Subgroups — C₅×#21855 #11944575

Order 1280.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×#529	—	2	4	no	—
19	C₅×#529	—	2	4	no	—
20	C₂×C₅×#126	C₄	1	1	yes	characteristic
21	C₂×C₅×#126	C₄	1	1	yes	characteristic
22	C₂×C₅×#125	C₄	1	1	yes	characteristic
23	C₂×C₅×#124	C₄	1	1	yes	characteristic
24	C₂×C₅×#123	C₄	1	1	yes	characteristic
25	C₂×C₅×#123	C₄	1	1	yes	characteristic
26	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
27	C₂×C₅×#121	C₄	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₂×C₅×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₅×#433	—	2	4	no	—
36	C₅×#424	—	2	4	no	—
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₅×#97	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₅×C₈	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	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	C₅×#336	C₂²	1	1	yes	characteristic
62	C₅×#336	C₂²	1	1	yes	characteristic
63	#21855	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₅×M₁₆	—	2	2	no	—
74	C₂×C₅×M₁₆	—	4	1	no	—
75	C₂×C₅×M₁₆	—	4	1	no	—
76	C₂²×C₅×C₈	—	2	2	no	—
77	C₂²×C₅×C₈	—	4	1	no	—
78	C₂²×C₅×C₈	—	4	1	no	—
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₅×#126	—	2	4	no	—
88	C₅×#126	—	2	4	no	—
89	C₅×#125	—	2	4	no	—
90	C₅×#124	—	2	4	no	—
91	C₅×#123	—	2	4	no	—
92	C₅×#123	—	2	4	no	—
93	C₅×C₂²⋊Q₈	—	2	4	no	—
94	C₅×#121	—	2	4	no	—
95	C₄×C₅×Q₈	—	2	2	no	—
96	C₄×C₅×Q₈	—	2	2	no	—
97	C₄×C₅×D₄	—	2	2	no	—
98	C₄×C₅×D₄	—	2	2	no	—
99	C₄×C₅×D₄	—	2	2	no	—
100	C₄×C₅×D₄	—	2	2	no	—
101	C₄×C₅×D₄	—	2	2	no	—
102	C₄×C₅×D₄	—	2	2	no	—
103	C₅×#117	—	2	2	no	—
104	C₅×#117	—	2	2	no	—
105	C₅×#117	D₄	1	4	yes	—
106	C₅×#117	D₄	1	4	yes	—
107	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
123	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
124	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
126	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₅	—	2	2	no	—
128	C₂×C₄²×C₅	—	2	2	no	—
129	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₅×C₄⋊C₈	—	2	2	no	—
136	C₅×C₄⋊C₈	—	2	2	no	—
137	C₅×C₄⋊C₈	—	2	2	no	—
138	C₅×C₄⋊C₈	—	2	2	no	—
139	C₅×C₄⋊C₈	—	2	2	no	—
140	C₅×C₄⋊C₈	—	2	2	no	—
141	C₅×C₂²⋊C₈	—	2	2	no	—
142	C₅×C₂²⋊C₈	—	2	2	no	—
143	C₅×C₂²⋊C₈	—	4	1	no	—
144	C₅×C₂²⋊C₈	—	4	1	no	—
145	C₅×C₂²⋊C₈	—	4	1	no	—
146	C₅×C₂²⋊C₈	—	4	1	no	—
147	C₅×C₂²⋊C₈	—	4	1	no	—
148	C₅×C₂²⋊C₈	—	4	1	no	—
149	C₅×C₂²⋊C₈	—	4	1	no	—
150	C₅×C₂²⋊C₈	—	4	1	no	—
151	C₅×#97	—	2	2	no	—
152	C₄×C₅×C₈	—	2	2	no	—
153	C₂×#529	C₂×C₅	1	1	yes	characteristic
154	C₂×#433	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#424	C₂×C₅	1	1	yes	characteristic, complemented
156	#1985	C₂×C₅	1	1	yes	characteristic, complemented
157	#1984	C₂×C₅	1	1	yes	characteristic, complemented
158	#1955	C₂×C₅	1	1	yes	characteristic, complemented
159	#1954	C₂×C₅	1	1	yes	characteristic, complemented
160	#1870	C₂×C₅	1	1	yes	characteristic, complemented
161	#1870	C₂×C₅	1	1	yes	characteristic, complemented
162	#1869	C₂×C₅	1	1	yes	characteristic, complemented
163	#1869	C₂×C₅	1	1	yes	characteristic, complemented
164	#1798	C₂×C₅	1	1	yes	characteristic, complemented
165	#1798	C₂×C₅	1	1	yes	characteristic, complemented
166	#1797	C₂×C₅	1	1	yes	characteristic, complemented
167	#1797	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₅×Q₈	—	2	2	no	—
172	C₂×C₅×Q₈	—	2	2	no	—
173	C₂×C₅×Q₈	—	4	1	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	2	2	no	—
176	C₂×C₅×D₄	—	2	2	no	—
177	C₂×C₅×D₄	—	2	2	no	—
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂×C₅×D₄	—	2	2	no	—
180	C₂×C₅×D₄	—	4	1	no	—
181	C₂×C₅×D₄	—	4	1	no	—
182	C₂×C₅×D₄	—	4	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	2	no	—
188	C₂²×C₄×C₅	—	2	2	no	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	2	2	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	—	2	1	no	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	4	1	no	—
204	C₂²×C₄×C₅	—	4	1	no	—
205	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₅×M₁₆	—	4	4	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	1	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	2	1	no	—
230	C₂×C₅×C₈	—	2	1	no	—
231	C₂×C₅×C₈	—	2	1	no	—
232	C₂×C₅×C₈	—	2	1	no	—
233	C₂×C₅×C₈	—	2	1	no	—
234	C₂×C₅×C₈	—	2	1	no	—
235	C₂×C₅×C₈	—	2	1	no	—
236	C₂×C₅×C₈	—	2	1	no	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	4	4	no	—
245	C₅×C₄⋊C₄	—	2	2	no	—
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	2	no	—
248	C₅×C₄⋊C₄	—	2	2	no	—
249	C₅×C₄⋊C₄	—	2	2	no	—
250	C₅×C₄⋊C₄	—	2	2	no	—
251	C₅×C₄⋊C₄	—	2	2	no	—
252	C₅×C₄⋊C₄	—	2	2	no	—
253	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
254	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
255	C₅×C₂²⋊C₄	—	2	2	no	—
256	C₅×C₂²⋊C₄	—	2	2	no	—
257	C₅×C₂²⋊C₄	—	2	2	no	—
258	C₅×C₂²⋊C₄	—	2	2	no	—
259	C₅×C₂²⋊C₄	—	2	2	no	—
260	C₅×C₂²⋊C₄	—	2	2	no	—
261	C₅×C₂²⋊C₄	—	2	2	no	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
264	C₅×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
265	C₄²×C₅	—	2	2	no	—
266	C₄²×C₅	—	2	2	no	—
267	C₄²×C₅	—	2	1	no	—
268	C₄²×C₅	—	2	1	no	—
269	C₄²×C₅	—	2	1	no	—
270	C₄²×C₅	—	2	1	no	—
271	C₄²×C₅	C₂×D₄	1	2	yes	—
272	C₄²×C₅	C₂×D₄	1	2	yes	—
273	C₄²×C₅	C₂×D₄	1	2	yes	—
274	C₄²×C₅	C₂×D₄	1	2	yes	—
275	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
276	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
277	#529	—	2	4	no	—
278	#529	—	2	4	no	—
279	C₂×#126	C₄×C₅	1	1	yes	characteristic
280	C₂×#126	C₄×C₅	1	1	yes	characteristic
281	C₂×#125	C₄×C₅	1	1	yes	characteristic
282	C₂×#124	C₄×C₅	1	1	yes	characteristic
283	C₂×#123	C₄×C₅	1	1	yes	characteristic
284	C₂×#123	C₄×C₅	1	1	yes	characteristic
285	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
286	C₂×#121	C₄×C₅	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×#117	C₂²×C₅	1	1	yes	characteristic
292	C₂×#117	C₂²×C₅	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
294	#433	—	2	4	no	—
295	#424	—	2	4	no	—
296	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
312	C₂×#97	C₂²×C₅	1	1	yes	characteristic
313	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
314	#336	C₂²×C₅	1	1	yes	characteristic
315	#336	C₂²×C₅	1	1	yes	characteristic
316	#336	C₂²×C₅	1	1	yes	characteristic
317	#336	C₂²×C₅	1	1	yes	characteristic
318	#336	C₂²×C₅	1	1	yes	characteristic
319	#336	C₂²×C₅	1	1	yes	characteristic
320	#336	C₂²×C₅	1	1	yes	characteristic
321	#336	C₂²×C₅	1	1	yes	characteristic
322	C₂³×C₅	—	2	1	no	—
323	C₂³×C₅	—	2	1	no	—
324	C₂³×C₅	—	2	1	no	—
325	C₂³×C₅	—	2	1	no	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	2	1	no	—
328	C₂³×C₅	—	2	1	no	—
329	C₂³×C₅	—	2	1	no	—
330	C₂³×C₅	—	2	1	no	—
331	C₂³×C₅	—	2	1	no	—
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	2	1	no	—
334	C₂³×C₅	—	2	1	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	2	1	no	—
337	C₂³×C₅	—	2	1	no	—
338	C₂³×C₅	—	2	1	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	2	1	no	—
341	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³×C₅	#131	1	2	yes	—
343	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
344	C₅×Q₈	—	4	4	no	—
345	C₅×D₄	—	4	4	no	—
346	C₅×D₄	—	4	4	no	—
347	C₅×D₄	—	4	4	no	—
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	1	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	1	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	1	no	—
357	C₂×C₄×C₅	—	2	1	no	—
358	C₂×C₄×C₅	—	2	1	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	2	2	no	—
363	C₂×C₄×C₅	—	2	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	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	1	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	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	4	4	no	—
380	C₂×C₄×C₅	—	4	4	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	4	1	no	—
383	C₂×C₄×C₅	—	4	1	no	—
384	C₂×C₄×C₅	—	4	1	no	—
385	C₂×C₄×C₅	—	4	1	no	—
386	C₂×C₄×C₅	—	4	1	no	—
387	C₂×C₄×C₅	—	4	1	no	—
388	C₂×C₄×C₅	—	4	1	no	—
389	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
390	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
392	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
393	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
394	C₂×C₄×C₅	#131	1	2	yes	—
395	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
400	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
401	C₅×C₈	—	4	1	no	—
402	C₅×C₈	—	4	1	no	—
403	C₅×C₈	—	4	1	no	—
404	C₅×C₈	—	4	1	no	—
405	C₅×C₈	—	4	1	no	—
406	C₅×C₈	—	4	1	no	—
407	C₅×C₈	—	4	1	no	—
408	C₅×C₈	—	4	1	no	—
409	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
411	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
412	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
413	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
414	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	4	1	no	—
420	C₂×M₁₆	—	4	1	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	4	1	no	—
423	C₂²×C₈	—	4	1	no	—
424	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
432	#126	—	2	4	no	—
433	#126	—	2	4	no	—
434	#125	—	2	4	no	—
435	#124	—	2	4	no	—
436	#123	—	2	4	no	—
437	#123	—	2	4	no	—
438	C₂²⋊Q₈	—	2	4	no	—
439	#121	—	2	4	no	—
440	C₄×Q₈	—	2	2	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	—	2	2	no	—
450	#117	C₅×D₄	1	4	yes	—
451	#117	C₅×D₄	1	4	yes	—
452	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
472	C₂×C₄²	—	2	2	no	—
473	C₂×C₄²	—	2	2	no	—
474	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
475	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
480	C₄⋊C₈	—	2	2	no	—
481	C₄⋊C₈	—	2	2	no	—
482	C₄⋊C₈	—	2	2	no	—
483	C₄⋊C₈	—	2	2	no	—
484	C₄⋊C₈	—	2	2	no	—
485	C₄⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₂²⋊C₈	—	2	2	no	—
488	C₂²⋊C₈	—	4	1	no	—
489	C₂²⋊C₈	—	4	1	no	—
490	C₂²⋊C₈	—	4	1	no	—
491	C₂²⋊C₈	—	4	1	no	—
492	C₂²⋊C₈	—	4	1	no	—
493	C₂²⋊C₈	—	4	1	no	—
494	C₂²⋊C₈	—	4	1	no	—
495	C₂²⋊C₈	—	4	1	no	—
496	#97	—	2	2	no	—
497	C₄×C₈	—	2	2	no	—
498	C₂²×C₅	—	2	2	no	—
499	C₂²×C₅	—	2	2	no	—
500	C₂²×C₅	—	2	2	no	—
501	C₂²×C₅	—	2	2	no	—
502	C₂²×C₅	—	2	2	no	—
503	C₂²×C₅	—	2	2	no	—
504	C₂²×C₅	—	4	1	no	—
505	C₂²×C₅	—	4	1	no	—
506	C₂²×C₅	—	4	1	no	—
507	C₂²×C₅	—	4	1	no	—
508	C₂²×C₅	—	4	1	no	—
509	C₂²×C₅	—	4	1	no	—
510	C₂²×C₅	—	4	1	no	—
511	C₂²×C₅	—	4	1	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	4	1	no	—
515	C₂²×C₅	—	4	1	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	1	no	—
519	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
520	C₂²×C₅	#520	1	1	yes	characteristic
521	C₂²×C₅	#520	1	1	yes	characteristic
522	C₂²×C₅	C₂×#131	1	1	yes	characteristic
523	C₂²×C₅	C₂×#131	1	1	yes	characteristic
524	C₂²×C₅	#568	1	1	yes	characteristic
525	C₂²×C₅	#568	1	1	yes	characteristic
526	C₄×C₅	—	2	2	no	—
527	C₄×C₅	—	2	2	no	—
528	C₄×C₅	—	2	2	no	—
529	C₄×C₅	—	2	2	no	—
530	C₄×C₅	—	2	2	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	4	1	no	—
533	C₄×C₅	—	4	1	no	—
534	C₄×C₅	—	4	1	no	—
535	C₄×C₅	—	4	1	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	#535	1	1	yes	characteristic
538	C₄×C₅	#536	1	1	yes	characteristic
539	C₄×C₅	#537	1	1	yes	characteristic
540	C₄×C₅	#537	1	1	yes	characteristic
541	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
542	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
543	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	4	1	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	1	no	—
555	C₂×D₄	—	4	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	4	1	no	—
577	C₂²×C₄	—	4	1	no	—
578	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
579	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
581	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
582	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
583	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
584	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
585	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
586	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
587	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
588	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
590	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
592	M₁₆	—	4	4	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	4	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
627	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
637	C₂²⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	—	2	1	no	—
644	C₄²	C₂×C₅×D₄	1	2	yes	—
645	C₄²	C₂×C₅×D₄	1	2	yes	—
646	C₄²	C₂×C₅×D₄	1	2	yes	—
647	C₄²	C₂×C₅×D₄	1	2	yes	—
648	C₂×C₅	—	4	2	no	—
649	C₂×C₅	—	4	2	no	—
650	C₂×C₅	—	8	1	no	—
651	C₂×C₅	#2311	1	1	yes	characteristic
652	C₂×C₅	#2880	1	1	yes	characteristic
653	C₂×C₅	#2880	1	1	yes	characteristic
654	C₂×C₅	#2992	1	1	yes	characteristic
655	C₂×C₅	#2993	1	1	yes	characteristic
656	C₂×C₅	#2994	1	1	yes	characteristic
657	C₂×C₅	#2995	1	1	yes	characteristic
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
678	C₂³	C₅×#131	1	2	yes	—
679	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
680	Q₈	—	4	4	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
726	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
727	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
728	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
729	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
730	C₂×C₄	C₅×#131	1	2	yes	—
731	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
732	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
733	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₈	—	4	1	no	—
742	C₈	—	4	1	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₅	#21855	1	1	yes	characteristic, direct product factor, Sylow
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
768	C₂²	C₅×#520	1	1	yes	characteristic
769	C₂²	C₅×#520	1	1	yes	characteristic
770	C₂²	C₂×C₅×#131	1	1	yes	characteristic
771	C₂²	C₂×C₅×#131	1	1	yes	characteristic
772	C₂²	C₅×#568	1	1	yes	characteristic
773	C₂²	C₅×#568	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	C₅×#535	1	1	yes	characteristic
786	C₄	C₅×#536	1	1	yes	characteristic
787	C₄	C₅×#537	1	1	yes	characteristic
788	C₄	C₅×#537	1	1	yes	characteristic
789	C₂	—	4	2	no	—
790	C₂	—	4	2	no	—
791	C₂	—	8	1	no	—
792	C₂	C₅×#2311	1	1	yes	characteristic
793	C₂	C₅×#2880	1	1	yes	characteristic
794	C₂	C₅×#2880	1	1	yes	characteristic
795	C₂	C₅×#2992	1	1	yes	characteristic
796	C₂	C₅×#2993	1	1	yes	characteristic
797	C₂	C₅×#2994	1	1	yes	characteristic
798	C₂	C₅×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂×C₅×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#433	C₂	semidirect
3. C₂×C₅×#424	C₂	semidirect
4. C₅×#1985	C₂	semidirect
5. C₅×#1984	C₂	semidirect
6. C₅×#1955	C₂	semidirect
7. C₅×#1954	C₂	semidirect
8. C₅×#1870	C₂	semidirect
9. C₅×#1870	C₂	semidirect
10. C₅×#1869	C₂	semidirect
11. C₅×#1869	C₂	semidirect
12. C₅×#1798	C₂	semidirect
13. C₅×#1798	C₂	semidirect
14. C₅×#1797	C₂	semidirect
15. C₅×#1797	C₂	semidirect
63. #21855	C₅	direct (N × H)
154. C₂×#433	C₂×C₅	semidirect
155. C₂×#424	C₂×C₅	semidirect
156. #1985	C₂×C₅	semidirect
157. #1984	C₂×C₅	semidirect
158. #1955	C₂×C₅	semidirect
159. #1954	C₂×C₅	semidirect
160. #1870	C₂×C₅	semidirect
161. #1870	C₂×C₅	semidirect
162. #1869	C₂×C₅	semidirect
163. #1869	C₂×C₅	semidirect
164. #1798	C₂×C₅	semidirect
165. #1798	C₂×C₅	semidirect
166. #1797	C₂×C₅	semidirect
167. #1797	C₂×C₅	semidirect
745. C₅	#21855	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×#529	2
C₂×C₅×#433	2
C₂×C₅×#424	2
C₅×#1985	2
C₅×#1984	2
C₅×#1955	2
C₅×#1954	2
C₅×#1870	2
C₅×#1869	2
C₅×#1798	2
C₅×#1797	2
#21855	5

Subgroups — C5×#21855 #11944575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21855 #11944575