Subgroups — C₅×#34261 #11956981

Order 1280.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#518	C₂	1	1	yes	maximal, characteristic
2	C₅×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2353	C₂	1	2	yes	maximal, complemented
5	C₅×#2352	C₂	1	2	yes	maximal, complemented
6	C₅×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2342	C₂	1	2	yes	maximal, complemented
11	C₅×#2342	C₂	1	2	yes	maximal, complemented
12	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2318	C₂	1	2	yes	maximal, complemented
16	C₅×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2312	C₂	1	2	yes	maximal, complemented
18	C₅×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×C₅×#388	C₂	1	2	yes	maximal, complemented
22	C₅×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₅×#518	C₄	1	16	yes	complemented
26	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₄	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×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×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×#117	C₂²	1	1	yes	characteristic
37	C₂×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₅×#117	C₂²	1	2	yes	complemented
39	C₂×C₅×#117	C₂²	1	2	yes	complemented
40	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
44	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
46	C₅×#390	C₂²	1	1	yes	characteristic
47	C₅×#390	C₂²	1	1	yes	characteristic
48	C₅×#390	C₂²	1	1	yes	characteristic
49	C₅×#390	C₂²	1	1	yes	characteristic
50	C₅×#389	C₂²	1	1	yes	characteristic, complemented
51	C₅×#389	C₂²	1	1	yes	characteristic, complemented
52	C₅×#389	C₂²	1	1	yes	characteristic, complemented
53	C₅×#389	C₂²	1	1	yes	characteristic, complemented
54	C₅×#388	C₂²	1	1	yes	characteristic
55	C₅×#388	C₂²	1	2	yes	—
56	C₅×#388	C₂²	1	2	yes	—
57	C₅×#388	C₂²	1	2	yes	—
58	C₅×#388	C₂²	1	1	yes	characteristic
59	C₅×#388	C₂²	1	1	yes	characteristic
60	C₅×#388	C₂²	1	1	yes	characteristic
61	C₅×#388	C₂²	1	2	yes	—
62	C₅×#388	C₂²	1	2	yes	—
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#388	C₂²	1	2	yes	complemented
65	C₅×#388	C₂²	1	2	yes	complemented
66	C₅×#388	C₂²	1	2	yes	complemented
67	C₅×#388	C₂²	1	2	yes	complemented
68	C₅×#388	C₂²	1	2	yes	complemented
69	C₅×#388	C₂²	1	2	yes	complemented
70	C₅×#388	C₂²	1	2	yes	complemented
71	C₅×#388	C₂²	1	2	yes	complemented
72	C₅×#387	C₂²	1	1	yes	characteristic, complemented
73	C₅×#387	C₂²	1	2	yes	complemented
74	C₅×#387	C₂²	1	1	yes	characteristic, complemented
75	C₅×#387	C₂²	1	1	yes	characteristic, complemented
76	C₅×#387	C₂²	1	1	yes	characteristic, complemented
77	C₅×#387	C₂²	1	2	yes	complemented
78	C₅×#386	C₂²	1	2	yes	—
79	C₅×#386	C₂²	1	2	yes	—
80	C₅×#386	C₂²	1	2	yes	—
81	C₅×#386	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	complemented
83	C₅×#385	C₂²	1	2	yes	complemented
84	C₅×#385	C₂²	1	2	yes	complemented
85	C₅×#385	C₂²	1	2	yes	complemented
86	C₅×#384	C₂²	1	1	yes	characteristic, complemented
87	C₅×#383	C₂²	1	2	yes	complemented
88	C₅×#382	C₂²	1	1	yes	characteristic, complemented
89	C₅×#382	C₂²	1	2	yes	complemented
90	C₅×#381	C₂²	1	2	yes	complemented
91	C₅×#381	C₂²	1	2	yes	complemented
92	C₅×#380	C₂²	1	1	yes	characteristic
93	C₅×#380	C₂²	1	1	yes	characteristic
94	C₅×#380	C₂²	1	2	yes	complemented
95	C₅×#380	C₂²	1	2	yes	complemented
96	C₅×#380	C₂²	1	2	yes	complemented
97	C₅×#380	C₂²	1	2	yes	complemented
98	C₅×#379	C₂²	1	2	yes	—
99	C₅×#379	C₂²	1	2	yes	—
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
107	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₅×#376	C₂²	1	1	yes	characteristic, complemented
120	C₅×#376	C₂²	1	2	yes	complemented
121	C₂×C₅×#95	C₂²	1	2	yes	complemented
122	C₂×C₅×#95	C₂²	1	2	yes	complemented
123	C₄³×C₅	C₂²	1	1	yes	characteristic, complemented
124	#34261	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₅	C₂³	1	2	yes	—
126	C₂²×C₅×D₄	—	2	4	no	—
127	C₂²×C₅×D₄	—	2	4	no	—
128	C₂²×C₅×D₄	C₂×C₄	1	8	yes	—
129	C₂²×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
131	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₅	C₂³	1	2	yes	—
133	C₂³×C₄×C₅	C₂³	1	2	yes	—
134	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂³	1	2	yes	—
136	C₂³×C₄×C₅	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	2	yes	—
138	C₂³×C₄×C₅	C₂³	1	2	yes	—
139	C₂³×C₄×C₅	C₂³	1	2	yes	—
140	C₂³×C₄×C₅	C₂³	1	2	yes	—
141	C₄×C₅×D₄	—	2	4	no	—
142	C₄×C₅×D₄	—	2	4	no	—
143	C₄×C₅×D₄	—	2	4	no	—
144	C₄×C₅×D₄	—	2	4	no	—
145	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
146	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
148	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
149	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
150	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
151	C₅×#117	—	4	4	no	—
152	C₅×#117	—	4	4	no	—
153	C₅×#117	C₂×C₄	1	8	yes	complemented
154	C₅×#117	C₂×C₄	1	8	yes	complemented
155	C₂×C₅×C₄⋊C₄	—	4	4	no	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
175	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
176	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
177	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
178	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	—	4	4	no	—
204	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₅	C₂³	1	2	yes	—
211	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₅	C₂³	1	2	yes	—
214	C₂×C₄²×C₅	C₂³	1	2	yes	—
215	C₂×C₄²×C₅	C₂³	1	2	yes	—
216	C₂×C₄²×C₅	C₂³	1	2	yes	—
217	C₂×C₄²×C₅	C₂³	1	2	yes	—
218	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₅	C₂³	1	2	yes	—
220	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
221	C₅×#95	C₂³	1	1	yes	characteristic
222	C₅×#95	C₂³	1	1	yes	characteristic
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	2	yes	—
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	1	yes	characteristic
231	C₅×#95	C₂³	1	1	yes	characteristic
232	C₅×#95	C₂³	1	1	yes	characteristic
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	1	yes	characteristic
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	1	yes	characteristic
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	2	yes	—
244	C₅×#95	C₂³	1	2	yes	—
245	C₅×#95	C₂³	1	1	yes	characteristic
246	C₅×#95	C₂³	1	1	yes	characteristic
247	C₂×#518	C₂×C₅	1	1	yes	characteristic
248	#2357	C₂×C₅	1	1	yes	characteristic, complemented
249	#2354	C₂×C₅	1	1	yes	characteristic, complemented
250	#2353	C₂×C₅	1	2	yes	complemented
251	#2352	C₂×C₅	1	2	yes	complemented
252	#2349	C₂×C₅	1	1	yes	characteristic, complemented
253	D₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
254	#2347	C₂×C₅	1	1	yes	characteristic, complemented
255	#2346	C₂×C₅	1	1	yes	characteristic, complemented
256	#2342	C₂×C₅	1	2	yes	complemented
257	#2342	C₂×C₅	1	2	yes	complemented
258	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
259	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
260	#2319	C₂×C₅	1	1	yes	characteristic, complemented
261	#2318	C₂×C₅	1	2	yes	complemented
262	#2314	C₂×C₅	1	1	yes	characteristic, complemented
263	#2312	C₂×C₅	1	2	yes	complemented
264	#2298	C₂×C₅	1	1	yes	characteristic, complemented
265	#2293	C₂×C₅	1	1	yes	characteristic, complemented
266	#2290	C₂×C₅	1	2	yes	complemented
267	C₂×#388	C₂×C₅	1	2	yes	complemented
268	#2275	C₂×C₅	1	1	yes	characteristic, complemented
269	C₄²×D₄	C₂×C₅	1	1	yes	characteristic, complemented
270	C₂⁴×C₅	—	2	4	no	—
271	C₂⁴×C₅	—	2	4	no	—
272	C₂⁴×C₅	—	4	2	no	—
273	C₂⁴×C₅	—	4	2	no	—
274	C₂⁴×C₅	—	4	2	no	—
275	C₂⁴×C₅	—	4	2	no	—
276	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
277	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
278	C₂⁴×C₅	C₂⁴	1	2	yes	—
279	C₂⁴×C₅	C₂⁴	1	2	yes	—
280	C₂×C₅×D₄	—	2	4	no	—
281	C₂×C₅×D₄	—	2	4	no	—
282	C₂×C₅×D₄	—	2	32	no	—
283	C₂×C₅×D₄	—	2	2	no	—
284	C₂×C₅×D₄	—	2	2	no	—
285	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
286	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
287	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
288	C₂×C₅×D₄	#41	1	4	yes	—
289	C₂×C₅×D₄	#41	1	4	yes	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	4	no	—
293	C₂²×C₄×C₅	—	2	4	no	—
294	C₂²×C₄×C₅	—	2	4	no	—
295	C₂²×C₄×C₅	—	2	4	no	—
296	C₂²×C₄×C₅	—	2	4	no	—
297	C₂²×C₄×C₅	—	2	4	no	—
298	C₂²×C₄×C₅	—	4	2	no	—
299	C₂²×C₄×C₅	—	4	2	no	—
300	C₂²×C₄×C₅	—	4	2	no	—
301	C₂²×C₄×C₅	—	4	2	no	—
302	C₂²×C₄×C₅	—	4	2	no	—
303	C₂²×C₄×C₅	—	4	2	no	—
304	C₂²×C₄×C₅	—	4	2	no	—
305	C₂²×C₄×C₅	—	4	2	no	—
306	C₂²×C₄×C₅	—	4	2	no	—
307	C₂²×C₄×C₅	—	4	2	no	—
308	C₂²×C₄×C₅	—	4	2	no	—
309	C₂²×C₄×C₅	—	4	2	no	—
310	C₂²×C₄×C₅	—	4	2	no	—
311	C₂²×C₄×C₅	—	4	2	no	—
312	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
313	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
314	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
316	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
317	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₅×C₄⋊C₄	—	2	2	no	—
338	C₅×C₄⋊C₄	—	2	2	no	—
339	C₅×C₄⋊C₄	—	2	2	no	—
340	C₅×C₄⋊C₄	—	2	2	no	—
341	C₅×C₄⋊C₄	—	2	2	no	—
342	C₅×C₄⋊C₄	—	2	4	no	—
343	C₅×C₄⋊C₄	—	2	2	no	—
344	C₅×C₄⋊C₄	—	4	2	no	—
345	C₅×C₄⋊C₄	—	4	2	no	—
346	C₅×C₄⋊C₄	—	4	1	no	—
347	C₅×C₄⋊C₄	—	4	1	no	—
348	C₅×C₄⋊C₄	—	4	2	no	—
349	C₅×C₄⋊C₄	—	4	2	no	—
350	C₅×C₄⋊C₄	—	4	2	no	—
351	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
352	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
353	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
354	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
355	C₅×C₂²⋊C₄	—	2	4	no	—
356	C₅×C₂²⋊C₄	—	2	4	no	—
357	C₅×C₂²⋊C₄	—	2	4	no	—
358	C₅×C₂²⋊C₄	—	2	4	no	—
359	C₅×C₂²⋊C₄	—	2	2	no	—
360	C₅×C₂²⋊C₄	—	2	2	no	—
361	C₅×C₂²⋊C₄	—	2	4	no	—
362	C₅×C₂²⋊C₄	—	2	4	no	—
363	C₅×C₂²⋊C₄	—	4	2	no	—
364	C₅×C₂²⋊C₄	—	4	2	no	—
365	C₅×C₂²⋊C₄	—	4	2	no	—
366	C₅×C₂²⋊C₄	—	4	2	no	—
367	C₅×C₂²⋊C₄	—	4	1	no	—
368	C₅×C₂²⋊C₄	—	4	2	no	—
369	C₅×C₂²⋊C₄	—	4	1	no	—
370	C₅×C₂²⋊C₄	—	4	2	no	—
371	C₅×C₂²⋊C₄	—	4	2	no	—
372	C₅×C₂²⋊C₄	—	4	2	no	—
373	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
374	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
375	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
376	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
377	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
378	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
379	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
380	C₄²×C₅	—	2	2	no	—
381	C₄²×C₅	—	2	2	no	—
382	C₄²×C₅	—	2	2	no	—
383	C₄²×C₅	—	2	2	no	—
384	C₄²×C₅	—	2	2	no	—
385	C₄²×C₅	—	2	4	no	—
386	C₄²×C₅	—	2	2	no	—
387	C₄²×C₅	—	4	2	no	—
388	C₄²×C₅	—	4	2	no	—
389	C₄²×C₅	—	4	1	no	—
390	C₄²×C₅	—	4	2	no	—
391	C₄²×C₅	—	4	1	no	—
392	C₄²×C₅	—	4	2	no	—
393	C₄²×C₅	—	4	2	no	—
394	C₄²×C₅	C₂²×C₄	1	4	yes	—
395	C₄²×C₅	C₂²×C₄	1	4	yes	—
396	C₄²×C₅	C₂²×C₄	1	8	yes	—
397	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
398	#518	C₄×C₅	1	16	yes	complemented
399	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
403	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
409	C₂×#117	C₂²×C₅	1	1	yes	characteristic
410	C₂×#117	C₂²×C₅	1	1	yes	characteristic
411	C₂×#117	C₂²×C₅	1	2	yes	complemented
412	C₂×#117	C₂²×C₅	1	2	yes	complemented
413	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
414	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
415	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
418	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
419	#390	C₂²×C₅	1	1	yes	characteristic
420	#390	C₂²×C₅	1	1	yes	characteristic
421	#390	C₂²×C₅	1	1	yes	characteristic
422	#390	C₂²×C₅	1	1	yes	characteristic
423	#389	C₂²×C₅	1	1	yes	characteristic, complemented
424	#389	C₂²×C₅	1	1	yes	characteristic, complemented
425	#389	C₂²×C₅	1	1	yes	characteristic, complemented
426	#389	C₂²×C₅	1	1	yes	characteristic, complemented
427	#388	C₂²×C₅	1	1	yes	characteristic
428	#388	C₂²×C₅	1	2	yes	—
429	#388	C₂²×C₅	1	2	yes	—
430	#388	C₂²×C₅	1	2	yes	—
431	#388	C₂²×C₅	1	2	yes	—
432	#388	C₂²×C₅	1	1	yes	characteristic
433	#388	C₂²×C₅	1	1	yes	characteristic
434	#388	C₂²×C₅	1	2	yes	—
435	#388	C₂²×C₅	1	2	yes	—
436	#388	C₂²×C₅	1	1	yes	characteristic
437	#388	C₂²×C₅	1	2	yes	complemented
438	#388	C₂²×C₅	1	2	yes	complemented
439	#388	C₂²×C₅	1	2	yes	complemented
440	#388	C₂²×C₅	1	2	yes	complemented
441	#388	C₂²×C₅	1	2	yes	complemented
442	#388	C₂²×C₅	1	2	yes	complemented
443	#388	C₂²×C₅	1	2	yes	complemented
444	#388	C₂²×C₅	1	2	yes	complemented
445	#387	C₂²×C₅	1	2	yes	complemented
446	#387	C₂²×C₅	1	2	yes	complemented
447	#387	C₂²×C₅	1	1	yes	characteristic, complemented
448	#387	C₂²×C₅	1	1	yes	characteristic, complemented
449	#387	C₂²×C₅	1	1	yes	characteristic, complemented
450	#387	C₂²×C₅	1	1	yes	characteristic, complemented
451	#386	C₂²×C₅	1	2	yes	—
452	#386	C₂²×C₅	1	2	yes	—
453	#386	C₂²×C₅	1	2	yes	—
454	#386	C₂²×C₅	1	2	yes	—
455	#385	C₂²×C₅	1	2	yes	complemented
456	#385	C₂²×C₅	1	2	yes	complemented
457	#385	C₂²×C₅	1	2	yes	complemented
458	#385	C₂²×C₅	1	2	yes	complemented
459	#384	C₂²×C₅	1	1	yes	characteristic, complemented
460	#383	C₂²×C₅	1	2	yes	complemented
461	#382	C₂²×C₅	1	1	yes	characteristic, complemented
462	#382	C₂²×C₅	1	2	yes	complemented
463	#381	C₂²×C₅	1	2	yes	complemented
464	#381	C₂²×C₅	1	2	yes	complemented
465	#380	C₂²×C₅	1	1	yes	characteristic
466	#380	C₂²×C₅	1	1	yes	characteristic
467	#380	C₂²×C₅	1	2	yes	complemented
468	#380	C₂²×C₅	1	2	yes	complemented
469	#380	C₂²×C₅	1	2	yes	complemented
470	#380	C₂²×C₅	1	2	yes	complemented
471	#379	C₂²×C₅	1	2	yes	—
472	#379	C₂²×C₅	1	2	yes	—
473	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
474	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
475	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
476	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
477	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
478	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
479	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
480	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
481	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
482	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
484	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
485	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
486	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
487	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
488	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
489	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
490	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
491	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
492	#376	C₂²×C₅	1	1	yes	characteristic, complemented
493	#376	C₂²×C₅	1	2	yes	complemented
494	C₂×#95	C₂²×C₅	1	2	yes	complemented
495	C₂×#95	C₂²×C₅	1	2	yes	complemented
496	C₄³	C₂²×C₅	1	1	yes	characteristic, complemented
497	C₂³×C₅	—	2	2	no	—
498	C₂³×C₅	—	2	2	no	—
499	C₂³×C₅	—	2	2	no	—
500	C₂³×C₅	—	2	2	no	—
501	C₂³×C₅	—	2	1	no	—
502	C₂³×C₅	—	2	1	no	—
503	C₂³×C₅	—	2	2	no	—
504	C₂³×C₅	—	2	2	no	—
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	2	no	—
510	C₂³×C₅	—	2	2	no	—
511	C₂³×C₅	—	2	1	no	—
512	C₂³×C₅	—	2	1	no	—
513	C₂³×C₅	—	2	16	no	—
514	C₂³×C₅	—	4	8	no	—
515	C₂³×C₅	—	4	8	no	—
516	C₂³×C₅	—	8	4	no	—
517	C₂³×C₅	—	8	4	no	—
518	C₂³×C₅	—	8	4	no	—
519	C₂³×C₅	—	8	4	no	—
520	C₂³×C₅	C₂³×C₄	1	2	yes	—
521	C₂³×C₅	C₂³×C₄	1	4	yes	—
522	C₂³×C₅	C₂³×C₄	1	4	yes	—
523	C₂³×C₅	C₂×#41	1	4	yes	—
524	C₂³×C₅	C₂×#41	1	4	yes	—
525	C₂³×C₅	C₂⁵	1	1	yes	characteristic
526	C₅×D₄	—	2	16	no	—
527	C₅×D₄	—	2	8	no	—
528	C₅×D₄	#117	1	16	yes	complemented
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	2	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	2	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	2	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	8	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	2	1	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	1	no	—
554	C₂×C₄×C₅	—	2	2	no	—
555	C₂×C₄×C₅	—	2	2	no	—
556	C₂×C₄×C₅	—	2	2	no	—
557	C₂×C₄×C₅	—	2	2	no	—
558	C₂×C₄×C₅	—	2	2	no	—
559	C₂×C₄×C₅	—	2	1	no	—
560	C₂×C₄×C₅	—	2	1	no	—
561	C₂×C₄×C₅	—	2	2	no	—
562	C₂×C₄×C₅	—	2	2	no	—
563	C₂×C₄×C₅	—	2	2	no	—
564	C₂×C₄×C₅	—	2	2	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	1	no	—
567	C₂×C₄×C₅	—	2	2	no	—
568	C₂×C₄×C₅	—	2	1	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	2	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	1	no	—
576	C₂×C₄×C₅	—	2	2	no	—
577	C₂×C₄×C₅	—	2	1	no	—
578	C₂×C₄×C₅	—	4	8	no	—
579	C₂×C₄×C₅	—	4	8	no	—
580	C₂×C₄×C₅	—	4	8	no	—
581	C₂×C₄×C₅	—	4	8	no	—
582	C₂×C₄×C₅	—	4	8	no	—
583	C₂×C₄×C₅	—	4	8	no	—
584	C₂×C₄×C₅	—	8	4	no	—
585	C₂×C₄×C₅	—	8	4	no	—
586	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
587	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
589	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
590	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
592	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
593	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
594	C₂×C₄×C₅	C₂×#41	1	2	yes	—
595	C₂×C₄×C₅	C₂×#41	1	2	yes	—
596	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
597	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
598	C₂⁵	C₂³×C₅	1	2	yes	—
599	C₂²×D₄	—	2	4	no	—
600	C₂²×D₄	—	2	4	no	—
601	C₂²×D₄	C₂×C₄×C₅	1	8	yes	—
602	C₂²×D₄	C₂³×C₅	1	2	yes	—
603	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₅	1	2	yes	—
606	C₂³×C₄	C₂³×C₅	1	2	yes	—
607	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₅	1	2	yes	—
609	C₂³×C₄	C₂³×C₅	1	2	yes	—
610	C₂³×C₄	C₂³×C₅	1	2	yes	—
611	C₂³×C₄	C₂³×C₅	1	2	yes	—
612	C₂³×C₄	C₂³×C₅	1	2	yes	—
613	C₂³×C₄	C₂³×C₅	1	2	yes	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	4	no	—
618	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
619	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
620	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
621	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
622	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
623	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
624	#117	—	4	4	no	—
625	#117	—	4	4	no	—
626	#117	C₂×C₄×C₅	1	8	yes	complemented
627	#117	C₂×C₄×C₅	1	8	yes	complemented
628	C₂×C₄⋊C₄	—	4	4	no	—
629	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	4	4	no	—
648	C₂×C₂²⋊C₄	—	4	4	no	—
649	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
650	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
651	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₂×C₄²	—	4	4	no	—
677	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₅	1	2	yes	—
679	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₅	1	2	yes	—
685	C₂×C₄²	C₂³×C₅	1	2	yes	—
686	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₅	1	2	yes	—
689	C₂×C₄²	C₂³×C₅	1	2	yes	—
690	C₂×C₄²	C₂³×C₅	1	2	yes	—
691	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₅	1	2	yes	—
693	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
694	#95	C₂³×C₅	1	1	yes	characteristic
695	#95	C₂³×C₅	1	1	yes	characteristic
696	#95	C₂³×C₅	1	2	yes	—
697	#95	C₂³×C₅	1	2	yes	—
698	#95	C₂³×C₅	1	2	yes	—
699	#95	C₂³×C₅	1	2	yes	—
700	#95	C₂³×C₅	1	2	yes	—
701	#95	C₂³×C₅	1	2	yes	—
702	#95	C₂³×C₅	1	1	yes	characteristic
703	#95	C₂³×C₅	1	1	yes	characteristic
704	#95	C₂³×C₅	1	1	yes	characteristic
705	#95	C₂³×C₅	1	1	yes	characteristic
706	#95	C₂³×C₅	1	2	yes	—
707	#95	C₂³×C₅	1	2	yes	—
708	#95	C₂³×C₅	1	1	yes	characteristic
709	#95	C₂³×C₅	1	1	yes	characteristic
710	#95	C₂³×C₅	1	1	yes	characteristic
711	#95	C₂³×C₅	1	2	yes	—
712	#95	C₂³×C₅	1	2	yes	—
713	#95	C₂³×C₅	1	2	yes	—
714	#95	C₂³×C₅	1	1	yes	characteristic
715	#95	C₂³×C₅	1	2	yes	—
716	#95	C₂³×C₅	1	2	yes	—
717	#95	C₂³×C₅	1	2	yes	—
718	#95	C₂³×C₅	1	1	yes	characteristic
719	#95	C₂³×C₅	1	1	yes	characteristic
720	C₂²×C₅	—	2	4	no	—
721	C₂²×C₅	—	2	4	no	—
722	C₂²×C₅	—	2	4	no	—
723	C₂²×C₅	—	2	4	no	—
724	C₂²×C₅	—	2	4	no	—
725	C₂²×C₅	—	2	4	no	—
726	C₂²×C₅	—	2	2	no	—
727	C₂²×C₅	—	2	4	no	—
728	C₂²×C₅	—	2	4	no	—
729	C₂²×C₅	—	2	4	no	—
730	C₂²×C₅	—	2	2	no	—
731	C₂²×C₅	—	2	2	no	—
732	C₂²×C₅	—	4	2	no	—
733	C₂²×C₅	—	4	1	no	—
734	C₂²×C₅	—	4	2	no	—
735	C₂²×C₅	—	4	1	no	—
736	C₂²×C₅	—	4	2	no	—
737	C₂²×C₅	—	4	1	no	—
738	C₂²×C₅	—	4	2	no	—
739	C₂²×C₅	—	4	1	no	—
740	C₂²×C₅	—	8	16	no	—
741	C₂²×C₅	C₂×#117	1	8	yes	—
742	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
743	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
744	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
745	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²×C₅	#585	1	1	yes	characteristic
748	C₂²×C₅	#585	1	1	yes	characteristic
749	C₄×C₅	—	2	2	no	—
750	C₄×C₅	—	2	2	no	—
751	C₄×C₅	—	2	4	no	—
752	C₄×C₅	—	2	2	no	—
753	C₄×C₅	—	2	2	no	—
754	C₄×C₅	—	2	2	no	—
755	C₄×C₅	—	2	4	no	—
756	C₄×C₅	—	2	2	no	—
757	C₄×C₅	—	2	2	no	—
758	C₄×C₅	—	4	1	no	—
759	C₄×C₅	—	4	2	no	—
760	C₄×C₅	—	4	1	no	—
761	C₄×C₅	—	4	2	no	—
762	C₄×C₅	—	4	1	no	—
763	C₄×C₅	—	4	2	no	—
764	C₄×C₅	—	4	2	no	—
765	C₄×C₅	—	4	1	no	—
766	C₄×C₅	—	4	1	no	—
767	C₄×C₅	—	4	1	no	—
768	C₄×C₅	C₂×#117	1	4	yes	—
769	C₂⁴	—	2	4	no	—
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	4	2	no	—
772	C₂⁴	—	4	2	no	—
773	C₂⁴	—	4	2	no	—
774	C₂⁴	—	4	2	no	—
775	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
776	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₅	1	2	yes	—
778	C₂⁴	C₂⁴×C₅	1	2	yes	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	32	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
785	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
786	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
787	C₂×D₄	C₅×#41	1	4	yes	—
788	C₂×D₄	C₅×#41	1	4	yes	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	4	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
812	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
813	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
814	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
815	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
816	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	4	2	no	—
844	C₄⋊C₄	—	4	2	no	—
845	C₄⋊C₄	—	4	2	no	—
846	C₄⋊C₄	—	4	2	no	—
847	C₄⋊C₄	—	4	1	no	—
848	C₄⋊C₄	—	4	1	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
851	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
852	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
853	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	1	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
873	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
874	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
875	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
876	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
877	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	4	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	2	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	1	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	1	no	—
893	C₄²	C₂²×C₄×C₅	1	4	yes	—
894	C₄²	C₂²×C₄×C₅	1	4	yes	—
895	C₄²	C₂²×C₄×C₅	1	8	yes	—
896	C₂×C₅	—	2	8	no	—
897	C₂×C₅	—	4	4	no	—
898	C₂×C₅	—	4	2	no	—
899	C₂×C₅	C₂²×#117	1	1	yes	characteristic
900	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂×C₅	#3513	1	1	yes	characteristic
903	C₂×C₅	#3514	1	1	yes	characteristic
904	C₂×C₅	#3519	1	1	yes	characteristic
905	C₂×C₅	#3521	1	1	yes	characteristic
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	16	no	—
923	C₂³	—	4	8	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	8	4	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	C₂³×C₄×C₅	1	2	yes	—
930	C₂³	C₂³×C₄×C₅	1	4	yes	—
931	C₂³	C₂³×C₄×C₅	1	4	yes	—
932	C₂³	C₂×C₅×#41	1	4	yes	—
933	C₂³	C₂×C₅×#41	1	4	yes	—
934	C₂³	C₂⁵×C₅	1	1	yes	characteristic
935	D₄	—	2	16	no	—
936	D₄	—	2	8	no	—
937	D₄	C₅×#117	1	16	yes	complemented
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	4	8	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	8	4	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
996	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1001	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1002	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1003	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1004	C₂×C₄	C₂×C₅×#41	1	2	yes	—
1005	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1006	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1007	C₅	#34261	1	1	yes	characteristic, direct product factor, Sylow
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	C₂×C₅×#117	1	8	yes	—
1030	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1031	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1032	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
1033	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂²	C₅×#585	1	1	yes	characteristic
1036	C₂²	C₅×#585	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	C₂×C₅×#117	1	4	yes	—
1057	C₂	—	2	8	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	4	no	—
1060	C₂	C₂²×C₅×#117	1	1	yes	characteristic
1061	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1062	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1063	C₂	C₅×#3513	1	1	yes	characteristic
1064	C₂	C₅×#3514	1	1	yes	characteristic
1065	C₂	C₅×#3519	1	1	yes	characteristic
1066	C₂	C₅×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂³×C₅×D₄	C₂²
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×#2357	C₂	semidirect
3. C₅×#2354	C₂	semidirect
4. C₅×#2353	C₂	semidirect
5. C₅×#2352	C₂	semidirect
6. C₅×#2349	C₂	semidirect
7. C₅×D₄×C₄⋊C₄	C₂	semidirect
8. C₅×#2347	C₂	semidirect
9. C₅×#2346	C₂	semidirect
10. C₅×#2342	C₂	semidirect
11. C₅×#2342	C₂	semidirect
14. C₅×#2319	C₂	semidirect
15. C₅×#2318	C₂	semidirect
16. C₅×#2314	C₂	semidirect
17. C₅×#2312	C₂	semidirect
18. C₅×#2298	C₂	semidirect
19. C₅×#2293	C₂	semidirect
20. C₅×#2290	C₂	semidirect
21. C₂×C₅×#388	C₂	semidirect
22. C₅×#2275	C₂	semidirect
23. C₄²×C₅×D₄	C₂	semidirect
25. C₅×#518	C₄	semidirect
38. C₂×C₅×#117	C₂²	semidirect
39. C₂×C₅×#117	C₂²	semidirect
40. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
45. C₂²×C₄²×C₅	C₂²	semidirect
50. C₅×#389	C₂²	semidirect
51. C₅×#389	C₂²	semidirect
52. C₅×#389	C₂²	semidirect
53. C₅×#389	C₂²	semidirect
64. C₅×#388	C₂²	semidirect
65. C₅×#388	C₂²	semidirect
66. C₅×#388	C₂²	semidirect
67. C₅×#388	C₂²	semidirect
68. C₅×#388	C₂²	semidirect
69. C₅×#388	C₂²	semidirect
70. C₅×#388	C₂²	semidirect
71. C₅×#388	C₂²	semidirect
72. C₅×#387	C₂²	semidirect
73. C₅×#387	C₂²	semidirect
74. C₅×#387	C₂²	semidirect
75. C₅×#387	C₂²	semidirect
76. C₅×#387	C₂²	semidirect
77. C₅×#387	C₂²	semidirect
82. C₅×#385	C₂²	semidirect
83. C₅×#385	C₂²	semidirect
84. C₅×#385	C₂²	semidirect
85. C₅×#385	C₂²	semidirect
86. C₅×#384	C₂²	semidirect
87. C₅×#383	C₂²	semidirect
88. C₅×#382	C₂²	semidirect
89. C₅×#382	C₂²	semidirect
90. C₅×#381	C₂²	semidirect
91. C₅×#381	C₂²	semidirect
94. C₅×#380	C₂²	semidirect
95. C₅×#380	C₂²	semidirect
96. C₅×#380	C₂²	semidirect
97. C₅×#380	C₂²	semidirect
100. C₄×C₅×C₄⋊C₄	C₂²	semidirect
101. C₄×C₅×C₄⋊C₄	C₂²	semidirect
102. C₄×C₅×C₄⋊C₄	C₂²	semidirect
103. C₄×C₅×C₄⋊C₄	C₂²	semidirect
104. C₄×C₅×C₄⋊C₄	C₂²	semidirect
105. C₄×C₅×C₄⋊C₄	C₂²	semidirect
106. C₄×C₅×C₄⋊C₄	C₂²	semidirect
107. C₄×C₅×C₄⋊C₄	C₂²	semidirect
108. C₄×C₅×C₄⋊C₄	C₂²	semidirect
111. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
112. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
113. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
114. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
115. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
116. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
117. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
118. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
119. C₅×#376	C₂²	semidirect
120. C₅×#376	C₂²	semidirect
121. C₂×C₅×#95	C₂²	semidirect
122. C₂×C₅×#95	C₂²	semidirect
123. C₄³×C₅	C₂²	semidirect
124. #34261	C₅	direct (N × H)
147. C₄×C₅×D₄	C₂×C₄	semidirect
148. C₄×C₅×D₄	C₂×C₄	semidirect
149. C₄×C₅×D₄	C₂×C₄	semidirect
150. C₄×C₅×D₄	C₂×C₄	semidirect
153. C₅×#117	C₂×C₄	semidirect
154. C₅×#117	C₂×C₄	semidirect
176. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
177. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
248. #2357	C₂×C₅	semidirect
249. #2354	C₂×C₅	semidirect
250. #2353	C₂×C₅	semidirect
251. #2352	C₂×C₅	semidirect
252. #2349	C₂×C₅	semidirect
253. D₄×C₄⋊C₄	C₂×C₅	semidirect
254. #2347	C₂×C₅	semidirect
255. #2346	C₂×C₅	semidirect
256. #2342	C₂×C₅	semidirect
257. #2342	C₂×C₅	semidirect
260. #2319	C₂×C₅	semidirect
261. #2318	C₂×C₅	semidirect
262. #2314	C₂×C₅	semidirect
263. #2312	C₂×C₅	semidirect
264. #2298	C₂×C₅	semidirect
265. #2293	C₂×C₅	semidirect
266. #2290	C₂×C₅	semidirect
267. C₂×#388	C₂×C₅	semidirect
268. #2275	C₂×C₅	semidirect
269. C₄²×D₄	C₂×C₅	semidirect
398. #518	C₄×C₅	semidirect
411. C₂×#117	C₂²×C₅	semidirect
412. C₂×#117	C₂²×C₅	semidirect
413. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
418. C₂²×C₄²	C₂²×C₅	semidirect
423. #389	C₂²×C₅	semidirect
424. #389	C₂²×C₅	semidirect
425. #389	C₂²×C₅	semidirect
426. #389	C₂²×C₅	semidirect
437. #388	C₂²×C₅	semidirect
438. #388	C₂²×C₅	semidirect
439. #388	C₂²×C₅	semidirect
440. #388	C₂²×C₅	semidirect
441. #388	C₂²×C₅	semidirect
442. #388	C₂²×C₅	semidirect
443. #388	C₂²×C₅	semidirect
444. #388	C₂²×C₅	semidirect
445. #387	C₂²×C₅	semidirect
446. #387	C₂²×C₅	semidirect
447. #387	C₂²×C₅	semidirect
448. #387	C₂²×C₅	semidirect
449. #387	C₂²×C₅	semidirect
450. #387	C₂²×C₅	semidirect
455. #385	C₂²×C₅	semidirect
456. #385	C₂²×C₅	semidirect
457. #385	C₂²×C₅	semidirect
458. #385	C₂²×C₅	semidirect
459. #384	C₂²×C₅	semidirect
460. #383	C₂²×C₅	semidirect
461. #382	C₂²×C₅	semidirect
462. #382	C₂²×C₅	semidirect
463. #381	C₂²×C₅	semidirect
464. #381	C₂²×C₅	semidirect
467. #380	C₂²×C₅	semidirect
468. #380	C₂²×C₅	semidirect
469. #380	C₂²×C₅	semidirect
470. #380	C₂²×C₅	semidirect
473. C₄×C₄⋊C₄	C₂²×C₅	semidirect
474. C₄×C₄⋊C₄	C₂²×C₅	semidirect
475. C₄×C₄⋊C₄	C₂²×C₅	semidirect
476. C₄×C₄⋊C₄	C₂²×C₅	semidirect
477. C₄×C₄⋊C₄	C₂²×C₅	semidirect
478. C₄×C₄⋊C₄	C₂²×C₅	semidirect
479. C₄×C₄⋊C₄	C₂²×C₅	semidirect
480. C₄×C₄⋊C₄	C₂²×C₅	semidirect
481. C₄×C₄⋊C₄	C₂²×C₅	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
485. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
486. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
487. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
488. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
489. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
490. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
491. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
492. #376	C₂²×C₅	semidirect
493. #376	C₂²×C₅	semidirect
494. C₂×#95	C₂²×C₅	semidirect
495. C₂×#95	C₂²×C₅	semidirect
496. C₄³	C₂²×C₅	semidirect
528. C₅×D₄	#117	semidirect
620. C₄×D₄	C₂×C₄×C₅	semidirect
621. C₄×D₄	C₂×C₄×C₅	semidirect
622. C₄×D₄	C₂×C₄×C₅	semidirect
623. C₄×D₄	C₂×C₄×C₅	semidirect
626. #117	C₂×C₄×C₅	semidirect
627. #117	C₂×C₄×C₅	semidirect
649. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
650. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
937. D₄	C₅×#117	semidirect
1007. C₅	#34261	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×#518	2
C₅×#2357	2
C₅×#2354	2
C₅×#2353	2
C₅×#2352	2
C₅×#2349	2
C₅×D₄×C₄⋊C₄	2
C₅×#2347	2
C₅×#2346	2
C₅×#2342	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2319	2
C₅×#2318	2
C₅×#2314	2
C₅×#2312	2
C₅×#2298	2
C₅×#2293	2
C₅×#2290	2
C₂×C₅×#388	2
C₅×#2275	2
C₄²×C₅×D₄	2
#34261	5

Subgroups — C5×#34261 #11956981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34261 #11956981