Subgroups — C₅×#25285 #11948005

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2544	C₂	1	1	yes	maximal, characteristic
4	C₅×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2041	C₂	1	1	yes	maximal, characteristic
9	C₅×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1982	C₂	1	1	yes	maximal, characteristic
12	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1928	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#127	C₂²	1	1	yes	characteristic
18	C₂×C₅×#124	C₂²	1	1	yes	characteristic
19	C₂×C₅×#124	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₅×#489	—	2	4	no	—
22	C₅×#474	—	2	4	no	—
23	C₂×C₅×#107	C₂²	1	1	yes	characteristic
24	C₂×C₅×#107	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	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×#103	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×#102	C₂²	1	1	yes	characteristic
37	C₂×C₅×#102	C₂²	1	1	yes	characteristic
38	C₂×C₅×#102	C₂²	1	1	yes	characteristic
39	C₂×C₅×#102	C₂²	1	1	yes	characteristic
40	C₂×C₅×#97	C₂²	1	1	yes	characteristic
41	C₅×#394	—	2	1	no	—
42	C₅×#394	—	2	1	no	—
43	C₅×#391	—	2	1	no	—
44	C₅×#391	—	2	1	no	—
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#389	—	2	1	no	—
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#389	C₂²	1	1	yes	characteristic
50	C₅×#386	—	2	1	no	—
51	C₅×#386	—	2	1	no	—
52	C₄×C₅×C₄⋊C₄	—	2	1	no	—
53	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
54	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₅×#340	C₂²	1	1	yes	characteristic
58	C₅×#340	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#25285	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	—	2	1	no	—
63	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₅	—	2	1	no	—
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	—	2	2	no	—
74	C₅×C₄⋊Q₈	D₄	1	4	yes	complemented
75	C₅×#127	—	2	2	no	—
76	C₅×#127	—	4	1	no	—
77	C₅×#124	—	2	2	no	—
78	C₅×#124	—	2	2	no	—
79	C₅×#124	—	2	2	no	—
80	C₅×#124	—	4	1	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	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	D₄	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	—	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	—	2	2	no	—
107	C₅×#107	—	2	2	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	—	4	1	no	—
110	C₅×C₄⋊C₈	—	4	1	no	—
111	C₅×#103	—	2	2	no	—
112	C₅×#103	—	2	2	no	—
113	C₅×#103	—	2	2	no	—
114	C₅×#103	—	4	1	no	—
115	C₅×#102	—	2	2	no	—
116	C₅×#102	—	2	2	no	—
117	C₅×#102	—	2	2	no	—
118	C₅×#102	—	2	2	no	—
119	C₅×#102	—	2	2	no	—
120	C₅×#102	—	2	2	no	—
121	C₅×#102	—	2	2	no	—
122	C₅×#102	—	4	1	no	—
123	C₅×#97	—	2	2	no	—
124	C₅×#95	—	2	1	no	—
125	C₅×#95	—	2	1	no	—
126	C₅×#95	—	2	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	D₄	1	1	yes	characteristic
132	C₅×#95	D₄	1	1	yes	characteristic
133	C₂×#489	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×#474	C₂×C₅	1	1	yes	characteristic, complemented
135	#2544	C₂×C₅	1	1	yes	characteristic
136	#2369	C₂×C₅	1	1	yes	characteristic, complemented
137	#2068	C₂×C₅	1	1	yes	characteristic, complemented
138	#2067	C₂×C₅	1	1	yes	characteristic, complemented
139	#2042	C₂×C₅	1	1	yes	characteristic, complemented
140	#2041	C₂×C₅	1	1	yes	characteristic
141	#1983	C₂×C₅	1	1	yes	characteristic, complemented
142	#1983	C₂×C₅	1	1	yes	characteristic, complemented
143	#1982	C₂×C₅	1	1	yes	characteristic
144	#1940	C₂×C₅	1	1	yes	characteristic, complemented
145	#1928	C₂×C₅	1	1	yes	characteristic, complemented
146	#1925	C₂×C₅	1	1	yes	characteristic, complemented
147	#1762	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁴×C₅	—	2	1	no	—
149	C₂⁴×C₅	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	4	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
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	—	8	1	no	—
158	C₂×C₅×Q₈	—	8	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	—	8	1	no	—
175	C₂×C₅×D₄	—	8	1	no	—
176	C₂×C₅×D₄	#41	1	2	yes	—
177	C₂²×C₄×C₅	—	2	1	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	—	4	2	no	—
184	C₂²×C₄×C₅	—	8	1	no	—
185	C₂²×C₄×C₅	—	8	1	no	—
186	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
200	C₂×C₅×C₈	—	2	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	4	no	—
206	C₅×C₄⋊C₄	—	2	2	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	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	4	1	no	—
215	C₅×C₄⋊C₄	—	8	1	no	—
216	C₅×C₄⋊C₄	—	8	1	no	—
217	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
219	C₅×C₄⋊C₄	#41	1	2	yes	—
220	C₅×C₂²⋊C₄	—	4	2	no	—
221	C₅×C₂²⋊C₄	—	4	2	no	—
222	C₅×C₂²⋊C₄	—	4	2	no	—
223	C₅×C₂²⋊C₄	—	4	2	no	—
224	C₅×C₂²⋊C₄	—	4	2	no	—
225	C₅×C₂²⋊C₄	—	8	1	no	—
226	C₅×C₂²⋊C₄	—	8	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	—	4	2	no	—
232	C₄²×C₅	—	8	1	no	—
233	C₄²×C₅	—	8	1	no	—
234	C₄²×C₅	C₂×D₄	1	2	yes	—
235	C₄²×C₅	#41	1	2	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×#127	C₂²×C₅	1	1	yes	characteristic
238	C₂×#124	C₂²×C₅	1	1	yes	characteristic
239	C₂×#124	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
241	#489	—	2	4	no	—
242	#474	—	2	4	no	—
243	C₂×#107	C₂²×C₅	1	1	yes	characteristic
244	C₂×#107	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅	1	1	yes	characteristic
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic
251	C₂×#103	C₂²×C₅	1	1	yes	characteristic
252	C₂×#102	C₂²×C₅	1	1	yes	characteristic
253	C₂×#102	C₂²×C₅	1	1	yes	characteristic
254	C₂×#102	C₂²×C₅	1	1	yes	characteristic
255	C₂×#102	C₂²×C₅	1	1	yes	characteristic
256	C₂×#102	C₂²×C₅	1	1	yes	characteristic
257	C₂×#102	C₂²×C₅	1	1	yes	characteristic
258	C₂×#102	C₂²×C₅	1	1	yes	characteristic
259	C₂×#102	C₂²×C₅	1	1	yes	characteristic
260	C₂×#97	C₂²×C₅	1	1	yes	characteristic
261	#394	—	2	1	no	—
262	#394	—	2	1	no	—
263	#391	—	2	1	no	—
264	#391	—	2	1	no	—
265	#391	C₂²×C₅	1	1	yes	characteristic
266	#390	C₂²×C₅	1	1	yes	characteristic
267	#389	—	2	1	no	—
268	#389	C₂²×C₅	1	1	yes	characteristic
269	#389	C₂²×C₅	1	1	yes	characteristic
270	#386	—	2	1	no	—
271	#386	—	2	1	no	—
272	C₄×C₄⋊C₄	—	2	1	no	—
273	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	#340	C₂²×C₅	1	1	yes	characteristic
278	#340	C₂²×C₅	1	1	yes	characteristic
279	#336	C₂²×C₅	1	1	yes	characteristic
280	#336	C₂²×C₅	1	1	yes	characteristic
281	C₂³×C₅	—	2	2	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	C₂²×D₄	1	1	yes	characteristic
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×Q₈	—	4	1	no	—
299	C₅×Q₈	—	4	1	no	—
300	C₅×Q₈	—	8	4	no	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	2	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	2	no	—
318	C₂×C₄×C₅	—	2	2	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	2	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	#121	1	2	yes	—
346	C₂×C₄×C₅	#121	1	2	yes	—
347	C₂×C₄×C₅	#137	1	2	yes	—
348	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
352	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
354	C₅×C₈	—	4	1	no	—
355	C₅×C₈	—	4	1	no	—
356	C₅×C₈	—	4	1	no	—
357	C₅×C₈	—	4	1	no	—
358	C₂²×Q₈	—	2	1	no	—
359	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊Q₈	—	2	2	no	—
370	C₄⋊Q₈	C₅×D₄	1	4	yes	complemented
371	#127	—	2	2	no	—
372	#127	—	4	1	no	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#124	—	4	1	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	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	C₅×D₄	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₅×D₄	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×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	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	—	2	2	no	—
403	#107	—	2	2	no	—
404	C₄⋊C₈	—	2	2	no	—
405	C₄⋊C₈	—	4	1	no	—
406	C₄⋊C₈	—	4	1	no	—
407	#103	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	4	1	no	—
411	#102	—	2	2	no	—
412	#102	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	#102	—	4	1	no	—
419	#97	—	2	2	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	C₅×D₄	1	1	yes	characteristic
428	#95	C₅×D₄	1	1	yes	characteristic
429	C₂²×C₅	—	4	2	no	—
430	C₂²×C₅	—	4	2	no	—
431	C₂²×C₅	—	4	2	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	C₂×#121	1	1	yes	characteristic
444	C₂²×C₅	#546	1	1	yes	characteristic
445	C₂²×C₅	#548	1	1	yes	characteristic
446	C₂²×C₅	C₂×#137	1	1	yes	characteristic
447	C₂²×C₅	#575	1	1	yes	characteristic
448	C₂²×C₅	#576	1	1	yes	characteristic
449	C₂²×C₅	#576	1	1	yes	characteristic
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	4	1	no	—
457	C₄×C₅	—	4	1	no	—
458	C₄×C₅	—	4	1	no	—
459	C₄×C₅	—	8	1	no	—
460	C₄×C₅	—	8	1	no	—
461	C₄×C₅	—	8	1	no	—
462	C₄×C₅	#529	1	1	yes	characteristic
463	C₄×C₅	#542	1	1	yes	characteristic
464	C₄×C₅	#548	1	1	yes	characteristic
465	C₄×C₅	#550	1	1	yes	characteristic
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	2	1	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	8	1	no	—
476	C₂×Q₈	—	8	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	—	2	1	no	—
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	4	2	no	—
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	8	1	no	—
493	C₂×D₄	—	8	1	no	—
494	C₂×D₄	C₅×#41	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	4	2	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	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	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	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	—	8	1	no	—
535	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
536	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
537	C₄⋊C₄	C₅×#41	1	2	yes	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₂²⋊C₄	—	4	2	no	—
540	C₂²⋊C₄	—	4	2	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	8	1	no	—
544	C₂²⋊C₄	—	8	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	4	2	no	—
550	C₄²	—	8	1	no	—
551	C₄²	—	8	1	no	—
552	C₄²	C₂×C₅×D₄	1	2	yes	—
553	C₄²	C₅×#41	1	2	yes	—
554	C₂×C₅	—	8	2	no	—
555	C₂×C₅	—	16	1	no	—
556	C₂×C₅	#2426	1	1	yes	characteristic
557	C₂×C₅	#3037	1	1	yes	characteristic
558	C₂×C₅	#3041	1	1	yes	characteristic
559	C₂×C₅	#3314	1	1	yes	characteristic
560	C₂×C₅	#3319	1	1	yes	characteristic
561	C₂×C₅	#3370	1	1	yes	characteristic
562	C₂×C₅	#3375	1	1	yes	characteristic
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	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	C₂²×C₅×D₄	1	1	yes	characteristic
578	Q₈	—	4	1	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	8	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	D₄	—	8	4	no	—
592	D₄	—	8	4	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	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	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	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	—	8	4	no	—
627	C₂×C₄	C₅×#121	1	2	yes	—
628	C₂×C₄	C₅×#121	1	2	yes	—
629	C₂×C₄	C₅×#137	1	2	yes	—
630	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
631	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
632	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
633	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
634	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₈	—	4	1	no	—
640	C₅	#25285	1	1	yes	characteristic, direct product factor, Sylow
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	C₂×C₅×#121	1	1	yes	characteristic
656	C₂²	C₅×#546	1	1	yes	characteristic
657	C₂²	C₅×#548	1	1	yes	characteristic
658	C₂²	C₂×C₅×#137	1	1	yes	characteristic
659	C₂²	C₅×#575	1	1	yes	characteristic
660	C₂²	C₅×#576	1	1	yes	characteristic
661	C₂²	C₅×#576	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	C₅×#529	1	1	yes	characteristic
675	C₄	C₅×#542	1	1	yes	characteristic
676	C₄	C₅×#548	1	1	yes	characteristic
677	C₄	C₅×#550	1	1	yes	characteristic
678	C₂	—	8	2	no	—
679	C₂	—	16	1	no	—
680	C₂	C₅×#2426	1	1	yes	characteristic
681	C₂	C₅×#3037	1	1	yes	characteristic
682	C₂	C₅×#3041	1	1	yes	characteristic
683	C₂	C₅×#3314	1	1	yes	characteristic
684	C₂	C₅×#3319	1	1	yes	characteristic
685	C₂	C₅×#3370	1	1	yes	characteristic
686	C₂	C₅×#3375	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#489	C₂	semidirect
2. C₂×C₅×#474	C₂	semidirect
4. C₅×#2369	C₂	semidirect
5. C₅×#2068	C₂	semidirect
6. C₅×#2067	C₂	semidirect
7. C₅×#2042	C₂	semidirect
9. C₅×#1983	C₂	semidirect
10. C₅×#1983	C₂	semidirect
12. C₅×#1940	C₂	semidirect
13. C₅×#1928	C₂	semidirect
14. C₅×#1925	C₂	semidirect
15. C₅×#1762	C₂	semidirect
61. #25285	C₅	direct (N × H)
74. C₅×C₄⋊Q₈	D₄	semidirect
133. C₂×#489	C₂×C₅	semidirect
134. C₂×#474	C₂×C₅	semidirect
136. #2369	C₂×C₅	semidirect
137. #2068	C₂×C₅	semidirect
138. #2067	C₂×C₅	semidirect
139. #2042	C₂×C₅	semidirect
141. #1983	C₂×C₅	semidirect
142. #1983	C₂×C₅	semidirect
144. #1940	C₂×C₅	semidirect
145. #1928	C₂×C₅	semidirect
146. #1925	C₂×C₅	semidirect
147. #1762	C₂×C₅	semidirect
370. C₄⋊Q₈	C₅×D₄	semidirect
640. C₅	#25285	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#489	2
C₂×C₅×#474	2
C₅×#2544	2
C₅×#2369	2
C₅×#2068	2
C₅×#2067	2
C₅×#2042	2
C₅×#2041	2
C₅×#1983	2
C₅×#1982	2
C₅×#1940	2
C₅×#1928	2
C₅×#1925	2
C₅×#1762	2
#25285	5

Subgroups — C5×#25285 #11948005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#25285 #11948005