350	C₂²×C₅	—	2	4	no	—
351	C₂²×C₅	—	2	4	no	—
352	C₂²×C₅	—	2	4	no	—
353	C₂²×C₅	—	4	32	no	—
354	C₂²×C₅	—	4	16	no	—
355	C₂²×C₅	—	4	16	no	—
356	C₂²×C₅	—	4	32	no	—
357	C₂²×C₅	—	4	16	no	—
358	C₂²×C₅	—	4	4	no	—
359	C₂²×C₅	—	4	4	no	—
360	C₂²×C₅	—	4	8	no	—
361	C₂²×C₅	—	4	4	no	—
362	C₂²×C₅	—	4	4	no	—
363	C₂²×C₅	—	8	8	no	—
364	C₂²×C₅	#518	1	4	yes	—
365	C₂²×C₅	#518	1	8	yes	—
366	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
367	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
368	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
369	C₄×C₅	—	2	4	no	—
370	C₄×C₅	—	2	8	no	—
371	C₄×C₅	—	4	8	no	—
372	C₄×C₅	—	4	8	no	—
373	C₂⁴	—	2	8	no	—
374	C₂⁴	—	2	8	no	—
375	C₂⁴	—	2	8	no	—
376	C₂⁴	—	2	8	no	—
377	C₂⁴	—	2	4	no	—
378	C₂⁴	—	2	4	no	—
379	C₂⁴	—	4	32	no	—
380	C₂⁴	—	4	16	no	—
381	C₂⁴	—	4	2	no	—
382	C₂⁴	—	4	4	no	—
383	C₂⁴	—	4	4	no	—
384	C₂⁴	—	4	4	no	—
385	C₂⁴	—	4	4	no	—
386	C₂⁴	—	4	2	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	—	4	4	no	—
389	C₂⁴	—	4	64	no	—
390	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
391	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
392	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
393	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
394	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
395	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
396	C₂⁴	C₂⁴×C₅	1	2	yes	—
397	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
398	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
399	C₂⁴	C₂⁴×C₅	1	2	yes	—
400	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
401	C₂⁴	C₂⁴×C₅	1	2	yes	—
402	C₂×D₄	—	2	16	no	—
403	C₂×D₄	—	4	16	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	32	no	—
410	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
411	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
412	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
413	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	16	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	8	no	—
418	C₂²×C₄	—	4	8	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
422	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
423	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
424	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
425	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	16	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	8	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	8	no	—
440	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
441	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
442	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
443	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
444	C₄²	—	4	4	no	—
445	C₄²	—	4	8	no	—
446	C₂×C₅	—	2	4	no	—
447	C₂×C₅	—	2	8	no	—
448	C₂×C₅	—	4	4	no	—
449	C₂×C₅	—	4	2	no	—
450	C₂×C₅	—	4	2	no	—
451	C₂×C₅	—	4	4	no	—
452	C₂×C₅	C₂×#518	1	1	yes	characteristic
453	C₂×C₅	C₂×#518	1	2	yes	—
454	C₂×C₅	#3532	1	4	yes	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	16	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	16	no	—
461	C₂³	—	2	16	no	—
462	C₂³	—	2	16	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	8	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	4	8	no	—
475	C₂³	—	4	8	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	8	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	16	no	—
483	C₂³	—	4	32	no	—
484	C₂³	—	4	32	no	—
485	C₂³	—	4	16	no	—
486	C₂³	—	4	128	no	—
487	C₂³	—	4	16	no	—
488	C₂³	—	8	8	no	—
489	C₂³	C₂³×C₄×C₅	1	4	yes	—
490	C₂³	C₂³×C₄×C₅	1	2	yes	—
491	C₂³	C₂³×C₄×C₅	1	2	yes	—
492	C₂³	C₂³×C₄×C₅	1	4	yes	—
493	C₂³	C₂³×C₄×C₅	1	4	yes	—
494	C₂³	C₂³×C₄×C₅	1	2	yes	—
495	C₂³	C₅×H(5,𝔽₂)	1	4	yes	—
496	C₂³	C₅×H(5,𝔽₂)	1	8	yes	—
497	C₂³	C₂⁵×C₅	1	1	yes	characteristic
498	D₄	—	2	32	no	—
499	D₄	—	4	8	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	16	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	8	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	8	16	no	—
514	C₂×C₄	—	8	8	no	—
515	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
516	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
517	C₅	#34356	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	16	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	32	no	—
533	C₂²	—	4	16	no	—
534	C₂²	—	4	16	no	—
535	C₂²	—	4	32	no	—
536	C₂²	—	4	16	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	8	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	8	8	no	—
543	C₂²	C₅×#518	1	4	yes	—
544	C₂²	C₅×#518	1	8	yes	—
545	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
546	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
547	C₂²	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
548	C₄	—	2	4	no	—
549	C₄	—	2	8	no	—
550	C₄	—	4	8	no	—
551	C₄	—	4	8	no	—
552	C₂	—	2	4	no	—
553	C₂	—	2	8	no	—
554	C₂	—	4	4	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	4	4	no	—
558	C₂	C₂×C₅×#518	1	1	yes	characteristic
559	C₂	C₂×C₅×#518	1	2	yes	—
560	C₂	C₅×#3532	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2375	C₂	semidirect
3. C₅×#2358	C₂	semidirect
4. C₅×#2342	C₂	semidirect
5. C₅×D₄×C₂²⋊C₄	C₂	semidirect
6. C₅×#2321	C₂	semidirect
7. C₅×#2312	C₂	semidirect
8. C₅×#2309	C₂	semidirect
9. C₅×#2308	C₂	semidirect
10. C₂×C₅×#379	C₂	semidirect
14. C₂×C₅×#120	C₄	semidirect
18. C₂×C₄×C₅×D₄	C₂²	semidirect
19. C₂×C₅×#117	C₂²	semidirect
23. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₅×#390	C₂²	semidirect
27. C₅×#390	C₂²	semidirect
28. C₅×#390	C₂²	semidirect
29. C₅×#388	C₂²	semidirect
30. C₅×#388	C₂²	semidirect
31. C₅×#388	C₂²	semidirect
32. C₅×#388	C₂²	semidirect
33. C₅×#386	C₂²	semidirect
34. C₅×#386	C₂²	semidirect
35. C₅×#386	C₂²	semidirect
36. C₅×#386	C₂²	semidirect
37. C₅×#385	C₂²	semidirect
38. C₅×#381	C₂²	semidirect
39. C₅×#380	C₂²	semidirect
43. C₅×#379	C₂²	semidirect
44. C₅×#379	C₂²	semidirect
45. C₅×#379	C₂²	semidirect
46. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
47. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
48. #34356	C₅	direct (N × H)
51. C₂⁵×C₅	C₂×C₄	semidirect
60. C₂²×C₅×D₄	C₂×C₄	semidirect
61. C₂²×C₅×D₄	C₂×C₄	semidirect
69. C₂³×C₄×C₅	C₂³	semidirect
70. C₅×#120	C₂×C₄	semidirect
71. C₅×#120	C₂×C₄	semidirect
72. C₅×#120	C₂×C₄	semidirect
75. C₂×C₅×C₄⋊C₄	C₂³	semidirect
76. C₂×C₅×C₄⋊C₄	C₂³	semidirect
81. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
82. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
96. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
97. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
98. C₂×C₄²×C₅	C₂³	semidirect
99. C₂×C₄²×C₅	C₂³	semidirect
100. C₅×#95	C₂³	semidirect
101. C₅×#95	C₂³	semidirect
102. C₅×#95	C₂³	semidirect
104. #2375	C₂×C₅	semidirect
105. #2358	C₂×C₅	semidirect
106. #2342	C₂×C₅	semidirect
107. D₄×C₂²⋊C₄	C₂×C₅	semidirect
108. #2321	C₂×C₅	semidirect
109. #2312	C₂×C₅	semidirect
110. #2309	C₂×C₅	semidirect
111. #2308	C₂×C₅	semidirect
112. C₂×#379	C₂×C₅	semidirect
189. C₂×#120	C₄×C₅	semidirect
193. C₂×C₄×D₄	C₂²×C₅	semidirect
194. C₂×#117	C₂²×C₅	semidirect
198. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
199. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
200. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
201. #390	C₂²×C₅	semidirect
202. #390	C₂²×C₅	semidirect
203. #390	C₂²×C₅	semidirect
204. #388	C₂²×C₅	semidirect
205. #388	C₂²×C₅	semidirect
206. #388	C₂²×C₅	semidirect
207. #388	C₂²×C₅	semidirect
208. #386	C₂²×C₅	semidirect
209. #386	C₂²×C₅	semidirect
210. #386	C₂²×C₅	semidirect
211. #386	C₂²×C₅	semidirect
212. #385	C₂²×C₅	semidirect
213. #381	C₂²×C₅	semidirect
214. #380	C₂²×C₅	semidirect
218. #379	C₂²×C₅	semidirect
219. #379	C₂²×C₅	semidirect
220. #379	C₂²×C₅	semidirect
221. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
222. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
287. C₂⁵	C₂×C₄×C₅	semidirect
296. C₂²×D₄	C₂×C₄×C₅	semidirect
297. C₂²×D₄	C₂×C₄×C₅	semidirect
305. C₂³×C₄	C₂³×C₅	semidirect
306. #120	C₂×C₄×C₅	semidirect
307. #120	C₂×C₄×C₅	semidirect
308. #120	C₂×C₄×C₅	semidirect
311. C₂×C₄⋊C₄	C₂³×C₅	semidirect
312. C₂×C₄⋊C₄	C₂³×C₅	semidirect
317. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
318. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
332. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
333. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
334. C₂×C₄²	C₂³×C₅	semidirect
335. C₂×C₄²	C₂³×C₅	semidirect
336. #95	C₂³×C₅	semidirect
337. #95	C₂³×C₅	semidirect
338. #95	C₂³×C₅	semidirect
517. C₅	#34356	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
C₅×#2375	2
C₅×#2358	2
C₅×#2342	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2321	2
C₅×#2312	2
C₅×#2309	2
C₅×#2308	2
C₂×C₅×#379	2
#34356	5

Subgroups — C5×#34356 #11957076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34356 #11957076