Subgroups — C₅×#34473 #11957193

Order 1280.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₅×#2377	C₂	1	2	yes	maximal, complemented
3	C₅×#2376	C₂	1	2	yes	maximal, complemented
4	C₅×#2374	C₂	1	2	yes	maximal, complemented
5	C₅×#2365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2345	C₂	1	2	yes	maximal, complemented
11	C₅×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2341	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2335	C₂	1	2	yes	maximal, complemented
14	C₅×#2335	C₂	1	2	yes	maximal, complemented
15	C₅×#2333	C₂	1	2	yes	maximal, complemented
16	C₅×#2327	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#2323	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#2313	C₂	1	2	yes	maximal, complemented
20	C₅×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
25	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
26	C₅×#547	C₄	1	16	yes	complemented
27	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×#123	C₂²	1	2	yes	—
29	C₂×C₅×#123	C₂²	1	2	yes	—
30	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₅×#121	C₂²	1	2	yes	—
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×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×D₄	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	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₄²×C₅	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×#390	C₂²	1	1	yes	characteristic
49	C₅×#390	C₂²	1	1	yes	characteristic
50	C₅×#390	C₂²	1	1	yes	characteristic
51	C₅×#390	C₂²	1	1	yes	characteristic
52	C₅×#390	C₂²	1	2	yes	—
53	C₅×#390	C₂²	1	2	yes	—
54	C₅×#390	C₂²	1	2	yes	—
55	C₅×#390	C₂²	1	2	yes	—
56	C₅×#389	C₂²	1	1	yes	characteristic
57	C₅×#389	C₂²	1	1	yes	characteristic
58	C₅×#389	C₂²	1	2	yes	—
59	C₅×#389	C₂²	1	2	yes	—
60	C₅×#389	C₂²	1	2	yes	—
61	C₅×#388	C₂²	1	1	yes	characteristic
62	C₅×#388	C₂²	1	1	yes	characteristic
63	C₅×#388	C₂²	1	2	yes	—
64	C₅×#388	C₂²	1	2	yes	—
65	C₅×#388	C₂²	1	2	yes	—
66	C₅×#388	C₂²	1	2	yes	—
67	C₅×#388	C₂²	1	2	yes	—
68	C₅×#388	C₂²	1	2	yes	—
69	C₅×#388	C₂²	1	2	yes	—
70	C₅×#388	C₂²	1	2	yes	—
71	C₅×#388	C₂²	1	2	yes	—
72	C₅×#387	C₂²	1	1	yes	characteristic
73	C₅×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
85	C₅×#386	C₂²	1	1	yes	characteristic
86	C₅×#386	C₂²	1	1	yes	characteristic
87	C₅×#386	C₂²	1	2	yes	—
88	C₅×#386	C₂²	1	2	yes	—
89	C₅×#386	C₂²	1	2	yes	—
90	C₅×#386	C₂²	1	2	yes	—
91	C₅×#386	C₂²	1	2	yes	—
92	C₅×#385	C₂²	1	1	yes	characteristic
93	C₅×#385	C₂²	1	1	yes	characteristic
94	C₅×#385	C₂²	1	2	yes	—
95	C₅×#385	C₂²	1	2	yes	—
96	C₅×#382	C₂²	1	1	yes	characteristic
97	C₅×#381	C₂²	1	2	yes	—
98	C₅×#381	C₂²	1	2	yes	—
99	C₅×#380	C₂²	1	1	yes	characteristic
100	C₅×#380	C₂²	1	2	yes	—
101	C₅×#380	C₂²	1	2	yes	—
102	C₅×#380	C₂²	1	2	yes	—
103	C₅×#380	C₂²	1	2	yes	—
104	C₅×#380	C₂²	1	1	yes	characteristic
105	C₅×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
109	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
114	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
116	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
123	C₅×#376	C₂²	1	1	yes	characteristic
124	#34473	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂×C₅×#41	—	4	2	no	—
126	C₂×C₅×#41	—	4	2	no	—
127	C₂×C₅×#41	—	4	2	no	—
128	C₂×C₅×#41	—	4	2	no	—
129	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
130	C₂×C₅×#41	C₂×C₄	1	8	yes	complemented
131	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
132	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
133	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₅×D₄	C₂³	1	2	yes	—
136	C₂²×C₅×D₄	C₂³	1	2	yes	—
137	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂³	1	2	yes	—
141	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅	C₂³	1	2	yes	—
143	C₂³×C₄×C₅	C₂³	1	2	yes	—
144	C₂³×C₄×C₅	C₂³	1	2	yes	—
145	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
146	C₅×#123	C₂×C₄	1	16	yes	complemented
147	C₅×#123	C₂×C₄	1	16	yes	complemented
148	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
149	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
150	C₅×#121	C₂×C₄	1	16	yes	—
151	C₄×C₅×Q₈	—	4	2	no	—
152	C₄×C₅×Q₈	—	4	2	no	—
153	C₄×C₅×Q₈	—	4	2	no	—
154	C₄×C₅×Q₈	—	4	2	no	—
155	C₄×C₅×D₄	C₂×C₄	1	8	yes	—
156	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
157	C₅×#117	—	4	2	no	—
158	C₅×#117	—	4	2	no	—
159	C₂×C₅×C₄⋊C₄	—	4	2	no	—
160	C₂×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₄²×C₅	—	4	2	no	—
205	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₅	C₂³	1	2	yes	—
210	C₂×C₄²×C₅	C₂³	1	2	yes	—
211	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₅	C₂³	1	2	yes	—
213	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₅	C₂³	1	2	yes	—
215	C₂×C₄²×C₅	C₂³	1	2	yes	—
216	C₂×C₄²×C₅	C₂³	1	2	yes	—
217	C₂×C₄²×C₅	C₂³	1	2	yes	—
218	C₂×C₄²×C₅	C₂³	1	2	yes	—
219	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
220	C₅×#95	C₂³	1	1	yes	characteristic
221	C₅×#95	C₂³	1	1	yes	characteristic
222	C₅×#95	C₂³	1	1	yes	characteristic
223	C₅×#95	C₂³	1	1	yes	characteristic
224	C₅×#95	C₂³	1	1	yes	characteristic
225	C₅×#95	C₂³	1	1	yes	characteristic
226	C₅×#95	C₂³	1	2	yes	—
227	C₅×#95	C₂³	1	1	yes	characteristic
228	C₅×#95	C₂³	1	2	yes	—
229	C₅×#95	C₂³	1	1	yes	characteristic
230	C₅×#95	C₂³	1	1	yes	characteristic
231	C₅×#95	C₂³	1	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	2	yes	—
237	C₅×#95	C₂³	1	2	yes	—
238	C₅×#95	C₂³	1	2	yes	—
239	C₅×#95	C₂³	1	2	yes	—
240	C₅×#95	C₂³	1	2	yes	—
241	C₅×#95	C₂³	1	2	yes	—
242	C₅×#95	C₂³	1	2	yes	—
243	C₅×#95	C₂³	1	2	yes	—
244	C₅×#95	C₂³	1	1	yes	characteristic
245	C₅×#95	C₂³	1	2	yes	—
246	C₅×#95	C₂³	1	2	yes	—
247	C₂×#547	C₂×C₅	1	1	yes	characteristic
248	#2377	C₂×C₅	1	2	yes	complemented
249	#2376	C₂×C₅	1	2	yes	complemented
250	#2374	C₂×C₅	1	2	yes	complemented
251	#2365	C₂×C₅	1	1	yes	characteristic, complemented
252	#2362	C₂×C₅	1	1	yes	characteristic, complemented
253	#2360	C₂×C₅	1	1	yes	characteristic, complemented
254	#2357	C₂×C₅	1	1	yes	characteristic, complemented
255	#2352	C₂×C₅	1	1	yes	characteristic, complemented
256	#2345	C₂×C₅	1	2	yes	complemented
257	#2341	C₂×C₅	1	1	yes	characteristic, complemented
258	#2341	C₂×C₅	1	1	yes	characteristic, complemented
259	#2335	C₂×C₅	1	2	yes	complemented
260	#2335	C₂×C₅	1	2	yes	complemented
261	#2333	C₂×C₅	1	2	yes	complemented
262	#2327	C₂×C₅	1	1	yes	characteristic, complemented
263	#2323	C₂×C₅	1	1	yes	characteristic, complemented
264	#2319	C₂×C₅	1	1	yes	characteristic, complemented
265	#2313	C₂×C₅	1	2	yes	complemented
266	#2311	C₂×C₅	1	1	yes	characteristic, complemented
267	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
268	#2297	C₂×C₅	1	1	yes	characteristic, complemented
269	#2290	C₂×C₅	1	1	yes	characteristic, complemented
270	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
272	C₂⁴×C₅	C₂⁴	1	2	yes	—
273	C₅×#41	—	4	16	no	—
274	C₅×#41	—	4	16	no	—
275	C₂×C₅×Q₈	—	2	2	no	—
276	C₂×C₅×Q₈	—	2	2	no	—
277	C₂×C₅×Q₈	—	2	2	no	—
278	C₂×C₅×Q₈	—	2	2	no	—
279	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
280	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
281	C₂×C₅×D₄	—	2	2	no	—
282	C₂×C₅×D₄	—	2	2	no	—
283	C₂×C₅×D₄	—	4	1	no	—
284	C₂×C₅×D₄	—	4	1	no	—
285	C₂×C₅×D₄	—	4	2	no	—
286	C₂×C₅×D₄	—	4	2	no	—
287	C₂×C₅×D₄	—	4	2	no	—
288	C₂×C₅×D₄	—	4	2	no	—
289	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
290	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
291	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
292	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₅	—	2	2	no	—
294	C₂²×C₄×C₅	—	2	2	no	—
295	C₂²×C₄×C₅	—	2	2	no	—
296	C₂²×C₄×C₅	—	2	2	no	—
297	C₂²×C₄×C₅	—	2	2	no	—
298	C₂²×C₄×C₅	—	4	1	no	—
299	C₂²×C₄×C₅	—	4	1	no	—
300	C₂²×C₄×C₅	—	4	1	no	—
301	C₂²×C₄×C₅	—	4	2	no	—
302	C₂²×C₄×C₅	—	4	2	no	—
303	C₂²×C₄×C₅	—	4	1	no	—
304	C₂²×C₄×C₅	—	4	1	no	—
305	C₂²×C₄×C₅	—	4	2	no	—
306	C₂²×C₄×C₅	—	4	2	no	—
307	C₂²×C₄×C₅	—	4	2	no	—
308	C₂²×C₄×C₅	—	4	2	no	—
309	C₂²×C₄×C₅	—	4	2	no	—
310	C₂²×C₄×C₅	—	4	2	no	—
311	C₂²×C₄×C₅	—	4	2	no	—
312	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
313	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
314	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
316	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
317	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₅×C₄⋊C₄	—	2	2	no	—
338	C₅×C₄⋊C₄	—	2	2	no	—
339	C₅×C₄⋊C₄	—	2	2	no	—
340	C₅×C₄⋊C₄	—	2	2	no	—
341	C₅×C₄⋊C₄	—	2	2	no	—
342	C₅×C₄⋊C₄	—	4	2	no	—
343	C₅×C₄⋊C₄	—	4	1	no	—
344	C₅×C₄⋊C₄	—	4	2	no	—
345	C₅×C₄⋊C₄	—	4	2	no	—
346	C₅×C₄⋊C₄	—	4	1	no	—
347	C₅×C₄⋊C₄	—	4	1	no	—
348	C₅×C₄⋊C₄	—	4	2	no	—
349	C₅×C₄⋊C₄	—	4	2	no	—
350	C₅×C₄⋊C₄	—	4	2	no	—
351	C₅×C₄⋊C₄	—	4	2	no	—
352	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
353	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
354	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
355	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
356	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
357	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
358	C₅×C₂²⋊C₄	—	2	2	no	—
359	C₅×C₂²⋊C₄	—	2	4	no	—
360	C₅×C₂²⋊C₄	—	4	1	no	—
361	C₅×C₂²⋊C₄	—	4	2	no	—
362	C₅×C₂²⋊C₄	—	4	2	no	—
363	C₅×C₂²⋊C₄	—	4	2	no	—
364	C₅×C₂²⋊C₄	—	4	2	no	—
365	C₅×C₂²⋊C₄	—	4	2	no	—
366	C₅×C₂²⋊C₄	—	4	2	no	—
367	C₅×C₂²⋊C₄	—	4	2	no	—
368	C₅×C₂²⋊C₄	—	4	1	no	—
369	C₅×C₂²⋊C₄	—	4	1	no	—
370	C₅×C₂²⋊C₄	—	4	2	no	—
371	C₅×C₂²⋊C₄	—	4	2	no	—
372	C₅×C₂²⋊C₄	—	4	1	no	—
373	C₅×C₂²⋊C₄	—	4	1	no	—
374	C₅×C₂²⋊C₄	—	4	2	no	—
375	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
376	C₅×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
377	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
378	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
379	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
380	C₄²×C₅	—	2	2	no	—
381	C₄²×C₅	—	2	2	no	—
382	C₄²×C₅	—	2	2	no	—
383	C₄²×C₅	—	2	2	no	—
384	C₄²×C₅	—	4	1	no	—
385	C₄²×C₅	—	4	1	no	—
386	C₄²×C₅	—	4	2	no	—
387	C₄²×C₅	—	4	2	no	—
388	C₄²×C₅	—	4	2	no	—
389	C₄²×C₅	—	4	2	no	—
390	C₄²×C₅	—	4	2	no	—
391	C₄²×C₅	—	4	2	no	—
392	C₄²×C₅	—	4	2	no	—
393	C₄²×C₅	—	4	2	no	—
394	C₄²×C₅	C₂²×C₄	1	4	yes	—
395	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
396	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
397	#547	C₄×C₅	1	16	yes	complemented
398	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
399	C₂×#123	C₂²×C₅	1	2	yes	—
400	C₂×#123	C₂²×C₅	1	2	yes	—
401	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
403	C₂×#121	C₂²×C₅	1	2	yes	—
404	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
410	C₂×#117	C₂²×C₅	1	1	yes	characteristic
411	C₂×#117	C₂²×C₅	1	1	yes	characteristic
412	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
414	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
415	#391	C₂²×C₅	1	1	yes	characteristic
416	#391	C₂²×C₅	1	1	yes	characteristic
417	#391	C₂²×C₅	1	1	yes	characteristic
418	#391	C₂²×C₅	1	1	yes	characteristic
419	#390	C₂²×C₅	1	1	yes	characteristic
420	#390	C₂²×C₅	1	1	yes	characteristic
421	#390	C₂²×C₅	1	1	yes	characteristic
422	#390	C₂²×C₅	1	2	yes	—
423	#390	C₂²×C₅	1	2	yes	—
424	#390	C₂²×C₅	1	2	yes	—
425	#390	C₂²×C₅	1	2	yes	—
426	#390	C₂²×C₅	1	1	yes	characteristic
427	#389	C₂²×C₅	1	1	yes	characteristic
428	#389	C₂²×C₅	1	1	yes	characteristic
429	#389	C₂²×C₅	1	2	yes	—
430	#389	C₂²×C₅	1	2	yes	—
431	#389	C₂²×C₅	1	2	yes	—
432	#388	C₂²×C₅	1	2	yes	—
433	#388	C₂²×C₅	1	2	yes	—
434	#388	C₂²×C₅	1	2	yes	—
435	#388	C₂²×C₅	1	2	yes	—
436	#388	C₂²×C₅	1	2	yes	—
437	#388	C₂²×C₅	1	1	yes	characteristic
438	#388	C₂²×C₅	1	2	yes	—
439	#388	C₂²×C₅	1	2	yes	—
440	#388	C₂²×C₅	1	2	yes	—
441	#388	C₂²×C₅	1	2	yes	—
442	#388	C₂²×C₅	1	1	yes	characteristic
443	#387	C₂²×C₅	1	1	yes	characteristic
444	#387	C₂²×C₅	1	2	yes	—
445	#387	C₂²×C₅	1	2	yes	—
446	#387	C₂²×C₅	1	2	yes	—
447	#387	C₂²×C₅	1	2	yes	—
448	#387	C₂²×C₅	1	2	yes	—
449	#387	C₂²×C₅	1	2	yes	—
450	#387	C₂²×C₅	1	2	yes	—
451	#387	C₂²×C₅	1	2	yes	—
452	#387	C₂²×C₅	1	2	yes	—
453	#387	C₂²×C₅	1	2	yes	—
454	#387	C₂²×C₅	1	2	yes	—
455	#387	C₂²×C₅	1	1	yes	characteristic
456	#386	C₂²×C₅	1	2	yes	—
457	#386	C₂²×C₅	1	2	yes	—
458	#386	C₂²×C₅	1	1	yes	characteristic
459	#386	C₂²×C₅	1	2	yes	—
460	#386	C₂²×C₅	1	2	yes	—
461	#386	C₂²×C₅	1	2	yes	—
462	#386	C₂²×C₅	1	1	yes	characteristic
463	#385	C₂²×C₅	1	1	yes	characteristic
464	#385	C₂²×C₅	1	2	yes	—
465	#385	C₂²×C₅	1	1	yes	characteristic
466	#385	C₂²×C₅	1	2	yes	—
467	#382	C₂²×C₅	1	1	yes	characteristic
468	#381	C₂²×C₅	1	2	yes	—
469	#381	C₂²×C₅	1	2	yes	—
470	#380	C₂²×C₅	1	2	yes	—
471	#380	C₂²×C₅	1	2	yes	—
472	#380	C₂²×C₅	1	2	yes	—
473	#380	C₂²×C₅	1	2	yes	—
474	#380	C₂²×C₅	1	1	yes	characteristic
475	#380	C₂²×C₅	1	2	yes	—
476	#380	C₂²×C₅	1	1	yes	characteristic
477	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
478	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
483	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
484	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
488	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
492	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
493	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
494	#376	C₂²×C₅	1	1	yes	characteristic
495	C₂³×C₅	—	2	1	no	—
496	C₂³×C₅	—	2	1	no	—
497	C₂³×C₅	—	2	1	no	—
498	C₂³×C₅	—	2	1	no	—
499	C₂³×C₅	—	2	2	no	—
500	C₂³×C₅	—	2	2	no	—
501	C₂³×C₅	—	2	2	no	—
502	C₂³×C₅	—	2	1	no	—
503	C₂³×C₅	—	2	1	no	—
504	C₂³×C₅	—	2	2	no	—
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	1	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	2	1	no	—
512	C₂³×C₅	—	2	1	no	—
513	C₂³×C₅	C₂³×C₄	1	2	yes	—
514	C₂³×C₅	C₂³×C₄	1	2	yes	—
515	C₂³×C₅	C₂³×C₄	1	4	yes	—
516	C₂³×C₅	C₂⁵	1	1	yes	characteristic
517	C₅×Q₈	—	2	8	no	—
518	C₅×Q₈	—	2	8	no	—
519	C₅×D₄	—	2	8	no	—
520	C₅×D₄	—	4	4	no	—
521	C₅×D₄	—	4	8	no	—
522	C₅×D₄	—	4	8	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	2	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	2	no	—
529	C₂×C₄×C₅	—	2	2	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	8	no	—
540	C₂×C₄×C₅	—	2	8	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	2	2	no	—
549	C₂×C₄×C₅	—	2	2	no	—
550	C₂×C₄×C₅	—	2	2	no	—
551	C₂×C₄×C₅	—	2	2	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	2	no	—
554	C₂×C₄×C₅	—	2	1	no	—
555	C₂×C₄×C₅	—	2	1	no	—
556	C₂×C₄×C₅	—	2	1	no	—
557	C₂×C₄×C₅	—	2	2	no	—
558	C₂×C₄×C₅	—	2	2	no	—
559	C₂×C₄×C₅	—	2	2	no	—
560	C₂×C₄×C₅	—	2	2	no	—
561	C₂×C₄×C₅	—	2	1	no	—
562	C₂×C₄×C₅	—	2	1	no	—
563	C₂×C₄×C₅	—	2	1	no	—
564	C₂×C₄×C₅	—	2	2	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	1	no	—
567	C₂×C₄×C₅	—	2	1	no	—
568	C₂×C₄×C₅	—	2	1	no	—
569	C₂×C₄×C₅	—	2	2	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	2	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	4	8	no	—
575	C₂×C₄×C₅	—	4	8	no	—
576	C₂×C₄×C₅	—	4	8	no	—
577	C₂×C₄×C₅	—	4	4	no	—
578	C₂×C₄×C₅	—	4	4	no	—
579	C₂×C₄×C₅	—	8	4	no	—
580	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
581	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
583	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
585	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
586	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
587	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
589	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
590	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
591	C₂×#41	—	4	2	no	—
592	C₂×#41	—	4	2	no	—
593	C₂×#41	—	4	2	no	—
594	C₂×#41	—	4	2	no	—
595	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
596	C₂×#41	C₂×C₄×C₅	1	8	yes	complemented
597	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
598	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
599	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₅	1	2	yes	—
602	C₂²×D₄	C₂³×C₅	1	2	yes	—
603	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₅	1	2	yes	—
607	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₅	1	2	yes	—
609	C₂³×C₄	C₂³×C₅	1	2	yes	—
610	C₂³×C₄	C₂³×C₅	1	2	yes	—
611	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
612	#123	C₂×C₄×C₅	1	16	yes	complemented
613	#123	C₂×C₄×C₅	1	16	yes	complemented
614	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
615	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	complemented
616	#121	C₂×C₄×C₅	1	16	yes	—
617	C₄×Q₈	—	4	2	no	—
618	C₄×Q₈	—	4	2	no	—
619	C₄×Q₈	—	4	2	no	—
620	C₄×Q₈	—	4	2	no	—
621	C₄×D₄	C₂×C₄×C₅	1	8	yes	—
622	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
623	#117	—	4	2	no	—
624	#117	—	4	2	no	—
625	C₂×C₄⋊C₄	—	4	2	no	—
626	C₂×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
627	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
670	C₂×C₄²	—	4	2	no	—
671	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₅	1	2	yes	—
676	C₂×C₄²	C₂³×C₅	1	2	yes	—
677	C₂×C₄²	C₂³×C₅	1	2	yes	—
678	C₂×C₄²	C₂³×C₅	1	2	yes	—
679	C₂×C₄²	C₂³×C₅	1	2	yes	—
680	C₂×C₄²	C₂³×C₅	1	2	yes	—
681	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₅	1	2	yes	—
684	C₂×C₄²	C₂³×C₅	1	2	yes	—
685	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
686	#95	C₂³×C₅	1	1	yes	characteristic
687	#95	C₂³×C₅	1	1	yes	characteristic
688	#95	C₂³×C₅	1	1	yes	characteristic
689	#95	C₂³×C₅	1	1	yes	characteristic
690	#95	C₂³×C₅	1	1	yes	characteristic
691	#95	C₂³×C₅	1	1	yes	characteristic
692	#95	C₂³×C₅	1	2	yes	—
693	#95	C₂³×C₅	1	1	yes	characteristic
694	#95	C₂³×C₅	1	2	yes	—
695	#95	C₂³×C₅	1	1	yes	characteristic
696	#95	C₂³×C₅	1	1	yes	characteristic
697	#95	C₂³×C₅	1	2	yes	—
698	#95	C₂³×C₅	1	2	yes	—
699	#95	C₂³×C₅	1	2	yes	—
700	#95	C₂³×C₅	1	2	yes	—
701	#95	C₂³×C₅	1	2	yes	—
702	#95	C₂³×C₅	1	2	yes	—
703	#95	C₂³×C₅	1	2	yes	—
704	#95	C₂³×C₅	1	2	yes	—
705	#95	C₂³×C₅	1	2	yes	—
706	#95	C₂³×C₅	1	2	yes	—
707	#95	C₂³×C₅	1	2	yes	—
708	#95	C₂³×C₅	1	2	yes	—
709	#95	C₂³×C₅	1	2	yes	—
710	#95	C₂³×C₅	1	1	yes	characteristic
711	#95	C₂³×C₅	1	2	yes	—
712	#95	C₂³×C₅	1	2	yes	—
713	C₂²×C₅	—	2	2	no	—
714	C₂²×C₅	—	2	2	no	—
715	C₂²×C₅	—	2	4	no	—
716	C₂²×C₅	—	2	4	no	—
717	C₂²×C₅	—	2	2	no	—
718	C₂²×C₅	—	2	2	no	—
719	C₂²×C₅	—	2	4	no	—
720	C₂²×C₅	—	2	2	no	—
721	C₂²×C₅	—	2	2	no	—
722	C₂²×C₅	—	4	1	no	—
723	C₂²×C₅	—	4	1	no	—
724	C₂²×C₅	—	4	2	no	—
725	C₂²×C₅	—	4	1	no	—
726	C₂²×C₅	—	4	1	no	—
727	C₂²×C₅	—	4	2	no	—
728	C₂²×C₅	—	4	1	no	—
729	C₂²×C₅	—	4	1	no	—
730	C₂²×C₅	—	4	2	no	—
731	C₂²×C₅	—	4	1	no	—
732	C₂²×C₅	—	4	1	no	—
733	C₂²×C₅	—	4	2	no	—
734	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
735	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
738	C₂²×C₅	#585	1	1	yes	characteristic
739	C₂²×C₅	#585	1	1	yes	characteristic
740	C₂²×C₅	#585	1	1	yes	characteristic
741	C₄×C₅	—	2	2	no	—
742	C₄×C₅	—	2	2	no	—
743	C₄×C₅	—	2	4	no	—
744	C₄×C₅	—	2	4	no	—
745	C₄×C₅	—	2	2	no	—
746	C₄×C₅	—	2	4	no	—
747	C₄×C₅	—	2	2	no	—
748	C₄×C₅	—	2	2	no	—
749	C₄×C₅	—	4	1	no	—
750	C₄×C₅	—	4	2	no	—
751	C₄×C₅	—	4	1	no	—
752	C₄×C₅	—	4	1	no	—
753	C₄×C₅	—	4	1	no	—
754	C₄×C₅	—	4	1	no	—
755	C₄×C₅	—	4	1	no	—
756	C₄×C₅	—	4	2	no	—
757	C₄×C₅	—	4	1	no	—
758	C₄×C₅	—	4	2	no	—
759	C₄×C₅	—	4	2	no	—
760	C₄×C₅	#518	1	4	yes	—
761	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
763	C₂⁴	C₂⁴×C₅	1	2	yes	—
764	#41	—	4	16	no	—
765	#41	—	4	16	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
771	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
781	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
782	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
783	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	1	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	—	4	1	no	—
796	C₂²×C₄	—	4	2	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	1	no	—
799	C₂²×C₄	—	4	1	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
804	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
805	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
806	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
807	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
808	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	1	no	—
835	C₄⋊C₄	—	4	1	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	1	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	—	4	2	no	—
843	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
844	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
845	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
846	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
847	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
848	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	4	1	no	—
852	C₂²⋊C₄	—	4	1	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	1	no	—
863	C₂²⋊C₄	—	4	1	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
867	C₂²⋊C₄	C₂²×C₄×C₅	1	4	yes	—
868	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
869	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
870	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	4	1	no	—
876	C₄²	—	4	1	no	—
877	C₄²	—	4	2	no	—
878	C₄²	—	4	2	no	—
879	C₄²	—	4	2	no	—
880	C₄²	—	4	2	no	—
881	C₄²	—	4	2	no	—
882	C₄²	—	4	2	no	—
883	C₄²	—	4	2	no	—
884	C₄²	—	4	2	no	—
885	C₄²	C₂²×C₄×C₅	1	4	yes	—
886	C₂×C₅	—	4	2	no	—
887	C₂×C₅	—	4	2	no	—
888	C₂×C₅	—	4	4	no	—
889	C₂×C₅	C₂×#518	1	1	yes	characteristic
890	C₂×C₅	#3428	1	1	yes	characteristic
891	C₂×C₅	C₄×2₋¹⁺⁴	1	1	yes	characteristic
892	C₂×C₅	#3539	1	1	yes	characteristic
893	C₂×C₅	#3541	1	1	yes	characteristic
894	C₂×C₅	#3554	1	1	yes	characteristic
895	C₂×C₅	#3562	1	1	yes	characteristic
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	C₂³×C₄×C₅	1	2	yes	—
915	C₂³	C₂³×C₄×C₅	1	2	yes	—
916	C₂³	C₂³×C₄×C₅	1	4	yes	—
917	C₂³	C₂⁵×C₅	1	1	yes	characteristic
918	Q₈	—	2	8	no	—
919	Q₈	—	2	8	no	—
920	D₄	—	2	8	no	—
921	D₄	—	4	8	no	—
922	D₄	—	4	8	no	—
923	D₄	—	4	4	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	8	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	8	4	no	—
981	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
984	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
987	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
989	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
990	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
991	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
992	C₅	#34473	1	1	yes	characteristic, direct product factor, Sylow
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	4	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	1	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
1015	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1016	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1017	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1018	C₂²	C₅×#585	1	1	yes	characteristic
1019	C₂²	C₅×#585	1	1	yes	characteristic
1020	C₂²	C₅×#585	1	1	yes	characteristic
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	4	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	2	2	no	—
1028	C₄	—	2	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	—	4	1	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	2	no	—
1033	C₄	—	4	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	2	no	—
1039	C₄	—	4	1	no	—
1040	C₄	C₅×#518	1	4	yes	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	4	4	no	—
1044	C₂	C₂×C₅×#518	1	1	yes	characteristic
1045	C₂	C₅×#3428	1	1	yes	characteristic
1046	C₂	C₄×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1047	C₂	C₅×#3539	1	1	yes	characteristic
1048	C₂	C₅×#3541	1	1	yes	characteristic
1049	C₂	C₅×#3554	1	1	yes	characteristic
1050	C₂	C₅×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂×C₅×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#2377	C₂	semidirect
3. C₅×#2376	C₂	semidirect
4. C₅×#2374	C₂	semidirect
5. C₅×#2365	C₂	semidirect
6. C₅×#2362	C₂	semidirect
7. C₅×#2360	C₂	semidirect
8. C₅×#2357	C₂	semidirect
9. C₅×#2352	C₂	semidirect
10. C₅×#2345	C₂	semidirect
11. C₅×#2341	C₂	semidirect
12. C₅×#2341	C₂	semidirect
13. C₅×#2335	C₂	semidirect
14. C₅×#2335	C₂	semidirect
15. C₅×#2333	C₂	semidirect
16. C₅×#2327	C₂	semidirect
17. C₅×#2323	C₂	semidirect
18. C₅×#2319	C₂	semidirect
19. C₅×#2313	C₂	semidirect
20. C₅×#2311	C₂	semidirect
21. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
22. C₅×#2297	C₂	semidirect
23. C₅×#2290	C₂	semidirect
26. C₅×#547	C₄	semidirect
124. #34473	C₅	direct (N × H)
129. C₂×C₅×#41	C₂×C₄	semidirect
130. C₂×C₅×#41	C₂×C₄	semidirect
145. C₅×C₄⋊Q₈	C₂×C₄	semidirect
146. C₅×#123	C₂×C₄	semidirect
147. C₅×#123	C₂×C₄	semidirect
148. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
149. C₅×C₂²⋊Q₈	C₂×C₄	semidirect
156. C₄×C₅×D₄	C₂×C₄	semidirect
160. C₂×C₅×C₄⋊C₄	C₂×C₄	semidirect
248. #2377	C₂×C₅	semidirect
249. #2376	C₂×C₅	semidirect
250. #2374	C₂×C₅	semidirect
251. #2365	C₂×C₅	semidirect
252. #2362	C₂×C₅	semidirect
253. #2360	C₂×C₅	semidirect
254. #2357	C₂×C₅	semidirect
255. #2352	C₂×C₅	semidirect
256. #2345	C₂×C₅	semidirect
257. #2341	C₂×C₅	semidirect
258. #2341	C₂×C₅	semidirect
259. #2335	C₂×C₅	semidirect
260. #2335	C₂×C₅	semidirect
261. #2333	C₂×C₅	semidirect
262. #2327	C₂×C₅	semidirect
263. #2323	C₂×C₅	semidirect
264. #2319	C₂×C₅	semidirect
265. #2313	C₂×C₅	semidirect
266. #2311	C₂×C₅	semidirect
267. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
268. #2297	C₂×C₅	semidirect
269. #2290	C₂×C₅	semidirect
397. #547	C₄×C₅	semidirect
595. C₂×#41	C₂×C₄×C₅	semidirect
596. C₂×#41	C₂×C₄×C₅	semidirect
611. C₄⋊Q₈	C₂×C₄×C₅	semidirect
612. #123	C₂×C₄×C₅	semidirect
613. #123	C₂×C₄×C₅	semidirect
614. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
615. C₂²⋊Q₈	C₂×C₄×C₅	semidirect
622. C₄×D₄	C₂×C₄×C₅	semidirect
626. C₂×C₄⋊C₄	C₂×C₄×C₅	semidirect
992. C₅	#34473	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×#547	2
C₅×#2377	2
C₅×#2376	2
C₅×#2374	2
C₅×#2365	2
C₅×#2362	2
C₅×#2360	2
C₅×#2357	2
C₅×#2352	2
C₅×#2345	2
C₅×#2341	2
C₅×#2335	2
C₅×#2333	2
C₅×#2327	2
C₅×#2323	2
C₅×#2319	2
C₅×#2313	2
C₅×#2311	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#2297	2
C₅×#2290	2
#34473	5

Subgroups — C5×#34473 #11957193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34473 #11957193