Subgroups — C₅×#34269 #11956989

Order 1280.

3426 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2367	C₂	1	4	yes	maximal, complemented
5	C₅×#2366	C₂	1	4	yes	maximal, complemented
6	C₅×#2358	C₂	1	8	yes	maximal, complemented
7	C₅×#2324	C₂	1	4	yes	maximal, complemented
8	C₅×#2311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#121	C₂	1	4	yes	maximal, complemented
10	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#535	C₄	1	16	yes	complemented
16	C₂×C₅×#127	C₂²	1	2	yes	—
17	C₂×C₅×#124	C₂²	1	2	yes	—
18	C₂×C₅×#121	C₂²	1	4	yes	—
19	C₂×C₅×#120	C₂²	1	4	yes	—
20	C₅×#518	—	2	8	no	—
21	C₄×C₅×#41	—	2	8	no	—
22	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
23	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
24	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
25	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
26	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
27	C₂×C₄×C₅×D₄	C₂²	1	8	yes	complemented
28	C₂×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₅×#117	C₂²	1	1	yes	characteristic
30	C₂×C₅×#117	C₂²	1	1	yes	characteristic
31	C₂×C₅×#117	C₂²	1	2	yes	complemented
32	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
34	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
37	C₅×#391	C₂²	1	2	yes	complemented
38	C₅×#390	C₂²	1	2	yes	—
39	C₅×#390	C₂²	1	2	yes	—
40	C₅×#390	C₂²	1	4	yes	—
41	C₅×#390	C₂²	1	2	yes	complemented
42	C₅×#390	C₂²	1	8	yes	complemented
43	C₅×#389	C₂²	1	2	yes	complemented
44	C₅×#389	C₂²	1	2	yes	complemented
45	C₅×#388	C₂²	1	8	yes	complemented
46	C₅×#388	C₂²	1	8	yes	complemented
47	C₅×#386	C₂²	1	4	yes	—
48	C₅×#386	C₂²	1	8	yes	complemented
49	C₅×#386	C₂²	1	8	yes	complemented
50	C₅×#385	C₂²	1	4	yes	—
51	C₅×#385	C₂²	1	8	yes	complemented
52	C₅×#380	C₂²	1	4	yes	complemented
53	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
54	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
55	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
56	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
57	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
58	#34269	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁵×C₅	C₂³	1	2	yes	—
60	C₂×C₅×#41	—	2	4	no	—
61	C₂×C₅×#41	—	2	4	no	—
62	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	—	2	4	no	—
65	C₂²×C₅×D₄	—	2	4	no	—
66	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
67	C₂²×C₅×D₄	C₂³	1	2	yes	—
68	C₂²×C₅×D₄	C₂³	1	2	yes	—
69	C₂²×C₅×D₄	C₂³	1	2	yes	—
70	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₄	C₂³	1	8	yes	—
72	C₂³×C₄×C₅	C₂³	1	2	yes	—
73	C₂³×C₄×C₅	C₂³	1	4	yes	—
74	C₂³×C₄×C₅	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	2	yes	—
76	C₂³×C₄×C₅	C₂³	1	8	yes	—
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₅×#127	C₂×C₄	1	16	yes	complemented
79	C₅×#124	C₂×C₄	1	16	yes	complemented
80	C₅×#121	C₂×C₄	1	32	yes	complemented
81	C₅×#120	C₂×C₄	1	32	yes	complemented
82	C₄×C₅×Q₈	—	2	8	no	—
83	C₄×C₅×D₄	—	2	16	no	—
84	C₄×C₅×D₄	—	2	8	no	—
85	C₄×C₅×D₄	—	2	16	no	—
86	C₄×C₅×D₄	—	2	16	no	—
87	C₄×C₅×D₄	—	4	16	no	—
88	C₅×#117	—	2	4	no	—
89	C₅×#117	—	2	8	no	—
90	C₅×#117	C₂×C₄	1	8	yes	complemented
91	C₅×#117	D₄	1	8	yes	complemented
92	C₂×C₅×C₄⋊C₄	—	2	4	no	—
93	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
102	C₂×C₅×C₂²⋊C₄	—	4	8	no	—
103	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₄²×C₅	—	2	4	no	—
113	C₂×C₄²×C₅	—	2	8	no	—
114	C₂×C₄²×C₅	C₂³	1	4	yes	—
115	C₂×C₄²×C₅	C₂³	1	2	yes	—
116	C₂×C₄²×C₅	C₂³	1	2	yes	—
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	8	yes	—
120	C₂×C₄²×C₅	C₂³	1	2	yes	—
121	C₂×C₄²×C₅	C₂³	1	2	yes	—
122	C₅×#95	C₂³	1	8	yes	—
123	C₅×#95	C₂³	1	4	yes	—
124	C₅×#95	C₂³	1	8	yes	—
125	C₅×#95	C₂³	1	4	yes	—
126	C₂×#535	C₂×C₅	1	1	yes	characteristic
127	C₂×#518	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
129	#2367	C₂×C₅	1	4	yes	complemented
130	#2366	C₂×C₅	1	4	yes	complemented
131	#2358	C₂×C₅	1	8	yes	complemented
132	#2324	C₂×C₅	1	4	yes	complemented
133	#2311	C₂×C₅	1	1	yes	characteristic, complemented
134	C₄×#121	C₂×C₅	1	4	yes	complemented
135	#2296	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×#390	C₂×C₅	1	1	yes	characteristic, complemented
137	#2274	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	—	2	4	no	—
139	C₂⁴×C₅	—	2	4	no	—
140	C₂⁴×C₅	—	4	4	no	—
141	C₂⁴×C₅	—	4	4	no	—
142	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
143	C₂⁴×C₅	C₂⁴	1	4	yes	—
144	C₂⁴×C₅	C₂⁴	1	2	yes	—
145	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
146	C₅×#41	—	2	32	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
150	C₂×C₅×D₄	—	2	4	no	—
151	C₂×C₅×D₄	—	2	4	no	—
152	C₂×C₅×D₄	—	2	32	no	—
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	2	2	no	—
156	C₂×C₅×D₄	—	2	4	no	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	4	8	no	—
160	C₂×C₅×D₄	—	4	8	no	—
161	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
162	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
163	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
164	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
165	C₂×C₅×D₄	C₂²×C₄	1	32	yes	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	2	4	no	—
170	C₂²×C₄×C₅	—	2	8	no	—
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	2	8	no	—
173	C₂²×C₄×C₅	—	2	16	no	—
174	C₂²×C₄×C₅	—	4	4	no	—
175	C₂²×C₄×C₅	—	4	2	no	—
176	C₂²×C₄×C₅	—	4	4	no	—
177	C₂²×C₄×C₅	—	4	8	no	—
178	C₂²×C₄×C₅	—	4	8	no	—
179	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
180	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₅	#41	1	4	yes	—
183	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
192	C₅×C₄⋊C₄	—	2	4	no	—
193	C₅×C₄⋊C₄	—	2	8	no	—
194	C₅×C₄⋊C₄	—	2	4	no	—
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	8	no	—
197	C₅×C₄⋊C₄	—	4	4	no	—
198	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
199	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
200	C₅×C₂²⋊C₄	—	2	4	no	—
201	C₅×C₂²⋊C₄	—	2	16	no	—
202	C₅×C₂²⋊C₄	—	2	8	no	—
203	C₅×C₂²⋊C₄	—	2	16	no	—
204	C₅×C₂²⋊C₄	—	4	8	no	—
205	C₅×C₂²⋊C₄	—	4	8	no	—
206	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
207	C₅×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
208	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
209	C₄²×C₅	—	2	2	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	8	no	—
212	C₄²×C₅	—	2	4	no	—
213	C₄²×C₅	—	2	4	no	—
214	C₄²×C₅	—	4	8	no	—
215	C₄²×C₅	C₂²×C₄	1	8	yes	—
216	C₄²×C₅	C₂×D₄	1	8	yes	—
217	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
218	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
219	#535	C₄×C₅	1	16	yes	complemented
220	C₂×#127	C₂²×C₅	1	2	yes	—
221	C₂×#124	C₂²×C₅	1	2	yes	—
222	C₂×#121	C₂²×C₅	1	4	yes	—
223	C₂×#120	C₂²×C₅	1	4	yes	—
224	#518	—	2	8	no	—
225	C₄×#41	—	2	8	no	—
226	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
227	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
228	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
229	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
230	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
231	C₂×C₄×D₄	C₂²×C₅	1	8	yes	complemented
232	C₂×#117	C₂²×C₅	1	1	yes	characteristic
233	C₂×#117	C₂²×C₅	1	1	yes	characteristic
234	C₂×#117	C₂²×C₅	1	1	yes	characteristic
235	C₂×#117	C₂²×C₅	1	2	yes	complemented
236	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
239	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
241	#391	C₂²×C₅	1	2	yes	complemented
242	#390	C₂²×C₅	1	2	yes	—
243	#390	C₂²×C₅	1	4	yes	—
244	#390	C₂²×C₅	1	2	yes	—
245	#390	C₂²×C₅	1	2	yes	complemented
246	#390	C₂²×C₅	1	8	yes	complemented
247	#389	C₂²×C₅	1	2	yes	complemented
248	#389	C₂²×C₅	1	2	yes	complemented
249	#388	C₂²×C₅	1	8	yes	complemented
250	#388	C₂²×C₅	1	8	yes	complemented
251	#386	C₂²×C₅	1	4	yes	—
252	#386	C₂²×C₅	1	8	yes	complemented
253	#386	C₂²×C₅	1	8	yes	complemented
254	#385	C₂²×C₅	1	4	yes	—
255	#385	C₂²×C₅	1	8	yes	complemented
256	#380	C₂²×C₅	1	4	yes	complemented
257	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
258	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
259	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
260	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
261	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	4	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	2	4	no	—
268	C₂³×C₅	—	2	8	no	—
269	C₂³×C₅	—	2	4	no	—
270	C₂³×C₅	—	2	4	no	—
271	C₂³×C₅	—	2	8	no	—
272	C₂³×C₅	—	2	16	no	—
273	C₂³×C₅	—	4	16	no	—
274	C₂³×C₅	—	8	8	no	—
275	C₂³×C₅	—	8	4	no	—
276	C₂³×C₅	—	8	4	no	—
277	C₂³×C₅	C₂³×C₄	1	8	yes	—
278	C₂³×C₅	C₂³×C₄	1	4	yes	—
279	C₂³×C₅	C₂³×C₄	1	2	yes	—
280	C₂³×C₅	C₂²×D₄	1	2	yes	—
281	C₂³×C₅	C₂×#41	1	2	yes	—
282	C₂³×C₅	C₂⁵	1	1	yes	characteristic
283	C₅×Q₈	—	2	8	no	—
284	C₅×D₄	—	2	16	no	—
285	C₅×D₄	—	2	16	no	—
286	C₅×D₄	—	2	16	no	—
287	C₅×D₄	—	2	8	no	—
288	C₅×D₄	—	4	32	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	4	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	2	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	4	no	—
297	C₂×C₄×C₅	—	2	16	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	8	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	4	no	—
306	C₂×C₄×C₅	—	4	16	no	—
307	C₂×C₄×C₅	—	4	8	no	—
308	C₂×C₄×C₅	—	8	16	no	—
309	C₂×C₄×C₅	—	8	4	no	—
310	C₂×C₄×C₅	C₄×D₄	1	16	yes	complemented
311	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
312	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
313	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
314	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
316	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₅	C₂×#41	1	2	yes	—
319	C₂×C₄×C₅	C₂×#41	1	2	yes	—
320	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
321	C₂⁵	C₂³×C₅	1	2	yes	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
325	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
329	C₂²×D₄	C₂³×C₅	1	2	yes	—
330	C₂²×D₄	C₂³×C₅	1	2	yes	—
331	C₂²×D₄	C₂³×C₅	1	2	yes	—
332	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₅	1	8	yes	—
334	C₂³×C₄	C₂³×C₅	1	2	yes	—
335	C₂³×C₄	C₂³×C₅	1	4	yes	—
336	C₂³×C₄	C₂³×C₅	1	2	yes	—
337	C₂³×C₄	C₂³×C₅	1	2	yes	—
338	C₂³×C₄	C₂³×C₅	1	8	yes	—
339	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
340	#127	C₂×C₄×C₅	1	16	yes	complemented
341	#124	C₂×C₄×C₅	1	16	yes	complemented
342	#121	C₂×C₄×C₅	1	32	yes	complemented
343	#120	C₂×C₄×C₅	1	32	yes	complemented
344	C₄×Q₈	—	2	8	no	—
345	C₄×D₄	—	2	16	no	—
346	C₄×D₄	—	2	8	no	—
347	C₄×D₄	—	2	16	no	—
348	C₄×D₄	—	2	16	no	—
349	C₄×D₄	—	4	16	no	—
350	#117	—	2	4	no	—
351	#117	—	2	8	no	—
352	#117	C₂×C₄×C₅	1	8	yes	complemented
353	#117	C₅×D₄	1	8	yes	complemented
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	16	no	—
364	C₂×C₂²⋊C₄	—	4	8	no	—
365	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
374	C₂×C₄²	—	2	4	no	—
375	C₂×C₄²	—	2	8	no	—
376	C₂×C₄²	C₂³×C₅	1	2	yes	—
377	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₅	1	4	yes	—
379	C₂×C₄²	C₂³×C₅	1	2	yes	—
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	8	yes	—
382	C₂×C₄²	C₂³×C₅	1	2	yes	—
383	C₂×C₄²	C₂³×C₅	1	2	yes	—
384	#95	C₂³×C₅	1	8	yes	—
385	#95	C₂³×C₅	1	4	yes	—
386	#95	C₂³×C₅	1	8	yes	—
387	#95	C₂³×C₅	1	4	yes	—
388	C₂²×C₅	—	2	4	no	—
389	C₂²×C₅	—	2	4	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	4	no	—
393	C₂²×C₅	—	2	8	no	—
394	C₂²×C₅	—	2	8	no	—
395	C₂²×C₅	—	2	16	no	—
396	C₂²×C₅	—	4	4	no	—
397	C₂²×C₅	—	4	8	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	4	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	4	no	—
402	C₂²×C₅	—	8	16	no	—
403	C₂²×C₅	C₂×C₄×D₄	1	4	yes	—
404	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
405	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
406	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
408	C₂²×C₅	#585	1	2	yes	—
409	C₄×C₅	—	2	4	no	—
410	C₄×C₅	—	2	8	no	—
411	C₄×C₅	—	2	4	no	—
412	C₄×C₅	—	2	8	no	—
413	C₄×C₅	—	4	2	no	—
414	C₄×C₅	—	4	4	no	—
415	C₄×C₅	—	4	4	no	—
416	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
417	C₄×C₅	C₂×C₄×D₄	1	4	yes	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	2	4	no	—
420	C₂⁴	—	4	4	no	—
421	C₂⁴	—	4	4	no	—
422	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
423	C₂⁴	C₂⁴×C₅	1	4	yes	—
424	C₂⁴	C₂⁴×C₅	1	2	yes	—
425	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
426	#41	—	2	32	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	32	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	4	8	no	—
440	C₂×D₄	—	4	8	no	—
441	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
442	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
443	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
444	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
445	C₂×D₄	C₂²×C₄×C₅	1	32	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	16	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	8	no	—
458	C₂²×C₄	—	4	8	no	—
459	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
460	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
461	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
462	C₂²×C₄	C₅×#41	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
479	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	16	no	—
484	C₂²⋊C₄	—	4	8	no	—
485	C₂²⋊C₄	—	4	8	no	—
486	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
487	C₂²⋊C₄	C₂²×C₄×C₅	1	32	yes	—
488	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	8	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	4	no	—
494	C₄²	—	4	8	no	—
495	C₄²	C₂²×C₄×C₅	1	8	yes	—
496	C₄²	C₂×C₅×D₄	1	8	yes	—
497	C₂×C₅	—	2	4	no	—
498	C₂×C₅	—	4	4	no	—
499	C₂×C₅	—	4	8	no	—
500	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
501	C₂×C₅	C₄×H(5,𝔽₂)	1	2	yes	—
502	C₂×C₅	#3488	1	2	yes	—
503	C₂×C₅	#3508	1	1	yes	characteristic
504	C₂×C₅	#3510	1	1	yes	characteristic
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	2	8	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	8	no	—
515	C₂³	—	2	16	no	—
516	C₂³	—	4	16	no	—
517	C₂³	—	8	8	no	—
518	C₂³	—	8	4	no	—
519	C₂³	—	8	4	no	—
520	C₂³	C₂³×C₄×C₅	1	8	yes	—
521	C₂³	C₂³×C₄×C₅	1	4	yes	—
522	C₂³	C₂³×C₄×C₅	1	2	yes	—
523	C₂³	C₂²×C₅×D₄	1	2	yes	—
524	C₂³	C₂×C₅×#41	1	2	yes	—
525	C₂³	C₂⁵×C₅	1	1	yes	characteristic
526	Q₈	—	2	8	no	—
527	D₄	—	2	16	no	—
528	D₄	—	2	16	no	—
529	D₄	—	2	16	no	—
530	D₄	—	2	8	no	—
531	D₄	—	4	32	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	16	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	4	16	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	8	16	no	—
552	C₂×C₄	—	8	4	no	—
553	C₂×C₄	C₄×C₅×D₄	1	16	yes	complemented
554	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
555	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
556	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
557	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
558	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
559	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
560	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
561	C₂×C₄	C₂×C₅×#41	1	2	yes	—
562	C₂×C₄	C₂×C₅×#41	1	2	yes	—
563	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
564	C₅	#34269	1	1	yes	characteristic, direct product factor, Sylow
565	C₂²	—	2	4	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	16	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	8	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	16	no	—
580	C₂²	C₂×C₄×C₅×D₄	1	4	yes	—
581	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
582	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
583	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
584	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
585	C₂²	C₅×#585	1	2	yes	—
586	C₄	—	2	4	no	—
587	C₄	—	2	8	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	8	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
594	C₄	C₂×C₄×C₅×D₄	1	4	yes	—
595	C₂	—	2	4	no	—
596	C₂	—	4	8	no	—
597	C₂	—	4	4	no	—
598	C₂	C₂²×C₄×C₅×D₄	1	1	yes	characteristic
599	C₂	C₄×C₅×H(5,𝔽₂)	1	2	yes	—
600	C₂	C₅×#3488	1	2	yes	—
601	C₂	C₅×#3508	1	1	yes	characteristic
602	C₂	C₅×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#535	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. C₂×C₅×#518	C₂	semidirect
3. C₂×C₄×C₅×#41	C₂	semidirect
4. C₅×#2367	C₂	semidirect
5. C₅×#2366	C₂	semidirect
6. C₅×#2358	C₂	semidirect
7. C₅×#2324	C₂	semidirect
8. C₅×#2311	C₂	semidirect
9. C₄×C₅×#121	C₂	semidirect
10. C₅×#2296	C₂	semidirect
11. C₂×C₅×#390	C₂	semidirect
12. C₅×#2274	C₂	semidirect
15. C₅×#535	C₄	semidirect
22. C₂×C₄×C₅×Q₈	C₂²	semidirect
26. C₂×C₄×C₅×D₄	C₂²	semidirect
27. C₂×C₄×C₅×D₄	C₂²	semidirect
31. C₂×C₅×#117	C₂²	semidirect
36. C₂²×C₄²×C₅	C₂²	semidirect
37. C₅×#391	C₂²	semidirect
41. C₅×#390	C₂²	semidirect
42. C₅×#390	C₂²	semidirect
43. C₅×#389	C₂²	semidirect
44. C₅×#389	C₂²	semidirect
45. C₅×#388	C₂²	semidirect
46. C₅×#388	C₂²	semidirect
48. C₅×#386	C₂²	semidirect
49. C₅×#386	C₂²	semidirect
51. C₅×#385	C₂²	semidirect
52. C₅×#380	C₂²	semidirect
53. C₄×C₅×C₄⋊C₄	C₂²	semidirect
54. C₄×C₅×C₄⋊C₄	C₂²	semidirect
55. C₄×C₅×C₄⋊C₄	C₂²	semidirect
57. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
58. #34269	C₅	direct (N × H)
62. C₂×C₅×#41	C₂×C₄	semidirect
66. C₂²×C₅×D₄	C₂×C₄	semidirect
78. C₅×#127	C₂×C₄	semidirect
79. C₅×#124	C₂×C₄	semidirect
80. C₅×#121	C₂×C₄	semidirect
81. C₅×#120	C₂×C₄	semidirect
90. C₅×#117	C₂×C₄	semidirect
91. C₅×#117	D₄	semidirect
127. C₂×#518	C₂×C₅	semidirect
128. C₂×C₄×#41	C₂×C₅	semidirect
129. #2367	C₂×C₅	semidirect
130. #2366	C₂×C₅	semidirect
131. #2358	C₂×C₅	semidirect
132. #2324	C₂×C₅	semidirect
133. #2311	C₂×C₅	semidirect
134. C₄×#121	C₂×C₅	semidirect
135. #2296	C₂×C₅	semidirect
136. C₂×#390	C₂×C₅	semidirect
137. #2274	C₂×C₅	semidirect
219. #535	C₄×C₅	semidirect
226. C₂×C₄×Q₈	C₂²×C₅	semidirect
230. C₂×C₄×D₄	C₂²×C₅	semidirect
231. C₂×C₄×D₄	C₂²×C₅	semidirect
235. C₂×#117	C₂²×C₅	semidirect
240. C₂²×C₄²	C₂²×C₅	semidirect
241. #391	C₂²×C₅	semidirect
245. #390	C₂²×C₅	semidirect
246. #390	C₂²×C₅	semidirect
247. #389	C₂²×C₅	semidirect
248. #389	C₂²×C₅	semidirect
249. #388	C₂²×C₅	semidirect
250. #388	C₂²×C₅	semidirect
252. #386	C₂²×C₅	semidirect
253. #386	C₂²×C₅	semidirect
255. #385	C₂²×C₅	semidirect
256. #380	C₂²×C₅	semidirect
257. C₄×C₄⋊C₄	C₂²×C₅	semidirect
258. C₄×C₄⋊C₄	C₂²×C₅	semidirect
259. C₄×C₄⋊C₄	C₂²×C₅	semidirect
261. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
310. C₂×C₄×C₅	C₄×D₄	semidirect
324. C₂×#41	C₂×C₄×C₅	semidirect
328. C₂²×D₄	C₂×C₄×C₅	semidirect
340. #127	C₂×C₄×C₅	semidirect
341. #124	C₂×C₄×C₅	semidirect
342. #121	C₂×C₄×C₅	semidirect
343. #120	C₂×C₄×C₅	semidirect
352. #117	C₂×C₄×C₅	semidirect
353. #117	C₅×D₄	semidirect
553. C₂×C₄	C₄×C₅×D₄	semidirect
564. C₅	#34269	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×#535	2
C₂×C₅×#518	2
C₂×C₄×C₅×#41	2
C₅×#2367	2
C₅×#2366	2
C₅×#2358	2
C₅×#2324	2
C₅×#2311	2
C₄×C₅×#121	2
C₅×#2296	2
C₂×C₅×#390	2
C₅×#2274	2
#34269	5

Subgroups — C5×#34269 #11956989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34269 #11956989