Subgroups — C₂×C₅×#2650 #11957303

Order 1280.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2650	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#397	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#397	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#396	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#393	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic
13	C₂×C₅×#388	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₅×#400	C₂²	1	8	yes	complemented
37	C₅×#400	C₂²	1	8	yes	complemented
38	C₅×#400	C₂²	1	8	yes	complemented
39	C₅×#397	C₂²	1	8	yes	—
40	C₅×#397	C₂²	1	8	yes	—
41	C₅×#396	C₂²	1	8	yes	—
42	C₅×#395	C₂²	1	8	yes	complemented
43	C₅×#393	C₂²	1	8	yes	—
44	C₅×#391	C₂²	1	8	yes	complemented
45	C₅×#388	C₂²	1	8	yes	—
46	C₅×#388	C₂²	1	8	yes	—
47	C₅×#388	C₂²	1	8	yes	—
48	C₅×#387	C₂²	1	8	yes	complemented
49	C₅×#387	C₂²	1	8	yes	complemented
50	C₄×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
51	C₂×C₅×#95	C₂²	1	1	yes	characteristic
52	C₂×C₅×#95	C₂²	1	1	yes	characteristic
53	C₂×C₅×#95	C₂²	1	1	yes	characteristic
54	C₂×C₅×#95	C₂²	1	1	yes	characteristic
55	C₂×C₅×#95	C₂²	1	1	yes	characteristic
56	C₂×C₅×#95	C₂²	1	1	yes	characteristic
57	C₂×C₅×#95	C₂²	1	1	yes	characteristic
58	C₂×C₅×#95	C₂²	1	1	yes	characteristic
59	C₂×C₅×#95	C₂²	1	1	yes	characteristic
60	C₂×C₅×#95	C₂²	1	1	yes	characteristic
61	C₂×C₅×#95	C₂²	1	1	yes	characteristic
62	C₂×C₅×#95	C₂²	1	1	yes	characteristic
63	C₂×C₅×#95	C₂²	1	1	yes	characteristic
64	C₂×C₅×#95	C₂²	1	1	yes	characteristic
65	C₂×C₅×#95	C₂²	1	1	yes	characteristic
66	C₂×C₅×#95	C₂²	1	1	yes	characteristic
67	C₂×#2650	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁵×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Q₈	—	2	4	no	—
70	C₂²×C₅×Q₈	—	4	2	no	—
71	C₂²×C₅×Q₈	—	4	2	no	—
72	C₂²×C₅×Q₈	C₂³	1	4	yes	—
73	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	—	2	4	no	—
88	C₂×C₅×C₄⋊C₄	—	2	4	no	—
89	C₂×C₅×C₄⋊C₄	—	2	4	no	—
90	C₂×C₅×C₄⋊C₄	—	2	4	no	—
91	C₂×C₅×C₄⋊C₄	—	4	2	no	—
92	C₂×C₅×C₄⋊C₄	—	4	2	no	—
93	C₂×C₅×C₄⋊C₄	—	4	2	no	—
94	C₂×C₅×C₄⋊C₄	—	4	2	no	—
95	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
106	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
107	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
108	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
109	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
110	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₄²×C₅	—	2	4	no	—
118	C₂×C₄²×C₅	—	4	2	no	—
119	C₂×C₄²×C₅	—	4	2	no	—
120	C₂×C₄²×C₅	C₂³	1	4	yes	—
121	C₂×C₄²×C₅	C₂³	1	4	yes	—
122	C₂×C₄²×C₅	C₂³	1	4	yes	—
123	C₅×#95	C₂³	1	4	yes	—
124	C₅×#95	C₂³	1	4	yes	—
125	C₅×#95	C₂³	1	4	yes	—
126	C₅×#95	C₂³	1	4	yes	—
127	C₅×#95	C₂³	1	4	yes	—
128	C₅×#95	C₂³	1	4	yes	—
129	C₅×#95	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	4	yes	—
131	C₅×#95	C₂³	1	4	yes	—
132	C₅×#95	C₂³	1	4	yes	—
133	C₅×#95	C₂³	1	4	yes	—
134	C₅×#95	C₂³	1	4	yes	—
135	C₅×#95	C₂³	1	4	yes	—
136	C₅×#95	C₂³	1	4	yes	—
137	C₅×#95	C₂³	1	4	yes	—
138	C₅×#95	C₂³	1	4	yes	—
139	#2650	C₂×C₅	1	16	yes	direct product factor
140	C₂×#400	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#400	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#400	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×#397	C₂×C₅	1	1	yes	characteristic
144	C₂×#397	C₂×C₅	1	1	yes	characteristic
145	C₂×#396	C₂×C₅	1	1	yes	characteristic
146	C₂×#395	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#393	C₂×C₅	1	1	yes	characteristic
148	C₂×#391	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#388	C₂×C₅	1	1	yes	characteristic
150	C₂×#388	C₂×C₅	1	1	yes	characteristic
151	C₂×#388	C₂×C₅	1	1	yes	characteristic
152	C₂×#387	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#387	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂⁴×C₅	—	2	2	no	—
156	C₂⁴×C₅	—	2	2	no	—
157	C₂⁴×C₅	—	2	2	no	—
158	C₂⁴×C₅	—	2	2	no	—
159	C₂⁴×C₅	—	2	2	no	—
160	C₂⁴×C₅	—	2	2	no	—
161	C₂⁴×C₅	—	2	2	no	—
162	C₂⁴×C₅	C₂⁴	1	2	yes	—
163	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
164	C₂×C₅×Q₈	—	2	8	no	—
165	C₂×C₅×Q₈	—	4	4	no	—
166	C₂×C₅×Q₈	—	4	4	no	—
167	C₂×C₅×Q₈	—	4	16	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	2	no	—
172	C₂²×C₄×C₅	—	2	2	no	—
173	C₂²×C₄×C₅	—	2	2	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	—	2	2	no	—
178	C₂²×C₄×C₅	—	2	2	no	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	2	2	no	—
184	C₂²×C₄×C₅	—	2	2	no	—
185	C₂²×C₄×C₅	—	2	2	no	—
186	C₂²×C₄×C₅	—	2	2	no	—
187	C₂²×C₄×C₅	—	2	2	no	—
188	C₂²×C₄×C₅	—	2	2	no	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	—	2	2	no	—
192	C₂²×C₄×C₅	—	2	2	no	—
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	—	2	2	no	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	—	2	2	no	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	#41	1	4	yes	—
208	C₂²×C₄×C₅	#41	1	4	yes	—
209	C₂²×C₄×C₅	#41	1	4	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
224	C₅×C₄⋊C₄	—	2	8	no	—
225	C₅×C₄⋊C₄	—	2	8	no	—
226	C₅×C₄⋊C₄	—	2	8	no	—
227	C₅×C₄⋊C₄	—	2	8	no	—
228	C₅×C₄⋊C₄	—	4	4	no	—
229	C₅×C₄⋊C₄	—	4	4	no	—
230	C₅×C₄⋊C₄	—	4	4	no	—
231	C₅×C₄⋊C₄	—	4	4	no	—
232	C₅×C₂²⋊C₄	—	2	8	no	—
233	C₅×C₂²⋊C₄	—	2	8	no	—
234	C₅×C₂²⋊C₄	—	2	8	no	—
235	C₅×C₂²⋊C₄	—	4	4	no	—
236	C₅×C₂²⋊C₄	—	4	4	no	—
237	C₅×C₂²⋊C₄	—	4	4	no	—
238	C₅×C₂²⋊C₄	—	4	4	no	—
239	C₄²×C₅	—	2	8	no	—
240	C₄²×C₅	—	4	4	no	—
241	C₄²×C₅	—	4	4	no	—
242	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
259	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
261	#400	C₂²×C₅	1	8	yes	complemented
262	#400	C₂²×C₅	1	8	yes	complemented
263	#400	C₂²×C₅	1	8	yes	complemented
264	#397	C₂²×C₅	1	8	yes	—
265	#397	C₂²×C₅	1	8	yes	—
266	#396	C₂²×C₅	1	8	yes	—
267	#395	C₂²×C₅	1	8	yes	complemented
268	#393	C₂²×C₅	1	8	yes	—
269	#391	C₂²×C₅	1	8	yes	complemented
270	#388	C₂²×C₅	1	8	yes	—
271	#388	C₂²×C₅	1	8	yes	—
272	#388	C₂²×C₅	1	8	yes	—
273	#387	C₂²×C₅	1	8	yes	complemented
274	#387	C₂²×C₅	1	8	yes	complemented
275	C₄×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
276	C₂×#95	C₂²×C₅	1	1	yes	characteristic
277	C₂×#95	C₂²×C₅	1	1	yes	characteristic
278	C₂×#95	C₂²×C₅	1	1	yes	characteristic
279	C₂×#95	C₂²×C₅	1	1	yes	characteristic
280	C₂×#95	C₂²×C₅	1	1	yes	characteristic
281	C₂×#95	C₂²×C₅	1	1	yes	characteristic
282	C₂×#95	C₂²×C₅	1	1	yes	characteristic
283	C₂×#95	C₂²×C₅	1	1	yes	characteristic
284	C₂×#95	C₂²×C₅	1	1	yes	characteristic
285	C₂×#95	C₂²×C₅	1	1	yes	characteristic
286	C₂×#95	C₂²×C₅	1	1	yes	characteristic
287	C₂×#95	C₂²×C₅	1	1	yes	characteristic
288	C₂×#95	C₂²×C₅	1	1	yes	characteristic
289	C₂×#95	C₂²×C₅	1	1	yes	characteristic
290	C₂×#95	C₂²×C₅	1	1	yes	characteristic
291	C₂×#95	C₂²×C₅	1	1	yes	characteristic
292	C₂³×C₅	—	2	2	no	—
293	C₂³×C₅	—	2	2	no	—
294	C₂³×C₅	—	2	2	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	2	no	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	4	4	no	—
300	C₂³×C₅	—	4	4	no	—
301	C₂³×C₅	—	4	4	no	—
302	C₂³×C₅	—	4	4	no	—
303	C₂³×C₅	—	4	4	no	—
304	C₂³×C₅	—	4	4	no	—
305	C₂³×C₅	—	4	4	no	—
306	C₂³×C₅	C₂×#41	1	2	yes	—
307	C₂³×C₅	C₂×#41	1	2	yes	—
308	C₂³×C₅	C₂×#41	1	2	yes	—
309	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
310	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
311	C₂³×C₅	2₋¹⁺⁴	1	2	yes	—
312	C₂³×C₅	2₋¹⁺⁴	1	2	yes	—
313	C₂³×C₅	C₂⁵	1	1	yes	characteristic
314	C₅×Q₈	—	4	16	no	—
315	C₂×C₄×C₅	—	2	8	no	—
316	C₂×C₄×C₅	—	2	8	no	—
317	C₂×C₄×C₅	—	2	8	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	2	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	4	4	no	—
358	C₂×C₄×C₅	—	4	4	no	—
359	C₂×C₄×C₅	—	4	4	no	—
360	C₂×C₄×C₅	—	4	4	no	—
361	C₂×C₄×C₅	—	4	4	no	—
362	C₂×C₄×C₅	—	4	4	no	—
363	C₂×C₄×C₅	—	4	4	no	—
364	C₂×C₄×C₅	—	4	4	no	—
365	C₂×C₄×C₅	—	4	4	no	—
366	C₂×C₄×C₅	—	4	4	no	—
367	C₂×C₄×C₅	—	4	4	no	—
368	C₂×C₄×C₅	C₂×#41	1	4	yes	—
369	C₂×C₄×C₅	C₂×#41	1	4	yes	—
370	C₂×C₄×C₅	C₂×#41	1	4	yes	—
371	C₂⁵	C₂³×C₅	1	1	yes	characteristic
372	C₂²×Q₈	—	2	4	no	—
373	C₂²×Q₈	—	4	2	no	—
374	C₂²×Q₈	—	4	2	no	—
375	C₂²×Q₈	C₂³×C₅	1	4	yes	—
376	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	2	4	no	—
391	C₂×C₄⋊C₄	—	2	4	no	—
392	C₂×C₄⋊C₄	—	2	4	no	—
393	C₂×C₄⋊C₄	—	2	4	no	—
394	C₂×C₄⋊C₄	—	4	2	no	—
395	C₂×C₄⋊C₄	—	4	2	no	—
396	C₂×C₄⋊C₄	—	4	2	no	—
397	C₂×C₄⋊C₄	—	4	2	no	—
398	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
406	C₂×C₂²⋊C₄	—	2	4	no	—
407	C₂×C₂²⋊C₄	—	2	4	no	—
408	C₂×C₂²⋊C₄	—	2	4	no	—
409	C₂×C₂²⋊C₄	—	4	2	no	—
410	C₂×C₂²⋊C₄	—	4	2	no	—
411	C₂×C₂²⋊C₄	—	4	2	no	—
412	C₂×C₂²⋊C₄	—	4	2	no	—
413	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
420	C₂×C₄²	—	2	4	no	—
421	C₂×C₄²	—	4	2	no	—
422	C₂×C₄²	—	4	2	no	—
423	C₂×C₄²	C₂³×C₅	1	4	yes	—
424	C₂×C₄²	C₂³×C₅	1	4	yes	—
425	C₂×C₄²	C₂³×C₅	1	4	yes	—
426	#95	C₂³×C₅	1	4	yes	—
427	#95	C₂³×C₅	1	4	yes	—
428	#95	C₂³×C₅	1	4	yes	—
429	#95	C₂³×C₅	1	4	yes	—
430	#95	C₂³×C₅	1	4	yes	—
431	#95	C₂³×C₅	1	4	yes	—
432	#95	C₂³×C₅	1	4	yes	—
433	#95	C₂³×C₅	1	4	yes	—
434	#95	C₂³×C₅	1	4	yes	—
435	#95	C₂³×C₅	1	4	yes	—
436	#95	C₂³×C₅	1	4	yes	—
437	#95	C₂³×C₅	1	4	yes	—
438	#95	C₂³×C₅	1	4	yes	—
439	#95	C₂³×C₅	1	4	yes	—
440	#95	C₂³×C₅	1	4	yes	—
441	#95	C₂³×C₅	1	4	yes	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	8	8	no	—
450	C₂²×C₅	#529	1	4	yes	—
451	C₂²×C₅	#538	1	4	yes	—
452	C₂²×C₅	#539	1	4	yes	—
453	C₂²×C₅	#541	1	4	yes	—
454	C₂²×C₅	#542	1	4	yes	—
455	C₂²×C₅	#542	1	4	yes	—
456	C₂²×C₅	#542	1	4	yes	—
457	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₄×C₅	—	2	4	no	—
465	C₄×C₅	—	2	4	no	—
466	C₄×C₅	—	2	4	no	—
467	C₄×C₅	—	4	2	no	—
468	C₄×C₅	—	4	2	no	—
469	C₄×C₅	—	4	2	no	—
470	C₄×C₅	—	4	2	no	—
471	C₄×C₅	—	4	2	no	—
472	C₄×C₅	—	4	2	no	—
473	C₄×C₅	—	4	2	no	—
474	C₄×C₅	—	4	2	no	—
475	C₄×C₅	—	4	2	no	—
476	C₄×C₅	—	4	2	no	—
477	C₄×C₅	—	4	2	no	—
478	C₂⁴	—	2	2	no	—
479	C₂⁴	—	2	2	no	—
480	C₂⁴	—	2	2	no	—
481	C₂⁴	—	2	2	no	—
482	C₂⁴	—	2	2	no	—
483	C₂⁴	—	2	2	no	—
484	C₂⁴	—	2	2	no	—
485	C₂⁴	C₂⁴×C₅	1	2	yes	—
486	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
487	C₂×Q₈	—	2	8	no	—
488	C₂×Q₈	—	4	4	no	—
489	C₂×Q₈	—	4	4	no	—
490	C₂×Q₈	—	4	16	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	C₅×#41	1	4	yes	—
531	C₂²×C₄	C₅×#41	1	4	yes	—
532	C₂²×C₄	C₅×#41	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
547	C₄⋊C₄	—	2	8	no	—
548	C₄⋊C₄	—	2	8	no	—
549	C₄⋊C₄	—	2	8	no	—
550	C₄⋊C₄	—	2	8	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	2	8	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₄²	—	2	8	no	—
563	C₄²	—	4	4	no	—
564	C₄²	—	4	4	no	—
565	C₂×C₅	—	8	2	no	—
566	C₂×C₅	#2650	1	8	yes	direct product factor
567	C₂×C₅	C₂×#529	1	1	yes	characteristic
568	C₂×C₅	C₂×#538	1	1	yes	characteristic
569	C₂×C₅	C₂×#539	1	1	yes	characteristic
570	C₂×C₅	C₂×#541	1	1	yes	characteristic
571	C₂×C₅	C₂×#542	1	1	yes	characteristic
572	C₂×C₅	C₂×#542	1	1	yes	characteristic
573	C₂×C₅	C₂×#542	1	1	yes	characteristic
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	4	4	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	4	no	—
584	C₂³	—	4	4	no	—
585	C₂³	—	4	4	no	—
586	C₂³	—	4	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	C₂×C₅×#41	1	2	yes	—
589	C₂³	C₂×C₅×#41	1	2	yes	—
590	C₂³	C₂×C₅×#41	1	2	yes	—
591	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
592	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
593	C₂³	C₅×2₋¹⁺⁴	1	2	yes	—
594	C₂³	C₅×2₋¹⁺⁴	1	2	yes	—
595	C₂³	C₂⁵×C₅	1	1	yes	characteristic
596	Q₈	—	4	16	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	8	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	4	no	—
650	C₂×C₄	C₂×C₅×#41	1	4	yes	—
651	C₂×C₄	C₂×C₅×#41	1	4	yes	—
652	C₂×C₄	C₂×C₅×#41	1	4	yes	—
653	C₅	C₂×#2650	1	1	yes	characteristic, direct product factor, Sylow
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	2	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	8	8	no	—
662	C₂²	C₅×#529	1	4	yes	—
663	C₂²	C₅×#538	1	4	yes	—
664	C₂²	C₅×#539	1	4	yes	—
665	C₂²	C₅×#541	1	4	yes	—
666	C₂²	C₅×#542	1	4	yes	—
667	C₂²	C₅×#542	1	4	yes	—
668	C₂²	C₅×#542	1	4	yes	—
669	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
670	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
671	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
672	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
675	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
676	C₄	—	2	4	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	4	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₂	—	8	2	no	—
691	C₂	C₅×#2650	1	8	yes	direct product factor
692	C₂	C₂×C₅×#529	1	1	yes	characteristic
693	C₂	C₂×C₅×#538	1	1	yes	characteristic
694	C₂	C₂×C₅×#539	1	1	yes	characteristic
695	C₂	C₂×C₅×#541	1	1	yes	characteristic
696	C₂	C₂×C₅×#542	1	1	yes	characteristic
697	C₂	C₂×C₅×#542	1	1	yes	characteristic
698	C₂	C₂×C₅×#542	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅×#2650	C₂	direct (N × H)
2. C₂×C₅×#400	C₂	semidirect
3. C₂×C₅×#400	C₂	semidirect
4. C₂×C₅×#400	C₂	semidirect
8. C₂×C₅×#395	C₂	semidirect
10. C₂×C₅×#391	C₂	semidirect
14. C₂×C₅×#387	C₂	semidirect
15. C₂×C₅×#387	C₂	semidirect
16. C₂×C₄×C₅×C₄⋊C₄	C₂	semidirect
36. C₅×#400	C₂²	semidirect
37. C₅×#400	C₂²	semidirect
38. C₅×#400	C₂²	semidirect
42. C₅×#395	C₂²	semidirect
44. C₅×#391	C₂²	semidirect
48. C₅×#387	C₂²	semidirect
49. C₅×#387	C₂²	semidirect
50. C₄×C₅×C₄⋊C₄	C₂²	semidirect
67. C₂×#2650	C₅	direct (N × H)
139. #2650	C₂×C₅	direct (N × H)
140. C₂×#400	C₂×C₅	semidirect
141. C₂×#400	C₂×C₅	semidirect
142. C₂×#400	C₂×C₅	semidirect
146. C₂×#395	C₂×C₅	semidirect
148. C₂×#391	C₂×C₅	semidirect
152. C₂×#387	C₂×C₅	semidirect
153. C₂×#387	C₂×C₅	semidirect
154. C₂×C₄×C₄⋊C₄	C₂×C₅	semidirect
261. #400	C₂²×C₅	semidirect
262. #400	C₂²×C₅	semidirect
263. #400	C₂²×C₅	semidirect
267. #395	C₂²×C₅	semidirect
269. #391	C₂²×C₅	semidirect
273. #387	C₂²×C₅	semidirect
274. #387	C₂²×C₅	semidirect
275. C₄×C₄⋊C₄	C₂²×C₅	semidirect
566. C₂×C₅	#2650	direct (N × H)
653. C₅	C₂×#2650	direct (N × H)
691. C₂	C₅×#2650	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2650	2
C₂×C₅×#400	2
C₂×C₅×#397	2
C₂×C₅×#396	2
C₂×C₅×#395	2
C₂×C₅×#393	2
C₂×C₅×#391	2
C₂×C₅×#388	2
C₂×C₅×#387	2
C₂×C₄×C₅×C₄⋊C₄	2
C₂×#2650	5

Subgroups — C2×C5×#2650 #11957303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2650 #11957303