Subgroups — C₅×#34330 #11957050

Order 1280.

2772 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#550	C₂	1	1	yes	maximal, characteristic
2	C₅×#2366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2366	C₂	1	2	yes	maximal, complemented
4	C₅×#2364	C₂	1	4	yes	maximal, complemented
5	C₅×#2363	C₂	1	2	yes	maximal, complemented
6	C₅×#2357	C₂	1	2	yes	maximal, complemented
7	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2339	C₂	1	2	yes	maximal, complemented
10	C₅×#2333	C₂	1	4	yes	maximal, complemented
11	C₅×#2328	C₂	1	2	yes	maximal, complemented
12	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₅×#121	C₂	1	2	yes	maximal, complemented
14	C₅×#2297	C₂	1	2	yes	maximal, complemented
15	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2275	C₂	1	2	yes	maximal, complemented
17	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	2	yes	—
19	C₅×#550	C₄	1	16	yes	complemented
20	C₂×C₅×#127	C₂²	1	1	yes	characteristic
21	C₂×C₅×#127	C₂²	1	2	yes	—
22	C₂×C₅×#121	C₂²	1	2	yes	—
23	C₂×C₅×#121	C₂²	1	4	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
35	C₂×C₅×#117	C₂²	1	2	yes	—
36	C₂²×C₄²×C₅	C₂²	1	2	yes	—
37	C₅×#391	C₂²	1	1	yes	characteristic
38	C₅×#391	C₂²	1	1	yes	characteristic
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#390	C₂²	1	2	yes	—
41	C₅×#390	C₂²	1	2	yes	—
42	C₅×#390	C₂²	1	2	yes	—
43	C₅×#390	C₂²	1	2	yes	—
44	C₅×#390	C₂²	1	2	yes	—
45	C₅×#390	C₂²	1	2	yes	—
46	C₅×#390	C₂²	1	4	yes	—
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	1	yes	characteristic
49	C₅×#388	C₂²	1	4	yes	—
50	C₅×#388	C₂²	1	4	yes	—
51	C₅×#388	C₂²	1	4	yes	—
52	C₅×#387	C₂²	1	2	yes	—
53	C₅×#387	C₂²	1	2	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#386	C₂²	1	4	yes	—
56	C₅×#386	C₂²	1	4	yes	—
57	C₅×#386	C₂²	1	4	yes	—
58	C₅×#386	C₂²	1	4	yes	—
59	C₅×#386	C₂²	1	4	yes	—
60	C₅×#386	C₂²	1	4	yes	—
61	C₅×#386	C₂²	1	4	yes	—
62	C₅×#384	C₂²	1	1	yes	characteristic
63	C₅×#382	C₂²	1	2	yes	—
64	C₅×#381	C₂²	1	4	yes	—
65	C₅×#380	C₂²	1	2	yes	—
66	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₅×#376	C₂²	1	2	yes	—
82	C₂×C₅×#95	C₂²	1	4	yes	—
83	C₄³×C₅	C₂²	1	1	yes	characteristic
84	#34330	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂×C₅×#41	—	4	4	no	—
86	C₂×C₅×#41	—	4	4	no	—
87	C₂×C₅×#41	C₂×C₄	1	16	yes	complemented
88	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
89	C₂²×C₅×D₄	C₂³	1	2	yes	—
90	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂²×C₅×D₄	C₂³	1	2	yes	—
92	C₂²×C₅×D₄	C₂³	1	4	yes	—
93	C₂²×C₅×D₄	C₂³	1	4	yes	—
94	C₂²×C₅×D₄	C₂³	1	2	yes	—
95	C₂³×C₄×C₅	C₂³	1	2	yes	—
96	C₂³×C₄×C₅	C₂³	1	2	yes	—
97	C₂³×C₄×C₅	C₂³	1	4	yes	—
98	C₂³×C₄×C₅	C₂³	1	4	yes	—
99	C₂³×C₄×C₅	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	4	yes	—
101	C₅×#127	C₂×C₄	1	8	yes	complemented
102	C₅×#127	C₂×C₄	1	16	yes	complemented
103	C₅×#121	C₂×C₄	1	16	yes	complemented
104	C₅×#121	C₂×C₄	1	32	yes	complemented
105	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
106	C₄×C₅×D₄	—	2	4	no	—
107	C₄×C₅×D₄	—	2	8	no	—
108	C₄×C₅×D₄	—	2	4	no	—
109	C₄×C₅×D₄	—	2	8	no	—
110	C₄×C₅×D₄	—	4	4	no	—
111	C₄×C₅×D₄	—	4	4	no	—
112	C₄×C₅×D₄	—	4	4	no	—
113	C₄×C₅×D₄	—	4	8	no	—
114	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
115	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
116	C₅×#117	—	4	4	no	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₄²×C₅	—	4	4	no	—
142	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂³	1	2	yes	—
147	C₂×C₄²×C₅	C₂³	1	2	yes	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₅	C₂³	1	2	yes	—
150	C₂×C₄²×C₅	C₂³	1	2	yes	—
151	C₂×C₄²×C₅	C₂³	1	4	yes	—
152	C₂×C₄²×C₅	C₂³	1	4	yes	—
153	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂³	1	2	yes	—
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	C₅×#95	C₂³	1	2	yes	—
157	C₅×#95	C₂³	1	2	yes	—
158	C₅×#95	C₂³	1	4	yes	—
159	C₅×#95	C₂³	1	4	yes	—
160	C₅×#95	C₂³	1	2	yes	—
161	C₅×#95	C₂³	1	2	yes	—
162	C₅×#95	C₂³	1	2	yes	—
163	C₅×#95	C₂³	1	2	yes	—
164	C₅×#95	C₂³	1	2	yes	—
165	C₅×#95	C₂³	1	2	yes	—
166	C₅×#95	C₂³	1	4	yes	—
167	C₅×#95	C₂³	1	2	yes	—
168	C₅×#95	C₂³	1	4	yes	—
169	C₅×#95	C₂³	1	2	yes	—
170	C₂×#550	C₂×C₅	1	1	yes	characteristic
171	#2366	C₂×C₅	1	2	yes	complemented
172	#2366	C₂×C₅	1	1	yes	characteristic, complemented
173	#2364	C₂×C₅	1	4	yes	complemented
174	#2363	C₂×C₅	1	2	yes	complemented
175	#2357	C₂×C₅	1	2	yes	complemented
176	#2355	C₂×C₅	1	1	yes	characteristic, complemented
177	#2354	C₂×C₅	1	1	yes	characteristic, complemented
178	#2339	C₂×C₅	1	2	yes	complemented
179	#2333	C₂×C₅	1	4	yes	complemented
180	#2328	C₂×C₅	1	2	yes	complemented
181	C₄×#127	C₂×C₅	1	1	yes	characteristic, complemented
182	C₄×#121	C₂×C₅	1	2	yes	complemented
183	#2297	C₂×C₅	1	2	yes	complemented
184	#2295	C₂×C₅	1	1	yes	characteristic, complemented
185	#2275	C₂×C₅	1	2	yes	complemented
186	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
187	C₂⁴×C₅	C₂⁴	1	4	yes	—
188	C₂⁴×C₅	C₂⁴	1	2	yes	—
189	C₅×#41	—	4	32	no	—
190	C₂×C₅×Q₈	—	2	2	no	—
191	C₂×C₅×Q₈	—	2	2	no	—
192	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	2	4	no	—
195	C₂×C₅×D₄	—	2	2	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	—	2	4	no	—
198	C₂×C₅×D₄	—	2	4	no	—
199	C₂×C₅×D₄	—	4	2	no	—
200	C₂×C₅×D₄	—	4	4	no	—
201	C₂×C₅×D₄	—	4	2	no	—
202	C₂×C₅×D₄	—	4	4	no	—
203	C₂×C₅×D₄	—	4	4	no	—
204	C₂×C₅×D₄	—	4	4	no	—
205	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
206	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
207	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
208	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
209	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
210	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
211	C₂²×C₄×C₅	—	2	4	no	—
212	C₂²×C₄×C₅	—	2	4	no	—
213	C₂²×C₄×C₅	—	2	4	no	—
214	C₂²×C₄×C₅	—	2	4	no	—
215	C₂²×C₄×C₅	—	2	4	no	—
216	C₂²×C₄×C₅	—	2	8	no	—
217	C₂²×C₄×C₅	—	2	8	no	—
218	C₂²×C₄×C₅	—	4	2	no	—
219	C₂²×C₄×C₅	—	4	2	no	—
220	C₂²×C₄×C₅	—	4	2	no	—
221	C₂²×C₄×C₅	—	4	4	no	—
222	C₂²×C₄×C₅	—	4	4	no	—
223	C₂²×C₄×C₅	—	4	4	no	—
224	C₂²×C₄×C₅	—	4	4	no	—
225	C₂²×C₄×C₅	—	4	4	no	—
226	C₂²×C₄×C₅	—	4	4	no	—
227	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
228	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
229	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
232	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₅×C₄⋊C₄	—	2	2	no	—
245	C₅×C₄⋊C₄	—	2	4	no	—
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	4	no	—
248	C₅×C₄⋊C₄	—	2	4	no	—
249	C₅×C₄⋊C₄	—	2	2	no	—
250	C₅×C₄⋊C₄	—	4	2	no	—
251	C₅×C₄⋊C₄	—	4	2	no	—
252	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
253	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
254	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
255	C₅×C₄⋊C₄	#41	1	4	yes	complemented
256	C₅×C₂²⋊C₄	—	2	4	no	—
257	C₅×C₂²⋊C₄	—	2	8	no	—
258	C₅×C₂²⋊C₄	—	2	8	no	—
259	C₅×C₂²⋊C₄	—	2	4	no	—
260	C₅×C₂²⋊C₄	—	2	8	no	—
261	C₅×C₂²⋊C₄	—	4	4	no	—
262	C₅×C₂²⋊C₄	—	4	4	no	—
263	C₅×C₂²⋊C₄	—	4	4	no	—
264	C₅×C₂²⋊C₄	—	4	4	no	—
265	C₅×C₂²⋊C₄	—	4	4	no	—
266	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
267	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
268	C₄²×C₅	—	2	2	no	—
269	C₄²×C₅	—	2	4	no	—
270	C₄²×C₅	—	2	2	no	—
271	C₄²×C₅	—	2	4	no	—
272	C₄²×C₅	—	2	2	no	—
273	C₄²×C₅	—	2	2	no	—
274	C₄²×C₅	—	4	2	no	—
275	C₄²×C₅	—	4	2	no	—
276	C₄²×C₅	—	4	1	no	—
277	C₄²×C₅	—	4	4	no	—
278	C₄²×C₅	—	4	4	no	—
279	C₄²×C₅	C₂²×C₄	1	8	yes	—
280	C₄²×C₅	C₂²×C₄	1	4	yes	—
281	C₄²×C₅	#41	1	4	yes	complemented
282	C₂²×#41	C₂²×C₅	1	2	yes	—
283	#550	C₄×C₅	1	16	yes	complemented
284	C₂×#127	C₂²×C₅	1	1	yes	characteristic
285	C₂×#127	C₂²×C₅	1	2	yes	—
286	C₂×#121	C₂²×C₅	1	4	yes	—
287	C₂×#121	C₂²×C₅	1	2	yes	—
288	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
290	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
293	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
294	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
296	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
297	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
299	C₂×#117	C₂²×C₅	1	2	yes	—
300	C₂²×C₄²	C₂²×C₅	1	2	yes	—
301	#391	C₂²×C₅	1	1	yes	characteristic
302	#391	C₂²×C₅	1	2	yes	—
303	#391	C₂²×C₅	1	1	yes	characteristic
304	#390	C₂²×C₅	1	2	yes	—
305	#390	C₂²×C₅	1	2	yes	—
306	#390	C₂²×C₅	1	2	yes	—
307	#390	C₂²×C₅	1	2	yes	—
308	#390	C₂²×C₅	1	2	yes	—
309	#390	C₂²×C₅	1	4	yes	—
310	#390	C₂²×C₅	1	2	yes	—
311	#389	C₂²×C₅	1	1	yes	characteristic
312	#389	C₂²×C₅	1	1	yes	characteristic
313	#388	C₂²×C₅	1	4	yes	—
314	#388	C₂²×C₅	1	4	yes	—
315	#388	C₂²×C₅	1	4	yes	—
316	#387	C₂²×C₅	1	2	yes	—
317	#387	C₂²×C₅	1	4	yes	—
318	#387	C₂²×C₅	1	2	yes	—
319	#386	C₂²×C₅	1	4	yes	—
320	#386	C₂²×C₅	1	4	yes	—
321	#386	C₂²×C₅	1	4	yes	—
322	#386	C₂²×C₅	1	4	yes	—
323	#386	C₂²×C₅	1	4	yes	—
324	#386	C₂²×C₅	1	4	yes	—
325	#386	C₂²×C₅	1	4	yes	—
326	#384	C₂²×C₅	1	1	yes	characteristic
327	#382	C₂²×C₅	1	2	yes	—
328	#381	C₂²×C₅	1	4	yes	—
329	#380	C₂²×C₅	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
331	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
333	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
335	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
339	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
340	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
341	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
342	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
343	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
344	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
345	#376	C₂²×C₅	1	2	yes	—
346	C₂×#95	C₂²×C₅	1	4	yes	—
347	C₄³	C₂²×C₅	1	1	yes	characteristic
348	C₂³×C₅	—	2	2	no	—
349	C₂³×C₅	—	2	4	no	—
350	C₂³×C₅	—	2	2	no	—
351	C₂³×C₅	—	2	4	no	—
352	C₂³×C₅	—	2	4	no	—
353	C₂³×C₅	—	2	2	no	—
354	C₂³×C₅	—	2	2	no	—
355	C₂³×C₅	—	2	4	no	—
356	C₂³×C₅	—	2	4	no	—
357	C₂³×C₅	—	2	2	no	—
358	C₂³×C₅	—	2	4	no	—
359	C₂³×C₅	—	2	2	no	—
360	C₂³×C₅	C₂³×C₄	1	4	yes	—
361	C₂³×C₅	C₂³×C₄	1	8	yes	—
362	C₂³×C₅	C₂⁵	1	1	yes	characteristic
363	C₅×Q₈	—	2	8	no	—
364	C₅×D₄	—	2	8	no	—
365	C₅×D₄	—	2	16	no	—
366	C₅×D₄	—	2	16	no	—
367	C₅×D₄	—	4	8	no	—
368	C₅×D₄	—	4	16	no	—
369	C₅×D₄	—	4	16	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	2	1	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	2	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	2	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	2	no	—
382	C₂×C₄×C₅	—	2	2	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	16	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	2	no	—
389	C₂×C₄×C₅	—	2	2	no	—
390	C₂×C₄×C₅	—	2	2	no	—
391	C₂×C₄×C₅	—	2	4	no	—
392	C₂×C₄×C₅	—	2	2	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	4	no	—
396	C₂×C₄×C₅	—	2	4	no	—
397	C₂×C₄×C₅	—	2	2	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	4	16	no	—
403	C₂×C₄×C₅	—	4	8	no	—
404	C₂×C₄×C₅	—	4	8	no	—
405	C₂×C₄×C₅	—	8	8	no	—
406	C₂×C₄×C₅	—	8	8	no	—
407	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
409	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
410	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
411	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
413	C₂×C₄×C₅	C₂×#41	1	2	yes	—
414	C₂×C₄×C₅	C₂×#41	1	2	yes	—
415	C₂×C₄×C₅	C₂×#41	1	4	yes	—
416	C₂×C₄×C₅	C₂×#41	1	2	yes	—
417	C₂×C₄×C₅	C₂×#41	1	2	yes	—
418	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
420	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
421	C₂×#41	—	4	4	no	—
422	C₂×#41	—	4	4	no	—
423	C₂×#41	C₂×C₄×C₅	1	16	yes	complemented
424	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₅	1	2	yes	—
426	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₅	1	2	yes	—
428	C₂²×D₄	C₂³×C₅	1	2	yes	—
429	C₂²×D₄	C₂³×C₅	1	4	yes	—
430	C₂²×D₄	C₂³×C₅	1	4	yes	—
431	C₂³×C₄	C₂³×C₅	1	2	yes	—
432	C₂³×C₄	C₂³×C₅	1	2	yes	—
433	C₂³×C₄	C₂³×C₅	1	4	yes	—
434	C₂³×C₄	C₂³×C₅	1	4	yes	—
435	C₂³×C₄	C₂³×C₅	1	2	yes	—
436	C₂³×C₄	C₂³×C₅	1	4	yes	—
437	#127	C₂×C₄×C₅	1	8	yes	complemented
438	#127	C₂×C₄×C₅	1	16	yes	complemented
439	#121	C₂×C₄×C₅	1	16	yes	complemented
440	#121	C₂×C₄×C₅	1	32	yes	complemented
441	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
442	C₄×D₄	—	2	4	no	—
443	C₄×D₄	—	2	8	no	—
444	C₄×D₄	—	2	4	no	—
445	C₄×D₄	—	2	8	no	—
446	C₄×D₄	—	4	4	no	—
447	C₄×D₄	—	4	4	no	—
448	C₄×D₄	—	4	4	no	—
449	C₄×D₄	—	4	8	no	—
450	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
451	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
452	#117	—	4	4	no	—
453	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
460	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
477	C₂×C₄²	—	4	4	no	—
478	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₅	1	2	yes	—
482	C₂×C₄²	C₂³×C₅	1	2	yes	—
483	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₅	1	4	yes	—
485	C₂×C₄²	C₂³×C₅	1	4	yes	—
486	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₅	1	2	yes	—
488	C₂×C₄²	C₂³×C₅	1	2	yes	—
489	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₅	1	2	yes	—
491	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
492	#95	C₂³×C₅	1	2	yes	—
493	#95	C₂³×C₅	1	2	yes	—
494	#95	C₂³×C₅	1	4	yes	—
495	#95	C₂³×C₅	1	4	yes	—
496	#95	C₂³×C₅	1	2	yes	—
497	#95	C₂³×C₅	1	2	yes	—
498	#95	C₂³×C₅	1	2	yes	—
499	#95	C₂³×C₅	1	2	yes	—
500	#95	C₂³×C₅	1	2	yes	—
501	#95	C₂³×C₅	1	2	yes	—
502	#95	C₂³×C₅	1	4	yes	—
503	#95	C₂³×C₅	1	2	yes	—
504	#95	C₂³×C₅	1	4	yes	—
505	#95	C₂³×C₅	1	2	yes	—
506	C₂²×C₅	—	2	4	no	—
507	C₂²×C₅	—	2	8	no	—
508	C₂²×C₅	—	2	4	no	—
509	C₂²×C₅	—	2	8	no	—
510	C₂²×C₅	—	2	8	no	—
511	C₂²×C₅	—	2	4	no	—
512	C₂²×C₅	—	4	2	no	—
513	C₂²×C₅	—	4	4	no	—
514	C₂²×C₅	—	4	4	no	—
515	C₂²×C₅	—	4	2	no	—
516	C₂²×C₅	—	4	2	no	—
517	C₂²×C₅	—	4	4	no	—
518	C₂²×C₅	—	4	2	no	—
519	C₂²×C₅	—	4	4	no	—
520	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
521	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₅	#585	1	1	yes	characteristic
527	C₄×C₅	—	2	4	no	—
528	C₄×C₅	—	2	4	no	—
529	C₄×C₅	—	2	2	no	—
530	C₄×C₅	—	2	4	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	2	2	no	—
534	C₄×C₅	—	2	4	no	—
535	C₄×C₅	—	4	2	no	—
536	C₄×C₅	—	4	4	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	2	no	—
539	C₄×C₅	—	4	2	no	—
540	C₄×C₅	C₄×#41	1	4	yes	—
541	C₄×C₅	#518	1	4	yes	—
542	C₂⁴	C₂⁴×C₅	1	4	yes	—
543	C₂⁴	C₂⁴×C₅	1	2	yes	—
544	#41	—	4	32	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	2	no	—
547	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
561	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
562	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
563	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
564	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
565	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	2	8	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	4	4	no	—
580	C₂²×C₄	—	4	4	no	—
581	C₂²×C₄	—	4	4	no	—
582	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
583	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
584	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
589	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
608	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
609	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
610	C₄⋊C₄	C₅×#41	1	4	yes	complemented
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	8	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
622	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
623	C₄²	—	2	2	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	4	2	no	—
630	C₄²	—	4	2	no	—
631	C₄²	—	4	4	no	—
632	C₄²	—	4	4	no	—
633	C₄²	—	4	1	no	—
634	C₄²	C₂²×C₄×C₅	1	8	yes	—
635	C₄²	C₂²×C₄×C₅	1	4	yes	—
636	C₄²	C₅×#41	1	4	yes	complemented
637	C₂×C₅	—	4	4	no	—
638	C₂×C₅	—	4	8	no	—
639	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
640	C₂×C₅	C₂×#518	1	1	yes	characteristic
641	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
642	C₂×C₅	#3506	1	1	yes	characteristic
643	C₂×C₅	#3508	1	1	yes	characteristic
644	C₂×C₅	#3517	1	1	yes	characteristic
645	C₂×C₅	#3519	1	1	yes	characteristic
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	4	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	C₂³×C₄×C₅	1	4	yes	—
659	C₂³	C₂³×C₄×C₅	1	8	yes	—
660	C₂³	C₂⁵×C₅	1	1	yes	characteristic
661	Q₈	—	2	8	no	—
662	D₄	—	2	8	no	—
663	D₄	—	2	16	no	—
664	D₄	—	2	16	no	—
665	D₄	—	4	16	no	—
666	D₄	—	4	8	no	—
667	D₄	—	4	16	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	16	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	4	16	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	8	8	no	—
704	C₂×C₄	—	8	8	no	—
705	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
707	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
708	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
709	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
710	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
711	C₂×C₄	C₂×C₅×#41	1	2	yes	—
712	C₂×C₄	C₂×C₅×#41	1	2	yes	—
713	C₂×C₄	C₂×C₅×#41	1	4	yes	—
714	C₂×C₄	C₂×C₅×#41	1	2	yes	—
715	C₂×C₄	C₂×C₅×#41	1	2	yes	—
716	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
717	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
718	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
719	C₅	#34330	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	4	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	8	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	4	no	—
734	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
735	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
736	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
737	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
739	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂²	C₅×#585	1	1	yes	characteristic
741	C₄	—	2	4	no	—
742	C₄	—	2	4	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	4	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	C₄×C₅×#41	1	4	yes	—
755	C₄	C₅×#518	1	4	yes	—
756	C₂	—	4	4	no	—
757	C₂	—	4	8	no	—
758	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
759	C₂	C₂×C₅×#518	1	1	yes	characteristic
760	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂	C₅×#3506	1	1	yes	characteristic
762	C₂	C₅×#3508	1	1	yes	characteristic
763	C₂	C₅×#3517	1	1	yes	characteristic
764	C₂	C₅×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#550	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2366	C₂	semidirect
3. C₅×#2366	C₂	semidirect
4. C₅×#2364	C₂	semidirect
5. C₅×#2363	C₂	semidirect
6. C₅×#2357	C₂	semidirect
7. C₅×#2355	C₂	semidirect
8. C₅×#2354	C₂	semidirect
9. C₅×#2339	C₂	semidirect
10. C₅×#2333	C₂	semidirect
11. C₅×#2328	C₂	semidirect
12. C₄×C₅×#127	C₂	semidirect
13. C₄×C₅×#121	C₂	semidirect
14. C₅×#2297	C₂	semidirect
15. C₅×#2295	C₂	semidirect
16. C₅×#2275	C₂	semidirect
17. C₄²×C₅×D₄	C₂	semidirect
19. C₅×#550	C₄	semidirect
84. #34330	C₅	direct (N × H)
87. C₂×C₅×#41	C₂×C₄	semidirect
101. C₅×#127	C₂×C₄	semidirect
102. C₅×#127	C₂×C₄	semidirect
103. C₅×#121	C₂×C₄	semidirect
104. C₅×#121	C₂×C₄	semidirect
105. C₄×C₅×Q₈	C₂×C₄	semidirect
114. C₄×C₅×D₄	C₂×C₄	semidirect
115. C₄×C₅×D₄	C₂×C₄	semidirect
171. #2366	C₂×C₅	semidirect
172. #2366	C₂×C₅	semidirect
173. #2364	C₂×C₅	semidirect
174. #2363	C₂×C₅	semidirect
175. #2357	C₂×C₅	semidirect
176. #2355	C₂×C₅	semidirect
177. #2354	C₂×C₅	semidirect
178. #2339	C₂×C₅	semidirect
179. #2333	C₂×C₅	semidirect
180. #2328	C₂×C₅	semidirect
181. C₄×#127	C₂×C₅	semidirect
182. C₄×#121	C₂×C₅	semidirect
183. #2297	C₂×C₅	semidirect
184. #2295	C₂×C₅	semidirect
185. #2275	C₂×C₅	semidirect
186. C₄²×D₄	C₂×C₅	semidirect
255. C₅×C₄⋊C₄	#41	semidirect
281. C₄²×C₅	#41	semidirect
283. #550	C₄×C₅	semidirect
423. C₂×#41	C₂×C₄×C₅	semidirect
437. #127	C₂×C₄×C₅	semidirect
438. #127	C₂×C₄×C₅	semidirect
439. #121	C₂×C₄×C₅	semidirect
440. #121	C₂×C₄×C₅	semidirect
441. C₄×Q₈	C₂×C₄×C₅	semidirect
450. C₄×D₄	C₂×C₄×C₅	semidirect
451. C₄×D₄	C₂×C₄×C₅	semidirect
610. C₄⋊C₄	C₅×#41	semidirect
636. C₄²	C₅×#41	semidirect
719. C₅	#34330	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×#550	2
C₅×#2366	2
C₅×#2364	2
C₅×#2363	2
C₅×#2357	2
C₅×#2355	2
C₅×#2354	2
C₅×#2339	2
C₅×#2333	2
C₅×#2328	2
C₄×C₅×#127	2
C₄×C₅×#121	2
C₅×#2297	2
C₅×#2295	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34330	5

Subgroups — C5×#34330 #11957050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34330 #11957050