Subgroups — C₅×#34814 #11957534

Order 1280.

1994 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2497	C₂	1	2	yes	maximal, complemented
2	C₅×#2496	C₂	1	2	yes	maximal, complemented
3	C₅×#2495	C₂	1	2	yes	maximal, complemented
4	C₅×#2494	C₂	1	2	yes	maximal, complemented
5	C₅×#2493	C₂	1	4	yes	maximal, complemented
6	C₅×#2480	C₂	1	4	yes	maximal
7	C₅×#2401	C₂	1	4	yes	maximal, complemented
8	C₄×C₅×#126	C₂	1	4	yes	maximal, complemented
9	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2280	C₂	1	1	yes	maximal, characteristic
13	C₅×#2280	C₂	1	1	yes	maximal, characteristic
14	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#126	C₂²	1	4	yes	—
18	C₂×C₅×#117	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	C₂²	1	1	yes	characteristic
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#401	C₂²	1	4	yes	complemented
26	C₅×#400	C₂²	1	4	yes	complemented
27	C₅×#400	C₂²	1	4	yes	complemented
28	C₅×#400	C₂²	1	4	yes	complemented
29	C₅×#397	C₂²	1	4	yes	—
30	C₅×#397	C₂²	1	4	yes	—
31	C₅×#397	C₂²	1	4	yes	—
32	C₅×#396	C₂²	1	4	yes	—
33	C₅×#389	C₂²	1	2	yes	complemented
34	C₅×#389	C₂²	1	2	yes	complemented
35	C₅×#389	C₂²	1	2	yes	complemented
36	C₅×#389	C₂²	1	2	yes	complemented
37	C₅×#388	C₂²	1	4	yes	—
38	C₅×#388	C₂²	1	4	yes	—
39	C₅×#388	C₂²	1	4	yes	—
40	C₅×#387	C₂²	1	4	yes	complemented
41	C₅×#387	C₂²	1	4	yes	complemented
42	C₅×#387	C₂²	1	4	yes	complemented
43	C₅×#385	C₂²	1	4	yes	—
44	C₅×#385	C₂²	1	4	yes	—
45	C₅×#384	C₂²	1	1	yes	characteristic, complemented
46	C₅×#384	C₂²	1	1	yes	characteristic, complemented
47	C₅×#383	C₂²	1	4	yes	complemented
48	C₅×#382	C₂²	1	1	yes	characteristic, complemented
49	C₅×#382	C₂²	1	1	yes	characteristic, complemented
50	C₅×#381	C₂²	1	2	yes	—
51	C₅×#381	C₂²	1	2	yes	—
52	C₅×#380	C₂²	1	4	yes	—
53	C₅×#380	C₂²	1	2	yes	—
54	C₅×#380	C₂²	1	2	yes	—
55	C₅×#380	C₂²	1	2	yes	—
56	C₅×#380	C₂²	1	2	yes	—
57	C₅×#379	C₂²	1	2	yes	—
58	C₅×#379	C₂²	1	2	yes	—
59	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
64	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
65	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
68	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₅×#376	C₂²	1	2	yes	complemented
73	C₂×C₅×#95	C₂²	1	2	yes	—
74	C₄³×C₅	C₂²	1	2	yes	complemented
75	#34814	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁵×C₅	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅	—	2	4	no	—
78	C₂³×C₄×C₅	—	2	4	no	—
79	C₂³×C₄×C₅	—	2	4	no	—
80	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂³	1	2	yes	—
82	C₂³×C₄×C₅	C₂³	1	2	yes	—
83	C₂³×C₄×C₅	C₂³	1	2	yes	—
84	C₂³×C₄×C₅	C₂³	1	2	yes	—
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₅×#126	—	2	16	no	—
87	C₅×#117	—	2	4	no	—
88	C₅×#117	—	2	4	no	—
89	C₅×#117	—	2	4	no	—
90	C₅×#117	—	2	4	no	—
91	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
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	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	2	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	8	no	—
104	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₅×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
116	C₂×C₄²×C₅	—	2	4	no	—
117	C₂×C₄²×C₅	—	2	4	no	—
118	C₂×C₄²×C₅	C₂³	1	4	yes	—
119	C₂×C₄²×C₅	C₂³	1	2	yes	—
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂³	1	2	yes	—
124	C₂×C₄²×C₅	C₂³	1	2	yes	—
125	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂³	1	2	yes	—
127	C₂×C₄²×C₅	C₂³	1	2	yes	—
128	C₂×C₄²×C₅	C₂³	1	2	yes	—
129	C₂×C₄²×C₅	C₂³	1	4	yes	—
130	C₅×#95	C₂³	1	2	yes	—
131	C₅×#95	C₂³	1	2	yes	—
132	C₅×#95	C₂³	1	2	yes	—
133	C₅×#95	C₂³	1	2	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	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	4	yes	—
144	C₅×#95	C₂³	1	4	yes	—
145	C₅×#95	C₂³	1	4	yes	—
146	#2497	C₂×C₅	1	2	yes	complemented
147	#2496	C₂×C₅	1	2	yes	complemented
148	#2495	C₂×C₅	1	2	yes	complemented
149	#2494	C₂×C₅	1	2	yes	complemented
150	#2493	C₂×C₅	1	4	yes	complemented
151	#2480	C₂×C₅	1	4	yes	—
152	#2401	C₂×C₅	1	4	yes	complemented
153	C₄×#126	C₂×C₅	1	4	yes	complemented
154	#2296	C₂×C₅	1	1	yes	characteristic, complemented
155	#2296	C₂×C₅	1	1	yes	characteristic, complemented
156	#2285	C₂×C₅	1	1	yes	characteristic, complemented
157	#2280	C₂×C₅	1	1	yes	characteristic
158	#2280	C₂×C₅	1	1	yes	characteristic
159	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
161	C₂⁴×C₅	—	2	4	no	—
162	C₂⁴×C₅	—	2	2	no	—
163	C₂⁴×C₅	—	2	2	no	—
164	C₂⁴×C₅	—	2	2	no	—
165	C₂⁴×C₅	—	4	2	no	—
166	C₂⁴×C₅	C₂⁴	1	2	yes	—
167	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	2	4	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	4	no	—
174	C₂²×C₄×C₅	—	2	4	no	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	2	4	no	—
177	C₂²×C₄×C₅	—	2	4	no	—
178	C₂²×C₄×C₅	—	2	4	no	—
179	C₂²×C₄×C₅	—	2	4	no	—
180	C₂²×C₄×C₅	—	2	4	no	—
181	C₂²×C₄×C₅	—	4	2	no	—
182	C₂²×C₄×C₅	—	4	2	no	—
183	C₂²×C₄×C₅	—	4	16	no	—
184	C₂²×C₄×C₅	#41	1	4	yes	—
185	C₂²×C₄×C₅	#41	1	4	yes	—
186	C₂²×C₄×C₅	#41	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	2	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	4	no	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	—	2	8	no	—
207	C₅×C₄⋊C₄	—	2	8	no	—
208	C₅×C₄⋊C₄	—	2	8	no	—
209	C₅×C₄⋊C₄	—	4	4	no	—
210	C₅×C₄⋊C₄	—	4	4	no	—
211	C₅×C₄⋊C₄	—	4	4	no	—
212	C₅×C₂²⋊C₄	—	2	4	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₅×C₂²⋊C₄	—	2	4	no	—
215	C₅×C₂²⋊C₄	—	2	4	no	—
216	C₅×C₂²⋊C₄	—	2	4	no	—
217	C₅×C₂²⋊C₄	—	2	8	no	—
218	C₅×C₂²⋊C₄	—	2	8	no	—
219	C₅×C₂²⋊C₄	—	2	4	no	—
220	C₅×C₂²⋊C₄	—	2	4	no	—
221	C₅×C₂²⋊C₄	—	4	4	no	—
222	C₅×C₂²⋊C₄	—	4	4	no	—
223	C₅×C₂²⋊C₄	#41	1	8	yes	—
224	C₄²×C₅	—	2	2	no	—
225	C₄²×C₅	—	2	2	no	—
226	C₄²×C₅	—	2	4	no	—
227	C₄²×C₅	—	2	4	no	—
228	C₄²×C₅	—	2	2	no	—
229	C₄²×C₅	—	2	2	no	—
230	C₄²×C₅	—	2	4	no	—
231	C₄²×C₅	—	2	4	no	—
232	C₄²×C₅	—	2	4	no	—
233	C₄²×C₅	—	2	4	no	—
234	C₄²×C₅	—	2	8	no	—
235	C₄²×C₅	—	4	4	no	—
236	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×#126	C₂²×C₅	1	4	yes	—
238	C₂×#117	C₂²×C₅	1	1	yes	characteristic
239	C₂×#117	C₂²×C₅	1	1	yes	characteristic
240	C₂×#117	C₂²×C₅	1	1	yes	characteristic
241	C₂×#117	C₂²×C₅	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
243	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
245	#401	C₂²×C₅	1	4	yes	complemented
246	#400	C₂²×C₅	1	4	yes	complemented
247	#400	C₂²×C₅	1	4	yes	complemented
248	#400	C₂²×C₅	1	4	yes	complemented
249	#397	C₂²×C₅	1	4	yes	—
250	#397	C₂²×C₅	1	4	yes	—
251	#397	C₂²×C₅	1	4	yes	—
252	#396	C₂²×C₅	1	4	yes	—
253	#389	C₂²×C₅	1	2	yes	complemented
254	#389	C₂²×C₅	1	2	yes	complemented
255	#389	C₂²×C₅	1	2	yes	complemented
256	#389	C₂²×C₅	1	2	yes	complemented
257	#388	C₂²×C₅	1	4	yes	—
258	#388	C₂²×C₅	1	4	yes	—
259	#388	C₂²×C₅	1	4	yes	—
260	#387	C₂²×C₅	1	4	yes	complemented
261	#387	C₂²×C₅	1	4	yes	complemented
262	#387	C₂²×C₅	1	4	yes	complemented
263	#385	C₂²×C₅	1	4	yes	—
264	#385	C₂²×C₅	1	4	yes	—
265	#384	C₂²×C₅	1	1	yes	characteristic, complemented
266	#384	C₂²×C₅	1	1	yes	characteristic, complemented
267	#383	C₂²×C₅	1	4	yes	complemented
268	#382	C₂²×C₅	1	1	yes	characteristic, complemented
269	#382	C₂²×C₅	1	1	yes	characteristic, complemented
270	#381	C₂²×C₅	1	2	yes	—
271	#381	C₂²×C₅	1	2	yes	—
272	#380	C₂²×C₅	1	4	yes	—
273	#380	C₂²×C₅	1	2	yes	—
274	#380	C₂²×C₅	1	2	yes	—
275	#380	C₂²×C₅	1	2	yes	—
276	#380	C₂²×C₅	1	2	yes	—
277	#379	C₂²×C₅	1	2	yes	—
278	#379	C₂²×C₅	1	2	yes	—
279	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
280	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
281	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
282	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
283	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
284	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
285	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
286	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
288	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
290	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
291	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
292	#376	C₂²×C₅	1	2	yes	complemented
293	C₂×#95	C₂²×C₅	1	2	yes	—
294	C₄³	C₂²×C₅	1	2	yes	complemented
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	8	no	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	2	2	no	—
301	C₂³×C₅	—	2	2	no	—
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	—	4	8	no	—
305	C₂³×C₅	—	4	8	no	—
306	C₂³×C₅	—	4	4	no	—
307	C₂³×C₅	—	4	4	no	—
308	C₂³×C₅	C₂×#41	1	4	yes	—
309	C₂³×C₅	C₂×#41	1	2	yes	—
310	C₂³×C₅	C₂×#41	1	2	yes	—
311	C₂³×C₅	C₂×#41	1	2	yes	—
312	C₂³×C₅	C₂⁵	1	1	yes	characteristic
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	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	4	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	4	no	—
325	C₂×C₄×C₅	—	2	4	no	—
326	C₂×C₄×C₅	—	2	4	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	4	no	—
330	C₂×C₄×C₅	—	2	4	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	4	no	—
335	C₂×C₄×C₅	—	2	4	no	—
336	C₂×C₄×C₅	—	2	4	no	—
337	C₂×C₄×C₅	—	2	4	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	4	8	no	—
341	C₂×C₄×C₅	—	4	8	no	—
342	C₂×C₄×C₅	—	4	4	no	—
343	C₂×C₄×C₅	—	4	8	no	—
344	C₂×C₄×C₅	—	4	8	no	—
345	C₂×C₄×C₅	#126	1	16	yes	complemented
346	C₂×C₄×C₅	C₂×#41	1	4	yes	—
347	C₂×C₄×C₅	C₂×#41	1	4	yes	—
348	C₂×C₄×C₅	C₂×#41	1	2	yes	—
349	C₂×C₄×C₅	C₂×#41	1	2	yes	—
350	C₂×C₄×C₅	C₂×#41	1	2	yes	—
351	C₂×C₄×C₅	C₂×#41	1	2	yes	—
352	C₂×C₄×C₅	C₂×#41	1	2	yes	—
353	C₂×C₄×C₅	C₂×#41	1	2	yes	—
354	C₂⁵	C₂³×C₅	1	1	yes	characteristic
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	—	2	4	no	—
358	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₅	1	2	yes	—
360	C₂³×C₄	C₂³×C₅	1	2	yes	—
361	C₂³×C₄	C₂³×C₅	1	2	yes	—
362	C₂³×C₄	C₂³×C₅	1	2	yes	—
363	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
364	#126	—	2	16	no	—
365	#117	—	2	4	no	—
366	#117	—	2	4	no	—
367	#117	—	2	4	no	—
368	#117	—	2	4	no	—
369	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
394	C₂×C₄²	—	2	4	no	—
395	C₂×C₄²	—	2	4	no	—
396	C₂×C₄²	C₂³×C₅	1	2	yes	—
397	C₂×C₄²	C₂³×C₅	1	2	yes	—
398	C₂×C₄²	C₂³×C₅	1	2	yes	—
399	C₂×C₄²	C₂³×C₅	1	2	yes	—
400	C₂×C₄²	C₂³×C₅	1	4	yes	—
401	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₅	1	2	yes	—
404	C₂×C₄²	C₂³×C₅	1	2	yes	—
405	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₅	1	4	yes	—
408	#95	C₂³×C₅	1	2	yes	—
409	#95	C₂³×C₅	1	2	yes	—
410	#95	C₂³×C₅	1	2	yes	—
411	#95	C₂³×C₅	1	2	yes	—
412	#95	C₂³×C₅	1	4	yes	—
413	#95	C₂³×C₅	1	4	yes	—
414	#95	C₂³×C₅	1	4	yes	—
415	#95	C₂³×C₅	1	4	yes	—
416	#95	C₂³×C₅	1	4	yes	—
417	#95	C₂³×C₅	1	4	yes	—
418	#95	C₂³×C₅	1	4	yes	—
419	#95	C₂³×C₅	1	4	yes	—
420	#95	C₂³×C₅	1	4	yes	—
421	#95	C₂³×C₅	1	4	yes	—
422	#95	C₂³×C₅	1	4	yes	—
423	#95	C₂³×C₅	1	4	yes	—
424	C₂²×C₅	—	2	2	no	—
425	C₂²×C₅	—	2	2	no	—
426	C₂²×C₅	—	2	4	no	—
427	C₂²×C₅	—	2	4	no	—
428	C₂²×C₅	—	2	4	no	—
429	C₂²×C₅	—	2	4	no	—
430	C₂²×C₅	—	2	4	no	—
431	C₂²×C₅	—	4	16	no	—
432	C₂²×C₅	—	4	2	no	—
433	C₂²×C₅	—	4	2	no	—
434	C₂²×C₅	—	4	2	no	—
435	C₂²×C₅	—	4	2	no	—
436	C₂²×C₅	C₂×#126	1	4	yes	—
437	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
439	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₅	C₂²×#41	1	2	yes	—
441	C₂²×C₅	#585	1	2	yes	—
442	C₄×C₅	—	2	4	no	—
443	C₄×C₅	—	2	4	no	—
444	C₄×C₅	—	4	2	no	—
445	C₄×C₅	—	4	2	no	—
446	C₄×C₅	—	4	2	no	—
447	C₄×C₅	—	4	2	no	—
448	C₄×C₅	—	4	2	no	—
449	C₄×C₅	—	4	4	no	—
450	C₄×C₅	—	4	4	no	—
451	C₄×C₅	—	4	2	no	—
452	C₄×C₅	—	4	2	no	—
453	C₄×C₅	C₂×#126	1	4	yes	—
454	C₄×C₅	C₂×#126	1	4	yes	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	2	no	—
457	C₂⁴	—	2	2	no	—
458	C₂⁴	—	2	2	no	—
459	C₂⁴	—	4	2	no	—
460	C₂⁴	C₂⁴×C₅	1	2	yes	—
461	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	16	no	—
478	C₂²×C₄	C₅×#41	1	4	yes	—
479	C₂²×C₄	C₅×#41	1	4	yes	—
480	C₂²×C₄	C₅×#41	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	8	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄⋊C₄	—	4	4	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₂²⋊C₄	C₅×#41	1	8	yes	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	8	no	—
529	C₄²	—	4	4	no	—
530	C₂×C₅	—	2	4	no	—
531	C₂×C₅	—	4	4	no	—
532	C₂×C₅	C₂²×#126	1	1	yes	characteristic
533	C₂×C₅	#3444	1	1	yes	characteristic
534	C₂×C₅	#3455	1	1	yes	characteristic
535	C₂×C₅	#3475	1	2	yes	—
536	C₂×C₅	#3475	1	2	yes	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	C₂×C₅×#41	1	4	yes	—
551	C₂³	C₂×C₅×#41	1	2	yes	—
552	C₂³	C₂×C₅×#41	1	2	yes	—
553	C₂³	C₂×C₅×#41	1	2	yes	—
554	C₂³	C₂⁵×C₅	1	1	yes	characteristic
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	8	no	—
586	C₂×C₄	—	4	8	no	—
587	C₂×C₄	C₅×#126	1	16	yes	complemented
588	C₂×C₄	C₂×C₅×#41	1	4	yes	—
589	C₂×C₄	C₂×C₅×#41	1	4	yes	—
590	C₂×C₄	C₂×C₅×#41	1	2	yes	—
591	C₂×C₄	C₂×C₅×#41	1	2	yes	—
592	C₂×C₄	C₂×C₅×#41	1	2	yes	—
593	C₂×C₄	C₂×C₅×#41	1	2	yes	—
594	C₂×C₄	C₂×C₅×#41	1	2	yes	—
595	C₂×C₄	C₂×C₅×#41	1	2	yes	—
596	C₅	#34814	1	1	yes	characteristic, direct product factor, Sylow
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	4	16	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	C₂×C₅×#126	1	4	yes	—
610	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
611	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
612	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
613	C₂²	C₂²×C₅×#41	1	2	yes	—
614	C₂²	C₅×#585	1	2	yes	—
615	C₄	—	2	4	no	—
616	C₄	—	2	4	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	4	no	—
625	C₄	—	4	4	no	—
626	C₄	C₂×C₅×#126	1	4	yes	—
627	C₄	C₂×C₅×#126	1	4	yes	—
628	C₂	—	2	4	no	—
629	C₂	—	4	4	no	—
630	C₂	C₂²×C₅×#126	1	1	yes	characteristic
631	C₂	C₅×#3444	1	1	yes	characteristic
632	C₂	C₅×#3455	1	1	yes	characteristic
633	C₂	C₅×#3475	1	2	yes	—
634	C₂	C₅×#3475	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₅×#2497	C₂	semidirect
2. C₅×#2496	C₂	semidirect
3. C₅×#2495	C₂	semidirect
4. C₅×#2494	C₂	semidirect
5. C₅×#2493	C₂	semidirect
7. C₅×#2401	C₂	semidirect
8. C₄×C₅×#126	C₂	semidirect
9. C₅×#2296	C₂	semidirect
10. C₅×#2296	C₂	semidirect
11. C₅×#2285	C₂	semidirect
14. C₄×C₅×#117	C₂	semidirect
25. C₅×#401	C₂²	semidirect
26. C₅×#400	C₂²	semidirect
27. C₅×#400	C₂²	semidirect
28. C₅×#400	C₂²	semidirect
33. C₅×#389	C₂²	semidirect
34. C₅×#389	C₂²	semidirect
35. C₅×#389	C₂²	semidirect
36. C₅×#389	C₂²	semidirect
40. C₅×#387	C₂²	semidirect
41. C₅×#387	C₂²	semidirect
42. C₅×#387	C₂²	semidirect
45. C₅×#384	C₂²	semidirect
46. C₅×#384	C₂²	semidirect
47. C₅×#383	C₂²	semidirect
48. C₅×#382	C₂²	semidirect
49. C₅×#382	C₂²	semidirect
59. C₄×C₅×C₄⋊C₄	C₂²	semidirect
60. C₄×C₅×C₄⋊C₄	C₂²	semidirect
61. C₄×C₅×C₄⋊C₄	C₂²	semidirect
62. C₄×C₅×C₄⋊C₄	C₂²	semidirect
63. C₄×C₅×C₄⋊C₄	C₂²	semidirect
64. C₄×C₅×C₄⋊C₄	C₂²	semidirect
72. C₅×#376	C₂²	semidirect
74. C₄³×C₅	C₂²	semidirect
75. #34814	C₅	direct (N × H)
146. #2497	C₂×C₅	semidirect
147. #2496	C₂×C₅	semidirect
148. #2495	C₂×C₅	semidirect
149. #2494	C₂×C₅	semidirect
150. #2493	C₂×C₅	semidirect
152. #2401	C₂×C₅	semidirect
153. C₄×#126	C₂×C₅	semidirect
154. #2296	C₂×C₅	semidirect
155. #2296	C₂×C₅	semidirect
156. #2285	C₂×C₅	semidirect
159. C₄×#117	C₂×C₅	semidirect
245. #401	C₂²×C₅	semidirect
246. #400	C₂²×C₅	semidirect
247. #400	C₂²×C₅	semidirect
248. #400	C₂²×C₅	semidirect
253. #389	C₂²×C₅	semidirect
254. #389	C₂²×C₅	semidirect
255. #389	C₂²×C₅	semidirect
256. #389	C₂²×C₅	semidirect
260. #387	C₂²×C₅	semidirect
261. #387	C₂²×C₅	semidirect
262. #387	C₂²×C₅	semidirect
265. #384	C₂²×C₅	semidirect
266. #384	C₂²×C₅	semidirect
267. #383	C₂²×C₅	semidirect
268. #382	C₂²×C₅	semidirect
269. #382	C₂²×C₅	semidirect
279. C₄×C₄⋊C₄	C₂²×C₅	semidirect
280. C₄×C₄⋊C₄	C₂²×C₅	semidirect
281. C₄×C₄⋊C₄	C₂²×C₅	semidirect
282. C₄×C₄⋊C₄	C₂²×C₅	semidirect
283. C₄×C₄⋊C₄	C₂²×C₅	semidirect
284. C₄×C₄⋊C₄	C₂²×C₅	semidirect
292. #376	C₂²×C₅	semidirect
294. C₄³	C₂²×C₅	semidirect
345. C₂×C₄×C₅	#126	semidirect
587. C₂×C₄	C₅×#126	semidirect
596. C₅	#34814	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×#2497	2
C₅×#2496	2
C₅×#2495	2
C₅×#2494	2
C₅×#2493	2
C₅×#2480	2
C₅×#2401	2
C₄×C₅×#126	2
C₅×#2296	2
C₅×#2285	2
C₅×#2280	2
C₄×C₅×#117	2
C₂×C₄×C₅×C₂²⋊C₄	2
#34814	5

Subgroups — C5×#34814 #11957534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34814 #11957534