Subgroups — C₅×#17680 #11940400

Order 1280.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3515	C₂	1	1	yes	maximal, characteristic
2	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1534	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1529	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1528	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1528	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1524	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#330	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#557	C₄	1	1	yes	characteristic
17	C₅×#554	C₄	1	1	yes	characteristic
18	C₅×#554	C₄	1	1	yes	characteristic
19	C₅×#553	C₄	1	1	yes	characteristic
20	C₅×#553	C₄	1	1	yes	characteristic
21	C₅×#552	—	2	1	no	—
22	C₅×#552	—	2	1	no	—
23	C₅×#552	—	2	1	no	—
24	C₅×#552	C₄	1	1	yes	characteristic
25	C₅×#552	C₄	1	1	yes	characteristic
26	C₅×#547	—	2	1	no	—
27	C₅×#547	C₄	1	1	yes	characteristic
28	C₅×#541	—	2	1	no	—
29	C₅×#539	—	2	1	no	—
30	C₅×#539	—	2	1	no	—
31	C₅×#533	C₂²	1	1	yes	characteristic
32	C₅×#529	C₂²	1	1	yes	characteristic
33	C₅×#529	C₂²	1	1	yes	characteristic
34	C₅×#529	C₂²	1	1	yes	characteristic
35	C₂×C₅×#125	C₂²	1	1	yes	characteristic
36	C₂×C₅×#125	C₂²	1	1	yes	characteristic
37	C₅×#520	—	2	1	no	—
38	C₄×C₅×#41	C₂²	1	1	yes	characteristic
39	C₅×#446	—	2	1	no	—
40	C₅×#435	—	2	1	no	—
41	C₅×#435	—	2	1	no	—
42	C₅×C₈×D₄	—	2	1	no	—
43	C₅×#433	—	2	1	no	—
44	C₅×#433	—	2	1	no	—
45	C₅×#432	C₂²	1	1	yes	characteristic
46	C₅×#432	C₂²	1	1	yes	characteristic
47	C₅×#432	C₂²	1	1	yes	characteristic
48	C₅×#432	C₂²	1	1	yes	characteristic
49	C₅×#432	C₂²	1	1	yes	characteristic
50	C₅×#432	C₂²	1	1	yes	characteristic
51	C₅×#432	C₂²	1	1	yes	characteristic
52	C₅×#424	—	2	1	no	—
53	C₅×#408	—	2	1	no	—
54	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
55	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
56	C₂×C₅×#97	C₂²	1	1	yes	characteristic
57	C₂×C₅×#97	C₂²	1	1	yes	characteristic
58	C₂×C₅×#97	C₂²	1	1	yes	characteristic
59	C₅×#330	C₂²	1	1	yes	characteristic
60	C₅×#330	C₂²	1	1	yes	characteristic
61	C₅×#330	C₂²	1	1	yes	characteristic
62	C₅×#330	C₂²	1	1	yes	characteristic
63	C₅×#330	C₂²	1	1	yes	characteristic
64	C₅×#330	C₂²	1	1	yes	characteristic
65	C₅×#330	C₂²	1	1	yes	characteristic
66	C₅×#330	C₂²	1	1	yes	characteristic
67	C₅×#330	C₂²	1	1	yes	characteristic
68	C₅×#330	C₂²	1	1	yes	characteristic
69	C₅×#330	C₂²	1	1	yes	characteristic
70	C₅×#330	C₂²	1	1	yes	characteristic
71	C₅×#329	C₂²	1	1	yes	characteristic
72	C₅×#329	C₂²	1	1	yes	characteristic
73	C₅×#329	C₂²	1	1	yes	characteristic
74	C₅×#329	C₂²	1	1	yes	characteristic
75	#17680	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×C₅×#41	—	2	1	no	—
77	C₂×C₅×#41	D₄	1	1	yes	characteristic
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂×C₅×M₁₆	—	2	1	no	—
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₅×#126	—	2	1	no	—
87	C₅×#126	—	2	1	no	—
88	C₅×#126	—	2	1	no	—
89	C₅×#126	—	2	1	no	—
90	C₅×#126	—	2	1	no	—
91	C₅×#126	—	2	1	no	—
92	C₅×#126	—	2	1	no	—
93	C₅×#125	—	2	1	no	—
94	C₅×#125	—	2	1	no	—
95	C₅×#125	—	2	1	no	—
96	C₅×#125	—	2	1	no	—
97	C₅×#125	—	2	1	no	—
98	C₅×#125	—	2	1	no	—
99	C₅×#125	—	2	1	no	—
100	C₅×#125	—	2	1	no	—
101	C₅×#125	—	2	1	no	—
102	C₅×#125	C₂×C₄	1	1	yes	characteristic
103	C₅×#125	C₂×C₄	1	1	yes	characteristic
104	C₅×#125	C₂×C₄	1	1	yes	characteristic
105	C₅×#125	C₂×C₄	1	1	yes	characteristic
106	C₅×#125	C₂³	1	1	yes	characteristic
107	C₅×#125	C₂³	1	1	yes	characteristic
108	C₅×#125	C₂³	1	1	yes	characteristic
109	C₅×#124	C₂³	1	1	yes	characteristic
110	C₅×#123	—	2	1	no	—
111	C₅×#123	—	2	1	no	—
112	C₅×#123	—	2	1	no	—
113	C₅×#123	—	2	1	no	—
114	C₅×#123	—	2	1	no	—
115	C₅×#123	—	2	1	no	—
116	C₅×#123	—	2	1	no	—
117	C₅×#123	—	2	1	no	—
118	C₅×#123	—	2	1	no	—
119	C₅×C₂²⋊Q₈	—	2	1	no	—
120	C₅×C₂²⋊Q₈	—	2	1	no	—
121	C₅×C₂²⋊Q₈	—	2	1	no	—
122	C₅×C₂²⋊Q₈	—	2	1	no	—
123	C₅×C₂²⋊Q₈	—	2	1	no	—
124	C₅×C₂²⋊Q₈	—	2	1	no	—
125	C₅×C₂²⋊Q₈	—	2	1	no	—
126	C₅×C₂²⋊Q₈	—	2	1	no	—
127	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
129	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
130	C₅×#121	—	2	1	no	—
131	C₅×#121	—	2	1	no	—
132	C₅×#121	C₂×C₄	1	1	yes	characteristic
133	C₅×#121	C₂×C₄	1	1	yes	characteristic
134	C₅×#121	C₂×C₄	1	1	yes	characteristic
135	C₄×C₅×Q₈	—	2	1	no	—
136	C₄×C₅×Q₈	—	2	1	no	—
137	C₄×C₅×Q₈	—	2	1	no	—
138	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
139	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
141	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
142	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
143	C₄×C₅×D₄	—	2	1	no	—
144	C₄×C₅×D₄	—	2	1	no	—
145	C₄×C₅×D₄	—	2	1	no	—
146	C₄×C₅×D₄	—	2	1	no	—
147	C₄×C₅×D₄	—	2	1	no	—
148	C₄×C₅×D₄	—	2	1	no	—
149	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
151	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
152	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
153	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
154	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
155	C₄×C₅×D₄	D₄	1	1	yes	characteristic
156	C₄×C₅×D₄	D₄	1	1	yes	characteristic
157	C₄×C₅×D₄	D₄	1	1	yes	characteristic
158	C₅×#117	—	2	1	no	—
159	C₅×#117	—	2	1	no	—
160	C₅×#117	—	2	1	no	—
161	C₅×#117	—	2	1	no	—
162	C₅×#117	—	2	1	no	—
163	C₅×#117	C₂×C₄	1	1	yes	characteristic
164	C₅×#117	C₂×C₄	1	1	yes	characteristic
165	C₅×#117	D₄	1	1	yes	characteristic
166	C₅×#117	D₄	1	1	yes	characteristic
167	C₅×#117	D₄	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	—	2	1	no	—
169	C₂×C₅×C₄⋊C₄	—	2	1	no	—
170	C₂×C₅×C₄⋊C₄	—	2	1	no	—
171	C₂×C₅×C₄⋊C₄	—	2	1	no	—
172	C₂×C₅×C₄⋊C₄	—	2	1	no	—
173	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
175	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
176	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
177	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₈	—	2	1	no	—
181	C₅×C₄⋊C₈	—	2	1	no	—
182	C₅×C₄⋊C₈	—	2	1	no	—
183	C₅×C₄⋊C₈	—	2	1	no	—
184	C₅×C₄⋊C₈	—	2	1	no	—
185	C₅×C₄⋊C₈	—	2	1	no	—
186	C₅×C₄⋊C₈	—	2	1	no	—
187	C₅×C₂²⋊C₈	—	2	1	no	—
188	C₅×C₂²⋊C₈	—	2	1	no	—
189	C₅×C₂²⋊C₈	—	2	1	no	—
190	C₅×C₂²⋊C₈	—	2	1	no	—
191	C₅×C₂²⋊C₈	—	2	1	no	—
192	C₅×C₂²⋊C₈	—	2	1	no	—
193	C₅×C₂²⋊C₈	—	2	1	no	—
194	C₅×#97	—	2	1	no	—
195	C₅×#97	—	2	1	no	—
196	C₅×#97	—	2	1	no	—
197	C₅×#97	C₂³	1	1	yes	characteristic
198	C₅×#97	C₂³	1	1	yes	characteristic
199	C₅×#97	C₂³	1	1	yes	characteristic
200	C₅×#97	C₂³	1	1	yes	characteristic
201	C₅×#97	C₂³	1	1	yes	characteristic
202	C₅×#97	C₂³	1	1	yes	characteristic
203	C₅×#97	C₂³	1	1	yes	characteristic
204	C₅×#97	C₂³	1	1	yes	characteristic
205	C₄×C₅×C₈	—	2	1	no	—
206	C₄×C₅×C₈	—	2	1	no	—
207	#3515	C₂×C₅	1	1	yes	characteristic
208	#2970	C₂×C₅	1	1	yes	characteristic, complemented
209	#2923	C₂×C₅	1	1	yes	characteristic, complemented
210	#1537	C₂×C₅	1	1	yes	characteristic, complemented
211	#1535	C₂×C₅	1	1	yes	characteristic, complemented
212	#1535	C₂×C₅	1	1	yes	characteristic, complemented
213	#1534	C₂×C₅	1	1	yes	characteristic, complemented
214	#1532	C₂×C₅	1	1	yes	characteristic, complemented
215	#1532	C₂×C₅	1	1	yes	characteristic, complemented
216	#1531	C₂×C₅	1	1	yes	characteristic, complemented
217	#1529	C₂×C₅	1	1	yes	characteristic, complemented
218	#1528	C₂×C₅	1	1	yes	characteristic, complemented
219	#1528	C₂×C₅	1	1	yes	characteristic, complemented
220	#1524	C₂×C₅	1	1	yes	characteristic, complemented
221	C₂×#330	C₂×C₅	1	1	yes	characteristic, complemented
222	C₅×#41	—	4	2	no	—
223	C₅×#41	—	4	4	no	—
224	C₂×C₅×Q₈	—	2	1	no	—
225	C₂×C₅×Q₈	—	2	1	no	—
226	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×D₄	—	2	1	no	—
229	C₂×C₅×D₄	—	2	1	no	—
230	C₂×C₅×D₄	—	2	1	no	—
231	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄×C₅	—	2	1	no	—
236	C₂²×C₄×C₅	—	2	1	no	—
237	C₂²×C₄×C₅	—	2	1	no	—
238	C₂²×C₄×C₅	—	2	1	no	—
239	C₂²×C₄×C₅	—	2	1	no	—
240	C₂²×C₄×C₅	—	2	1	no	—
241	C₂²×C₄×C₅	—	2	1	no	—
242	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
251	C₅×M₁₆	—	4	2	no	—
252	C₅×M₁₆	—	4	2	no	—
253	C₂×C₅×C₈	—	2	1	no	—
254	C₂×C₅×C₈	—	2	1	no	—
255	C₂×C₅×C₈	—	2	1	no	—
256	C₂×C₅×C₈	—	2	1	no	—
257	C₂×C₅×C₈	—	2	1	no	—
258	C₂×C₅×C₈	—	2	1	no	—
259	C₂×C₅×C₈	—	2	1	no	—
260	C₂×C₅×C₈	—	2	1	no	—
261	C₂×C₅×C₈	—	4	2	no	—
262	C₂×C₅×C₈	—	4	2	no	—
263	C₂×C₅×C₈	—	4	2	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	—	2	1	no	—
266	C₅×C₄⋊C₄	—	2	1	no	—
267	C₅×C₄⋊C₄	—	2	1	no	—
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	2	1	no	—
271	C₅×C₄⋊C₄	—	2	1	no	—
272	C₅×C₄⋊C₄	—	2	1	no	—
273	C₅×C₄⋊C₄	—	2	1	no	—
274	C₅×C₄⋊C₄	—	2	1	no	—
275	C₅×C₄⋊C₄	—	2	1	no	—
276	C₅×C₄⋊C₄	—	2	1	no	—
277	C₅×C₄⋊C₄	—	2	1	no	—
278	C₅×C₄⋊C₄	—	2	1	no	—
279	C₅×C₄⋊C₄	—	2	1	no	—
280	C₅×C₄⋊C₄	—	2	1	no	—
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	2	1	no	—
283	C₅×C₄⋊C₄	—	2	1	no	—
284	C₅×C₄⋊C₄	—	2	1	no	—
285	C₅×C₄⋊C₄	—	2	1	no	—
286	C₅×C₄⋊C₄	—	2	1	no	—
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	2	1	no	—
289	C₅×C₄⋊C₄	—	2	1	no	—
290	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
300	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
316	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
317	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
318	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₅×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₄²×C₅	—	2	1	no	—
322	C₄²×C₅	—	2	1	no	—
323	C₄²×C₅	—	2	1	no	—
324	C₄²×C₅	—	2	1	no	—
325	C₄²×C₅	—	2	1	no	—
326	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
327	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
328	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
329	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₅	C₂⁴	1	1	yes	characteristic
336	#557	C₄×C₅	1	1	yes	characteristic
337	#554	C₄×C₅	1	1	yes	characteristic
338	#554	C₄×C₅	1	1	yes	characteristic
339	#553	C₄×C₅	1	1	yes	characteristic
340	#553	C₄×C₅	1	1	yes	characteristic
341	#552	—	2	1	no	—
342	#552	—	2	1	no	—
343	#552	—	2	1	no	—
344	#552	C₄×C₅	1	1	yes	characteristic
345	#552	C₄×C₅	1	1	yes	characteristic
346	#547	—	2	1	no	—
347	#547	C₄×C₅	1	1	yes	characteristic
348	#541	—	2	1	no	—
349	#539	—	2	1	no	—
350	#539	—	2	1	no	—
351	#533	C₂²×C₅	1	1	yes	characteristic
352	#529	C₂²×C₅	1	1	yes	characteristic
353	#529	C₂²×C₅	1	1	yes	characteristic
354	#529	C₂²×C₅	1	1	yes	characteristic
355	C₂×#125	C₂²×C₅	1	1	yes	characteristic
356	C₂×#125	C₂²×C₅	1	1	yes	characteristic
357	#520	—	2	1	no	—
358	C₄×#41	C₂²×C₅	1	1	yes	characteristic
359	#446	—	2	1	no	—
360	#435	—	2	1	no	—
361	#435	—	2	1	no	—
362	C₈×D₄	—	2	1	no	—
363	#433	—	2	1	no	—
364	#433	—	2	1	no	—
365	#432	C₂²×C₅	1	1	yes	characteristic
366	#432	C₂²×C₅	1	1	yes	characteristic
367	#432	C₂²×C₅	1	1	yes	characteristic
368	#432	C₂²×C₅	1	1	yes	characteristic
369	#432	C₂²×C₅	1	1	yes	characteristic
370	#432	C₂²×C₅	1	1	yes	characteristic
371	#432	C₂²×C₅	1	1	yes	characteristic
372	#424	—	2	1	no	—
373	#408	—	2	1	no	—
374	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
375	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
376	C₂×#97	C₂²×C₅	1	1	yes	characteristic
377	C₂×#97	C₂²×C₅	1	1	yes	characteristic
378	C₂×#97	C₂²×C₅	1	1	yes	characteristic
379	#330	C₂²×C₅	1	1	yes	characteristic
380	#330	C₂²×C₅	1	1	yes	characteristic
381	#330	C₂²×C₅	1	1	yes	characteristic
382	#330	C₂²×C₅	1	1	yes	characteristic
383	#330	C₂²×C₅	1	1	yes	characteristic
384	#330	C₂²×C₅	1	1	yes	characteristic
385	#330	C₂²×C₅	1	1	yes	characteristic
386	#330	C₂²×C₅	1	1	yes	characteristic
387	#330	C₂²×C₅	1	1	yes	characteristic
388	#330	C₂²×C₅	1	1	yes	characteristic
389	#330	C₂²×C₅	1	1	yes	characteristic
390	#330	C₂²×C₅	1	1	yes	characteristic
391	#329	C₂²×C₅	1	1	yes	characteristic
392	#329	C₂²×C₅	1	1	yes	characteristic
393	#329	C₂²×C₅	1	1	yes	characteristic
394	#329	C₂²×C₅	1	1	yes	characteristic
395	C₂³×C₅	—	2	1	no	—
396	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₅×Q₈	—	4	1	no	—
400	C₅×Q₈	—	4	1	no	—
401	C₅×Q₈	—	4	2	no	—
402	C₅×Q₈	—	8	1	no	—
403	C₅×D₄	—	2	2	no	—
404	C₅×D₄	—	2	2	no	—
405	C₅×D₄	—	4	1	no	—
406	C₅×D₄	—	4	1	no	—
407	C₅×D₄	—	4	2	no	—
408	C₅×D₄	—	4	2	no	—
409	C₅×D₄	—	8	1	no	—
410	C₂×C₄×C₅	—	2	2	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	4	1	no	—
419	C₂×C₄×C₅	—	4	1	no	—
420	C₂×C₄×C₅	—	4	1	no	—
421	C₂×C₄×C₅	—	4	1	no	—
422	C₂×C₄×C₅	—	4	1	no	—
423	C₂×C₄×C₅	—	4	1	no	—
424	C₂×C₄×C₅	—	4	1	no	—
425	C₂×C₄×C₅	—	4	1	no	—
426	C₂×C₄×C₅	—	4	2	no	—
427	C₂×C₄×C₅	—	4	2	no	—
428	C₂×C₄×C₅	—	4	2	no	—
429	C₂×C₄×C₅	—	8	1	no	—
430	C₂×C₄×C₅	—	8	1	no	—
431	C₂×C₄×C₅	—	8	1	no	—
432	C₂×C₄×C₅	—	8	1	no	—
433	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
435	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
436	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
438	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
445	C₅×C₈	—	2	2	no	—
446	C₅×C₈	—	4	1	no	—
447	C₅×C₈	—	4	1	no	—
448	C₅×C₈	—	4	1	no	—
449	C₅×C₈	—	4	1	no	—
450	C₅×C₈	—	4	1	no	—
451	C₅×C₈	—	4	1	no	—
452	C₅×C₈	—	4	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	C₅×D₄	1	1	yes	characteristic
455	C₂×M₁₆	—	2	1	no	—
456	C₂×M₁₆	—	2	1	no	—
457	C₂²×C₈	—	2	1	no	—
458	C₂²×C₈	—	2	1	no	—
459	C₂²×C₈	—	2	1	no	—
460	C₄⋊Q₈	—	2	1	no	—
461	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
462	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
463	#126	—	2	1	no	—
464	#126	—	2	1	no	—
465	#126	—	2	1	no	—
466	#126	—	2	1	no	—
467	#126	—	2	1	no	—
468	#126	—	2	1	no	—
469	#126	—	2	1	no	—
470	#125	—	2	1	no	—
471	#125	—	2	1	no	—
472	#125	—	2	1	no	—
473	#125	—	2	1	no	—
474	#125	—	2	1	no	—
475	#125	—	2	1	no	—
476	#125	—	2	1	no	—
477	#125	—	2	1	no	—
478	#125	—	2	1	no	—
479	#125	C₂×C₄×C₅	1	1	yes	characteristic
480	#125	C₂×C₄×C₅	1	1	yes	characteristic
481	#125	C₂×C₄×C₅	1	1	yes	characteristic
482	#125	C₂×C₄×C₅	1	1	yes	characteristic
483	#125	C₂³×C₅	1	1	yes	characteristic
484	#125	C₂³×C₅	1	1	yes	characteristic
485	#125	C₂³×C₅	1	1	yes	characteristic
486	#124	C₂³×C₅	1	1	yes	characteristic
487	#123	—	2	1	no	—
488	#123	—	2	1	no	—
489	#123	—	2	1	no	—
490	#123	—	2	1	no	—
491	#123	—	2	1	no	—
492	#123	—	2	1	no	—
493	#123	—	2	1	no	—
494	#123	—	2	1	no	—
495	#123	—	2	1	no	—
496	C₂²⋊Q₈	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
505	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
506	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
507	#121	—	2	1	no	—
508	#121	—	2	1	no	—
509	#121	C₂×C₄×C₅	1	1	yes	characteristic
510	#121	C₂×C₄×C₅	1	1	yes	characteristic
511	#121	C₂×C₄×C₅	1	1	yes	characteristic
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
516	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
517	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
518	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
519	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
527	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
528	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
529	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
530	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
531	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
532	C₄×D₄	C₅×D₄	1	1	yes	characteristic
533	C₄×D₄	C₅×D₄	1	1	yes	characteristic
534	C₄×D₄	C₅×D₄	1	1	yes	characteristic
535	#117	—	2	1	no	—
536	#117	—	2	1	no	—
537	#117	—	2	1	no	—
538	#117	—	2	1	no	—
539	#117	—	2	1	no	—
540	#117	C₂×C₄×C₅	1	1	yes	characteristic
541	#117	C₂×C₄×C₅	1	1	yes	characteristic
542	#117	C₅×D₄	1	1	yes	characteristic
543	#117	C₅×D₄	1	1	yes	characteristic
544	#117	C₅×D₄	1	1	yes	characteristic
545	C₂×C₄⋊C₄	—	2	1	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	1	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
557	C₄⋊C₈	—	2	1	no	—
558	C₄⋊C₈	—	2	1	no	—
559	C₄⋊C₈	—	2	1	no	—
560	C₄⋊C₈	—	2	1	no	—
561	C₄⋊C₈	—	2	1	no	—
562	C₄⋊C₈	—	2	1	no	—
563	C₄⋊C₈	—	2	1	no	—
564	C₂²⋊C₈	—	2	1	no	—
565	C₂²⋊C₈	—	2	1	no	—
566	C₂²⋊C₈	—	2	1	no	—
567	C₂²⋊C₈	—	2	1	no	—
568	C₂²⋊C₈	—	2	1	no	—
569	C₂²⋊C₈	—	2	1	no	—
570	C₂²⋊C₈	—	2	1	no	—
571	#97	—	2	1	no	—
572	#97	—	2	1	no	—
573	#97	—	2	1	no	—
574	#97	C₂³×C₅	1	1	yes	characteristic
575	#97	C₂³×C₅	1	1	yes	characteristic
576	#97	C₂³×C₅	1	1	yes	characteristic
577	#97	C₂³×C₅	1	1	yes	characteristic
578	#97	C₂³×C₅	1	1	yes	characteristic
579	#97	C₂³×C₅	1	1	yes	characteristic
580	#97	C₂³×C₅	1	1	yes	characteristic
581	#97	C₂³×C₅	1	1	yes	characteristic
582	C₄×C₈	—	2	1	no	—
583	C₄×C₈	—	2	1	no	—
584	C₂²×C₅	—	2	1	no	—
585	C₂²×C₅	—	2	1	no	—
586	C₂²×C₅	—	2	1	no	—
587	C₂²×C₅	—	2	1	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	1	no	—
591	C₂²×C₅	—	2	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	#421	1	2	yes	—
596	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
597	C₄×C₅	—	2	1	no	—
598	C₄×C₅	—	2	1	no	—
599	C₄×C₅	—	2	1	no	—
600	C₄×C₅	—	2	1	no	—
601	C₄×C₅	—	2	1	no	—
602	C₄×C₅	—	2	1	no	—
603	C₄×C₅	—	2	1	no	—
604	C₄×C₅	—	2	1	no	—
605	C₄×C₅	—	2	1	no	—
606	C₄×C₅	—	2	1	no	—
607	C₄×C₅	—	2	1	no	—
608	C₄×C₅	—	2	1	no	—
609	C₄×C₅	—	4	1	no	—
610	C₄×C₅	—	4	1	no	—
611	C₄×C₅	—	4	1	no	—
612	C₄×C₅	—	4	1	no	—
613	C₄×C₅	—	4	1	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	—	4	1	no	—
616	#41	—	4	2	no	—
617	#41	—	4	4	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
621	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
626	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
627	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
628	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
639	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
641	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
643	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
644	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
645	M₁₆	—	4	2	no	—
646	M₁₆	—	4	2	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	4	2	no	—
656	C₂×C₈	—	4	2	no	—
657	C₂×C₈	—	4	2	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
685	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
686	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
687	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
688	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
689	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
690	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
691	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
692	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
693	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
694	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
695	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
710	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
711	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
712	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
713	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
714	C₂²⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
721	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
722	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
723	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
724	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
725	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
726	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
727	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
728	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
729	C₄²	C₂⁴×C₅	1	1	yes	characteristic
730	C₂×C₅	—	2	2	no	—
731	C₂×C₅	—	4	1	no	—
732	C₂×C₅	—	4	1	no	—
733	C₂×C₅	—	8	1	no	—
734	C₂×C₅	#2889	1	1	yes	characteristic
735	C₂×C₅	C₂×#421	1	1	yes	characteristic
736	C₂×C₅	#2901	1	1	yes	characteristic
737	C₂³	—	2	1	no	—
738	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
739	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
740	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	2	no	—
744	Q₈	—	8	1	no	—
745	D₄	—	2	2	no	—
746	D₄	—	2	2	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	2	no	—
750	D₄	—	4	2	no	—
751	D₄	—	8	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	8	1	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
776	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
777	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
778	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
779	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
780	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
781	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
782	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
783	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
784	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
787	C₈	—	2	2	no	—
788	C₈	—	4	1	no	—
789	C₈	—	4	1	no	—
790	C₈	—	4	1	no	—
791	C₈	—	4	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₅	#17680	1	1	yes	characteristic, direct product factor, Sylow
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	C₅×#421	1	2	yes	—
808	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₂	—	2	2	no	—
829	C₂	—	4	1	no	—
830	C₂	—	4	1	no	—
831	C₂	—	8	1	no	—
832	C₂	C₅×#2889	1	1	yes	characteristic
833	C₂	C₂×C₅×#421	1	1	yes	characteristic
834	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2970	C₂	semidirect
3. C₅×#2923	C₂	semidirect
4. C₅×#1537	C₂	semidirect
5. C₅×#1535	C₂	semidirect
6. C₅×#1535	C₂	semidirect
7. C₅×#1534	C₂	semidirect
8. C₅×#1532	C₂	semidirect
9. C₅×#1532	C₂	semidirect
10. C₅×#1531	C₂	semidirect
11. C₅×#1529	C₂	semidirect
12. C₅×#1528	C₂	semidirect
13. C₅×#1528	C₂	semidirect
14. C₅×#1524	C₂	semidirect
15. C₂×C₅×#330	C₂	semidirect
75. #17680	C₅	direct (N × H)
208. #2970	C₂×C₅	semidirect
209. #2923	C₂×C₅	semidirect
210. #1537	C₂×C₅	semidirect
211. #1535	C₂×C₅	semidirect
212. #1535	C₂×C₅	semidirect
213. #1534	C₂×C₅	semidirect
214. #1532	C₂×C₅	semidirect
215. #1532	C₂×C₅	semidirect
216. #1531	C₂×C₅	semidirect
217. #1529	C₂×C₅	semidirect
218. #1528	C₂×C₅	semidirect
219. #1528	C₂×C₅	semidirect
220. #1524	C₂×C₅	semidirect
221. C₂×#330	C₂×C₅	semidirect
795. C₅	#17680	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3515	2
C₅×#2970	2
C₅×#2923	2
C₅×#1537	2
C₅×#1535	2
C₅×#1534	2
C₅×#1532	2
C₅×#1531	2
C₅×#1529	2
C₅×#1528	2
C₅×#1524	2
C₂×C₅×#330	2
#17680	5

Subgroups — C5×#17680 #11940400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17680 #11940400