Subgroups — C₅×#32727 #11955447

Order 1280.

838 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2854	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2065	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2035	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2033	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2012	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1999	C₂	1	1	yes	maximal, characteristic
15	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₅×#123	—	2	1	no	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#121	C₂²	1	1	yes	characteristic
22	C₂×C₅×#121	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×#106	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#103	C₂²	1	1	yes	characteristic
29	C₂×C₅×#103	C₂²	1	1	yes	characteristic
30	C₂×C₅×#103	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	C₂²	1	1	yes	characteristic
32	C₂×C₅×#102	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	C₂²	1	1	yes	characteristic
34	C₂×C₅×#102	C₂²	1	1	yes	characteristic
35	C₂×C₅×#102	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#391	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×#388	—	2	1	no	—
45	C₅×#388	—	2	1	no	—
46	C₅×#388	—	2	1	no	—
47	C₅×#388	—	2	1	no	—
48	C₅×#386	—	2	1	no	—
49	C₅×#386	—	2	1	no	—
50	C₅×#386	—	2	1	no	—
51	C₅×#382	C₂²	1	1	yes	characteristic
52	C₅×#380	C₂²	1	1	yes	characteristic
53	C₅×#340	C₂²	1	1	yes	characteristic
54	C₅×#340	C₂²	1	1	yes	characteristic
55	C₅×#340	C₂²	1	1	yes	characteristic
56	C₅×#340	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	#32727	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₂²×C₅×D₄	—	2	1	no	—
63	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×SD₁₆	—	4	1	no	—
69	C₂×C₅×SD₁₆	—	4	1	no	—
70	C₂×C₅×SD₁₆	—	4	1	no	—
71	C₂×C₅×D₈	—	4	1	no	—
72	C₂×C₅×D₈	—	4	1	no	—
73	C₂×C₅×D₈	—	4	1	no	—
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	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₅×#124	—	4	1	no	—
79	C₅×#124	—	4	1	no	—
80	C₅×#123	—	4	4	no	—
81	C₅×C₂²⋊Q₈	—	4	1	no	—
82	C₅×C₂²⋊Q₈	—	4	1	no	—
83	C₅×#121	—	4	1	no	—
84	C₅×#121	—	4	1	no	—
85	C₅×#121	—	4	1	no	—
86	C₅×#121	—	4	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	—	2	1	no	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₄²×C₅	—	4	1	no	—
108	C₂×C₄²×C₅	—	4	1	no	—
109	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₅×#107	—	4	1	no	—
114	C₅×#106	—	4	1	no	—
115	C₅×C₄⋊C₈	—	4	1	no	—
116	C₅×C₄⋊C₈	—	4	1	no	—
117	C₅×#103	—	4	1	no	—
118	C₅×#103	—	4	1	no	—
119	C₅×#103	—	4	1	no	—
120	C₅×#102	—	4	1	no	—
121	C₅×#102	—	4	1	no	—
122	C₅×#102	—	4	1	no	—
123	C₅×#102	—	4	1	no	—
124	C₅×#102	—	4	1	no	—
125	C₅×C₂²⋊C₈	—	4	1	no	—
126	C₅×C₂²⋊C₈	—	4	1	no	—
127	C₅×#95	—	2	1	no	—
128	C₅×#95	—	2	1	no	—
129	C₅×#95	—	2	1	no	—
130	C₅×#95	—	2	1	no	—
131	C₅×#95	—	2	1	no	—
132	C₅×#95	—	2	1	no	—
133	C₅×#95	—	2	1	no	—
134	#2854	C₂×C₅	1	1	yes	characteristic, complemented
135	#2850	C₂×C₅	1	1	yes	characteristic, complemented
136	#2101	C₂×C₅	1	1	yes	characteristic, complemented
137	#2092	C₂×C₅	1	1	yes	characteristic, complemented
138	#2068	C₂×C₅	1	1	yes	characteristic, complemented
139	#2065	C₂×C₅	1	1	yes	characteristic, complemented
140	#2055	C₂×C₅	1	1	yes	characteristic, complemented
141	#2054	C₂×C₅	1	1	yes	characteristic, complemented
142	#2042	C₂×C₅	1	1	yes	characteristic, complemented
143	#2035	C₂×C₅	1	1	yes	characteristic, complemented
144	#2033	C₂×C₅	1	1	yes	characteristic, complemented
145	#2012	C₂×C₅	1	1	yes	characteristic, complemented
146	#2000	C₂×C₅	1	1	yes	characteristic, complemented
147	#1999	C₂×C₅	1	1	yes	characteristic
148	#1797	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂⁴×C₅	—	2	1	no	—
150	C₂⁴×C₅	—	2	1	no	—
151	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	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	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	2	1	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	4	2	no	—
171	C₂×C₅×D₄	—	4	2	no	—
172	C₂×C₅×D₄	—	4	2	no	—
173	C₂×C₅×D₄	—	4	2	no	—
174	C₂×C₅×D₄	—	4	2	no	—
175	C₂×C₅×D₄	—	4	2	no	—
176	C₂²×C₄×C₅	—	2	2	no	—
177	C₂²×C₄×C₅	—	2	2	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	2	1	no	—
182	C₂²×C₄×C₅	—	2	1	no	—
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
191	C₂²×C₄×C₅	—	4	1	no	—
192	C₂²×C₄×C₅	—	4	1	no	—
193	C₂²×C₄×C₅	—	4	1	no	—
194	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₅×SD₁₆	—	4	4	no	—
201	C₅×D₈	—	4	4	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	2	1	no	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	4	2	no	—
225	C₅×C₄⋊C₄	—	4	2	no	—
226	C₅×C₄⋊C₄	—	4	2	no	—
227	C₅×C₂²⋊C₄	—	4	2	no	—
228	C₅×C₂²⋊C₄	—	4	2	no	—
229	C₅×C₂²⋊C₄	—	4	2	no	—
230	C₅×C₂²⋊C₄	—	4	2	no	—
231	C₅×C₂²⋊C₄	—	4	2	no	—
232	C₅×C₂²⋊C₄	—	4	2	no	—
233	C₅×C₂²⋊C₄	—	4	2	no	—
234	C₅×C₂²⋊C₄	—	4	2	no	—
235	C₅×C₂²⋊C₄	—	4	2	no	—
236	C₅×C₂²⋊C₄	—	4	2	no	—
237	C₅×C₂²⋊C₄	—	4	2	no	—
238	C₅×C₂²⋊C₄	—	4	2	no	—
239	C₄²×C₅	—	2	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	2	1	no	—
242	C₄²×C₅	—	2	1	no	—
243	C₄²×C₅	—	4	1	no	—
244	C₄²×C₅	—	4	1	no	—
245	C₂²×SD₁₆	C₂²×C₅	1	1	yes	characteristic
246	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×#124	C₂²×C₅	1	1	yes	characteristic
248	C₂×#123	—	2	1	no	—
249	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×#121	C₂²×C₅	1	1	yes	characteristic
251	C₂×#121	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
253	C₂×#107	C₂²×C₅	1	1	yes	characteristic
254	C₂×#106	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	C₂×#103	C₂²×C₅	1	1	yes	characteristic
258	C₂×#103	C₂²×C₅	1	1	yes	characteristic
259	C₂×#103	C₂²×C₅	1	1	yes	characteristic
260	C₂×#102	C₂²×C₅	1	1	yes	characteristic
261	C₂×#102	C₂²×C₅	1	1	yes	characteristic
262	C₂×#102	C₂²×C₅	1	1	yes	characteristic
263	C₂×#102	C₂²×C₅	1	1	yes	characteristic
264	C₂×#102	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	#391	C₂²×C₅	1	1	yes	characteristic
268	#390	C₂²×C₅	1	1	yes	characteristic
269	#390	C₂²×C₅	1	1	yes	characteristic
270	#390	C₂²×C₅	1	1	yes	characteristic
271	#389	C₂²×C₅	1	1	yes	characteristic
272	#389	C₂²×C₅	1	1	yes	characteristic
273	#388	—	2	1	no	—
274	#388	—	2	1	no	—
275	#388	—	2	1	no	—
276	#388	—	2	1	no	—
277	#386	—	2	1	no	—
278	#386	—	2	1	no	—
279	#386	—	2	1	no	—
280	#382	C₂²×C₅	1	1	yes	characteristic
281	#380	C₂²×C₅	1	1	yes	characteristic
282	#340	C₂²×C₅	1	1	yes	characteristic
283	#340	C₂²×C₅	1	1	yes	characteristic
284	#340	C₂²×C₅	1	1	yes	characteristic
285	#340	C₂²×C₅	1	1	yes	characteristic
286	#336	C₂²×C₅	1	1	yes	characteristic
287	#336	C₂²×C₅	1	1	yes	characteristic
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	4	1	no	—
296	C₂³×C₅	—	4	1	no	—
297	C₂³×C₅	—	4	1	no	—
298	C₂³×C₅	—	4	1	no	—
299	C₂³×C₅	—	4	1	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	4	1	no	—
303	C₂³×C₅	—	4	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂³×C₅	—	4	1	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	4	1	no	—
308	C₂³×C₅	AGL(1,ℤ/8)	1	2	yes	—
309	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
310	C₅×Q₈	—	4	1	no	—
311	C₅×Q₈	—	4	1	no	—
312	C₅×Q₈	—	4	1	no	—
313	C₅×Q₈	—	4	1	no	—
314	C₅×D₄	—	4	1	no	—
315	C₅×D₄	—	4	1	no	—
316	C₅×D₄	—	4	1	no	—
317	C₅×D₄	—	4	1	no	—
318	C₅×D₄	—	4	1	no	—
319	C₅×D₄	—	4	1	no	—
320	C₅×D₄	—	4	1	no	—
321	C₅×D₄	—	4	1	no	—
322	C₅×D₄	—	8	4	no	—
323	C₅×D₄	—	8	4	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	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	1	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	4	4	no	—
339	C₂×C₄×C₅	—	4	4	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	—	4	1	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	1	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	1	no	—
351	C₂×C₄×C₅	—	4	1	no	—
352	C₂×C₄×C₅	—	4	1	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	1	no	—
355	C₂×C₄×C₅	—	4	1	no	—
356	C₂×C₄×C₅	—	4	1	no	—
357	C₂×C₄×C₅	—	4	1	no	—
358	C₂×C₄×C₅	—	4	1	no	—
359	C₂×C₄×C₅	—	4	1	no	—
360	C₂×C₄×C₅	—	4	1	no	—
361	C₂×C₄×C₅	—	4	1	no	—
362	C₂×C₄×C₅	#135	1	2	yes	—
363	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
369	C₅×C₈	—	4	1	no	—
370	C₅×C₈	—	4	1	no	—
371	C₅×C₈	—	4	1	no	—
372	C₅×C₈	—	4	1	no	—
373	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	—	2	1	no	—
376	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
378	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
379	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂×SD₁₆	—	4	1	no	—
382	C₂×SD₁₆	—	4	1	no	—
383	C₂×SD₁₆	—	4	1	no	—
384	C₂×D₈	—	4	1	no	—
385	C₂×D₈	—	4	1	no	—
386	C₂×D₈	—	4	1	no	—
387	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
391	#124	—	4	1	no	—
392	#124	—	4	1	no	—
393	#123	—	4	4	no	—
394	C₂²⋊Q₈	—	4	1	no	—
395	C₂²⋊Q₈	—	4	1	no	—
396	#121	—	4	1	no	—
397	#121	—	4	1	no	—
398	#121	—	4	1	no	—
399	#121	—	4	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₄²	—	4	1	no	—
421	C₂×C₄²	—	4	1	no	—
422	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
423	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
426	#107	—	4	1	no	—
427	#106	—	4	1	no	—
428	C₄⋊C₈	—	4	1	no	—
429	C₄⋊C₈	—	4	1	no	—
430	#103	—	4	1	no	—
431	#103	—	4	1	no	—
432	#103	—	4	1	no	—
433	#102	—	4	1	no	—
434	#102	—	4	1	no	—
435	#102	—	4	1	no	—
436	#102	—	4	1	no	—
437	#102	—	4	1	no	—
438	C₂²⋊C₈	—	4	1	no	—
439	C₂²⋊C₈	—	4	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	2	2	no	—
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	4	1	no	—
451	C₂²×C₅	—	4	1	no	—
452	C₂²×C₅	—	4	1	no	—
453	C₂²×C₅	—	4	1	no	—
454	C₂²×C₅	—	8	1	no	—
455	C₂²×C₅	—	8	1	no	—
456	C₂²×C₅	—	8	1	no	—
457	C₂²×C₅	—	8	1	no	—
458	C₂²×C₅	—	8	1	no	—
459	C₂²×C₅	—	8	1	no	—
460	C₂²×C₅	—	8	1	no	—
461	C₂²×C₅	—	8	1	no	—
462	C₂²×C₅	—	8	1	no	—
463	C₂²×C₅	—	8	1	no	—
464	C₂²×C₅	—	8	1	no	—
465	C₂²×C₅	—	8	1	no	—
466	C₂²×C₅	—	8	1	no	—
467	C₂²×C₅	—	8	1	no	—
468	C₂²×C₅	#534	1	1	yes	characteristic
469	C₂²×C₅	#535	1	1	yes	characteristic
470	C₂²×C₅	#537	1	1	yes	characteristic
471	C₂²×C₅	C₂×#135	1	1	yes	characteristic
472	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂²×C₅	#575	1	1	yes	characteristic
474	C₂²×C₅	#575	1	1	yes	characteristic
475	C₄×C₅	—	2	2	no	—
476	C₄×C₅	—	4	1	no	—
477	C₄×C₅	—	4	1	no	—
478	C₄×C₅	—	4	1	no	—
479	C₄×C₅	—	4	1	no	—
480	C₄×C₅	—	8	1	no	—
481	C₄×C₅	—	8	1	no	—
482	C₄×C₅	—	8	1	no	—
483	C₄×C₅	—	8	1	no	—
484	C₄×C₅	—	8	1	no	—
485	C₄×C₅	—	8	1	no	—
486	C₄×C₅	#560	1	1	yes	characteristic
487	C₄×C₅	#560	1	1	yes	characteristic
488	C₄×C₅	#562	1	1	yes	characteristic
489	C₄×C₅	#562	1	1	yes	characteristic
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	1	no	—
492	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	1	no	—
535	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
537	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
538	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
541	SD₁₆	—	4	4	no	—
542	D₈	—	4	4	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	4	1	no	—
585	C₄²	—	4	1	no	—
586	C₂×C₅	—	4	2	no	—
587	C₂×C₅	—	16	1	no	—
588	C₂×C₅	—	16	1	no	—
589	C₂×C₅	#2813	1	1	yes	characteristic
590	C₂×C₅	#3191	1	1	yes	characteristic
591	C₂×C₅	#3194	1	1	yes	characteristic
592	C₂×C₅	#3212	1	1	yes	characteristic
593	C₂×C₅	#3213	1	1	yes	characteristic
594	C₂×C₅	#3247	1	1	yes	characteristic
595	C₂×C₅	#3256	1	1	yes	characteristic
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	C₅×AGL(1,ℤ/8)	1	2	yes	—
617	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	8	4	no	—
631	D₄	—	8	4	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	C₅×#135	1	2	yes	—
671	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₅	#32727	1	1	yes	characteristic, direct product factor, Sylow
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	C₅×#534	1	1	yes	characteristic
704	C₂²	C₅×#535	1	1	yes	characteristic
705	C₂²	C₅×#537	1	1	yes	characteristic
706	C₂²	C₂×C₅×#135	1	1	yes	characteristic
707	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₂²	C₅×#575	1	1	yes	characteristic
709	C₂²	C₅×#575	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	8	1	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	C₅×#560	1	1	yes	characteristic
722	C₄	C₅×#560	1	1	yes	characteristic
723	C₄	C₅×#562	1	1	yes	characteristic
724	C₄	C₅×#562	1	1	yes	characteristic
725	C₂	—	4	2	no	—
726	C₂	—	16	1	no	—
727	C₂	—	16	1	no	—
728	C₂	C₅×#2813	1	1	yes	characteristic
729	C₂	C₅×#3191	1	1	yes	characteristic
730	C₂	C₅×#3194	1	1	yes	characteristic
731	C₂	C₅×#3212	1	1	yes	characteristic
732	C₂	C₅×#3213	1	1	yes	characteristic
733	C₂	C₅×#3247	1	1	yes	characteristic
734	C₂	C₅×#3256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2854	C₂	semidirect
2. C₅×#2850	C₂	semidirect
3. C₅×#2101	C₂	semidirect
4. C₅×#2092	C₂	semidirect
5. C₅×#2068	C₂	semidirect
6. C₅×#2065	C₂	semidirect
7. C₅×#2055	C₂	semidirect
8. C₅×#2054	C₂	semidirect
9. C₅×#2042	C₂	semidirect
10. C₅×#2035	C₂	semidirect
11. C₅×#2033	C₂	semidirect
12. C₅×#2012	C₂	semidirect
13. C₅×#2000	C₂	semidirect
15. C₅×#1797	C₂	semidirect
59. #32727	C₅	direct (N × H)
134. #2854	C₂×C₅	semidirect
135. #2850	C₂×C₅	semidirect
136. #2101	C₂×C₅	semidirect
137. #2092	C₂×C₅	semidirect
138. #2068	C₂×C₅	semidirect
139. #2065	C₂×C₅	semidirect
140. #2055	C₂×C₅	semidirect
141. #2054	C₂×C₅	semidirect
142. #2042	C₂×C₅	semidirect
143. #2035	C₂×C₅	semidirect
144. #2033	C₂×C₅	semidirect
145. #2012	C₂×C₅	semidirect
146. #2000	C₂×C₅	semidirect
148. #1797	C₂×C₅	semidirect
681. C₅	#32727	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×#2854	2
C₅×#2850	2
C₅×#2101	2
C₅×#2092	2
C₅×#2068	2
C₅×#2065	2
C₅×#2055	2
C₅×#2054	2
C₅×#2042	2
C₅×#2035	2
C₅×#2033	2
C₅×#2012	2
C₅×#2000	2
C₅×#1999	2
C₅×#1797	2
#32727	5

Subgroups — C5×#32727 #11955447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#32727 #11955447