Subgroups — C₅×#29536 #11952256

Order 1280.

840 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2054	C₂	1	1	yes	maximal, characteristic
7	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1879	C₂	1	1	yes	maximal, characteristic
12	C₅×#1879	C₂	1	1	yes	maximal, characteristic
13	C₅×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#117	—	2	1	no	—
20	C₂×C₅×#117	—	2	1	no	—
21	C₂×C₅×#107	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#106	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	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×#102	C₂²	1	1	yes	characteristic
32	C₅×#390	C₂²	1	1	yes	characteristic
33	C₅×#390	C₂²	1	1	yes	characteristic
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#390	C₂²	1	1	yes	characteristic
36	C₅×#389	C₂²	1	1	yes	characteristic
37	C₅×#389	C₂²	1	1	yes	characteristic
38	C₅×#389	C₂²	1	1	yes	characteristic
39	C₅×#389	C₂²	1	1	yes	characteristic
40	C₅×#388	—	2	1	no	—
41	C₅×#388	—	2	1	no	—
42	C₅×#388	—	2	1	no	—
43	C₅×#388	—	2	1	no	—
44	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₄³×C₅	C₂²	1	1	yes	characteristic
49	C₅×#340	C₂²	1	1	yes	characteristic
50	C₅×#340	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	#29536	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₅	—	2	1	no	—
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂×C₅×D₈	—	2	2	no	—
65	C₂×C₅×D₈	—	2	2	no	—
66	C₂×C₅×D₈	—	4	1	no	—
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₄×C₅×D₄	—	2	2	no	—
75	C₅×#117	—	4	4	no	—
76	C₅×#117	—	4	4	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
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	—	2	2	no	—
107	C₅×#106	—	2	2	no	—
108	C₅×#106	—	4	1	no	—
109	C₅×C₄⋊C₈	—	4	1	no	—
110	C₅×C₄⋊C₈	—	4	1	no	—
111	C₅×#102	—	2	2	no	—
112	C₅×#102	—	2	2	no	—
113	C₅×#102	—	2	2	no	—
114	C₅×#102	—	2	2	no	—
115	C₅×#102	—	4	1	no	—
116	C₅×#102	—	4	1	no	—
117	C₅×#95	—	2	1	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	#2293	C₂×C₅	1	1	yes	characteristic, complemented
124	#2293	C₂×C₅	1	1	yes	characteristic, complemented
125	#2088	C₂×C₅	1	1	yes	characteristic, complemented
126	#2067	C₂×C₅	1	1	yes	characteristic, complemented
127	#2065	C₂×C₅	1	1	yes	characteristic, complemented
128	#2054	C₂×C₅	1	1	yes	characteristic
129	#1926	C₂×C₅	1	1	yes	characteristic, complemented
130	#1926	C₂×C₅	1	1	yes	characteristic, complemented
131	#1921	C₂×C₅	1	1	yes	characteristic, complemented
132	#1919	C₂×C₅	1	1	yes	characteristic, complemented
133	#1879	C₂×C₅	1	1	yes	characteristic
134	#1879	C₂×C₅	1	1	yes	characteristic
135	#1864	C₂×C₅	1	1	yes	characteristic, complemented
136	#1862	C₂×C₅	1	1	yes	characteristic, complemented
137	#1831	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂⁴×C₅	—	2	1	no	—
139	C₂⁴×C₅	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	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	#41	1	2	yes	—
151	C₂×C₅×D₄	#41	1	2	yes	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	—	2	4	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	4	2	no	—
161	C₂²×C₄×C₅	—	4	2	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	—	4	2	no	—
164	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₅×D₈	—	4	4	no	—
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	—	2	1	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₅×C₄⋊C₄	—	2	1	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	4	2	no	—
195	C₅×C₄⋊C₄	—	4	2	no	—
196	C₅×C₄⋊C₄	—	4	2	no	—
197	C₅×C₄⋊C₄	—	4	2	no	—
198	C₅×C₄⋊C₄	#41	1	2	yes	—
199	C₅×C₄⋊C₄	#41	1	2	yes	—
200	C₅×C₂²⋊C₄	—	2	4	no	—
201	C₅×C₂²⋊C₄	—	2	4	no	—
202	C₅×C₂²⋊C₄	—	4	2	no	—
203	C₅×C₂²⋊C₄	—	4	2	no	—
204	C₅×C₂²⋊C₄	—	4	2	no	—
205	C₅×C₂²⋊C₄	—	4	2	no	—
206	C₅×C₂²⋊C₄	—	4	2	no	—
207	C₅×C₂²⋊C₄	—	4	2	no	—
208	C₅×C₂²⋊C₄	—	4	2	no	—
209	C₅×C₂²⋊C₄	—	4	2	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	2	2	no	—
213	C₄²×C₅	—	2	1	no	—
214	C₄²×C₅	—	2	1	no	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	4	1	no	—
220	C₄²×C₅	—	4	2	no	—
221	C₄²×C₅	—	4	2	no	—
222	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×#117	—	2	1	no	—
226	C₂×#117	—	2	1	no	—
227	C₂×#107	C₂²×C₅	1	1	yes	characteristic
228	C₂×#106	C₂²×C₅	1	1	yes	characteristic
229	C₂×#106	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×#102	C₂²×C₅	1	1	yes	characteristic
233	C₂×#102	C₂²×C₅	1	1	yes	characteristic
234	C₂×#102	C₂²×C₅	1	1	yes	characteristic
235	C₂×#102	C₂²×C₅	1	1	yes	characteristic
236	C₂×#102	C₂²×C₅	1	1	yes	characteristic
237	C₂×#102	C₂²×C₅	1	1	yes	characteristic
238	#390	C₂²×C₅	1	1	yes	characteristic
239	#390	C₂²×C₅	1	1	yes	characteristic
240	#390	C₂²×C₅	1	1	yes	characteristic
241	#390	C₂²×C₅	1	1	yes	characteristic
242	#389	C₂²×C₅	1	1	yes	characteristic
243	#389	C₂²×C₅	1	1	yes	characteristic
244	#389	C₂²×C₅	1	1	yes	characteristic
245	#389	C₂²×C₅	1	1	yes	characteristic
246	#388	—	2	1	no	—
247	#388	—	2	1	no	—
248	#388	—	2	1	no	—
249	#388	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	—	2	1	no	—
253	C₄×C₂²⋊C₄	—	2	1	no	—
254	C₄³	C₂²×C₅	1	1	yes	characteristic
255	#340	C₂²×C₅	1	1	yes	characteristic
256	#340	C₂²×C₅	1	1	yes	characteristic
257	#340	C₂²×C₅	1	1	yes	characteristic
258	#340	C₂²×C₅	1	1	yes	characteristic
259	#340	C₂²×C₅	1	1	yes	characteristic
260	#340	C₂²×C₅	1	1	yes	characteristic
261	#336	C₂²×C₅	1	1	yes	characteristic
262	#336	C₂²×C₅	1	1	yes	characteristic
263	#336	C₂²×C₅	1	1	yes	characteristic
264	#336	C₂²×C₅	1	1	yes	characteristic
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	—	4	1	no	—
268	C₂³×C₅	—	4	1	no	—
269	C₂³×C₅	—	4	1	no	—
270	C₂³×C₅	—	4	1	no	—
271	C₂³×C₅	—	4	1	no	—
272	C₂³×C₅	—	4	1	no	—
273	C₂³×C₅	—	4	1	no	—
274	C₂³×C₅	—	4	1	no	—
275	C₂³×C₅	—	4	1	no	—
276	C₂³×C₅	—	4	1	no	—
277	C₂³×C₅	—	4	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	2	2	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	4	1	no	—
285	C₅×D₄	—	4	1	no	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	4	8	no	—
306	C₂×C₄×C₅	—	4	8	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	1	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	#135	1	2	yes	—
324	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
325	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
326	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂×D₈	—	2	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂×D₈	—	4	1	no	—
343	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	#117	—	4	4	no	—
352	#117	—	4	4	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
376	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
377	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
378	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
382	#107	—	2	2	no	—
383	#106	—	2	2	no	—
384	#106	—	4	1	no	—
385	C₄⋊C₈	—	4	1	no	—
386	C₄⋊C₈	—	4	1	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	4	1	no	—
392	#102	—	4	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	C₂²×C₅	—	4	2	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	2	no	—
402	C₂²×C₅	—	4	2	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	8	1	no	—
406	C₂²×C₅	—	8	1	no	—
407	C₂²×C₅	—	8	1	no	—
408	C₂²×C₅	—	8	1	no	—
409	C₂²×C₅	—	8	1	no	—
410	C₂²×C₅	—	8	1	no	—
411	C₂²×C₅	—	8	1	no	—
412	C₂²×C₅	—	8	1	no	—
413	C₂²×C₅	#525	1	1	yes	characteristic
414	C₂²×C₅	#525	1	1	yes	characteristic
415	C₂²×C₅	#537	1	1	yes	characteristic
416	C₂²×C₅	C₂×#135	1	1	yes	characteristic
417	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂²×C₅	#575	1	1	yes	characteristic
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	2	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	2	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	—	8	1	no	—
429	C₄×C₅	—	8	1	no	—
430	C₄×C₅	—	8	1	no	—
431	C₄×C₅	—	8	1	no	—
432	C₄×C₅	#551	1	1	yes	characteristic
433	C₄×C₅	#552	1	1	yes	characteristic
434	C₄×C₅	#552	1	1	yes	characteristic
435	C₄×C₅	#555	1	1	yes	characteristic
436	C₂⁴	—	2	1	no	—
437	C₂⁴	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	C₅×#41	1	2	yes	—
449	C₂×D₄	C₅×#41	1	2	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
469	D₈	—	4	4	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	C₅×#41	1	2	yes	—
497	C₄⋊C₄	C₅×#41	1	2	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	4	2	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	2	no	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	4	1	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₂×C₅	—	8	2	no	—
521	C₂×C₅	—	8	2	no	—
522	C₂×C₅	#2609	1	1	yes	characteristic
523	C₂×C₅	#3102	1	1	yes	characteristic
524	C₂×C₅	#3105	1	1	yes	characteristic
525	C₂×C₅	#3109	1	1	yes	characteristic
526	C₂×C₅	#3115	1	1	yes	characteristic
527	C₂×C₅	#3247	1	1	yes	characteristic
528	C₂×C₅	#3251	1	1	yes	characteristic
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	8	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	C₅×#135	1	2	yes	—
588	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
589	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
590	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
594	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₅	#29536	1	1	yes	characteristic, direct product factor, Sylow
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	C₅×#525	1	1	yes	characteristic
616	C₂²	C₅×#525	1	1	yes	characteristic
617	C₂²	C₅×#537	1	1	yes	characteristic
618	C₂²	C₂×C₅×#135	1	1	yes	characteristic
619	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
621	C₂²	C₅×#575	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	C₅×#551	1	1	yes	characteristic
635	C₄	C₅×#552	1	1	yes	characteristic
636	C₄	C₅×#552	1	1	yes	characteristic
637	C₄	C₅×#555	1	1	yes	characteristic
638	C₂	—	8	2	no	—
639	C₂	—	8	2	no	—
640	C₂	C₅×#2609	1	1	yes	characteristic
641	C₂	C₅×#3102	1	1	yes	characteristic
642	C₂	C₅×#3105	1	1	yes	characteristic
643	C₂	C₅×#3109	1	1	yes	characteristic
644	C₂	C₅×#3115	1	1	yes	characteristic
645	C₂	C₅×#3247	1	1	yes	characteristic
646	C₂	C₅×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2293	C₂	semidirect
2. C₅×#2293	C₂	semidirect
3. C₅×#2088	C₂	semidirect
4. C₅×#2067	C₂	semidirect
5. C₅×#2065	C₂	semidirect
7. C₅×#1926	C₂	semidirect
8. C₅×#1926	C₂	semidirect
9. C₅×#1921	C₂	semidirect
10. C₅×#1919	C₂	semidirect
13. C₅×#1864	C₂	semidirect
14. C₅×#1862	C₂	semidirect
15. C₅×#1831	C₂	semidirect
59. #29536	C₅	direct (N × H)
123. #2293	C₂×C₅	semidirect
124. #2293	C₂×C₅	semidirect
125. #2088	C₂×C₅	semidirect
126. #2067	C₂×C₅	semidirect
127. #2065	C₂×C₅	semidirect
129. #1926	C₂×C₅	semidirect
130. #1926	C₂×C₅	semidirect
131. #1921	C₂×C₅	semidirect
132. #1919	C₂×C₅	semidirect
135. #1864	C₂×C₅	semidirect
136. #1862	C₂×C₅	semidirect
137. #1831	C₂×C₅	semidirect
600. C₅	#29536	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×#2293	2
C₅×#2088	2
C₅×#2067	2
C₅×#2065	2
C₅×#2054	2
C₅×#1926	2
C₅×#1921	2
C₅×#1919	2
C₅×#1879	2
C₅×#1864	2
C₅×#1862	2
C₅×#1831	2
#29536	5

Subgroups — C5×#29536 #11952256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#29536 #11952256