Subgroups — C₅×#29505 #11952225

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2644	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2328	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2011	C₂	1	1	yes	maximal, characteristic
7	C₅×#1972	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1970	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1936	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#127	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#102	C₂²	1	1	yes	characteristic
24	C₂×C₅×#102	C₂²	1	1	yes	characteristic
25	C₂×C₅×#102	C₂²	1	1	yes	characteristic
26	C₂×C₅×#102	C₂²	1	1	yes	characteristic
27	C₂×C₅×#102	C₂²	1	1	yes	characteristic
28	C₂×C₅×#102	C₂²	1	1	yes	characteristic
29	C₂×C₅×#102	C₂²	1	1	yes	characteristic
30	C₂×C₅×#102	C₂²	1	1	yes	characteristic
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#397	—	2	1	no	—
34	C₅×#397	—	2	1	no	—
35	C₅×#397	—	2	1	no	—
36	C₅×#396	—	2	1	no	—
37	C₅×#390	C₂²	1	1	yes	characteristic
38	C₅×#390	C₂²	1	1	yes	characteristic
39	C₅×#390	C₂²	1	1	yes	characteristic
40	C₅×#390	C₂²	1	1	yes	characteristic
41	C₅×#390	C₂²	1	1	yes	characteristic
42	C₅×#389	C₂²	1	1	yes	characteristic
43	C₅×#389	C₂²	1	1	yes	characteristic
44	C₅×#389	C₂²	1	1	yes	characteristic
45	C₅×#386	—	2	1	no	—
46	C₅×#386	—	2	1	no	—
47	C₅×#386	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#382	C₂²	1	1	yes	characteristic
50	C₅×#376	C₂²	1	1	yes	characteristic
51	C₅×#340	C₂²	1	1	yes	characteristic
52	C₅×#340	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#29505	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	—	2	1	no	—
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	—	2	1	no	—
66	C₂³×C₄×C₅	—	2	1	no	—
67	C₂×C₅×D₈	—	2	2	no	—
68	C₂×C₅×D₈	—	2	2	no	—
69	C₂×C₅×D₈	—	2	2	no	—
70	C₂×C₅×D₈	—	2	2	no	—
71	C₂×C₅×D₈	—	4	1	no	—
72	C₂×C₅×D₈	—	4	1	no	—
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₅×#127	—	2	2	no	—
78	C₅×#127	—	2	2	no	—
79	C₄×C₅×D₄	—	4	1	no	—
80	C₄×C₅×D₄	—	4	1	no	—
81	C₄×C₅×D₄	—	4	1	no	—
82	C₄×C₅×D₄	—	4	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₅×#107	—	4	1	no	—
107	C₅×#106	—	4	1	no	—
108	C₅×#102	—	2	2	no	—
109	C₅×#102	—	2	2	no	—
110	C₅×#102	—	2	2	no	—
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	4	1	no	—
113	C₅×#102	—	4	1	no	—
114	C₅×#102	—	4	1	no	—
115	C₅×#102	—	4	1	no	—
116	C₅×#97	—	2	2	no	—
117	C₄×C₅×C₈	—	2	2	no	—
118	C₅×#95	—	2	1	no	—
119	C₅×#95	—	2	1	no	—
120	C₅×#95	—	2	1	no	—
121	C₅×#95	—	2	1	no	—
122	C₅×#95	—	2	1	no	—
123	C₅×#95	D₄	1	1	yes	characteristic
124	C₅×#95	D₄	1	1	yes	characteristic
125	C₅×#95	D₄	1	1	yes	characteristic
126	C₅×#95	D₄	1	1	yes	characteristic
127	#2644	C₂×C₅	1	1	yes	characteristic, complemented
128	#2328	C₂×C₅	1	1	yes	characteristic, complemented
129	#2085	C₂×C₅	1	1	yes	characteristic, complemented
130	#2073	C₂×C₅	1	1	yes	characteristic, complemented
131	#2041	C₂×C₅	1	1	yes	characteristic, complemented
132	#2011	C₂×C₅	1	1	yes	characteristic
133	#1972	C₂×C₅	1	1	yes	characteristic, complemented
134	#1970	C₂×C₅	1	1	yes	characteristic, complemented
135	#1936	C₂×C₅	1	1	yes	characteristic, complemented
136	#1934	C₂×C₅	1	1	yes	characteristic, complemented
137	#1879	C₂×C₅	1	1	yes	characteristic, complemented
138	#1879	C₂×C₅	1	1	yes	characteristic, complemented
139	#1864	C₂×C₅	1	1	yes	characteristic, complemented
140	#1862	C₂×C₅	1	1	yes	characteristic, complemented
141	#1746	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	1	no	—
143	C₂⁴×C₅	—	2	1	no	—
144	C₂⁴×C₅	—	2	1	no	—
145	C₂×C₅×D₄	—	2	4	no	—
146	C₂×C₅×D₄	—	2	4	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	—	2	1	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	—	2	1	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	—	2	1	no	—
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	8	1	no	—
164	C₂×C₅×D₄	—	8	1	no	—
165	C₂×C₅×D₄	—	8	1	no	—
166	C₂×C₅×D₄	—	8	1	no	—
167	C₂×C₅×D₄	#41	1	2	yes	—
168	C₂×C₅×D₄	#41	1	2	yes	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	4	2	no	—
175	C₂²×C₄×C₅	—	4	2	no	—
176	C₂²×C₄×C₅	—	8	1	no	—
177	C₂²×C₄×C₅	—	8	1	no	—
178	C₂²×C₄×C₅	—	8	1	no	—
179	C₂²×C₄×C₅	—	8	1	no	—
180	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₅×D₈	—	4	4	no	—
188	C₅×D₈	—	4	4	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	#41	1	2	yes	—
200	C₂×C₅×C₈	#41	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	8	1	no	—
212	C₅×C₄⋊C₄	—	8	1	no	—
213	C₅×C₄⋊C₄	—	8	1	no	—
214	C₅×C₂²⋊C₄	—	4	2	no	—
215	C₅×C₂²⋊C₄	—	4	2	no	—
216	C₅×C₂²⋊C₄	—	8	1	no	—
217	C₅×C₂²⋊C₄	—	8	1	no	—
218	C₅×C₂²⋊C₄	—	8	1	no	—
219	C₅×C₂²⋊C₄	—	8	1	no	—
220	C₅×C₂²⋊C₄	—	8	1	no	—
221	C₅×C₂²⋊C₄	—	8	1	no	—
222	C₅×C₂²⋊C₄	—	8	1	no	—
223	C₅×C₂²⋊C₄	—	8	1	no	—
224	C₅×C₂²⋊C₄	—	8	1	no	—
225	C₅×C₂²⋊C₄	—	8	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	2	1	no	—
232	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
233	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
234	C₂×#127	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×#107	C₂²×C₅	1	1	yes	characteristic
238	C₂×#106	C₂²×C₅	1	1	yes	characteristic
239	C₂×#102	C₂²×C₅	1	1	yes	characteristic
240	C₂×#102	C₂²×C₅	1	1	yes	characteristic
241	C₂×#102	C₂²×C₅	1	1	yes	characteristic
242	C₂×#102	C₂²×C₅	1	1	yes	characteristic
243	C₂×#102	C₂²×C₅	1	1	yes	characteristic
244	C₂×#102	C₂²×C₅	1	1	yes	characteristic
245	C₂×#102	C₂²×C₅	1	1	yes	characteristic
246	C₂×#102	C₂²×C₅	1	1	yes	characteristic
247	C₂×#97	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
249	#397	—	2	1	no	—
250	#397	—	2	1	no	—
251	#397	—	2	1	no	—
252	#396	—	2	1	no	—
253	#390	C₂²×C₅	1	1	yes	characteristic
254	#390	C₂²×C₅	1	1	yes	characteristic
255	#390	C₂²×C₅	1	1	yes	characteristic
256	#390	C₂²×C₅	1	1	yes	characteristic
257	#390	C₂²×C₅	1	1	yes	characteristic
258	#389	C₂²×C₅	1	1	yes	characteristic
259	#389	C₂²×C₅	1	1	yes	characteristic
260	#389	C₂²×C₅	1	1	yes	characteristic
261	#386	—	2	1	no	—
262	#386	—	2	1	no	—
263	#386	—	2	1	no	—
264	#386	—	2	1	no	—
265	#382	C₂²×C₅	1	1	yes	characteristic
266	#376	C₂²×C₅	1	1	yes	characteristic
267	#340	C₂²×C₅	1	1	yes	characteristic
268	#340	C₂²×C₅	1	1	yes	characteristic
269	#340	C₂²×C₅	1	1	yes	characteristic
270	#340	C₂²×C₅	1	1	yes	characteristic
271	#336	C₂²×C₅	1	1	yes	characteristic
272	#336	C₂²×C₅	1	1	yes	characteristic
273	#336	C₂²×C₅	1	1	yes	characteristic
274	#336	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	—	4	1	no	—
280	C₂³×C₅	—	4	1	no	—
281	C₂³×C₅	—	4	1	no	—
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	—	4	1	no	—
285	C₂³×C₅	—	4	1	no	—
286	C₂³×C₅	—	4	1	no	—
287	C₂³×C₅	—	4	1	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	—	4	1	no	—
291	C₂³×C₅	—	4	1	no	—
292	C₂³×C₅	—	4	1	no	—
293	C₂³×C₅	—	4	1	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	4	1	no	—
296	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	2	2	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	4	1	no	—
302	C₅×D₄	—	4	1	no	—
303	C₅×D₄	—	4	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	4	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	8	4	no	—
310	C₅×D₄	—	8	4	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	1	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	1	no	—
340	C₂×C₄×C₅	—	4	1	no	—
341	C₂×C₄×C₅	—	4	1	no	—
342	C₂×C₄×C₅	—	4	1	no	—
343	C₂×C₄×C₅	—	4	1	no	—
344	C₂×C₄×C₅	—	8	4	no	—
345	C₂×C₄×C₅	—	8	4	no	—
346	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
352	C₅×C₈	—	2	2	no	—
353	C₅×C₈	—	2	2	no	—
354	C₅×C₈	—	4	1	no	—
355	C₅×C₈	—	4	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×D₈	—	2	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	2	2	no	—
367	C₂×D₈	—	4	1	no	—
368	C₂×D₈	—	4	1	no	—
369	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
373	#127	—	2	2	no	—
374	#127	—	2	2	no	—
375	C₄×D₄	—	4	1	no	—
376	C₄×D₄	—	4	1	no	—
377	C₄×D₄	—	4	1	no	—
378	C₄×D₄	—	4	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
402	#107	—	4	1	no	—
403	#106	—	4	1	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#102	—	2	2	no	—
408	#102	—	4	1	no	—
409	#102	—	4	1	no	—
410	#102	—	4	1	no	—
411	#102	—	4	1	no	—
412	#97	—	2	2	no	—
413	C₄×C₈	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	C₅×D₄	1	1	yes	characteristic
420	#95	C₅×D₄	1	1	yes	characteristic
421	#95	C₅×D₄	1	1	yes	characteristic
422	#95	C₅×D₄	1	1	yes	characteristic
423	C₂²×C₅	—	4	2	no	—
424	C₂²×C₅	—	4	2	no	—
425	C₂²×C₅	—	4	2	no	—
426	C₂²×C₅	—	4	2	no	—
427	C₂²×C₅	—	4	2	no	—
428	C₂²×C₅	—	4	2	no	—
429	C₂²×C₅	—	8	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	—	8	1	no	—
436	C₂²×C₅	—	8	1	no	—
437	C₂²×C₅	—	8	1	no	—
438	C₂²×C₅	—	8	1	no	—
439	C₂²×C₅	—	8	1	no	—
440	C₂²×C₅	—	8	1	no	—
441	C₂²×C₅	—	8	1	no	—
442	C₂²×C₅	—	8	1	no	—
443	C₂²×C₅	—	8	1	no	—
444	C₂²×C₅	#525	1	1	yes	characteristic
445	C₂²×C₅	#532	1	1	yes	characteristic
446	C₂²×C₅	#535	1	1	yes	characteristic
447	C₂²×C₅	#576	1	1	yes	characteristic
448	C₂²×C₅	#576	1	1	yes	characteristic
449	C₂²×C₅	#576	1	1	yes	characteristic
450	C₂²×C₅	#577	1	1	yes	characteristic
451	C₄×C₅	—	4	1	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	8	1	no	—
458	C₄×C₅	—	8	1	no	—
459	C₄×C₅	—	8	1	no	—
460	C₄×C₅	—	8	1	no	—
461	C₄×C₅	—	8	1	no	—
462	C₄×C₅	#551	1	1	yes	characteristic
463	C₄×C₅	#551	1	1	yes	characteristic
464	C₄×C₅	#553	1	1	yes	characteristic
465	C₄×C₅	#553	1	1	yes	characteristic
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	1	no	—
468	C₂⁴	—	2	1	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	8	1	no	—
488	C₂×D₄	—	8	1	no	—
489	C₂×D₄	—	8	1	no	—
490	C₂×D₄	—	8	1	no	—
491	C₂×D₄	C₅×#41	1	2	yes	—
492	C₂×D₄	C₅×#41	1	2	yes	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	—	8	1	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
511	D₈	—	4	4	no	—
512	D₈	—	4	4	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	C₅×#41	1	2	yes	—
524	C₂×C₈	C₅×#41	1	2	yes	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	8	1	no	—
536	C₄⋊C₄	—	8	1	no	—
537	C₄⋊C₄	—	8	1	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	8	1	no	—
541	C₂²⋊C₄	—	8	1	no	—
542	C₂²⋊C₄	—	8	1	no	—
543	C₂²⋊C₄	—	8	1	no	—
544	C₂²⋊C₄	—	8	1	no	—
545	C₂²⋊C₄	—	8	1	no	—
546	C₂²⋊C₄	—	8	1	no	—
547	C₂²⋊C₄	—	8	1	no	—
548	C₂²⋊C₄	—	8	1	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₂×C₅	—	8	2	no	—
557	C₂×C₅	—	8	2	no	—
558	C₂×C₅	—	16	1	no	—
559	C₂×C₅	#2603	1	1	yes	characteristic
560	C₂×C₅	#3118	1	1	yes	characteristic
561	C₂×C₅	#3122	1	1	yes	characteristic
562	C₂×C₅	#3176	1	1	yes	characteristic
563	C₂×C₅	#3179	1	1	yes	characteristic
564	C₂×C₅	#3220	1	1	yes	characteristic
565	C₂×C₅	#3224	1	1	yes	characteristic
566	C₂³	—	2	2	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	—	4	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	1	no	—
580	C₂³	—	4	1	no	—
581	C₂³	—	4	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	8	4	no	—
601	D₄	—	8	4	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	8	4	no	—
636	C₂×C₄	—	8	4	no	—
637	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
638	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
639	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
640	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
641	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
643	C₈	—	2	2	no	—
644	C₈	—	2	2	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₅	#29505	1	1	yes	characteristic, direct product factor, Sylow
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	—	8	1	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	—	8	1	no	—
668	C₂²	—	8	1	no	—
669	C₂²	C₅×#525	1	1	yes	characteristic
670	C₂²	C₅×#532	1	1	yes	characteristic
671	C₂²	C₅×#535	1	1	yes	characteristic
672	C₂²	C₅×#576	1	1	yes	characteristic
673	C₂²	C₅×#576	1	1	yes	characteristic
674	C₂²	C₅×#576	1	1	yes	characteristic
675	C₂²	C₅×#577	1	1	yes	characteristic
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	—	8	1	no	—
687	C₄	C₅×#551	1	1	yes	characteristic
688	C₄	C₅×#551	1	1	yes	characteristic
689	C₄	C₅×#553	1	1	yes	characteristic
690	C₄	C₅×#553	1	1	yes	characteristic
691	C₂	—	8	2	no	—
692	C₂	—	8	2	no	—
693	C₂	—	16	1	no	—
694	C₂	C₅×#2603	1	1	yes	characteristic
695	C₂	C₅×#3118	1	1	yes	characteristic
696	C₂	C₅×#3122	1	1	yes	characteristic
697	C₂	C₅×#3176	1	1	yes	characteristic
698	C₂	C₅×#3179	1	1	yes	characteristic
699	C₂	C₅×#3220	1	1	yes	characteristic
700	C₂	C₅×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2644	C₂	semidirect
2. C₅×#2328	C₂	semidirect
3. C₅×#2085	C₂	semidirect
4. C₅×#2073	C₂	semidirect
5. C₅×#2041	C₂	semidirect
7. C₅×#1972	C₂	semidirect
8. C₅×#1970	C₂	semidirect
9. C₅×#1936	C₂	semidirect
10. C₅×#1934	C₂	semidirect
11. C₅×#1879	C₂	semidirect
12. C₅×#1879	C₂	semidirect
13. C₅×#1864	C₂	semidirect
14. C₅×#1862	C₂	semidirect
15. C₅×#1746	C₂	semidirect
59. #29505	C₅	direct (N × H)
127. #2644	C₂×C₅	semidirect
128. #2328	C₂×C₅	semidirect
129. #2085	C₂×C₅	semidirect
130. #2073	C₂×C₅	semidirect
131. #2041	C₂×C₅	semidirect
133. #1972	C₂×C₅	semidirect
134. #1970	C₂×C₅	semidirect
135. #1936	C₂×C₅	semidirect
136. #1934	C₂×C₅	semidirect
137. #1879	C₂×C₅	semidirect
138. #1879	C₂×C₅	semidirect
139. #1864	C₂×C₅	semidirect
140. #1862	C₂×C₅	semidirect
141. #1746	C₂×C₅	semidirect
647. C₅	#29505	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×#2644	2
C₅×#2328	2
C₅×#2085	2
C₅×#2073	2
C₅×#2041	2
C₅×#2011	2
C₅×#1972	2
C₅×#1970	2
C₅×#1936	2
C₅×#1934	2
C₅×#1879	2
C₅×#1864	2
C₅×#1862	2
C₅×#1746	2
#29505	5

Subgroups — C5×#29505 #11952225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29505 #11952225