Subgroups — C₅×#34326 #11957046

Order 1280.

2128 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#556	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	2	yes	maximal, complemented
3	C₅×#2373	C₂	1	2	yes	maximal, complemented
4	C₅×#2368	C₂	1	2	yes	maximal, complemented
5	C₅×#2367	C₂	1	1	yes	maximal, characteristic
6	C₅×#2367	C₂	1	1	yes	maximal, characteristic
7	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2357	C₂	1	1	yes	maximal, characteristic
9	C₅×#2356	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2355	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2343	C₂	1	2	yes	maximal, complemented
13	C₅×#2334	C₂	1	2	yes	maximal, complemented
14	C₅×#2332	C₂	1	2	yes	maximal, complemented
15	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2326	C₂	1	1	yes	maximal, characteristic
17	C₄×C₅×#126	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
19	C₅×#2298	C₂	1	2	yes	maximal, complemented
20	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#556	C₄	1	16	yes	complemented
25	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×#126	C₂²	1	2	yes	—
27	C₂×C₅×#126	C₂²	1	2	yes	—
28	C₂×C₅×#124	C₂²	1	1	yes	characteristic
29	C₂×C₅×#124	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×#117	C₂²	1	2	yes	—
42	C₅×#391	C₂²	1	1	yes	characteristic
43	C₅×#391	C₂²	1	1	yes	characteristic
44	C₅×#391	C₂²	1	1	yes	characteristic
45	C₅×#391	C₂²	1	1	yes	characteristic
46	C₅×#391	C₂²	1	1	yes	characteristic
47	C₅×#391	C₂²	1	1	yes	characteristic
48	C₅×#391	C₂²	1	2	yes	—
49	C₅×#390	C₂²	1	1	yes	characteristic
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	1	yes	characteristic
53	C₅×#389	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	—
58	C₅×#388	C₂²	1	2	yes	—
59	C₅×#388	C₂²	1	2	yes	—
60	C₅×#388	C₂²	1	2	yes	—
61	C₅×#388	C₂²	1	2	yes	—
62	C₅×#388	C₂²	1	2	yes	—
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#387	C₂²	1	1	yes	characteristic
65	C₅×#387	C₂²	1	1	yes	characteristic
66	C₅×#387	C₂²	1	1	yes	characteristic
67	C₅×#387	C₂²	1	1	yes	characteristic
68	C₅×#387	C₂²	1	2	yes	—
69	C₅×#387	C₂²	1	2	yes	—
70	C₅×#387	C₂²	1	2	yes	—
71	C₅×#387	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	2	yes	—
73	C₅×#387	C₂²	1	2	yes	—
74	C₅×#387	C₂²	1	2	yes	—
75	C₅×#387	C₂²	1	2	yes	—
76	C₅×#387	C₂²	1	2	yes	—
77	C₅×#387	C₂²	1	2	yes	—
78	C₅×#387	C₂²	1	2	yes	—
79	C₅×#387	C₂²	1	2	yes	—
80	C₅×#385	C₂²	1	2	yes	—
81	C₅×#385	C₂²	1	2	yes	—
82	C₅×#385	C₂²	1	2	yes	—
83	C₅×#385	C₂²	1	2	yes	—
84	C₅×#384	C₂²	1	1	yes	characteristic
85	C₅×#383	C₂²	1	2	yes	—
86	C₅×#382	C₂²	1	1	yes	characteristic
87	C₅×#382	C₂²	1	1	yes	characteristic
88	C₅×#382	C₂²	1	2	yes	—
89	C₅×#381	C₂²	1	2	yes	—
90	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
92	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
99	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₅×#376	C₂²	1	1	yes	characteristic
118	C₅×#376	C₂²	1	1	yes	characteristic
119	C₅×#376	C₂²	1	2	yes	—
120	C₅×#376	C₂²	1	2	yes	—
121	C₂×C₅×#95	C₂²	1	2	yes	—
122	C₄³×C₅	C₂²	1	1	yes	characteristic
123	C₄³×C₅	C₂²	1	2	yes	—
124	#34326	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₅	C₂³	1	2	yes	—
130	C₂³×C₄×C₅	C₂³	1	2	yes	—
131	C₂³×C₄×C₅	C₂³	1	2	yes	—
132	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
133	C₅×#126	C₂×C₄	1	16	yes	complemented
134	C₅×#126	C₂×C₄	1	16	yes	complemented
135	C₅×#124	C₂×C₄	1	8	yes	—
136	C₅×#124	C₂×C₄	1	8	yes	—
137	C₅×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
138	C₄×C₅×Q₈	—	2	4	no	—
139	C₄×C₅×Q₈	—	2	4	no	—
140	C₄×C₅×Q₈	—	2	4	no	—
141	C₄×C₅×Q₈	—	2	4	no	—
142	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
143	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
144	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
145	C₄×C₅×D₄	—	2	4	no	—
146	C₄×C₅×D₄	—	2	4	no	—
147	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
148	C₅×#117	C₂×C₄	1	16	yes	complemented
149	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×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×C₄²×C₅	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₅	C₂³	1	2	yes	—
186	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₅	C₂³	1	2	yes	—
188	C₂×C₄²×C₅	C₂³	1	2	yes	—
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₅	C₂³	1	2	yes	—
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	2	yes	—
196	C₂×C₄²×C₅	C₂³	1	2	yes	—
197	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅	C₂³	1	2	yes	—
199	C₂×C₄²×C₅	C₂³	1	2	yes	—
200	C₂×C₄²×C₅	C₂³	1	2	yes	—
201	C₂×C₄²×C₅	C₂³	1	2	yes	—
202	C₂×C₄²×C₅	C₂³	1	2	yes	—
203	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
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	C₅×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
213	C₅×#95	C₂³	1	1	yes	characteristic
214	C₅×#95	C₂³	1	1	yes	characteristic
215	C₅×#95	C₂³	1	1	yes	characteristic
216	C₅×#95	C₂³	1	1	yes	characteristic
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	1	yes	characteristic
220	C₅×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₅×#95	C₂³	1	1	yes	characteristic
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	2	yes	—
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	2	yes	—
232	C₅×#95	C₂³	1	2	yes	—
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
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	C₂×#556	C₂×C₅	1	1	yes	characteristic
242	#2373	C₂×C₅	1	2	yes	complemented
243	#2373	C₂×C₅	1	2	yes	complemented
244	#2368	C₂×C₅	1	2	yes	complemented
245	#2367	C₂×C₅	1	1	yes	characteristic
246	#2367	C₂×C₅	1	1	yes	characteristic
247	#2365	C₂×C₅	1	1	yes	characteristic, complemented
248	#2357	C₂×C₅	1	1	yes	characteristic
249	#2356	C₂×C₅	1	1	yes	characteristic, complemented
250	#2355	C₂×C₅	1	1	yes	characteristic, complemented
251	#2355	C₂×C₅	1	1	yes	characteristic, complemented
252	#2343	C₂×C₅	1	2	yes	complemented
253	#2334	C₂×C₅	1	2	yes	complemented
254	#2332	C₂×C₅	1	2	yes	complemented
255	#2327	C₂×C₅	1	1	yes	characteristic, complemented
256	#2326	C₂×C₅	1	1	yes	characteristic
257	C₄×#126	C₂×C₅	1	2	yes	complemented
258	C₄×#124	C₂×C₅	1	1	yes	characteristic
259	#2298	C₂×C₅	1	2	yes	complemented
260	#2295	C₂×C₅	1	1	yes	characteristic, complemented
261	#2276	C₂×C₅	1	1	yes	characteristic, complemented
262	#2275	C₂×C₅	1	1	yes	characteristic
263	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
264	C₂⁴×C₅	C₂⁴	1	2	yes	—
265	C₂×C₅×Q₈	—	2	2	no	—
266	C₂×C₅×Q₈	—	2	2	no	—
267	C₂×C₅×Q₈	—	2	2	no	—
268	C₂×C₅×Q₈	—	2	2	no	—
269	C₂×C₅×Q₈	—	4	1	no	—
270	C₂×C₅×Q₈	—	4	1	no	—
271	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
272	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
273	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
274	C₂×C₅×D₄	—	2	2	no	—
275	C₂×C₅×D₄	—	2	2	no	—
276	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₅	—	2	4	no	—
278	C₂²×C₄×C₅	—	2	4	no	—
279	C₂²×C₄×C₅	—	4	2	no	—
280	C₂²×C₄×C₅	—	4	2	no	—
281	C₂²×C₄×C₅	—	4	2	no	—
282	C₂²×C₄×C₅	—	4	2	no	—
283	C₂²×C₄×C₅	—	4	2	no	—
284	C₂²×C₄×C₅	—	4	2	no	—
285	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	4	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	4	no	—
313	C₅×C₄⋊C₄	—	2	2	no	—
314	C₅×C₄⋊C₄	—	2	2	no	—
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	2	no	—
317	C₅×C₄⋊C₄	—	4	1	no	—
318	C₅×C₄⋊C₄	—	4	1	no	—
319	C₅×C₄⋊C₄	—	4	1	no	—
320	C₅×C₄⋊C₄	—	4	2	no	—
321	C₅×C₄⋊C₄	—	4	1	no	—
322	C₅×C₄⋊C₄	—	4	2	no	—
323	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
324	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
325	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
326	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
327	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
328	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
330	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
331	C₅×C₄⋊C₄	#41	1	4	yes	—
332	C₅×C₂²⋊C₄	—	2	4	no	—
333	C₅×C₂²⋊C₄	—	2	4	no	—
334	C₅×C₂²⋊C₄	—	2	4	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	C₂²×C₄	1	8	yes	—
339	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
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	C₄²×C₅	—	2	2	no	—
344	C₄²×C₅	—	2	4	no	—
345	C₄²×C₅	—	2	2	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	2	4	no	—
348	C₄²×C₅	—	2	4	no	—
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	4	2	no	—
352	C₄²×C₅	—	4	2	no	—
353	C₄²×C₅	—	4	2	no	—
354	C₄²×C₅	—	4	1	no	—
355	C₄²×C₅	—	4	1	no	—
356	C₄²×C₅	—	4	1	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	—
362	C₄²×C₅	C₂²×C₄	1	8	yes	—
363	C₄²×C₅	C₂²×C₄	1	4	yes	—
364	C₄²×C₅	C₂²×C₄	1	4	yes	—
365	C₄²×C₅	C₂²×C₄	1	4	yes	—
366	C₄²×C₅	#41	1	4	yes	—
367	#556	C₄×C₅	1	16	yes	complemented
368	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
369	C₂×#126	C₂²×C₅	1	2	yes	—
370	C₂×#126	C₂²×C₅	1	2	yes	—
371	C₂×#124	C₂²×C₅	1	1	yes	characteristic
372	C₂×#124	C₂²×C₅	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
374	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
375	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
379	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
380	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
382	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
383	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
384	C₂×#117	C₂²×C₅	1	2	yes	—
385	#391	C₂²×C₅	1	1	yes	characteristic
386	#391	C₂²×C₅	1	1	yes	characteristic
387	#391	C₂²×C₅	1	1	yes	characteristic
388	#391	C₂²×C₅	1	1	yes	characteristic
389	#391	C₂²×C₅	1	2	yes	—
390	#391	C₂²×C₅	1	1	yes	characteristic
391	#391	C₂²×C₅	1	1	yes	characteristic
392	#390	C₂²×C₅	1	1	yes	characteristic
393	#390	C₂²×C₅	1	1	yes	characteristic
394	#389	C₂²×C₅	1	1	yes	characteristic
395	#389	C₂²×C₅	1	2	yes	—
396	#389	C₂²×C₅	1	1	yes	characteristic
397	#388	C₂²×C₅	1	2	yes	—
398	#388	C₂²×C₅	1	2	yes	—
399	#388	C₂²×C₅	1	2	yes	—
400	#388	C₂²×C₅	1	2	yes	—
401	#388	C₂²×C₅	1	2	yes	—
402	#388	C₂²×C₅	1	2	yes	—
403	#388	C₂²×C₅	1	2	yes	—
404	#388	C₂²×C₅	1	2	yes	—
405	#388	C₂²×C₅	1	2	yes	—
406	#388	C₂²×C₅	1	2	yes	—
407	#387	C₂²×C₅	1	1	yes	characteristic
408	#387	C₂²×C₅	1	2	yes	—
409	#387	C₂²×C₅	1	2	yes	—
410	#387	C₂²×C₅	1	2	yes	—
411	#387	C₂²×C₅	1	2	yes	—
412	#387	C₂²×C₅	1	2	yes	—
413	#387	C₂²×C₅	1	2	yes	—
414	#387	C₂²×C₅	1	2	yes	—
415	#387	C₂²×C₅	1	2	yes	—
416	#387	C₂²×C₅	1	2	yes	—
417	#387	C₂²×C₅	1	2	yes	—
418	#387	C₂²×C₅	1	1	yes	characteristic
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	2	yes	—
421	#387	C₂²×C₅	1	1	yes	characteristic
422	#387	C₂²×C₅	1	1	yes	characteristic
423	#385	C₂²×C₅	1	2	yes	—
424	#385	C₂²×C₅	1	2	yes	—
425	#385	C₂²×C₅	1	2	yes	—
426	#385	C₂²×C₅	1	2	yes	—
427	#384	C₂²×C₅	1	1	yes	characteristic
428	#383	C₂²×C₅	1	2	yes	—
429	#382	C₂²×C₅	1	1	yes	characteristic
430	#382	C₂²×C₅	1	2	yes	—
431	#382	C₂²×C₅	1	1	yes	characteristic
432	#381	C₂²×C₅	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
460	#376	C₂²×C₅	1	1	yes	characteristic
461	#376	C₂²×C₅	1	1	yes	characteristic
462	#376	C₂²×C₅	1	2	yes	—
463	#376	C₂²×C₅	1	2	yes	—
464	C₂×#95	C₂²×C₅	1	2	yes	—
465	C₄³	C₂²×C₅	1	2	yes	—
466	C₄³	C₂²×C₅	1	1	yes	characteristic
467	C₂³×C₅	—	2	2	no	—
468	C₂³×C₅	—	2	2	no	—
469	C₂³×C₅	—	2	2	no	—
470	C₂³×C₅	—	2	2	no	—
471	C₂³×C₅	—	2	2	no	—
472	C₂³×C₅	—	2	2	no	—
473	C₂³×C₅	C₂³×C₄	1	4	yes	—
474	C₂³×C₅	C₂⁵	1	1	yes	characteristic
475	C₅×Q₈	—	2	8	no	—
476	C₅×Q₈	—	2	8	no	—
477	C₅×Q₈	—	4	4	no	—
478	C₅×D₄	—	2	8	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	2	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	2	no	—
483	C₂×C₄×C₅	—	2	2	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	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	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	2	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	2	2	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	1	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	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	2	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	2	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	2	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	4	8	no	—
530	C₂×C₄×C₅	—	8	4	no	—
531	C₂×C₄×C₅	—	8	4	no	—
532	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
533	C₂×C₄×C₅	C₂³×C₄	1	2	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	4	yes	—
537	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
538	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
539	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
540	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
541	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
542	C₂×C₄×C₅	C₂×#41	1	2	yes	—
543	C₂×C₄×C₅	C₂×#41	1	2	yes	—
544	C₂×C₄×C₅	C₂×#41	1	4	yes	—
545	C₂×C₄×C₅	C₂×#41	1	2	yes	—
546	C₂×C₄×C₅	C₂×#41	1	2	yes	—
547	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
548	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
551	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₅	1	2	yes	—
553	C₂³×C₄	C₂³×C₅	1	2	yes	—
554	C₂³×C₄	C₂³×C₅	1	2	yes	—
555	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
556	#126	C₂×C₄×C₅	1	16	yes	complemented
557	#126	C₂×C₄×C₅	1	16	yes	complemented
558	#124	C₂×C₄×C₅	1	8	yes	—
559	#124	C₂×C₄×C₅	1	8	yes	—
560	C₂²⋊Q₈	C₂×C₄×C₅	1	16	yes	complemented
561	C₄×Q₈	—	2	4	no	—
562	C₄×Q₈	—	2	4	no	—
563	C₄×Q₈	—	2	4	no	—
564	C₄×Q₈	—	2	4	no	—
565	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
566	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
567	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	4	no	—
570	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
571	#117	C₂×C₄×C₅	1	16	yes	complemented
572	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
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	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₄²	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₅	1	2	yes	—
609	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₅	1	2	yes	—
611	C₂×C₄²	C₂³×C₅	1	2	yes	—
612	C₂×C₄²	C₂³×C₅	1	2	yes	—
613	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₅	1	2	yes	—
616	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
629	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
631	#95	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
636	#95	C₂³×C₅	1	1	yes	characteristic
637	#95	C₂³×C₅	1	1	yes	characteristic
638	#95	C₂³×C₅	1	1	yes	characteristic
639	#95	C₂³×C₅	1	1	yes	characteristic
640	#95	C₂³×C₅	1	2	yes	—
641	#95	C₂³×C₅	1	2	yes	—
642	#95	C₂³×C₅	1	1	yes	characteristic
643	#95	C₂³×C₅	1	2	yes	—
644	#95	C₂³×C₅	1	1	yes	characteristic
645	#95	C₂³×C₅	1	1	yes	characteristic
646	#95	C₂³×C₅	1	2	yes	—
647	#95	C₂³×C₅	1	2	yes	—
648	#95	C₂³×C₅	1	1	yes	characteristic
649	#95	C₂³×C₅	1	1	yes	characteristic
650	#95	C₂³×C₅	1	1	yes	characteristic
651	#95	C₂³×C₅	1	2	yes	—
652	#95	C₂³×C₅	1	2	yes	—
653	#95	C₂³×C₅	1	2	yes	—
654	#95	C₂³×C₅	1	2	yes	—
655	#95	C₂³×C₅	1	2	yes	—
656	#95	C₂³×C₅	1	2	yes	—
657	#95	C₂³×C₅	1	2	yes	—
658	#95	C₂³×C₅	1	2	yes	—
659	#95	C₂³×C₅	1	1	yes	characteristic
660	#95	C₂³×C₅	1	2	yes	—
661	#95	C₂³×C₅	1	2	yes	—
662	#95	C₂³×C₅	1	1	yes	characteristic
663	#95	C₂³×C₅	1	2	yes	—
664	C₂²×C₅	—	2	4	no	—
665	C₂²×C₅	—	2	4	no	—
666	C₂²×C₅	—	2	4	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	C₂⁴×C₄	1	1	yes	characteristic
672	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
673	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
674	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
675	C₂²×C₅	#585	1	1	yes	characteristic
676	C₂²×C₅	#585	1	1	yes	characteristic
677	C₂²×C₅	#585	1	1	yes	characteristic
678	C₄×C₅	—	2	4	no	—
679	C₄×C₅	—	2	4	no	—
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	2	4	no	—
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	2	2	no	—
684	C₄×C₅	—	2	2	no	—
685	C₄×C₅	—	2	2	no	—
686	C₄×C₅	—	2	2	no	—
687	C₄×C₅	—	2	2	no	—
688	C₄×C₅	—	2	2	no	—
689	C₄×C₅	—	2	2	no	—
690	C₄×C₅	—	2	4	no	—
691	C₄×C₅	—	4	2	no	—
692	C₄×C₅	—	4	2	no	—
693	C₄×C₅	—	4	2	no	—
694	C₄×C₅	—	4	1	no	—
695	C₄×C₅	—	4	1	no	—
696	C₄×C₅	—	4	1	no	—
697	C₄×C₅	—	4	1	no	—
698	C₄×C₅	—	4	1	no	—
699	C₄×C₅	C₄×#41	1	4	yes	—
700	C₂⁴	C₂⁴×C₅	1	2	yes	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	4	1	no	—
706	C₂×Q₈	—	4	1	no	—
707	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
708	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
709	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
722	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	1	no	—
755	C₄⋊C₄	—	4	1	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	1	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
760	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
761	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
762	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
763	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
764	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
765	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
766	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
767	C₄⋊C₄	C₅×#41	1	4	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
775	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
776	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
777	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
778	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	1	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	C₂²×C₄×C₅	1	8	yes	—
798	C₄²	C₂²×C₄×C₅	1	8	yes	—
799	C₄²	C₂²×C₄×C₅	1	4	yes	—
800	C₄²	C₂²×C₄×C₅	1	4	yes	—
801	C₄²	C₂²×C₄×C₅	1	4	yes	—
802	C₄²	C₅×#41	1	4	yes	—
803	C₂×C₅	—	4	4	no	—
804	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
805	C₂×C₅	#3428	1	1	yes	characteristic
806	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
807	C₂×C₅	#3507	1	1	yes	characteristic
808	C₂×C₅	#3510	1	1	yes	characteristic
809	C₂×C₅	#3516	1	1	yes	characteristic
810	C₂×C₅	#3521	1	1	yes	characteristic
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	C₂³×C₄×C₅	1	4	yes	—
818	C₂³	C₂⁵×C₅	1	1	yes	characteristic
819	Q₈	—	2	8	no	—
820	Q₈	—	2	8	no	—
821	Q₈	—	4	4	no	—
822	D₄	—	2	8	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	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	1	no	—
873	C₂×C₄	—	4	8	no	—
874	C₂×C₄	—	8	4	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
877	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
878	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
879	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
880	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
881	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
882	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
883	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
884	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
885	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
886	C₂×C₄	C₂×C₅×#41	1	2	yes	—
887	C₂×C₄	C₂×C₅×#41	1	2	yes	—
888	C₂×C₄	C₂×C₅×#41	1	4	yes	—
889	C₂×C₄	C₂×C₅×#41	1	2	yes	—
890	C₂×C₄	C₂×C₅×#41	1	2	yes	—
891	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
892	C₅	#34326	1	1	yes	characteristic, direct product factor, Sylow
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
901	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
902	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
903	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
904	C₂²	C₅×#585	1	1	yes	characteristic
905	C₂²	C₅×#585	1	1	yes	characteristic
906	C₂²	C₅×#585	1	1	yes	characteristic
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	C₄×C₅×#41	1	4	yes	—
929	C₂	—	4	4	no	—
930	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
931	C₂	C₅×#3428	1	1	yes	characteristic
932	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
933	C₂	C₅×#3507	1	1	yes	characteristic
934	C₂	C₅×#3510	1	1	yes	characteristic
935	C₂	C₅×#3516	1	1	yes	characteristic
936	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	C₂²×C₅×D₄	C₂³
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×#2373	C₂	semidirect
3. C₅×#2373	C₂	semidirect
4. C₅×#2368	C₂	semidirect
7. C₅×#2365	C₂	semidirect
9. C₅×#2356	C₂	semidirect
10. C₅×#2355	C₂	semidirect
11. C₅×#2355	C₂	semidirect
12. C₅×#2343	C₂	semidirect
13. C₅×#2334	C₂	semidirect
14. C₅×#2332	C₂	semidirect
15. C₅×#2327	C₂	semidirect
17. C₄×C₅×#126	C₂	semidirect
19. C₅×#2298	C₂	semidirect
20. C₅×#2295	C₂	semidirect
21. C₅×#2276	C₂	semidirect
23. C₄²×C₅×Q₈	C₂	semidirect
24. C₅×#556	C₄	semidirect
124. #34326	C₅	direct (N × H)
132. C₅×C₄⋊Q₈	C₂×C₄	semidirect
133. C₅×#126	C₂×C₄	semidirect
134. C₅×#126	C₂×C₄	semidirect
137. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
143. C₄×C₅×Q₈	C₂×C₄	semidirect
144. C₄×C₅×Q₈	C₂×C₄	semidirect
148. C₅×#117	C₂×C₄	semidirect
242. #2373	C₂×C₅	semidirect
243. #2373	C₂×C₅	semidirect
244. #2368	C₂×C₅	semidirect
247. #2365	C₂×C₅	semidirect
249. #2356	C₂×C₅	semidirect
250. #2355	C₂×C₅	semidirect
251. #2355	C₂×C₅	semidirect
252. #2343	C₂×C₅	semidirect
253. #2334	C₂×C₅	semidirect
254. #2332	C₂×C₅	semidirect
255. #2327	C₂×C₅	semidirect
257. C₄×#126	C₂×C₅	semidirect
259. #2298	C₂×C₅	semidirect
260. #2295	C₂×C₅	semidirect
261. #2276	C₂×C₅	semidirect
263. C₄²×Q₈	C₂×C₅	semidirect
367. #556	C₄×C₅	semidirect
555. C₄⋊Q₈	C₂×C₄×C₅	semidirect
556. #126	C₂×C₄×C₅	semidirect
557. #126	C₂×C₄×C₅	semidirect
560. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
565. C₄×Q₈	C₂×C₄×C₅	semidirect
566. C₄×Q₈	C₂×C₄×C₅	semidirect
567. C₄×Q₈	C₂×C₄×C₅	semidirect
571. #117	C₂×C₄×C₅	semidirect
892. C₅	#34326	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×#556	2
C₅×#2373	2
C₅×#2368	2
C₅×#2367	2
C₅×#2365	2
C₅×#2357	2
C₅×#2356	2
C₅×#2355	2
C₅×#2343	2
C₅×#2334	2
C₅×#2332	2
C₅×#2327	2
C₅×#2326	2
C₄×C₅×#126	2
C₄×C₅×#124	2
C₅×#2298	2
C₅×#2295	2
C₅×#2276	2
C₅×#2275	2
C₄²×C₅×Q₈	2
#34326	5

Subgroups — C5×#34326 #11957046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34326 #11957046