Subgroups — C₅×#34478 #11957198

Order 1280.

2608 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#546	C₂	1	1	yes	maximal, characteristic
2	C₅×#2377	C₂	1	2	yes	maximal, complemented
3	C₅×#2375	C₂	1	2	yes	maximal, complemented
4	C₅×#2374	C₂	1	2	yes	maximal, complemented
5	C₅×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2354	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2342	C₂	1	2	yes	maximal, complemented
11	C₅×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2335	C₂	1	2	yes	maximal, complemented
14	C₅×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2324	C₂	1	2	yes	maximal, complemented
16	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2321	C₂	1	2	yes	maximal, complemented
18	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2312	C₂	1	2	yes	maximal, complemented
20	C₅×#2309	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
26	C₅×#546	C₄	1	16	yes	complemented
27	C₂×C₅×#124	C₂²	1	1	yes	characteristic
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#121	C₂²	1	1	yes	characteristic
31	C₂×C₅×#121	C₂²	1	2	yes	—
32	C₂×C₅×#120	C₂²	1	2	yes	—
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
40	C₂×C₅×#117	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	1	yes	characteristic
42	C₂×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×#117	C₂²	1	2	yes	complemented
44	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
46	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
47	C₅×#391	C₂²	1	1	yes	characteristic, complemented
48	C₅×#391	C₂²	1	1	yes	characteristic, complemented
49	C₅×#390	C₂²	1	1	yes	characteristic
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	2	yes	—
53	C₅×#390	C₂²	1	1	yes	characteristic
54	C₅×#390	C₂²	1	1	yes	characteristic
55	C₅×#390	C₂²	1	2	yes	—
56	C₅×#390	C₂²	1	1	yes	characteristic
57	C₅×#390	C₂²	1	2	yes	—
58	C₅×#390	C₂²	1	2	yes	complemented
59	C₅×#390	C₂²	1	2	yes	complemented
60	C₅×#390	C₂²	1	2	yes	complemented
61	C₅×#389	C₂²	1	1	yes	characteristic, complemented
62	C₅×#389	C₂²	1	1	yes	characteristic, complemented
63	C₅×#389	C₂²	1	2	yes	complemented
64	C₅×#388	C₂²	1	1	yes	characteristic
65	C₅×#388	C₂²	1	1	yes	characteristic
66	C₅×#388	C₂²	1	2	yes	—
67	C₅×#388	C₂²	1	2	yes	—
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#388	C₂²	1	2	yes	—
71	C₅×#388	C₂²	1	2	yes	complemented
72	C₅×#388	C₂²	1	2	yes	complemented
73	C₅×#388	C₂²	1	2	yes	complemented
74	C₅×#388	C₂²	1	2	yes	complemented
75	C₅×#388	C₂²	1	2	yes	complemented
76	C₅×#388	C₂²	1	2	yes	complemented
77	C₅×#388	C₂²	1	2	yes	complemented
78	C₅×#388	C₂²	1	2	yes	complemented
79	C₅×#388	C₂²	1	2	yes	complemented
80	C₅×#388	C₂²	1	2	yes	complemented
81	C₅×#388	C₂²	1	2	yes	complemented
82	C₅×#387	C₂²	1	1	yes	characteristic, complemented
83	C₅×#387	C₂²	1	1	yes	characteristic, complemented
84	C₅×#387	C₂²	1	2	yes	complemented
85	C₅×#387	C₂²	1	2	yes	complemented
86	C₅×#386	C₂²	1	1	yes	characteristic
87	C₅×#386	C₂²	1	1	yes	characteristic
88	C₅×#386	C₂²	1	2	yes	—
89	C₅×#386	C₂²	1	2	yes	—
90	C₅×#386	C₂²	1	2	yes	complemented
91	C₅×#386	C₂²	1	2	yes	complemented
92	C₅×#386	C₂²	1	2	yes	complemented
93	C₅×#386	C₂²	1	2	yes	complemented
94	C₅×#385	C₂²	1	1	yes	characteristic, complemented
95	C₅×#385	C₂²	1	1	yes	characteristic, complemented
96	C₅×#385	C₂²	1	2	yes	complemented
97	C₅×#385	C₂²	1	2	yes	complemented
98	C₅×#385	C₂²	1	2	yes	complemented
99	C₅×#384	C₂²	1	1	yes	characteristic, complemented
100	C₅×#381	C₂²	1	2	yes	complemented
101	C₅×#380	C₂²	1	1	yes	characteristic
102	C₅×#380	C₂²	1	1	yes	characteristic, complemented
103	C₅×#380	C₂²	1	2	yes	complemented
104	C₅×#380	C₂²	1	2	yes	complemented
105	C₅×#380	C₂²	1	2	yes	complemented
106	C₅×#379	C₂²	1	2	yes	—
107	C₅×#379	C₂²	1	2	yes	—
108	C₅×#379	C₂²	1	2	yes	—
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
114	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₅×#376	C₂²	1	1	yes	characteristic, complemented
124	#34478	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁵×C₅	C₂³	1	2	yes	—
126	C₂×C₅×#41	—	4	2	no	—
127	C₂×C₅×#41	—	4	2	no	—
128	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
129	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂²×C₅×D₄	—	4	2	no	—
131	C₂²×C₅×D₄	—	4	2	no	—
132	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
133	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₅×D₄	C₂³	1	2	yes	—
138	C₂²×C₅×D₄	C₂³	1	2	yes	—
139	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₅	C₂³	1	2	yes	—
142	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₅	C₂³	1	2	yes	—
144	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₅	C₂³	1	2	yes	—
146	C₂³×C₄×C₅	C₂³	1	2	yes	—
147	C₅×#124	C₂×C₄	1	8	yes	complemented
148	C₅×#123	C₂×C₄	1	16	yes	complemented
149	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
150	C₅×#121	C₂×C₄	1	8	yes	—
151	C₅×#121	C₂×C₄	1	16	yes	complemented
152	C₅×#120	C₂×C₄	1	16	yes	complemented
153	C₄×C₅×Q₈	—	4	2	no	—
154	C₄×C₅×Q₈	—	4	2	no	—
155	C₄×C₅×D₄	—	4	2	no	—
156	C₄×C₅×D₄	—	4	2	no	—
157	C₄×C₅×D₄	—	4	4	no	—
158	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
159	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
160	C₅×#117	—	4	2	no	—
161	C₅×#117	—	4	4	no	—
162	C₅×#117	—	4	2	no	—
163	C₅×#117	—	4	2	no	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
182	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
183	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
195	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₄²×C₅	—	4	2	no	—
215	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₅	C₂³	1	2	yes	—
219	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₅	C₂³	1	2	yes	—
222	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₅	C₂³	1	2	yes	—
224	C₂×C₄²×C₅	C₂³	1	2	yes	—
225	C₂×C₄²×C₅	C₂³	1	2	yes	—
226	C₂×C₄²×C₅	C₂³	1	2	yes	—
227	C₂×C₄²×C₅	C₂³	1	2	yes	—
228	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
234	C₅×#95	C₂³	1	1	yes	characteristic
235	C₅×#95	C₂³	1	1	yes	characteristic
236	C₅×#95	C₂³	1	1	yes	characteristic
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	2	yes	—
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	2	yes	—
246	C₅×#95	C₂³	1	2	yes	—
247	C₅×#95	C₂³	1	2	yes	—
248	C₅×#95	C₂³	1	2	yes	—
249	C₅×#95	C₂³	1	1	yes	characteristic
250	C₂×#546	C₂×C₅	1	1	yes	characteristic
251	#2377	C₂×C₅	1	2	yes	complemented
252	#2375	C₂×C₅	1	2	yes	complemented
253	#2374	C₂×C₅	1	2	yes	complemented
254	#2367	C₂×C₅	1	1	yes	characteristic, complemented
255	#2363	C₂×C₅	1	1	yes	characteristic, complemented
256	#2362	C₂×C₅	1	1	yes	characteristic, complemented
257	#2354	C₂×C₅	1	1	yes	characteristic, complemented
258	#2354	C₂×C₅	1	1	yes	characteristic, complemented
259	#2342	C₂×C₅	1	2	yes	complemented
260	#2341	C₂×C₅	1	1	yes	characteristic, complemented
261	D₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
262	#2335	C₂×C₅	1	2	yes	complemented
263	#2326	C₂×C₅	1	1	yes	characteristic, complemented
264	#2324	C₂×C₅	1	2	yes	complemented
265	#2323	C₂×C₅	1	1	yes	characteristic, complemented
266	#2321	C₂×C₅	1	2	yes	complemented
267	#2319	C₂×C₅	1	1	yes	characteristic, complemented
268	#2312	C₂×C₅	1	2	yes	complemented
269	#2309	C₂×C₅	1	1	yes	characteristic, complemented
270	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
271	#2297	C₂×C₅	1	1	yes	characteristic, complemented
272	#2290	C₂×C₅	1	1	yes	characteristic, complemented
273	C₂⁴×C₅	—	4	2	no	—
274	C₂⁴×C₅	—	4	2	no	—
275	C₂⁴×C₅	—	4	2	no	—
276	C₂⁴×C₅	—	4	2	no	—
277	C₂⁴×C₅	—	4	2	no	—
278	C₂⁴×C₅	—	4	2	no	—
279	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
280	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₅	C₂⁴	1	2	yes	—
282	C₂⁴×C₅	C₂⁴	1	2	yes	—
283	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
284	C₅×#41	—	4	16	no	—
285	C₂×C₅×Q₈	—	2	2	no	—
286	C₂×C₅×Q₈	—	2	2	no	—
287	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
288	C₂×C₅×D₄	—	2	2	no	—
289	C₂×C₅×D₄	—	2	2	no	—
290	C₂×C₅×D₄	—	2	2	no	—
291	C₂×C₅×D₄	—	2	2	no	—
292	C₂×C₅×D₄	—	4	16	no	—
293	C₂×C₅×D₄	—	4	2	no	—
294	C₂×C₅×D₄	—	4	2	no	—
295	C₂×C₅×D₄	—	4	2	no	—
296	C₂×C₅×D₄	—	4	1	no	—
297	C₂×C₅×D₄	—	4	1	no	—
298	C₂×C₅×D₄	—	4	2	no	—
299	C₂×C₅×D₄	—	4	2	no	—
300	C₂×C₅×D₄	—	4	2	no	—
301	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
302	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
303	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
304	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
305	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
306	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
307	C₂²×C₄×C₅	—	2	2	no	—
308	C₂²×C₄×C₅	—	2	2	no	—
309	C₂²×C₄×C₅	—	2	2	no	—
310	C₂²×C₄×C₅	—	2	2	no	—
311	C₂²×C₄×C₅	—	2	2	no	—
312	C₂²×C₄×C₅	—	2	4	no	—
313	C₂²×C₄×C₅	—	4	1	no	—
314	C₂²×C₄×C₅	—	4	1	no	—
315	C₂²×C₄×C₅	—	4	2	no	—
316	C₂²×C₄×C₅	—	4	2	no	—
317	C₂²×C₄×C₅	—	4	1	no	—
318	C₂²×C₄×C₅	—	4	1	no	—
319	C₂²×C₄×C₅	—	4	1	no	—
320	C₂²×C₄×C₅	—	4	2	no	—
321	C₂²×C₄×C₅	—	4	2	no	—
322	C₂²×C₄×C₅	—	4	2	no	—
323	C₂²×C₄×C₅	—	4	2	no	—
324	C₂²×C₄×C₅	—	4	2	no	—
325	C₂²×C₄×C₅	—	4	2	no	—
326	C₂²×C₄×C₅	—	4	2	no	—
327	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
328	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
329	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
330	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
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	2	yes	—
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
350	C₅×C₄⋊C₄	—	2	2	no	—
351	C₅×C₄⋊C₄	—	2	2	no	—
352	C₅×C₄⋊C₄	—	2	2	no	—
353	C₅×C₄⋊C₄	—	2	2	no	—
354	C₅×C₄⋊C₄	—	2	2	no	—
355	C₅×C₄⋊C₄	—	4	2	no	—
356	C₅×C₄⋊C₄	—	4	1	no	—
357	C₅×C₄⋊C₄	—	4	2	no	—
358	C₅×C₄⋊C₄	—	4	2	no	—
359	C₅×C₄⋊C₄	—	4	1	no	—
360	C₅×C₄⋊C₄	—	4	1	no	—
361	C₅×C₄⋊C₄	—	4	2	no	—
362	C₅×C₄⋊C₄	—	4	2	no	—
363	C₅×C₄⋊C₄	—	4	2	no	—
364	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
365	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
366	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
367	C₅×C₂²⋊C₄	—	2	2	no	—
368	C₅×C₂²⋊C₄	—	2	4	no	—
369	C₅×C₂²⋊C₄	—	4	2	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	—	4	2	no	—
374	C₅×C₂²⋊C₄	—	4	1	no	—
375	C₅×C₂²⋊C₄	—	4	2	no	—
376	C₅×C₂²⋊C₄	—	4	1	no	—
377	C₅×C₂²⋊C₄	—	4	2	no	—
378	C₅×C₂²⋊C₄	—	4	2	no	—
379	C₅×C₂²⋊C₄	—	4	2	no	—
380	C₅×C₂²⋊C₄	—	4	2	no	—
381	C₅×C₂²⋊C₄	—	4	1	no	—
382	C₅×C₂²⋊C₄	—	4	1	no	—
383	C₅×C₂²⋊C₄	—	4	1	no	—
384	C₅×C₂²⋊C₄	—	4	2	no	—
385	C₅×C₂²⋊C₄	—	4	2	no	—
386	C₅×C₂²⋊C₄	—	4	2	no	—
387	C₅×C₂²⋊C₄	—	4	2	no	—
388	C₅×C₂²⋊C₄	—	4	2	no	—
389	C₅×C₂²⋊C₄	—	4	2	no	—
390	C₅×C₂²⋊C₄	—	4	2	no	—
391	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
392	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
393	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
394	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
395	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
396	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
397	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
398	C₄²×C₅	—	2	2	no	—
399	C₄²×C₅	—	2	2	no	—
400	C₄²×C₅	—	2	4	no	—
401	C₄²×C₅	—	2	2	no	—
402	C₄²×C₅	—	2	2	no	—
403	C₄²×C₅	—	4	1	no	—
404	C₄²×C₅	—	4	1	no	—
405	C₄²×C₅	—	4	2	no	—
406	C₄²×C₅	—	4	2	no	—
407	C₄²×C₅	—	4	2	no	—
408	C₄²×C₅	—	4	2	no	—
409	C₄²×C₅	—	4	2	no	—
410	C₄²×C₅	—	4	2	no	—
411	C₄²×C₅	C₂²×C₄	1	4	yes	—
412	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
413	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
414	#546	C₄×C₅	1	16	yes	complemented
415	C₂×#124	C₂²×C₅	1	1	yes	characteristic
416	C₂×#123	C₂²×C₅	1	2	yes	—
417	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
418	C₂×#121	C₂²×C₅	1	1	yes	characteristic
419	C₂×#121	C₂²×C₅	1	2	yes	—
420	C₂×#120	C₂²×C₅	1	2	yes	—
421	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
422	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
423	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
428	C₂×#117	C₂²×C₅	1	1	yes	characteristic
429	C₂×#117	C₂²×C₅	1	1	yes	characteristic
430	C₂×#117	C₂²×C₅	1	2	yes	complemented
431	C₂×#117	C₂²×C₅	1	1	yes	characteristic, complemented
432	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
433	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
434	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
435	#391	C₂²×C₅	1	1	yes	characteristic, complemented
436	#391	C₂²×C₅	1	1	yes	characteristic, complemented
437	#390	C₂²×C₅	1	1	yes	characteristic
438	#390	C₂²×C₅	1	2	yes	—
439	#390	C₂²×C₅	1	1	yes	characteristic
440	#390	C₂²×C₅	1	1	yes	characteristic
441	#390	C₂²×C₅	1	1	yes	characteristic
442	#390	C₂²×C₅	1	2	yes	—
443	#390	C₂²×C₅	1	1	yes	characteristic
444	#390	C₂²×C₅	1	2	yes	—
445	#390	C₂²×C₅	1	1	yes	characteristic
446	#390	C₂²×C₅	1	2	yes	complemented
447	#390	C₂²×C₅	1	2	yes	complemented
448	#390	C₂²×C₅	1	2	yes	complemented
449	#389	C₂²×C₅	1	1	yes	characteristic, complemented
450	#389	C₂²×C₅	1	1	yes	characteristic, complemented
451	#389	C₂²×C₅	1	2	yes	complemented
452	#388	C₂²×C₅	1	1	yes	characteristic
453	#388	C₂²×C₅	1	2	yes	—
454	#388	C₂²×C₅	1	2	yes	—
455	#388	C₂²×C₅	1	2	yes	—
456	#388	C₂²×C₅	1	2	yes	—
457	#388	C₂²×C₅	1	2	yes	—
458	#388	C₂²×C₅	1	1	yes	characteristic
459	#388	C₂²×C₅	1	2	yes	complemented
460	#388	C₂²×C₅	1	2	yes	complemented
461	#388	C₂²×C₅	1	2	yes	complemented
462	#388	C₂²×C₅	1	2	yes	complemented
463	#388	C₂²×C₅	1	2	yes	complemented
464	#388	C₂²×C₅	1	2	yes	complemented
465	#388	C₂²×C₅	1	2	yes	complemented
466	#388	C₂²×C₅	1	2	yes	complemented
467	#388	C₂²×C₅	1	2	yes	complemented
468	#388	C₂²×C₅	1	2	yes	complemented
469	#388	C₂²×C₅	1	2	yes	complemented
470	#387	C₂²×C₅	1	2	yes	complemented
471	#387	C₂²×C₅	1	1	yes	characteristic, complemented
472	#387	C₂²×C₅	1	2	yes	complemented
473	#387	C₂²×C₅	1	1	yes	characteristic, complemented
474	#386	C₂²×C₅	1	1	yes	characteristic
475	#386	C₂²×C₅	1	2	yes	—
476	#386	C₂²×C₅	1	2	yes	—
477	#386	C₂²×C₅	1	1	yes	characteristic
478	#386	C₂²×C₅	1	2	yes	complemented
479	#386	C₂²×C₅	1	2	yes	complemented
480	#386	C₂²×C₅	1	2	yes	complemented
481	#386	C₂²×C₅	1	2	yes	complemented
482	#385	C₂²×C₅	1	2	yes	complemented
483	#385	C₂²×C₅	1	1	yes	characteristic, complemented
484	#385	C₂²×C₅	1	2	yes	complemented
485	#385	C₂²×C₅	1	2	yes	complemented
486	#385	C₂²×C₅	1	1	yes	characteristic, complemented
487	#384	C₂²×C₅	1	1	yes	characteristic, complemented
488	#381	C₂²×C₅	1	2	yes	complemented
489	#380	C₂²×C₅	1	1	yes	characteristic
490	#380	C₂²×C₅	1	2	yes	complemented
491	#380	C₂²×C₅	1	2	yes	complemented
492	#380	C₂²×C₅	1	2	yes	complemented
493	#380	C₂²×C₅	1	1	yes	characteristic, complemented
494	#379	C₂²×C₅	1	2	yes	—
495	#379	C₂²×C₅	1	2	yes	—
496	#379	C₂²×C₅	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
498	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
499	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
500	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
501	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
502	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
503	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
505	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
506	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
507	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
508	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
509	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
510	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
511	#376	C₂²×C₅	1	1	yes	characteristic, complemented
512	C₂³×C₅	—	2	2	no	—
513	C₂³×C₅	—	2	1	no	—
514	C₂³×C₅	—	2	1	no	—
515	C₂³×C₅	—	2	1	no	—
516	C₂³×C₅	—	2	1	no	—
517	C₂³×C₅	—	2	1	no	—
518	C₂³×C₅	—	2	2	no	—
519	C₂³×C₅	—	2	2	no	—
520	C₂³×C₅	—	2	2	no	—
521	C₂³×C₅	—	2	1	no	—
522	C₂³×C₅	—	2	2	no	—
523	C₂³×C₅	—	2	2	no	—
524	C₂³×C₅	—	2	2	no	—
525	C₂³×C₅	—	2	2	no	—
526	C₂³×C₅	—	2	1	no	—
527	C₂³×C₅	—	2	1	no	—
528	C₂³×C₅	—	2	2	no	—
529	C₂³×C₅	—	2	2	no	—
530	C₂³×C₅	—	2	2	no	—
531	C₂³×C₅	—	2	2	no	—
532	C₂³×C₅	—	2	1	no	—
533	C₂³×C₅	—	2	1	no	—
534	C₂³×C₅	—	2	1	no	—
535	C₂³×C₅	—	2	1	no	—
536	C₂³×C₅	—	4	8	no	—
537	C₂³×C₅	—	4	8	no	—
538	C₂³×C₅	—	4	8	no	—
539	C₂³×C₅	—	8	4	no	—
540	C₂³×C₅	—	8	4	no	—
541	C₂³×C₅	—	8	4	no	—
542	C₂³×C₅	—	8	4	no	—
543	C₂³×C₅	C₂³×C₄	1	2	yes	—
544	C₂³×C₅	C₂³×C₄	1	4	yes	—
545	C₂³×C₅	C₂³×C₄	1	4	yes	—
546	C₂³×C₅	C₂³×C₄	1	2	yes	—
547	C₂³×C₅	C₂⁵	1	1	yes	characteristic
548	C₅×Q₈	—	2	8	no	—
549	C₅×D₄	—	2	8	no	—
550	C₅×D₄	—	2	8	no	—
551	C₅×D₄	—	4	8	no	—
552	C₅×D₄	—	4	4	no	—
553	C₅×D₄	—	4	8	no	—
554	C₅×D₄	—	4	8	no	—
555	C₂×C₄×C₅	—	2	2	no	—
556	C₂×C₄×C₅	—	2	1	no	—
557	C₂×C₄×C₅	—	2	1	no	—
558	C₂×C₄×C₅	—	2	1	no	—
559	C₂×C₄×C₅	—	2	1	no	—
560	C₂×C₄×C₅	—	2	2	no	—
561	C₂×C₄×C₅	—	2	2	no	—
562	C₂×C₄×C₅	—	2	1	no	—
563	C₂×C₄×C₅	—	2	1	no	—
564	C₂×C₄×C₅	—	2	1	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	8	no	—
570	C₂×C₄×C₅	—	2	8	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
579	C₂×C₄×C₅	—	2	1	no	—
580	C₂×C₄×C₅	—	2	2	no	—
581	C₂×C₄×C₅	—	2	2	no	—
582	C₂×C₄×C₅	—	2	2	no	—
583	C₂×C₄×C₅	—	2	2	no	—
584	C₂×C₄×C₅	—	2	2	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	2	2	no	—
587	C₂×C₄×C₅	—	2	1	no	—
588	C₂×C₄×C₅	—	2	2	no	—
589	C₂×C₄×C₅	—	2	2	no	—
590	C₂×C₄×C₅	—	2	1	no	—
591	C₂×C₄×C₅	—	2	1	no	—
592	C₂×C₄×C₅	—	2	1	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	2	no	—
595	C₂×C₄×C₅	—	2	2	no	—
596	C₂×C₄×C₅	—	2	1	no	—
597	C₂×C₄×C₅	—	2	1	no	—
598	C₂×C₄×C₅	—	2	1	no	—
599	C₂×C₄×C₅	—	2	1	no	—
600	C₂×C₄×C₅	—	2	1	no	—
601	C₂×C₄×C₅	—	2	1	no	—
602	C₂×C₄×C₅	—	2	2	no	—
603	C₂×C₄×C₅	—	2	1	no	—
604	C₂×C₄×C₅	—	4	8	no	—
605	C₂×C₄×C₅	—	4	8	no	—
606	C₂×C₄×C₅	—	4	4	no	—
607	C₂×C₄×C₅	—	4	4	no	—
608	C₂×C₄×C₅	—	8	4	no	—
609	C₂×C₄×C₅	—	8	4	no	—
610	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
611	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
612	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
613	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
614	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
615	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
617	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
618	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
619	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
620	C₂⁵	C₂³×C₅	1	2	yes	—
621	C₂×#41	—	4	2	no	—
622	C₂×#41	—	4	2	no	—
623	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
624	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
625	C₂²×D₄	—	4	2	no	—
626	C₂²×D₄	—	4	2	no	—
627	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
628	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
629	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
630	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
631	C₂²×D₄	C₂³×C₅	1	2	yes	—
632	C₂²×D₄	C₂³×C₅	1	2	yes	—
633	C₂²×D₄	C₂³×C₅	1	2	yes	—
634	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
636	C₂³×C₄	C₂³×C₅	1	2	yes	—
637	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
638	C₂³×C₄	C₂³×C₅	1	2	yes	—
639	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₅	1	2	yes	—
641	C₂³×C₄	C₂³×C₅	1	2	yes	—
642	#124	C₂×C₄×C₅	1	8	yes	complemented
643	#123	C₂×C₄×C₅	1	16	yes	complemented
644	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
645	#121	C₂×C₄×C₅	1	8	yes	—
646	#121	C₂×C₄×C₅	1	16	yes	complemented
647	#120	C₂×C₄×C₅	1	16	yes	complemented
648	C₄×Q₈	—	4	2	no	—
649	C₄×Q₈	—	4	2	no	—
650	C₄×D₄	—	4	2	no	—
651	C₄×D₄	—	4	2	no	—
652	C₄×D₄	—	4	4	no	—
653	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
654	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
655	#117	—	4	2	no	—
656	#117	—	4	4	no	—
657	#117	—	4	2	no	—
658	#117	—	4	2	no	—
659	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
676	C₂×C₂²⋊C₄	—	4	4	no	—
677	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
678	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
708	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
709	C₂×C₄²	—	4	2	no	—
710	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
711	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₅	1	2	yes	—
713	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₅	1	2	yes	—
716	C₂×C₄²	C₂³×C₅	1	2	yes	—
717	C₂×C₄²	C₂³×C₅	1	2	yes	—
718	C₂×C₄²	C₂³×C₅	1	2	yes	—
719	C₂×C₄²	C₂³×C₅	1	2	yes	—
720	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₅	1	2	yes	—
723	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
724	#95	C₂³×C₅	1	1	yes	characteristic
725	#95	C₂³×C₅	1	1	yes	characteristic
726	#95	C₂³×C₅	1	1	yes	characteristic
727	#95	C₂³×C₅	1	1	yes	characteristic
728	#95	C₂³×C₅	1	1	yes	characteristic
729	#95	C₂³×C₅	1	1	yes	characteristic
730	#95	C₂³×C₅	1	1	yes	characteristic
731	#95	C₂³×C₅	1	1	yes	characteristic
732	#95	C₂³×C₅	1	2	yes	—
733	#95	C₂³×C₅	1	2	yes	—
734	#95	C₂³×C₅	1	1	yes	characteristic
735	#95	C₂³×C₅	1	2	yes	—
736	#95	C₂³×C₅	1	2	yes	—
737	#95	C₂³×C₅	1	2	yes	—
738	#95	C₂³×C₅	1	2	yes	—
739	#95	C₂³×C₅	1	2	yes	—
740	#95	C₂³×C₅	1	2	yes	—
741	#95	C₂³×C₅	1	2	yes	—
742	#95	C₂³×C₅	1	2	yes	—
743	#95	C₂³×C₅	1	2	yes	—
744	#95	C₂³×C₅	1	1	yes	characteristic
745	C₂²×C₅	—	2	2	no	—
746	C₂²×C₅	—	2	2	no	—
747	C₂²×C₅	—	2	4	no	—
748	C₂²×C₅	—	2	4	no	—
749	C₂²×C₅	—	2	2	no	—
750	C₂²×C₅	—	2	2	no	—
751	C₂²×C₅	—	2	4	no	—
752	C₂²×C₅	—	2	4	no	—
753	C₂²×C₅	—	2	4	no	—
754	C₂²×C₅	—	2	2	no	—
755	C₂²×C₅	—	2	4	no	—
756	C₂²×C₅	—	2	2	no	—
757	C₂²×C₅	—	4	1	no	—
758	C₂²×C₅	—	4	2	no	—
759	C₂²×C₅	—	4	2	no	—
760	C₂²×C₅	—	4	1	no	—
761	C₂²×C₅	—	4	1	no	—
762	C₂²×C₅	—	4	2	no	—
763	C₂²×C₅	—	4	2	no	—
764	C₂²×C₅	—	4	1	no	—
765	C₂²×C₅	—	4	2	no	—
766	C₂²×C₅	—	4	1	no	—
767	C₂²×C₅	—	4	2	no	—
768	C₂²×C₅	—	4	1	no	—
769	C₂²×C₅	—	4	1	no	—
770	C₂²×C₅	—	4	2	no	—
771	C₂²×C₅	—	4	2	no	—
772	C₂²×C₅	—	4	1	no	—
773	C₂²×C₅	—	8	16	no	—
774	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
775	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
777	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂²×C₅	#585	1	1	yes	characteristic
779	C₂²×C₅	#585	1	1	yes	characteristic
780	C₂²×C₅	#585	1	1	yes	characteristic
781	C₄×C₅	—	2	2	no	—
782	C₄×C₅	—	2	2	no	—
783	C₄×C₅	—	2	4	no	—
784	C₄×C₅	—	2	2	no	—
785	C₄×C₅	—	2	2	no	—
786	C₄×C₅	—	2	4	no	—
787	C₄×C₅	—	2	2	no	—
788	C₄×C₅	—	4	1	no	—
789	C₄×C₅	—	4	1	no	—
790	C₄×C₅	—	4	1	no	—
791	C₄×C₅	—	4	1	no	—
792	C₄×C₅	—	4	1	no	—
793	C₄×C₅	—	4	2	no	—
794	C₄×C₅	—	4	2	no	—
795	C₄×C₅	—	4	2	no	—
796	C₄×C₅	—	4	1	no	—
797	C₄×C₅	—	4	1	no	—
798	C₄×C₅	—	4	2	no	—
799	C₄×C₅	#518	1	4	yes	—
800	C₂⁴	—	4	2	no	—
801	C₂⁴	—	4	2	no	—
802	C₂⁴	—	4	2	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
807	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
808	C₂⁴	C₂⁴×C₅	1	2	yes	—
809	C₂⁴	C₂⁴×C₅	1	2	yes	—
810	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
811	#41	—	4	16	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	4	16	no	—
820	C₂×D₄	—	4	2	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	4	2	no	—
823	C₂×D₄	—	4	2	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	4	1	no	—
826	C₂×D₄	—	4	1	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
829	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
830	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
831	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
832	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
833	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	4	1	no	—
841	C₂²×C₄	—	4	1	no	—
842	C₂²×C₄	—	4	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	—	4	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	4	2	no	—
853	C₂²×C₄	—	4	2	no	—
854	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
855	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
856	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
857	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
858	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
867	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₄⋊C₄	—	4	1	no	—
884	C₄⋊C₄	—	4	1	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	—	4	1	no	—
890	C₄⋊C₄	—	4	2	no	—
891	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
892	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
893	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	1	no	—
899	C₂²⋊C₄	—	4	1	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	1	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	1	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	1	no	—
918	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
919	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
920	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
921	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
923	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
924	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	4	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	4	1	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	2	no	—
933	C₄²	—	4	2	no	—
934	C₄²	—	4	2	no	—
935	C₄²	—	4	2	no	—
936	C₄²	—	4	2	no	—
937	C₄²	—	4	2	no	—
938	C₄²	C₂²×C₄×C₅	1	4	yes	—
939	C₂×C₅	—	4	2	no	—
940	C₂×C₅	—	4	4	no	—
941	C₂×C₅	—	4	4	no	—
942	C₂×C₅	—	4	2	no	—
943	C₂×C₅	C₂×#518	1	1	yes	characteristic
944	C₂×C₅	#3428	1	1	yes	characteristic
945	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂×C₅	#3540	1	1	yes	characteristic
947	C₂×C₅	#3542	1	1	yes	characteristic
948	C₂×C₅	#3546	1	1	yes	characteristic
949	C₂×C₅	#3562	1	1	yes	characteristic
950	C₂³	—	2	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	4	8	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	8	no	—
977	C₂³	—	8	4	no	—
978	C₂³	—	8	4	no	—
979	C₂³	—	8	4	no	—
980	C₂³	—	8	4	no	—
981	C₂³	C₂³×C₄×C₅	1	2	yes	—
982	C₂³	C₂³×C₄×C₅	1	4	yes	—
983	C₂³	C₂³×C₄×C₅	1	4	yes	—
984	C₂³	C₂³×C₄×C₅	1	2	yes	—
985	C₂³	C₂⁵×C₅	1	1	yes	characteristic
986	Q₈	—	2	8	no	—
987	D₄	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	4	8	no	—
990	D₄	—	4	8	no	—
991	D₄	—	4	4	no	—
992	D₄	—	4	8	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	4	8	no	—
1043	C₂×C₄	—	4	8	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	8	4	no	—
1047	C₂×C₄	—	8	4	no	—
1048	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1049	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1050	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1051	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1052	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
1053	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1054	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
1055	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1056	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1057	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
1058	C₅	#34478	1	1	yes	characteristic, direct product factor, Sylow
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	4	no	—
1062	C₂²	—	2	4	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	8	16	no	—
1088	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1089	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1090	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1091	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1092	C₂²	C₅×#585	1	1	yes	characteristic
1093	C₂²	C₅×#585	1	1	yes	characteristic
1094	C₂²	C₅×#585	1	1	yes	characteristic
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	4	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	C₅×#518	1	4	yes	—
1114	C₂	—	4	2	no	—
1115	C₂	—	4	4	no	—
1116	C₂	—	4	4	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₂×C₅×#518	1	1	yes	characteristic
1119	C₂	C₅×#3428	1	1	yes	characteristic
1120	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1121	C₂	C₅×#3540	1	1	yes	characteristic
1122	C₂	C₅×#3542	1	1	yes	characteristic
1123	C₂	C₅×#3546	1	1	yes	characteristic
1124	C₂	C₅×#3562	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×#546	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×#2377	C₂	semidirect
3. C₅×#2375	C₂	semidirect
4. C₅×#2374	C₂	semidirect
5. C₅×#2367	C₂	semidirect
6. C₅×#2363	C₂	semidirect
7. C₅×#2362	C₂	semidirect
8. C₅×#2354	C₂	semidirect
9. C₅×#2354	C₂	semidirect
10. C₅×#2342	C₂	semidirect
11. C₅×#2341	C₂	semidirect
12. C₅×D₄×C₂²⋊C₄	C₂	semidirect
13. C₅×#2335	C₂	semidirect
14. C₅×#2326	C₂	semidirect
15. C₅×#2324	C₂	semidirect
16. C₅×#2323	C₂	semidirect
17. C₅×#2321	C₂	semidirect
18. C₅×#2319	C₂	semidirect
19. C₅×#2312	C₂	semidirect
20. C₅×#2309	C₂	semidirect
21. C₄×C₅×#121	C₂	semidirect
22. C₅×#2297	C₂	semidirect
23. C₅×#2290	C₂	semidirect
26. C₅×#546	C₄	semidirect
33. C₂×C₄×C₅×Q₈	C₂²	semidirect
34. C₂×C₄×C₅×Q₈	C₂²	semidirect
39. C₂×C₄×C₅×D₄	C₂²	semidirect
42. C₂×C₅×#117	C₂²	semidirect
43. C₂×C₅×#117	C₂²	semidirect
46. C₂²×C₄²×C₅	C₂²	semidirect
47. C₅×#391	C₂²	semidirect
48. C₅×#391	C₂²	semidirect
58. C₅×#390	C₂²	semidirect
59. C₅×#390	C₂²	semidirect
60. C₅×#390	C₂²	semidirect
61. C₅×#389	C₂²	semidirect
62. C₅×#389	C₂²	semidirect
63. C₅×#389	C₂²	semidirect
71. C₅×#388	C₂²	semidirect
72. C₅×#388	C₂²	semidirect
73. C₅×#388	C₂²	semidirect
74. C₅×#388	C₂²	semidirect
75. C₅×#388	C₂²	semidirect
76. C₅×#388	C₂²	semidirect
77. C₅×#388	C₂²	semidirect
78. C₅×#388	C₂²	semidirect
79. C₅×#388	C₂²	semidirect
80. C₅×#388	C₂²	semidirect
81. C₅×#388	C₂²	semidirect
82. C₅×#387	C₂²	semidirect
83. C₅×#387	C₂²	semidirect
84. C₅×#387	C₂²	semidirect
85. C₅×#387	C₂²	semidirect
90. C₅×#386	C₂²	semidirect
91. C₅×#386	C₂²	semidirect
92. C₅×#386	C₂²	semidirect
93. C₅×#386	C₂²	semidirect
94. C₅×#385	C₂²	semidirect
95. C₅×#385	C₂²	semidirect
96. C₅×#385	C₂²	semidirect
97. C₅×#385	C₂²	semidirect
98. C₅×#385	C₂²	semidirect
99. C₅×#384	C₂²	semidirect
100. C₅×#381	C₂²	semidirect
102. C₅×#380	C₂²	semidirect
103. C₅×#380	C₂²	semidirect
104. C₅×#380	C₂²	semidirect
105. C₅×#380	C₂²	semidirect
109. C₄×C₅×C₄⋊C₄	C₂²	semidirect
110. C₄×C₅×C₄⋊C₄	C₂²	semidirect
111. C₄×C₅×C₄⋊C₄	C₂²	semidirect
112. C₄×C₅×C₄⋊C₄	C₂²	semidirect
113. C₄×C₅×C₄⋊C₄	C₂²	semidirect
114. C₄×C₅×C₄⋊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. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
120. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
121. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
122. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
123. C₅×#376	C₂²	semidirect
124. #34478	C₅	direct (N × H)
128. C₂×C₅×#41	C₂×C₄	semidirect
132. C₂²×C₅×D₄	C₂×C₄	semidirect
147. C₅×#124	C₂×C₄	semidirect
148. C₅×#123	C₂×C₄	semidirect
149. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₅×#121	C₂×C₄	semidirect
152. C₅×#120	C₂×C₄	semidirect
158. C₄×C₅×D₄	C₂×C₄	semidirect
159. C₄×C₅×D₄	C₂×C₄	semidirect
182. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
251. #2377	C₂×C₅	semidirect
252. #2375	C₂×C₅	semidirect
253. #2374	C₂×C₅	semidirect
254. #2367	C₂×C₅	semidirect
255. #2363	C₂×C₅	semidirect
256. #2362	C₂×C₅	semidirect
257. #2354	C₂×C₅	semidirect
258. #2354	C₂×C₅	semidirect
259. #2342	C₂×C₅	semidirect
260. #2341	C₂×C₅	semidirect
261. D₄×C₂²⋊C₄	C₂×C₅	semidirect
262. #2335	C₂×C₅	semidirect
263. #2326	C₂×C₅	semidirect
264. #2324	C₂×C₅	semidirect
265. #2323	C₂×C₅	semidirect
266. #2321	C₂×C₅	semidirect
267. #2319	C₂×C₅	semidirect
268. #2312	C₂×C₅	semidirect
269. #2309	C₂×C₅	semidirect
270. C₄×#121	C₂×C₅	semidirect
271. #2297	C₂×C₅	semidirect
272. #2290	C₂×C₅	semidirect
414. #546	C₄×C₅	semidirect
421. C₂×C₄×Q₈	C₂²×C₅	semidirect
422. C₂×C₄×Q₈	C₂²×C₅	semidirect
427. C₂×C₄×D₄	C₂²×C₅	semidirect
430. C₂×#117	C₂²×C₅	semidirect
431. C₂×#117	C₂²×C₅	semidirect
434. C₂²×C₄²	C₂²×C₅	semidirect
435. #391	C₂²×C₅	semidirect
436. #391	C₂²×C₅	semidirect
446. #390	C₂²×C₅	semidirect
447. #390	C₂²×C₅	semidirect
448. #390	C₂²×C₅	semidirect
449. #389	C₂²×C₅	semidirect
450. #389	C₂²×C₅	semidirect
451. #389	C₂²×C₅	semidirect
459. #388	C₂²×C₅	semidirect
460. #388	C₂²×C₅	semidirect
461. #388	C₂²×C₅	semidirect
462. #388	C₂²×C₅	semidirect
463. #388	C₂²×C₅	semidirect
464. #388	C₂²×C₅	semidirect
465. #388	C₂²×C₅	semidirect
466. #388	C₂²×C₅	semidirect
467. #388	C₂²×C₅	semidirect
468. #388	C₂²×C₅	semidirect
469. #388	C₂²×C₅	semidirect
470. #387	C₂²×C₅	semidirect
471. #387	C₂²×C₅	semidirect
472. #387	C₂²×C₅	semidirect
473. #387	C₂²×C₅	semidirect
478. #386	C₂²×C₅	semidirect
479. #386	C₂²×C₅	semidirect
480. #386	C₂²×C₅	semidirect
481. #386	C₂²×C₅	semidirect
482. #385	C₂²×C₅	semidirect
483. #385	C₂²×C₅	semidirect
484. #385	C₂²×C₅	semidirect
485. #385	C₂²×C₅	semidirect
486. #385	C₂²×C₅	semidirect
487. #384	C₂²×C₅	semidirect
488. #381	C₂²×C₅	semidirect
490. #380	C₂²×C₅	semidirect
491. #380	C₂²×C₅	semidirect
492. #380	C₂²×C₅	semidirect
493. #380	C₂²×C₅	semidirect
497. C₄×C₄⋊C₄	C₂²×C₅	semidirect
498. C₄×C₄⋊C₄	C₂²×C₅	semidirect
499. C₄×C₄⋊C₄	C₂²×C₅	semidirect
500. C₄×C₄⋊C₄	C₂²×C₅	semidirect
501. C₄×C₄⋊C₄	C₂²×C₅	semidirect
502. C₄×C₄⋊C₄	C₂²×C₅	semidirect
504. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
505. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
506. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
507. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
508. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
509. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
510. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
511. #376	C₂²×C₅	semidirect
623. C₂×#41	C₂×C₄×C₅	semidirect
627. C₂²×D₄	C₂×C₄×C₅	semidirect
642. #124	C₂×C₄×C₅	semidirect
643. #123	C₂×C₄×C₅	semidirect
644. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
646. #121	C₂×C₄×C₅	semidirect
647. #120	C₂×C₄×C₅	semidirect
653. C₄×D₄	C₂×C₄×C₅	semidirect
654. C₄×D₄	C₂×C₄×C₅	semidirect
677. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
1058. C₅	#34478	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×#546	2
C₅×#2377	2
C₅×#2375	2
C₅×#2374	2
C₅×#2367	2
C₅×#2363	2
C₅×#2362	2
C₅×#2354	2
C₅×#2342	2
C₅×#2341	2
C₅×D₄×C₂²⋊C₄	2
C₅×#2335	2
C₅×#2326	2
C₅×#2324	2
C₅×#2323	2
C₅×#2321	2
C₅×#2319	2
C₅×#2312	2
C₅×#2309	2
C₄×C₅×#121	2
C₅×#2297	2
C₅×#2290	2
#34478	5

Subgroups — C5×#34478 #11957198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34478 #11957198