Subgroups — C₅×#34286 #11957006

Order 1280.

2062 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#541	C₂	1	1	yes	maximal, characteristic
2	C₅×#2373	C₂	1	2	yes	maximal
3	C₅×#2373	C₂	1	2	yes	maximal
4	C₅×#2371	C₂	1	2	yes	maximal, complemented
5	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2370	C₂	1	2	yes	maximal, complemented
8	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2362	C₂	1	1	yes	maximal, characteristic
11	C₅×#2362	C₂	1	1	yes	maximal, characteristic
12	C₅×#2360	C₂	1	1	yes	maximal, characteristic
13	C₅×#2360	C₂	1	1	yes	maximal, characteristic
14	C₅×#2336	C₂	1	2	yes	maximal, complemented
15	C₅×#2334	C₂	1	2	yes	maximal
16	C₅×#2320	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#125	C₂	1	2	yes	maximal, complemented
18	C₄×C₅×#126	C₂	1	2	yes	maximal
19	C₅×#2298	C₂	1	1	yes	maximal, characteristic
20	C₅×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×#2276	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2274	C₂	1	1	yes	maximal, characteristic
23	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#541	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×#125	C₂²	1	2	yes	—
29	C₂×C₅×#125	C₂²	1	1	yes	characteristic
30	C₂×C₅×#125	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₂²⋊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×Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₅×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×#389	C₂²	1	1	yes	characteristic
47	C₅×#389	C₂²	1	1	yes	characteristic
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#389	C₂²	1	1	yes	characteristic
51	C₅×#389	C₂²	1	1	yes	characteristic
52	C₅×#389	C₂²	1	2	yes	—
53	C₅×#389	C₂²	1	2	yes	—
54	C₅×#389	C₂²	1	2	yes	—
55	C₅×#389	C₂²	1	2	yes	—
56	C₅×#388	C₂²	1	1	yes	characteristic
57	C₅×#388	C₂²	1	1	yes	characteristic
58	C₅×#388	C₂²	1	1	yes	characteristic
59	C₅×#388	C₂²	1	1	yes	characteristic
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	2	yes	—
65	C₅×#387	C₂²	1	2	yes	—
66	C₅×#387	C₂²	1	1	yes	characteristic
67	C₅×#387	C₂²	1	1	yes	characteristic
68	C₅×#387	C₂²	1	1	yes	characteristic
69	C₅×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
81	C₅×#387	C₂²	1	2	yes	—
82	C₅×#387	C₂²	1	2	yes	—
83	C₅×#387	C₂²	1	2	yes	—
84	C₅×#385	C₂²	1	2	yes	—
85	C₅×#385	C₂²	1	2	yes	—
86	C₅×#383	C₂²	1	2	yes	—
87	C₅×#382	C₂²	1	2	yes	—
88	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
89	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
90	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
91	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
101	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
105	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
110	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
111	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
112	C₄×C₅×C₄⋊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	1	yes	characteristic
116	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₅×#376	C₂²	1	1	yes	characteristic
120	C₅×#376	C₂²	1	2	yes	—
121	C₅×#376	C₂²	1	2	yes	—
122	C₄³×C₅	C₂²	1	1	yes	characteristic
123	C₄³×C₅	C₂²	1	2	yes	—
124	#34286	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	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₅	C₂³	1	2	yes	—
129	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
130	C₅×#126	C₂×C₄	1	16	yes	—
131	C₅×#126	C₂×C₄	1	16	yes	—
132	C₅×#125	C₂×C₄	1	8	yes	complemented
133	C₅×#125	C₂×C₄	1	16	yes	complemented
134	C₅×#125	C₂×C₄	1	16	yes	complemented
135	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
136	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
137	C₄×C₅×Q₈	—	2	4	no	—
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	C₂×C₄	1	8	yes	complemented
142	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
143	C₅×#117	—	2	4	no	—
144	C₅×#117	C₂×C₄	1	8	yes	—
145	C₂×C₅×C₄⋊C₄	—	2	4	no	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
150	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₅×C₄⋊C₄	C₂³	1	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	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	C₂×C₄²×C₅	C₂³	1	2	yes	—
187	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₅	C₂³	1	2	yes	—
190	C₂×C₄²×C₅	C₂³	1	2	yes	—
191	C₂×C₄²×C₅	C₂³	1	2	yes	—
192	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
204	C₂×C₄²×C₅	C₂³	1	2	yes	—
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₅×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
215	C₅×#95	C₂³	1	1	yes	characteristic
216	C₅×#95	C₂³	1	2	yes	—
217	C₅×#95	C₂³	1	2	yes	—
218	C₅×#95	C₂³	1	2	yes	—
219	C₅×#95	C₂³	1	2	yes	—
220	C₅×#95	C₂³	1	2	yes	—
221	C₅×#95	C₂³	1	1	yes	characteristic
222	C₅×#95	C₂³	1	2	yes	—
223	C₅×#95	C₂³	1	2	yes	—
224	C₅×#95	C₂³	1	1	yes	characteristic
225	C₅×#95	C₂³	1	2	yes	—
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	2	yes	—
228	C₅×#95	C₂³	1	1	yes	characteristic
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	2	yes	—
231	C₅×#95	C₂³	1	1	yes	characteristic
232	C₅×#95	C₂³	1	1	yes	characteristic
233	C₅×#95	C₂³	1	2	yes	—
234	C₅×#95	C₂³	1	2	yes	—
235	C₅×#95	C₂³	1	2	yes	—
236	C₅×#95	C₂³	1	2	yes	—
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	1	yes	characteristic
239	C₅×#95	C₂³	1	1	yes	characteristic
240	C₅×#95	C₂³	1	2	yes	—
241	C₂×#541	C₂×C₅	1	1	yes	characteristic
242	#2373	C₂×C₅	1	2	yes	—
243	#2373	C₂×C₅	1	2	yes	—
244	#2371	C₂×C₅	1	2	yes	complemented
245	#2370	C₂×C₅	1	1	yes	characteristic, complemented
246	#2370	C₂×C₅	1	1	yes	characteristic, complemented
247	#2370	C₂×C₅	1	2	yes	complemented
248	#2365	C₂×C₅	1	1	yes	characteristic, complemented
249	#2365	C₂×C₅	1	1	yes	characteristic, complemented
250	#2362	C₂×C₅	1	1	yes	characteristic
251	#2362	C₂×C₅	1	1	yes	characteristic
252	#2360	C₂×C₅	1	1	yes	characteristic
253	#2360	C₂×C₅	1	1	yes	characteristic
254	#2336	C₂×C₅	1	2	yes	complemented
255	#2334	C₂×C₅	1	2	yes	—
256	#2320	C₂×C₅	1	1	yes	characteristic, complemented
257	C₄×#125	C₂×C₅	1	2	yes	complemented
258	C₄×#126	C₂×C₅	1	2	yes	—
259	#2298	C₂×C₅	1	1	yes	characteristic
260	#2295	C₂×C₅	1	1	yes	characteristic, complemented
261	#2276	C₂×C₅	1	1	yes	characteristic, complemented
262	#2274	C₂×C₅	1	1	yes	characteristic
263	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
264	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄	1	4	yes	—
270	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₅	—	2	2	no	—
272	C₂²×C₄×C₅	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	4	no	—
274	C₂²×C₄×C₅	—	4	2	no	—
275	C₂²×C₄×C₅	—	4	2	no	—
276	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
299	C₅×C₄⋊C₄	—	2	4	no	—
300	C₅×C₄⋊C₄	—	2	2	no	—
301	C₅×C₄⋊C₄	—	2	2	no	—
302	C₅×C₄⋊C₄	—	2	4	no	—
303	C₅×C₄⋊C₄	—	2	4	no	—
304	C₅×C₄⋊C₄	—	2	4	no	—
305	C₅×C₄⋊C₄	—	2	4	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	4	no	—
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	4	1	no	—
310	C₅×C₄⋊C₄	—	4	1	no	—
311	C₅×C₄⋊C₄	—	4	2	no	—
312	C₅×C₄⋊C₄	—	4	2	no	—
313	C₅×C₄⋊C₄	—	4	2	no	—
314	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
315	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
316	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
317	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
318	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
319	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
320	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
321	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
322	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
323	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
324	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
325	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
326	C₅×C₄⋊C₄	#41	1	4	yes	—
327	C₅×C₄⋊C₄	#41	1	4	yes	—
328	C₅×C₂²⋊C₄	—	2	4	no	—
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	2	2	no	—
331	C₅×C₂²⋊C₄	—	4	1	no	—
332	C₅×C₂²⋊C₄	—	4	1	no	—
333	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
334	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
335	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
336	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
337	C₄²×C₅	—	2	4	no	—
338	C₄²×C₅	—	2	4	no	—
339	C₄²×C₅	—	2	4	no	—
340	C₄²×C₅	—	2	2	no	—
341	C₄²×C₅	—	2	2	no	—
342	C₄²×C₅	—	2	4	no	—
343	C₄²×C₅	—	2	4	no	—
344	C₄²×C₅	—	2	2	no	—
345	C₄²×C₅	—	2	2	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	2	2	no	—
348	C₄²×C₅	—	2	2	no	—
349	C₄²×C₅	—	4	2	no	—
350	C₄²×C₅	—	4	1	no	—
351	C₄²×C₅	—	4	2	no	—
352	C₄²×C₅	—	4	2	no	—
353	C₄²×C₅	—	4	2	no	—
354	C₄²×C₅	—	4	2	no	—
355	C₄²×C₅	—	4	1	no	—
356	C₄²×C₅	—	4	2	no	—
357	C₄²×C₅	—	4	2	no	—
358	C₄²×C₅	C₂²×C₄	1	4	yes	—
359	C₄²×C₅	C₂²×C₄	1	4	yes	—
360	C₄²×C₅	C₂²×C₄	1	8	yes	—
361	C₄²×C₅	C₂²×C₄	1	8	yes	—
362	#541	C₄×C₅	1	16	yes	complemented
363	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
364	C₂×#126	C₂²×C₅	1	2	yes	—
365	C₂×#126	C₂²×C₅	1	2	yes	—
366	C₂×#125	C₂²×C₅	1	2	yes	—
367	C₂×#125	C₂²×C₅	1	1	yes	characteristic
368	C₂×#125	C₂²×C₅	1	2	yes	—
369	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
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×#117	C₂²×C₅	1	1	yes	characteristic
378	C₂×#117	C₂²×C₅	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
380	#391	C₂²×C₅	1	1	yes	characteristic
381	#391	C₂²×C₅	1	1	yes	characteristic
382	#391	C₂²×C₅	1	1	yes	characteristic
383	#391	C₂²×C₅	1	1	yes	characteristic
384	#389	C₂²×C₅	1	2	yes	—
385	#389	C₂²×C₅	1	2	yes	—
386	#389	C₂²×C₅	1	1	yes	characteristic
387	#389	C₂²×C₅	1	1	yes	characteristic
388	#389	C₂²×C₅	1	2	yes	—
389	#389	C₂²×C₅	1	2	yes	—
390	#389	C₂²×C₅	1	2	yes	—
391	#389	C₂²×C₅	1	2	yes	—
392	#389	C₂²×C₅	1	1	yes	characteristic
393	#389	C₂²×C₅	1	1	yes	characteristic
394	#388	C₂²×C₅	1	1	yes	characteristic
395	#388	C₂²×C₅	1	2	yes	—
396	#388	C₂²×C₅	1	2	yes	—
397	#388	C₂²×C₅	1	1	yes	characteristic
398	#388	C₂²×C₅	1	2	yes	—
399	#388	C₂²×C₅	1	2	yes	—
400	#388	C₂²×C₅	1	1	yes	characteristic
401	#388	C₂²×C₅	1	1	yes	characteristic
402	#387	C₂²×C₅	1	2	yes	—
403	#387	C₂²×C₅	1	2	yes	—
404	#387	C₂²×C₅	1	2	yes	—
405	#387	C₂²×C₅	1	1	yes	characteristic
406	#387	C₂²×C₅	1	2	yes	—
407	#387	C₂²×C₅	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
419	#387	C₂²×C₅	1	2	yes	—
420	#387	C₂²×C₅	1	1	yes	characteristic
421	#387	C₂²×C₅	1	1	yes	characteristic
422	#385	C₂²×C₅	1	2	yes	—
423	#385	C₂²×C₅	1	2	yes	—
424	#383	C₂²×C₅	1	2	yes	—
425	#382	C₂²×C₅	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
427	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
432	C₄×C₄⋊C₄	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	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
437	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
447	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
449	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
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	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
457	#376	C₂²×C₅	1	1	yes	characteristic
458	#376	C₂²×C₅	1	2	yes	—
459	#376	C₂²×C₅	1	2	yes	—
460	C₄³	C₂²×C₅	1	2	yes	—
461	C₄³	C₂²×C₅	1	1	yes	characteristic
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	—	2	1	no	—
465	C₂³×C₅	—	2	1	no	—
466	C₂³×C₅	—	2	1	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	C₂³×C₄	1	2	yes	—
469	C₂³×C₅	C₂⁵	1	1	yes	characteristic
470	C₅×Q₈	—	2	8	no	—
471	C₅×Q₈	—	2	8	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	2	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	2	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	1	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	2	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	2	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	2	2	no	—
498	C₂×C₄×C₅	—	2	8	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	2	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	2	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	2	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	2	no	—
520	C₂×C₄×C₅	—	2	2	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	8	4	no	—
524	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
529	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
530	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
531	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
532	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
533	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
534	C₂×C₄×C₅	C₂×#41	1	4	yes	—
535	C₂×C₄×C₅	C₂×#41	1	4	yes	—
536	C₂×C₄×C₅	C₂×#41	1	2	yes	—
537	C₂×C₄×C₅	C₂×#41	1	2	yes	—
538	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
540	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₅	1	2	yes	—
544	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
545	#126	C₂×C₄×C₅	1	16	yes	—
546	#126	C₂×C₄×C₅	1	16	yes	—
547	#125	C₂×C₄×C₅	1	8	yes	complemented
548	#125	C₂×C₄×C₅	1	16	yes	complemented
549	#125	C₂×C₄×C₅	1	16	yes	complemented
550	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
551	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
552	C₄×Q₈	—	2	4	no	—
553	C₄×Q₈	—	2	4	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×Q₈	—	2	4	no	—
556	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
557	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
558	#117	—	2	4	no	—
559	#117	C₂×C₄×C₅	1	8	yes	—
560	C₂×C₄⋊C₄	—	2	4	no	—
561	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
590	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
594	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
599	C₂×C₄²	C₂³×C₅	1	2	yes	—
600	C₂×C₄²	C₂³×C₅	1	2	yes	—
601	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₅	1	2	yes	—
604	C₂×C₄²	C₂³×C₅	1	2	yes	—
605	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₅	1	2	yes	—
608	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	#95	C₂³×C₅	1	1	yes	characteristic
625	#95	C₂³×C₅	1	2	yes	—
626	#95	C₂³×C₅	1	2	yes	—
627	#95	C₂³×C₅	1	1	yes	characteristic
628	#95	C₂³×C₅	1	1	yes	characteristic
629	#95	C₂³×C₅	1	2	yes	—
630	#95	C₂³×C₅	1	2	yes	—
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	2	yes	—
636	#95	C₂³×C₅	1	1	yes	characteristic
637	#95	C₂³×C₅	1	2	yes	—
638	#95	C₂³×C₅	1	2	yes	—
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	2	yes	—
643	#95	C₂³×C₅	1	1	yes	characteristic
644	#95	C₂³×C₅	1	1	yes	characteristic
645	#95	C₂³×C₅	1	2	yes	—
646	#95	C₂³×C₅	1	1	yes	characteristic
647	#95	C₂³×C₅	1	1	yes	characteristic
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	#95	C₂³×C₅	1	2	yes	—
653	#95	C₂³×C₅	1	1	yes	characteristic
654	#95	C₂³×C₅	1	1	yes	characteristic
655	#95	C₂³×C₅	1	2	yes	—
656	C₂²×C₅	—	2	2	no	—
657	C₂²×C₅	—	2	2	no	—
658	C₂²×C₅	—	2	2	no	—
659	C₂²×C₅	—	4	1	no	—
660	C₂²×C₅	—	4	1	no	—
661	C₂²×C₅	—	4	1	no	—
662	C₂²×C₅	—	4	1	no	—
663	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
664	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
665	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
666	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
667	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
668	C₂²×C₅	#585	1	1	yes	characteristic
669	C₂²×C₅	#585	1	1	yes	characteristic
670	C₄×C₅	—	2	2	no	—
671	C₄×C₅	—	2	4	no	—
672	C₄×C₅	—	2	4	no	—
673	C₄×C₅	—	2	2	no	—
674	C₄×C₅	—	2	2	no	—
675	C₄×C₅	—	2	4	no	—
676	C₄×C₅	—	2	2	no	—
677	C₄×C₅	—	2	2	no	—
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	—	4	1	no	—
684	C₄×C₅	—	4	1	no	—
685	C₄×C₅	—	4	1	no	—
686	C₄×C₅	—	4	2	no	—
687	C₄×C₅	—	4	1	no	—
688	C₄×C₅	—	4	1	no	—
689	C₄×C₅	—	4	2	no	—
690	C₄×C₅	—	4	1	no	—
691	C₄×C₅	C₄×#41	1	4	yes	—
692	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
693	C₂×Q₈	—	2	2	no	—
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	2	no	—
697	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
698	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
714	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
743	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
744	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
745	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
746	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
747	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
748	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
749	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
750	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
751	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
752	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
753	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
754	C₄⋊C₄	C₅×#41	1	4	yes	—
755	C₄⋊C₄	C₅×#41	1	4	yes	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	4	1	no	—
760	C₂²⋊C₄	—	4	1	no	—
761	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
762	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
763	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
764	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	4	no	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	4	2	no	—
778	C₄²	—	4	1	no	—
779	C₄²	—	4	2	no	—
780	C₄²	—	4	2	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	1	no	—
784	C₄²	—	4	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	C₂²×C₄×C₅	1	4	yes	—
787	C₄²	C₂²×C₄×C₅	1	4	yes	—
788	C₄²	C₂²×C₄×C₅	1	8	yes	—
789	C₄²	C₂²×C₄×C₅	1	8	yes	—
790	C₂×C₅	—	4	2	no	—
791	C₂×C₅	C₂×C₄×#41	1	1	yes	characteristic
792	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
794	C₂×C₅	#3515	1	1	yes	characteristic
795	C₂×C₅	#3516	1	1	yes	characteristic
796	C₂×C₅	#3521	1	1	yes	characteristic
797	C₂×C₅	#3523	1	1	yes	characteristic
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	C₂³×C₄×C₅	1	2	yes	—
805	C₂³	C₂⁵×C₅	1	1	yes	characteristic
806	Q₈	—	2	8	no	—
807	Q₈	—	2	8	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	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	2	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	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
861	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
862	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
863	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
864	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
865	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
866	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
867	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
868	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
869	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
870	C₂×C₄	C₂×C₅×#41	1	4	yes	—
871	C₂×C₄	C₂×C₅×#41	1	4	yes	—
872	C₂×C₄	C₂×C₅×#41	1	2	yes	—
873	C₂×C₄	C₂×C₅×#41	1	2	yes	—
874	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
875	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
876	C₅	#34286	1	1	yes	characteristic, direct product factor, Sylow
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
885	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
886	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
887	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
888	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
889	C₂²	C₅×#585	1	1	yes	characteristic
890	C₂²	C₅×#585	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	1	no	—
912	C₄	C₄×C₅×#41	1	4	yes	—
913	C₂	—	4	2	no	—
914	C₂	C₂×C₄×C₅×#41	1	1	yes	characteristic
915	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
917	C₂	C₅×#3515	1	1	yes	characteristic
918	C₂	C₅×#3516	1	1	yes	characteristic
919	C₂	C₅×#3521	1	1	yes	characteristic
920	C₂	C₅×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂⁴
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
4. C₅×#2371	C₂	semidirect
5. C₅×#2370	C₂	semidirect
6. C₅×#2370	C₂	semidirect
7. C₅×#2370	C₂	semidirect
8. C₅×#2365	C₂	semidirect
9. C₅×#2365	C₂	semidirect
14. C₅×#2336	C₂	semidirect
16. C₅×#2320	C₂	semidirect
17. C₄×C₅×#125	C₂	semidirect
20. C₅×#2295	C₂	semidirect
21. C₅×#2276	C₂	semidirect
23. C₄²×C₅×Q₈	C₂	semidirect
24. C₅×#541	C₄	semidirect
124. #34286	C₅	direct (N × H)
129. C₅×C₄⋊Q₈	C₂×C₄	semidirect
132. C₅×#125	C₂×C₄	semidirect
133. C₅×#125	C₂×C₄	semidirect
134. C₅×#125	C₂×C₄	semidirect
141. C₄×C₅×Q₈	C₂×C₄	semidirect
142. C₄×C₅×Q₈	C₂×C₄	semidirect
244. #2371	C₂×C₅	semidirect
245. #2370	C₂×C₅	semidirect
246. #2370	C₂×C₅	semidirect
247. #2370	C₂×C₅	semidirect
248. #2365	C₂×C₅	semidirect
249. #2365	C₂×C₅	semidirect
254. #2336	C₂×C₅	semidirect
256. #2320	C₂×C₅	semidirect
257. C₄×#125	C₂×C₅	semidirect
260. #2295	C₂×C₅	semidirect
261. #2276	C₂×C₅	semidirect
263. C₄²×Q₈	C₂×C₅	semidirect
362. #541	C₄×C₅	semidirect
544. C₄⋊Q₈	C₂×C₄×C₅	semidirect
547. #125	C₂×C₄×C₅	semidirect
548. #125	C₂×C₄×C₅	semidirect
549. #125	C₂×C₄×C₅	semidirect
556. C₄×Q₈	C₂×C₄×C₅	semidirect
557. C₄×Q₈	C₂×C₄×C₅	semidirect
876. C₅	#34286	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×#541	2
C₅×#2373	2
C₅×#2371	2
C₅×#2370	2
C₅×#2365	2
C₅×#2362	2
C₅×#2360	2
C₅×#2336	2
C₅×#2334	2
C₅×#2320	2
C₄×C₅×#125	2
C₄×C₅×#126	2
C₅×#2298	2
C₅×#2295	2
C₅×#2276	2
C₅×#2274	2
C₄²×C₅×Q₈	2
#34286	5

Subgroups — C5×#34286 #11957006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34286 #11957006