Subgroups — C₅×#34277 #11956997

Order 1280.

2634 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#538	C₂	1	1	yes	maximal, characteristic
2	C₅×#2374	C₂	1	2	yes	maximal, complemented
3	C₅×#2373	C₂	1	2	yes	maximal, complemented
4	C₅×#2373	C₂	1	2	yes	maximal, complemented
5	C₅×#2372	C₂	1	2	yes	maximal, complemented
6	C₅×#2367	C₂	1	2	yes	maximal, complemented
7	C₅×#2364	C₂	1	2	yes	maximal, complemented
8	C₅×#2363	C₂	1	2	yes	maximal, complemented
9	C₅×#2359	C₂	1	2	yes	maximal, complemented
10	C₅×#2329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2321	C₂	1	2	yes	maximal, complemented
13	C₅×#2312	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#120	C₂	1	2	yes	maximal, complemented
17	C₅×#2290	C₂	1	2	yes	maximal, complemented
18	C₅×#2275	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₅×#538	C₄	1	16	yes	complemented
22	C₂×C₅×#126	C₂²	1	2	yes	—
23	C₂×C₅×#124	C₂²	1	2	yes	—
24	C₂×C₅×#123	C₂²	1	2	yes	—
25	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#121	C₂²	1	1	yes	characteristic
27	C₂×C₅×#121	C₂²	1	2	yes	—
28	C₂×C₅×#120	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
31	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
33	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
34	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
35	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#117	C₂²	1	2	yes	complemented
37	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
41	C₅×#391	C₂²	1	1	yes	characteristic, complemented
42	C₅×#391	C₂²	1	2	yes	complemented
43	C₅×#390	C₂²	1	2	yes	—
44	C₅×#390	C₂²	1	2	yes	—
45	C₅×#390	C₂²	1	1	yes	characteristic, complemented
46	C₅×#389	C₂²	1	1	yes	characteristic, complemented
47	C₅×#389	C₂²	1	1	yes	characteristic, complemented
48	C₅×#389	C₂²	1	2	yes	complemented
49	C₅×#388	C₂²	1	2	yes	—
50	C₅×#388	C₂²	1	2	yes	—
51	C₅×#388	C₂²	1	2	yes	—
52	C₅×#388	C₂²	1	2	yes	—
53	C₅×#388	C₂²	1	2	yes	—
54	C₅×#388	C₂²	1	2	yes	—
55	C₅×#388	C₂²	1	2	yes	—
56	C₅×#388	C₂²	1	2	yes	—
57	C₅×#388	C₂²	1	2	yes	complemented
58	C₅×#388	C₂²	1	2	yes	complemented
59	C₅×#388	C₂²	1	2	yes	complemented
60	C₅×#388	C₂²	1	2	yes	complemented
61	C₅×#387	C₂²	1	2	yes	complemented
62	C₅×#387	C₂²	1	2	yes	complemented
63	C₅×#387	C₂²	1	2	yes	complemented
64	C₅×#387	C₂²	1	2	yes	complemented
65	C₅×#387	C₂²	1	2	yes	complemented
66	C₅×#387	C₂²	1	2	yes	complemented
67	C₅×#386	C₂²	1	2	yes	—
68	C₅×#386	C₂²	1	2	yes	—
69	C₅×#386	C₂²	1	2	yes	—
70	C₅×#386	C₂²	1	2	yes	—
71	C₅×#386	C₂²	1	2	yes	—
72	C₅×#386	C₂²	1	2	yes	—
73	C₅×#386	C₂²	1	2	yes	complemented
74	C₅×#385	C₂²	1	2	yes	—
75	C₅×#385	C₂²	1	2	yes	—
76	C₅×#385	C₂²	1	2	yes	—
77	C₅×#385	C₂²	1	2	yes	—
78	C₅×#385	C₂²	1	2	yes	complemented
79	C₅×#380	C₂²	1	1	yes	characteristic
80	C₅×#380	C₂²	1	1	yes	characteristic
81	C₅×#379	C₂²	1	2	yes	—
82	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
83	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
84	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
86	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
88	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
90	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
91	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
92	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
93	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
100	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
101	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	C₅×#376	C₂²	1	2	yes	complemented
104	C₅×#376	C₂²	1	2	yes	complemented
105	C₂×C₅×#95	C₂²	1	1	yes	characteristic
106	C₂×C₅×#95	C₂²	1	1	yes	characteristic
107	C₂×C₅×#95	C₂²	1	2	yes	complemented
108	#34277	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁵×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₅×D₄	C₂³	1	2	yes	—
112	C₂²×C₅×D₄	C₂³	1	2	yes	—
113	C₂²×C₅×D₄	C₂³	1	2	yes	—
114	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₅	—	2	4	no	—
116	C₂³×C₄×C₅	—	4	2	no	—
117	C₂³×C₄×C₅	—	4	2	no	—
118	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₅	C₂³	1	2	yes	—
120	C₂³×C₄×C₅	C₂³	1	2	yes	—
121	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₅	C₂³	1	2	yes	—
123	C₂³×C₄×C₅	C₂³	1	2	yes	—
124	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₅	C₂³	1	2	yes	—
127	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
129	C₅×#126	C₂×C₄	1	16	yes	complemented
130	C₅×#124	C₂×C₄	1	16	yes	complemented
131	C₅×#123	C₂×C₄	1	16	yes	complemented
132	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
133	C₅×#121	C₂×C₄	1	16	yes	complemented
134	C₅×#121	C₂×C₄	1	8	yes	complemented
135	C₅×#120	C₂×C₄	1	16	yes	complemented
136	C₄×C₅×Q₈	—	4	2	no	—
137	C₄×C₅×D₄	—	2	8	no	—
138	C₄×C₅×D₄	—	2	8	no	—
139	C₄×C₅×D₄	—	4	2	no	—
140	C₄×C₅×D₄	—	4	4	no	—
141	C₄×C₅×D₄	—	4	4	no	—
142	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
143	C₅×#117	—	4	4	no	—
144	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
159	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
160	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₂×C₄²×C₅	—	4	2	no	—
182	C₂×C₄²×C₅	—	4	2	no	—
183	C₂×C₄²×C₅	C₂³	1	2	yes	—
184	C₂×C₄²×C₅	C₂³	1	2	yes	—
185	C₂×C₄²×C₅	C₂³	1	2	yes	—
186	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅	C₂³	1	2	yes	—
189	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₅	C₂³	1	2	yes	—
191	C₂×C₄²×C₅	C₂³	1	2	yes	—
192	C₂×C₄²×C₅	C₂³	1	2	yes	—
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	2	yes	—
195	C₂×C₄²×C₅	C₂³	1	2	yes	—
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
197	C₂×C₄²×C₅	C₂³	1	2	yes	—
198	C₅×#95	C₂³	1	2	yes	—
199	C₅×#95	C₂³	1	2	yes	—
200	C₅×#95	C₂³	1	2	yes	—
201	C₅×#95	C₂³	1	2	yes	—
202	C₅×#95	C₂³	1	2	yes	—
203	C₅×#95	C₂³	1	2	yes	—
204	C₅×#95	C₂³	1	2	yes	—
205	C₅×#95	C₂³	1	2	yes	—
206	C₅×#95	C₂³	1	2	yes	—
207	C₅×#95	C₂³	1	2	yes	—
208	C₅×#95	C₂³	1	2	yes	—
209	C₅×#95	C₂³	1	2	yes	—
210	C₅×#95	C₂³	1	2	yes	—
211	C₅×#95	C₂³	1	2	yes	—
212	C₅×#95	C₂³	1	2	yes	—
213	C₅×#95	C₂³	1	2	yes	—
214	C₅×#95	C₂³	1	2	yes	—
215	C₅×#95	C₂³	1	2	yes	—
216	C₅×#95	C₂³	1	2	yes	—
217	C₅×#95	C₂³	1	2	yes	—
218	C₂×#538	C₂×C₅	1	1	yes	characteristic
219	#2374	C₂×C₅	1	2	yes	complemented
220	#2373	C₂×C₅	1	2	yes	complemented
221	#2373	C₂×C₅	1	2	yes	complemented
222	#2372	C₂×C₅	1	2	yes	complemented
223	#2367	C₂×C₅	1	2	yes	complemented
224	#2364	C₂×C₅	1	2	yes	complemented
225	#2363	C₂×C₅	1	2	yes	complemented
226	#2359	C₂×C₅	1	2	yes	complemented
227	#2329	C₂×C₅	1	1	yes	characteristic, complemented
228	#2325	C₂×C₅	1	1	yes	characteristic, complemented
229	#2321	C₂×C₅	1	2	yes	complemented
230	#2312	C₂×C₅	1	1	yes	characteristic, complemented
231	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
232	C₄×#121	C₂×C₅	1	1	yes	characteristic, complemented
233	C₄×#120	C₂×C₅	1	2	yes	complemented
234	#2290	C₂×C₅	1	2	yes	complemented
235	#2275	C₂×C₅	1	2	yes	complemented
236	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
237	C₂⁴×C₅	—	2	2	no	—
238	C₂⁴×C₅	—	2	2	no	—
239	C₂⁴×C₅	—	4	1	no	—
240	C₂⁴×C₅	—	4	1	no	—
241	C₂⁴×C₅	—	4	1	no	—
242	C₂⁴×C₅	—	4	1	no	—
243	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
244	C₂⁴×C₅	C₂⁴	1	2	yes	—
245	C₂⁴×C₅	C₂⁴	1	2	yes	—
246	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
247	C₂×C₅×Q₈	—	4	1	no	—
248	C₂×C₅×Q₈	—	4	1	no	—
249	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
250	C₂×C₅×D₄	—	2	4	no	—
251	C₂×C₅×D₄	—	2	4	no	—
252	C₂×C₅×D₄	—	4	1	no	—
253	C₂×C₅×D₄	—	4	2	no	—
254	C₂×C₅×D₄	—	4	2	no	—
255	C₂×C₅×D₄	—	4	2	no	—
256	C₂×C₅×D₄	—	4	1	no	—
257	C₂×C₅×D₄	—	4	2	no	—
258	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
259	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
260	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
261	C₂×C₅×D₄	C₂²×C₄	1	4	yes	complemented
262	C₂²×C₄×C₅	—	2	2	no	—
263	C₂²×C₄×C₅	—	2	2	no	—
264	C₂²×C₄×C₅	—	2	2	no	—
265	C₂²×C₄×C₅	—	2	2	no	—
266	C₂²×C₄×C₅	—	2	4	no	—
267	C₂²×C₄×C₅	—	2	4	no	—
268	C₂²×C₄×C₅	—	2	4	no	—
269	C₂²×C₄×C₅	—	2	4	no	—
270	C₂²×C₄×C₅	—	2	4	no	—
271	C₂²×C₄×C₅	—	2	4	no	—
272	C₂²×C₄×C₅	—	4	1	no	—
273	C₂²×C₄×C₅	—	4	1	no	—
274	C₂²×C₄×C₅	—	4	1	no	—
275	C₂²×C₄×C₅	—	4	1	no	—
276	C₂²×C₄×C₅	—	4	2	no	—
277	C₂²×C₄×C₅	—	4	2	no	—
278	C₂²×C₄×C₅	—	4	2	no	—
279	C₂²×C₄×C₅	—	4	1	no	—
280	C₂²×C₄×C₅	—	4	1	no	—
281	C₂²×C₄×C₅	—	4	1	no	—
282	C₂²×C₄×C₅	—	4	1	no	—
283	C₂²×C₄×C₅	—	4	2	no	—
284	C₂²×C₄×C₅	—	4	1	no	—
285	C₂²×C₄×C₅	—	4	1	no	—
286	C₂²×C₄×C₅	—	4	2	no	—
287	C₂²×C₄×C₅	—	4	2	no	—
288	C₂²×C₄×C₅	—	4	2	no	—
289	C₂²×C₄×C₅	—	4	2	no	—
290	C₂²×C₄×C₅	—	4	16	no	—
291	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
292	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
293	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	complemented
294	C₂²×C₄×C₅	#41	1	4	yes	—
295	C₂²×C₄×C₅	#41	1	4	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
312	C₅×C₄⋊C₄	—	2	4	no	—
313	C₅×C₄⋊C₄	—	2	4	no	—
314	C₅×C₄⋊C₄	—	2	4	no	—
315	C₅×C₄⋊C₄	—	2	4	no	—
316	C₅×C₄⋊C₄	—	4	1	no	—
317	C₅×C₄⋊C₄	—	4	1	no	—
318	C₅×C₄⋊C₄	—	4	2	no	—
319	C₅×C₄⋊C₄	—	4	2	no	—
320	C₅×C₄⋊C₄	—	4	1	no	—
321	C₅×C₄⋊C₄	—	4	1	no	—
322	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
323	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
324	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
325	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
326	C₅×C₂²⋊C₄	—	2	4	no	—
327	C₅×C₂²⋊C₄	—	2	4	no	—
328	C₅×C₂²⋊C₄	—	2	4	no	—
329	C₅×C₂²⋊C₄	—	2	4	no	—
330	C₅×C₂²⋊C₄	—	2	4	no	—
331	C₅×C₂²⋊C₄	—	2	4	no	—
332	C₅×C₂²⋊C₄	—	2	4	no	—
333	C₅×C₂²⋊C₄	—	2	4	no	—
334	C₅×C₂²⋊C₄	—	4	2	no	—
335	C₅×C₂²⋊C₄	—	4	2	no	—
336	C₅×C₂²⋊C₄	—	4	2	no	—
337	C₅×C₂²⋊C₄	—	4	2	no	—
338	C₅×C₂²⋊C₄	—	4	2	no	—
339	C₅×C₂²⋊C₄	—	4	2	no	—
340	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
341	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
342	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
343	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
344	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
345	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
346	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
347	C₄²×C₅	—	2	4	no	—
348	C₄²×C₅	—	2	4	no	—
349	C₄²×C₅	—	2	4	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	2	2	no	—
352	C₄²×C₅	—	4	1	no	—
353	C₄²×C₅	—	4	2	no	—
354	C₄²×C₅	—	4	1	no	—
355	C₄²×C₅	—	4	2	no	—
356	C₄²×C₅	—	4	2	no	—
357	C₄²×C₅	—	4	2	no	—
358	C₄²×C₅	—	4	2	no	—
359	C₄²×C₅	—	4	2	no	—
360	C₄²×C₅	—	4	2	no	—
361	C₄²×C₅	C₂²×C₄	1	8	yes	complemented
362	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
363	#538	C₄×C₅	1	16	yes	complemented
364	C₂×#126	C₂²×C₅	1	2	yes	—
365	C₂×#124	C₂²×C₅	1	2	yes	—
366	C₂×#123	C₂²×C₅	1	2	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
368	C₂×#121	C₂²×C₅	1	1	yes	characteristic
369	C₂×#121	C₂²×C₅	1	2	yes	—
370	C₂×#120	C₂²×C₅	1	2	yes	—
371	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
372	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
378	C₂×#117	C₂²×C₅	1	2	yes	complemented
379	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
382	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
383	#391	C₂²×C₅	1	2	yes	complemented
384	#391	C₂²×C₅	1	1	yes	characteristic, complemented
385	#390	C₂²×C₅	1	2	yes	—
386	#390	C₂²×C₅	1	2	yes	—
387	#390	C₂²×C₅	1	1	yes	characteristic, complemented
388	#389	C₂²×C₅	1	2	yes	complemented
389	#389	C₂²×C₅	1	1	yes	characteristic, complemented
390	#389	C₂²×C₅	1	1	yes	characteristic, complemented
391	#388	C₂²×C₅	1	2	yes	—
392	#388	C₂²×C₅	1	2	yes	—
393	#388	C₂²×C₅	1	2	yes	—
394	#388	C₂²×C₅	1	2	yes	—
395	#388	C₂²×C₅	1	2	yes	—
396	#388	C₂²×C₅	1	2	yes	—
397	#388	C₂²×C₅	1	2	yes	—
398	#388	C₂²×C₅	1	2	yes	—
399	#388	C₂²×C₅	1	2	yes	complemented
400	#388	C₂²×C₅	1	2	yes	complemented
401	#388	C₂²×C₅	1	2	yes	complemented
402	#388	C₂²×C₅	1	2	yes	complemented
403	#387	C₂²×C₅	1	2	yes	complemented
404	#387	C₂²×C₅	1	2	yes	complemented
405	#387	C₂²×C₅	1	2	yes	complemented
406	#387	C₂²×C₅	1	2	yes	complemented
407	#387	C₂²×C₅	1	2	yes	complemented
408	#387	C₂²×C₅	1	2	yes	complemented
409	#386	C₂²×C₅	1	2	yes	—
410	#386	C₂²×C₅	1	2	yes	—
411	#386	C₂²×C₅	1	2	yes	—
412	#386	C₂²×C₅	1	2	yes	—
413	#386	C₂²×C₅	1	2	yes	—
414	#386	C₂²×C₅	1	2	yes	—
415	#386	C₂²×C₅	1	2	yes	complemented
416	#385	C₂²×C₅	1	2	yes	—
417	#385	C₂²×C₅	1	2	yes	—
418	#385	C₂²×C₅	1	2	yes	—
419	#385	C₂²×C₅	1	2	yes	—
420	#385	C₂²×C₅	1	2	yes	complemented
421	#380	C₂²×C₅	1	1	yes	characteristic
422	#380	C₂²×C₅	1	1	yes	characteristic
423	#379	C₂²×C₅	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
425	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
426	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
427	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
428	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
429	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
430	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
431	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
436	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
441	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
442	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
443	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
444	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
445	#376	C₂²×C₅	1	2	yes	complemented
446	#376	C₂²×C₅	1	2	yes	complemented
447	C₂×#95	C₂²×C₅	1	1	yes	characteristic
448	C₂×#95	C₂²×C₅	1	1	yes	characteristic
449	C₂×#95	C₂²×C₅	1	2	yes	complemented
450	C₂³×C₅	—	2	1	no	—
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	—	2	1	no	—
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	2	8	no	—
455	C₂³×C₅	—	2	2	no	—
456	C₂³×C₅	—	2	2	no	—
457	C₂³×C₅	—	2	2	no	—
458	C₂³×C₅	—	2	2	no	—
459	C₂³×C₅	—	2	2	no	—
460	C₂³×C₅	—	2	2	no	—
461	C₂³×C₅	—	2	2	no	—
462	C₂³×C₅	—	2	2	no	—
463	C₂³×C₅	—	2	2	no	—
464	C₂³×C₅	—	2	2	no	—
465	C₂³×C₅	—	2	2	no	—
466	C₂³×C₅	—	2	2	no	—
467	C₂³×C₅	—	4	4	no	—
468	C₂³×C₅	—	4	4	no	—
469	C₂³×C₅	—	4	4	no	—
470	C₂³×C₅	—	4	4	no	—
471	C₂³×C₅	—	4	4	no	—
472	C₂³×C₅	—	4	4	no	—
473	C₂³×C₅	C₂³×C₄	1	4	yes	—
474	C₂³×C₅	C₂³×C₄	1	4	yes	—
475	C₂³×C₅	C₂³×C₄	1	2	yes	—
476	C₂³×C₅	C₂×#41	1	2	yes	—
477	C₂³×C₅	C₂×#41	1	2	yes	—
478	C₂³×C₅	C₂⁵	1	1	yes	characteristic
479	C₅×Q₈	—	4	4	no	—
480	C₅×D₄	—	2	16	no	—
481	C₅×D₄	—	4	8	no	—
482	C₅×D₄	—	4	8	no	—
483	C₅×D₄	—	4	4	no	—
484	C₂×C₄×C₅	—	2	8	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	2	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	2	no	—
498	C₂×C₄×C₅	—	2	2	no	—
499	C₂×C₄×C₅	—	2	2	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	2	no	—
502	C₂×C₄×C₅	—	2	2	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	2	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	2	no	—
508	C₂×C₄×C₅	—	2	2	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	2	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	2	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	4	4	no	—
523	C₂×C₄×C₅	—	4	4	no	—
524	C₂×C₄×C₅	—	4	4	no	—
525	C₂×C₄×C₅	—	4	8	no	—
526	C₂×C₄×C₅	—	4	4	no	—
527	C₂×C₄×C₅	—	4	8	no	—
528	C₂×C₄×C₅	—	4	8	no	—
529	C₂×C₄×C₅	—	4	4	no	—
530	C₂×C₄×C₅	—	8	4	no	—
531	C₂×C₄×C₅	—	8	4	no	—
532	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
533	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
534	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
535	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
536	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
537	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
538	C₂×C₄×C₅	C₂×#41	1	2	yes	—
539	C₂×C₄×C₅	C₂×#41	1	4	yes	—
540	C₂×C₄×C₅	C₂×#41	1	2	yes	—
541	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
542	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
543	C₂⁵	C₂³×C₅	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₅	1	2	yes	—
546	C₂²×D₄	C₂³×C₅	1	2	yes	—
547	C₂²×D₄	C₂³×C₅	1	2	yes	—
548	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
549	C₂³×C₄	—	2	4	no	—
550	C₂³×C₄	—	4	2	no	—
551	C₂³×C₄	—	4	2	no	—
552	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₅	1	2	yes	—
554	C₂³×C₄	C₂³×C₅	1	2	yes	—
555	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₅	1	2	yes	—
557	C₂³×C₄	C₂³×C₅	1	2	yes	—
558	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₅	1	2	yes	—
561	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
563	#126	C₂×C₄×C₅	1	16	yes	complemented
564	#124	C₂×C₄×C₅	1	16	yes	complemented
565	#123	C₂×C₄×C₅	1	16	yes	complemented
566	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
567	#121	C₂×C₄×C₅	1	16	yes	complemented
568	#121	C₂×C₄×C₅	1	8	yes	complemented
569	#120	C₂×C₄×C₅	1	16	yes	complemented
570	C₄×Q₈	—	4	2	no	—
571	C₄×D₄	—	2	8	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	4	2	no	—
574	C₄×D₄	—	4	4	no	—
575	C₄×D₄	—	4	4	no	—
576	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
577	#117	—	4	4	no	—
578	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	—	2	4	no	—
593	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
594	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
615	C₂×C₄²	—	4	2	no	—
616	C₂×C₄²	—	4	2	no	—
617	C₂×C₄²	C₂³×C₅	1	2	yes	—
618	C₂×C₄²	C₂³×C₅	1	2	yes	—
619	C₂×C₄²	C₂³×C₅	1	2	yes	—
620	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₅	1	2	yes	—
623	C₂×C₄²	C₂³×C₅	1	2	yes	—
624	C₂×C₄²	C₂³×C₅	1	2	yes	—
625	C₂×C₄²	C₂³×C₅	1	2	yes	—
626	C₂×C₄²	C₂³×C₅	1	2	yes	—
627	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₅	1	2	yes	—
629	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅	1	2	yes	—
631	C₂×C₄²	C₂³×C₅	1	2	yes	—
632	#95	C₂³×C₅	1	2	yes	—
633	#95	C₂³×C₅	1	2	yes	—
634	#95	C₂³×C₅	1	2	yes	—
635	#95	C₂³×C₅	1	2	yes	—
636	#95	C₂³×C₅	1	2	yes	—
637	#95	C₂³×C₅	1	2	yes	—
638	#95	C₂³×C₅	1	2	yes	—
639	#95	C₂³×C₅	1	2	yes	—
640	#95	C₂³×C₅	1	2	yes	—
641	#95	C₂³×C₅	1	2	yes	—
642	#95	C₂³×C₅	1	2	yes	—
643	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	2	yes	—
645	#95	C₂³×C₅	1	2	yes	—
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	2	yes	—
649	#95	C₂³×C₅	1	2	yes	—
650	#95	C₂³×C₅	1	2	yes	—
651	#95	C₂³×C₅	1	2	yes	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	2	2	no	—
655	C₂²×C₅	—	2	2	no	—
656	C₂²×C₅	—	2	2	no	—
657	C₂²×C₅	—	2	2	no	—
658	C₂²×C₅	—	2	4	no	—
659	C₂²×C₅	—	2	4	no	—
660	C₂²×C₅	—	2	4	no	—
661	C₂²×C₅	—	2	4	no	—
662	C₂²×C₅	—	2	4	no	—
663	C₂²×C₅	—	2	4	no	—
664	C₂²×C₅	—	4	16	no	—
665	C₂²×C₅	—	4	2	no	—
666	C₂²×C₅	—	4	2	no	—
667	C₂²×C₅	—	4	2	no	—
668	C₂²×C₅	—	4	2	no	—
669	C₂²×C₅	—	4	2	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	—	4	2	no	—
672	C₂²×C₅	—	4	2	no	—
673	C₂²×C₅	C₄×#41	1	4	yes	—
674	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
675	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
676	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
677	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²×C₅	#585	1	1	yes	characteristic
680	C₂²×C₅	#585	1	1	yes	characteristic
681	C₄×C₅	—	2	4	no	—
682	C₄×C₅	—	2	4	no	—
683	C₄×C₅	—	2	2	no	—
684	C₄×C₅	—	2	4	no	—
685	C₄×C₅	—	2	2	no	—
686	C₄×C₅	—	2	4	no	—
687	C₄×C₅	—	2	2	no	—
688	C₄×C₅	—	2	2	no	—
689	C₄×C₅	—	2	4	no	—
690	C₄×C₅	—	2	2	no	—
691	C₄×C₅	—	2	2	no	—
692	C₄×C₅	—	4	2	no	—
693	C₄×C₅	—	4	2	no	—
694	C₄×C₅	—	4	2	no	—
695	C₄×C₅	—	4	2	no	—
696	C₄×C₅	—	4	2	no	—
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	4	1	no	—
700	C₂⁴	—	4	1	no	—
701	C₂⁴	—	4	1	no	—
702	C₂⁴	—	4	1	no	—
703	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
704	C₂⁴	C₂⁴×C₅	1	2	yes	—
705	C₂⁴	C₂⁴×C₅	1	2	yes	—
706	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
707	C₂×Q₈	—	4	1	no	—
708	C₂×Q₈	—	4	1	no	—
709	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
720	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₅	1	4	yes	complemented
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	1	no	—
740	C₂²×C₄	—	4	1	no	—
741	C₂²×C₄	—	4	1	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	16	no	—
751	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
752	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
753	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	complemented
754	C₂²×C₄	C₅×#41	1	4	yes	—
755	C₂²×C₄	C₅×#41	1	4	yes	—
756	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	1	no	—
780	C₄⋊C₄	—	4	1	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
783	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
784	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
785	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	complemented
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	2	no	—
799	C₂²⋊C₄	—	4	2	no	—
800	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
801	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
802	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
803	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
806	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	complemented
807	C₄²	—	2	4	no	—
808	C₄²	—	2	4	no	—
809	C₄²	—	2	4	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	1	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	2	no	—
820	C₄²	—	4	2	no	—
821	C₄²	C₂²×C₄×C₅	1	8	yes	complemented
822	C₂×C₅	—	2	4	no	—
823	C₂×C₅	—	4	4	no	—
824	C₂×C₅	—	4	4	no	—
825	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
826	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
827	C₂×C₅	C₄×H(5,𝔽₂)	1	1	yes	characteristic
828	C₂×C₅	#3490	1	1	yes	characteristic
829	C₂×C₅	#3493	1	1	yes	characteristic
830	C₂×C₅	#3505	1	1	yes	characteristic
831	C₂×C₅	#3506	1	1	yes	characteristic
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	8	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	4	4	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	4	no	—
855	C₂³	C₂³×C₄×C₅	1	4	yes	—
856	C₂³	C₂³×C₄×C₅	1	4	yes	—
857	C₂³	C₂³×C₄×C₅	1	2	yes	—
858	C₂³	C₂×C₅×#41	1	2	yes	—
859	C₂³	C₂×C₅×#41	1	2	yes	—
860	C₂³	C₂⁵×C₅	1	1	yes	characteristic
861	Q₈	—	4	4	no	—
862	D₄	—	2	16	no	—
863	D₄	—	4	8	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	C₂×C₄	—	2	8	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	8	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	—	8	4	no	—
914	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
915	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
916	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
917	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
918	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
919	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
920	C₂×C₄	C₂×C₅×#41	1	2	yes	—
921	C₂×C₄	C₂×C₅×#41	1	4	yes	—
922	C₂×C₄	C₂×C₅×#41	1	2	yes	—
923	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
924	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
925	C₅	#34277	1	1	yes	characteristic, direct product factor, Sylow
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	16	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	C₄×C₅×#41	1	4	yes	—
948	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
949	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
950	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
951	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₅×#585	1	1	yes	characteristic
954	C₂²	C₅×#585	1	1	yes	characteristic
955	C₄	—	2	4	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₂	—	2	4	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
975	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂	C₄×C₅×H(5,𝔽₂)	1	1	yes	characteristic
977	C₂	C₅×#3490	1	1	yes	characteristic
978	C₂	C₅×#3493	1	1	yes	characteristic
979	C₂	C₅×#3505	1	1	yes	characteristic
980	C₂	C₅×#3506	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×#538	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×#2374	C₂	semidirect
3. C₅×#2373	C₂	semidirect
4. C₅×#2373	C₂	semidirect
5. C₅×#2372	C₂	semidirect
6. C₅×#2367	C₂	semidirect
7. C₅×#2364	C₂	semidirect
8. C₅×#2363	C₂	semidirect
9. C₅×#2359	C₂	semidirect
10. C₅×#2329	C₂	semidirect
11. C₅×#2325	C₂	semidirect
12. C₅×#2321	C₂	semidirect
13. C₅×#2312	C₂	semidirect
14. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₅×#121	C₂	semidirect
16. C₄×C₅×#120	C₂	semidirect
17. C₅×#2290	C₂	semidirect
18. C₅×#2275	C₂	semidirect
19. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
21. C₅×#538	C₄	semidirect
29. C₂×C₄×C₅×Q₈	C₂²	semidirect
35. C₂×C₄×C₅×D₄	C₂²	semidirect
36. C₂×C₅×#117	C₂²	semidirect
41. C₅×#391	C₂²	semidirect
42. C₅×#391	C₂²	semidirect
45. C₅×#390	C₂²	semidirect
46. C₅×#389	C₂²	semidirect
47. C₅×#389	C₂²	semidirect
48. C₅×#389	C₂²	semidirect
57. C₅×#388	C₂²	semidirect
58. C₅×#388	C₂²	semidirect
59. C₅×#388	C₂²	semidirect
60. C₅×#388	C₂²	semidirect
61. C₅×#387	C₂²	semidirect
62. C₅×#387	C₂²	semidirect
63. C₅×#387	C₂²	semidirect
64. C₅×#387	C₂²	semidirect
65. C₅×#387	C₂²	semidirect
66. C₅×#387	C₂²	semidirect
73. C₅×#386	C₂²	semidirect
78. C₅×#385	C₂²	semidirect
82. C₄×C₅×C₄⋊C₄	C₂²	semidirect
83. C₄×C₅×C₄⋊C₄	C₂²	semidirect
84. C₄×C₅×C₄⋊C₄	C₂²	semidirect
85. C₄×C₅×C₄⋊C₄	C₂²	semidirect
86. C₄×C₅×C₄⋊C₄	C₂²	semidirect
87. C₄×C₅×C₄⋊C₄	C₂²	semidirect
88. C₄×C₅×C₄⋊C₄	C₂²	semidirect
98. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
99. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
100. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
101. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
102. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
103. C₅×#376	C₂²	semidirect
104. C₅×#376	C₂²	semidirect
107. C₂×C₅×#95	C₂²	semidirect
108. #34277	C₅	direct (N × H)
129. C₅×#126	C₂×C₄	semidirect
130. C₅×#124	C₂×C₄	semidirect
131. C₅×#123	C₂×C₄	semidirect
132. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
133. C₅×#121	C₂×C₄	semidirect
134. C₅×#121	C₂×C₄	semidirect
135. C₅×#120	C₂×C₄	semidirect
142. C₄×C₅×D₄	C₂×C₄	semidirect
159. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
219. #2374	C₂×C₅	semidirect
220. #2373	C₂×C₅	semidirect
221. #2373	C₂×C₅	semidirect
222. #2372	C₂×C₅	semidirect
223. #2367	C₂×C₅	semidirect
224. #2364	C₂×C₅	semidirect
225. #2363	C₂×C₅	semidirect
226. #2359	C₂×C₅	semidirect
227. #2329	C₂×C₅	semidirect
228. #2325	C₂×C₅	semidirect
229. #2321	C₂×C₅	semidirect
230. #2312	C₂×C₅	semidirect
231. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
232. C₄×#121	C₂×C₅	semidirect
233. C₄×#120	C₂×C₅	semidirect
234. #2290	C₂×C₅	semidirect
235. #2275	C₂×C₅	semidirect
236. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
249. C₂×C₅×Q₈	C₂²×C₄	semidirect
261. C₂×C₅×D₄	C₂²×C₄	semidirect
293. C₂²×C₄×C₅	C₂²×C₄	semidirect
322. C₅×C₄⋊C₄	C₂²×C₄	semidirect
323. C₅×C₄⋊C₄	C₂²×C₄	semidirect
324. C₅×C₄⋊C₄	C₂²×C₄	semidirect
325. C₅×C₄⋊C₄	C₂²×C₄	semidirect
345. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
346. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
361. C₄²×C₅	C₂²×C₄	semidirect
363. #538	C₄×C₅	semidirect
371. C₂×C₄×Q₈	C₂²×C₅	semidirect
377. C₂×C₄×D₄	C₂²×C₅	semidirect
378. C₂×#117	C₂²×C₅	semidirect
383. #391	C₂²×C₅	semidirect
384. #391	C₂²×C₅	semidirect
387. #390	C₂²×C₅	semidirect
388. #389	C₂²×C₅	semidirect
389. #389	C₂²×C₅	semidirect
390. #389	C₂²×C₅	semidirect
399. #388	C₂²×C₅	semidirect
400. #388	C₂²×C₅	semidirect
401. #388	C₂²×C₅	semidirect
402. #388	C₂²×C₅	semidirect
403. #387	C₂²×C₅	semidirect
404. #387	C₂²×C₅	semidirect
405. #387	C₂²×C₅	semidirect
406. #387	C₂²×C₅	semidirect
407. #387	C₂²×C₅	semidirect
408. #387	C₂²×C₅	semidirect
415. #386	C₂²×C₅	semidirect
420. #385	C₂²×C₅	semidirect
424. C₄×C₄⋊C₄	C₂²×C₅	semidirect
425. C₄×C₄⋊C₄	C₂²×C₅	semidirect
426. C₄×C₄⋊C₄	C₂²×C₅	semidirect
427. C₄×C₄⋊C₄	C₂²×C₅	semidirect
428. C₄×C₄⋊C₄	C₂²×C₅	semidirect
429. C₄×C₄⋊C₄	C₂²×C₅	semidirect
430. C₄×C₄⋊C₄	C₂²×C₅	semidirect
440. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
441. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
442. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
443. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
444. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
445. #376	C₂²×C₅	semidirect
446. #376	C₂²×C₅	semidirect
449. C₂×#95	C₂²×C₅	semidirect
563. #126	C₂×C₄×C₅	semidirect
564. #124	C₂×C₄×C₅	semidirect
565. #123	C₂×C₄×C₅	semidirect
566. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
567. #121	C₂×C₄×C₅	semidirect
568. #121	C₂×C₄×C₅	semidirect
569. #120	C₂×C₄×C₅	semidirect
576. C₄×D₄	C₂×C₄×C₅	semidirect
593. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
709. C₂×Q₈	C₂²×C₄×C₅	semidirect
721. C₂×D₄	C₂²×C₄×C₅	semidirect
753. C₂²×C₄	C₂²×C₄×C₅	semidirect
782. C₄⋊C₄	C₂²×C₄×C₅	semidirect
783. C₄⋊C₄	C₂²×C₄×C₅	semidirect
784. C₄⋊C₄	C₂²×C₄×C₅	semidirect
785. C₄⋊C₄	C₂²×C₄×C₅	semidirect
805. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
806. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
821. C₄²	C₂²×C₄×C₅	semidirect
925. C₅	#34277	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×#538	2
C₅×#2374	2
C₅×#2373	2
C₅×#2372	2
C₅×#2367	2
C₅×#2364	2
C₅×#2363	2
C₅×#2359	2
C₅×#2329	2
C₅×#2325	2
C₅×#2321	2
C₅×#2312	2
C₄×C₅×C₂²⋊Q₈	2
C₄×C₅×#121	2
C₄×C₅×#120	2
C₅×#2290	2
C₅×#2275	2
C₂×C₄×C₅×C₂²⋊C₄	2
#34277	5

Subgroups — C5×#34277 #11956997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34277 #11956997