Subgroups — C₅×#80727 #14453439

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5609	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5598	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5154	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5111	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5040	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4886	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4787	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4781	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3265	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×D₃×D₄	—	2	1	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#121	C₂²	1	1	yes	characteristic
25	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
26	C₅×#940	C₂²	1	1	yes	characteristic
27	C₅×#939	—	2	1	no	—
28	C₅×#937	—	2	1	no	—
29	C₅×#936	C₂²	1	1	yes	characteristic, complemented
30	C₅×D₄×Dic₃	—	2	1	no	—
31	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#213	C₂²	1	1	yes	characteristic
34	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₅×#67	C₂²	1	1	yes	characteristic
36	C₅×#911	—	2	4	no	—
37	C₂×C₅×#204	—	2	4	no	—
38	C₂×C₅×#204	C₂²	1	1	yes	characteristic
39	C₂×C₅×#204	C₂²	1	1	yes	characteristic
40	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
43	C₅×#897	C₂²	1	1	yes	characteristic, complemented
44	C₅×#895	C₂²	1	1	yes	characteristic
45	C₅×#893	C₂²	1	1	yes	characteristic
46	C₅×#887	C₂²	1	1	yes	characteristic, complemented
47	C₅×#885	—	2	1	no	—
48	C₅×#884	—	2	1	no	—
49	C₅×#882	—	2	1	no	—
50	C₅×#878	—	2	1	no	—
51	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₅×#830	C₂²	1	1	yes	characteristic, complemented
55	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×#815	C₂²	1	1	yes	characteristic, complemented
57	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₅×#810	C₂²	1	1	yes	characteristic, complemented
59	C₅×#810	C₂²	1	1	yes	characteristic, complemented
60	C₅×#809	C₂²	1	1	yes	characteristic
61	C₅×#809	C₂²	1	1	yes	characteristic, complemented
62	#80727	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂²×C₅×SD₁₆	—	3	1	no	—
65	C₅×#548	—	3	1	no	—
66	C₅×D₄²	—	3	1	no	—
67	C₅×#496	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#466	D₃	1	1	yes	characteristic, complemented
70	C₅×#463	—	3	1	no	—
71	C₅×#460	—	3	1	no	—
72	C₅×#450	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#448	—	3	1	no	—
75	C₅×#447	—	3	1	no	—
76	C₅×#440	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₂³×C₅×D₃	—	2	1	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₂×C₅×#67	—	2	1	no	—
88	C₂×C₅×#67	—	2	1	no	—
89	C₂×C₅×#67	D₄	1	1	yes	characteristic
90	C₂²×C₅×Dic₃	—	2	1	no	—
91	C₂²×C₅×Dic₃	—	2	1	no	—
92	C₅×#237	—	2	2	no	—
93	C₅×#237	—	4	1	no	—
94	C₅×D₃×D₄	—	2	2	no	—
95	C₅×D₃×D₄	—	4	1	no	—
96	C₅×D₃×D₄	—	4	4	no	—
97	C₂×C₅×D₁₂	—	2	2	no	—
98	C₂×C₅×D₁₂	—	2	1	no	—
99	C₂×C₅×D₁₂	—	2	1	no	—
100	C₂×C₅×D₁₂	—	4	1	no	—
101	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
102	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₅×D₃	—	2	1	no	—
104	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
105	C₂×C₅×Dic₆	—	2	2	no	—
106	C₂×C₅×Dic₆	—	2	1	no	—
107	C₂×C₅×Dic₆	—	4	1	no	—
108	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
109	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
110	C₃×C₅×D₈	—	2	2	no	—
111	C₂×C₃×C₅×C₈	—	2	2	no	—
112	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₅×#217	—	2	1	no	—
119	C₅×#217	—	2	1	no	—
120	C₅×#217	D₄	1	1	yes	characteristic
121	C₅×#214	—	2	2	no	—
122	C₅×#214	—	4	1	no	—
123	C₅×#213	—	2	2	no	—
124	C₅×#213	—	4	1	no	—
125	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
126	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
129	C₅×C₄⋊Dic₃	—	2	1	no	—
130	C₅×Dic₃⋊C₄	—	2	1	no	—
131	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
132	C₄×C₅×Dic₃	—	2	1	no	—
133	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₅×#204	—	2	2	no	—
137	C₅×#204	—	2	2	no	—
138	C₅×#204	—	2	2	no	—
139	C₅×#204	D₄	1	4	yes	complemented
140	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
141	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂²×#204	C₂×C₅	1	1	yes	characteristic, complemented
143	#5609	C₂×C₅	1	1	yes	characteristic, complemented
144	#5598	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
146	#5154	C₂×C₅	1	1	yes	characteristic, complemented
147	#5111	C₂×C₅	1	1	yes	characteristic, complemented
148	#5040	C₂×C₅	1	1	yes	characteristic, complemented
149	#5036	C₂×C₅	1	1	yes	characteristic, complemented
150	#4889	C₂×C₅	1	1	yes	characteristic, complemented
151	#4886	C₂×C₅	1	1	yes	characteristic, complemented
152	#4787	C₂×C₅	1	1	yes	characteristic, complemented
153	#4781	C₂×C₅	1	1	yes	characteristic, complemented
154	#4776	C₂×C₅	1	1	yes	characteristic, complemented
155	#4762	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×C₅×#41	—	3	1	no	—
157	C₂²×C₅×Q₈	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₂²×C₅×D₄	—	3	1	no	—
160	C₂²×C₅×D₄	—	6	1	no	—
161	C₅×AGL(1,ℤ/8)	—	6	4	no	—
162	C₂×C₅×SD₁₆	—	3	1	no	—
163	C₂×C₅×SD₁₆	—	3	1	no	—
164	C₂×C₅×SD₁₆	—	3	1	no	—
165	C₂×C₅×SD₁₆	—	3	1	no	—
166	C₂×C₅×SD₁₆	—	3	1	no	—
167	C₂×C₅×SD₁₆	—	3	1	no	—
168	C₂×C₅×SD₁₆	—	6	4	no	—
169	C₂×C₅×D₈	—	3	1	no	—
170	C₂×C₅×D₈	—	3	1	no	—
171	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂×C₅×M₁₆	—	3	1	no	—
173	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
174	C₅×#127	—	3	1	no	—
175	C₅×#124	—	3	1	no	—
176	C₅×#124	—	6	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	6	1	no	—
179	C₅×#121	—	3	1	no	—
180	C₅×#121	—	6	1	no	—
181	C₅×#121	—	6	1	no	—
182	C₅×#121	C₂×D₃	1	1	yes	characteristic
183	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
184	C₅×#120	—	6	1	no	—
185	C₅×#120	—	6	1	no	—
186	C₄×C₅×Q₈	—	3	1	no	—
187	C₄×C₅×D₄	—	3	1	no	—
188	C₄×C₅×D₄	—	3	1	no	—
189	C₄×C₅×D₄	—	6	1	no	—
190	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
191	C₅×C₄⋊C₈	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
197	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×C₂²⋊C₈	—	3	1	no	—
200	C₅×#97	—	3	1	no	—
201	#3265	—	3	1	no	Sylow
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	2	1	no	—
207	C₂²×C₅×D₃	—	4	2	no	—
208	C₂²×C₅×D₃	—	4	2	no	—
209	C₂²×C₅×D₃	—	4	2	no	—
210	C₂²×C₅×D₃	—	4	2	no	—
211	C₂²×C₅×D₃	—	8	1	no	—
212	C₂²×C₅×D₃	—	8	1	no	—
213	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
214	C₃×C₅×D₄	—	2	1	no	—
215	C₃×C₅×D₄	—	2	1	no	—
216	C₃×C₅×D₄	—	2	1	no	—
217	C₃×C₅×D₄	—	2	1	no	—
218	C₃×C₅×D₄	—	4	2	no	—
219	C₃×C₅×D₄	—	4	2	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₅×#67	—	2	2	no	—
227	C₅×#67	—	4	2	no	—
228	C₅×#67	—	4	2	no	—
229	C₅×#67	—	4	2	no	—
230	C₅×#67	—	8	1	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	2	1	no	—
233	C₂×C₅×Dic₃	—	4	2	no	—
234	C₂×C₅×Dic₃	—	4	2	no	—
235	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
236	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
237	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
238	C₅×D₁₂	—	2	1	no	—
239	C₅×D₁₂	—	2	1	no	—
240	C₅×D₁₂	—	2	1	no	—
241	C₅×D₁₂	—	4	2	no	—
242	C₅×D₁₂	—	4	2	no	—
243	C₅×D₁₂	C₂×D₄	1	2	yes	—
244	C₄×C₅×D₃	—	2	1	no	—
245	C₄×C₅×D₃	—	2	1	no	—
246	C₄×C₅×D₃	—	4	2	no	—
247	C₅×Dic₆	—	2	1	no	—
248	C₅×Dic₆	—	2	1	no	—
249	C₅×Dic₆	—	2	1	no	—
250	C₅×Dic₆	—	4	2	no	—
251	C₅×Dic₆	C₂×D₄	1	2	yes	complemented
252	C₃×C₅×C₈	—	2	1	no	—
253	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
254	C₅×C₃⋊C₈	—	2	1	no	—
255	C₅×C₃⋊C₈	—	2	1	no	—
256	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×D₃×D₄	—	2	1	no	—
258	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
260	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#121	C₂²×C₅	1	1	yes	characteristic
264	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
265	#940	C₂²×C₅	1	1	yes	characteristic
266	#939	—	2	1	no	—
267	#937	—	2	1	no	—
268	#936	C₂²×C₅	1	1	yes	characteristic, complemented
269	D₄×Dic₃	—	2	1	no	—
270	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×#213	C₂²×C₅	1	1	yes	characteristic
273	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₄×#67	C₂²×C₅	1	1	yes	characteristic
275	#911	—	2	4	no	—
276	C₂×#204	—	2	4	no	—
277	C₂×#204	C₂²×C₅	1	1	yes	characteristic
278	C₂×#204	C₂²×C₅	1	1	yes	characteristic
279	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
282	#897	C₂²×C₅	1	1	yes	characteristic, complemented
283	#895	C₂²×C₅	1	1	yes	characteristic
284	#893	C₂²×C₅	1	1	yes	characteristic
285	#887	C₂²×C₅	1	1	yes	characteristic, complemented
286	#885	—	2	1	no	—
287	#884	—	2	1	no	—
288	#882	—	2	1	no	—
289	#878	—	2	1	no	—
290	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
293	#830	C₂²×C₅	1	1	yes	characteristic, complemented
294	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
295	#815	C₂²×C₅	1	1	yes	characteristic, complemented
296	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
297	#810	C₂²×C₅	1	1	yes	characteristic, complemented
298	#810	C₂²×C₅	1	1	yes	characteristic, complemented
299	#809	C₂²×C₅	1	1	yes	characteristic
300	#809	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂⁴×C₅	—	6	1	no	—
302	C₂⁴×C₅	—	6	1	no	—
303	C₅×#41	—	6	2	no	—
304	C₅×#41	—	12	1	no	—
305	C₂×C₅×Q₈	—	3	1	no	—
306	C₂×C₅×Q₈	—	3	1	no	—
307	C₂×C₅×Q₈	—	6	2	no	—
308	C₂×C₅×Q₈	—	6	1	no	—
309	C₂×C₅×Q₈	—	12	1	no	—
310	C₂×C₅×D₄	—	2	1	no	—
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	3	1	no	—
313	C₂×C₅×D₄	—	3	1	no	—
314	C₂×C₅×D₄	—	3	1	no	—
315	C₂×C₅×D₄	—	6	2	no	—
316	C₂×C₅×D₄	—	6	1	no	—
317	C₂×C₅×D₄	—	6	1	no	—
318	C₂×C₅×D₄	—	6	1	no	—
319	C₂×C₅×D₄	—	6	1	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	1	no	—
322	C₂×C₅×D₄	—	6	1	no	—
323	C₂×C₅×D₄	—	12	1	no	—
324	C₂×C₅×D₄	—	12	1	no	—
325	C₂×C₅×D₄	—	12	4	no	—
326	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
327	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	—	3	1	no	—
329	C₂²×C₄×C₅	—	6	1	no	—
330	C₂²×C₄×C₅	—	6	1	no	—
331	C₂²×C₄×C₅	—	6	1	no	—
332	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
333	C₅×SD₁₆	—	3	4	no	—
334	C₅×SD₁₆	—	6	2	no	—
335	C₅×SD₁₆	—	6	2	no	—
336	C₅×SD₁₆	—	6	2	no	—
337	C₅×SD₁₆	—	6	2	no	—
338	C₅×SD₁₆	—	12	1	no	—
339	C₅×D₈	—	2	2	no	—
340	C₅×D₈	—	6	2	no	—
341	C₅×D₈	—	12	1	no	—
342	C₅×M₁₆	—	6	2	no	—
343	C₂×C₅×C₈	—	2	2	no	—
344	C₂×C₅×C₈	—	3	1	no	—
345	C₂×C₅×C₈	—	3	1	no	—
346	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
347	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	—	3	1	no	—
349	C₅×C₄⋊C₄	—	6	1	no	—
350	C₅×C₄⋊C₄	—	6	1	no	—
351	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
352	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
353	C₅×C₂²⋊C₄	—	2	1	no	—
354	C₅×C₂²⋊C₄	—	2	1	no	—
355	C₅×C₂²⋊C₄	—	3	1	no	—
356	C₅×C₂²⋊C₄	—	3	1	no	—
357	C₅×C₂²⋊C₄	—	6	1	no	—
358	C₅×C₂²⋊C₄	—	6	1	no	—
359	C₅×C₂²⋊C₄	—	6	1	no	—
360	C₅×C₂²⋊C₄	—	6	1	no	—
361	C₅×C₂²⋊C₄	—	6	1	no	—
362	C₄²×C₅	—	3	1	no	—
363	C₄²×C₅	—	6	1	no	—
364	C₂×AGL(1,ℤ/8)	—	3	1	no	—
365	C₂²×SD₁₆	—	3	1	no	—
366	#548	—	3	1	no	—
367	D₄²	—	3	1	no	—
368	#496	—	3	1	no	—
369	#468	—	3	1	no	—
370	#466	C₅×D₃	1	1	yes	characteristic, complemented
371	#463	—	3	1	no	—
372	#460	—	3	1	no	—
373	#450	—	3	1	no	—
374	#449	—	3	1	no	—
375	#448	—	3	1	no	—
376	#447	—	3	1	no	—
377	#440	—	3	1	no	—
378	#435	—	3	1	no	—
379	C₂²×C₃×C₅	—	2	1	no	—
380	C₂²×C₃×C₅	—	2	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
388	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₅×D₃	—	2	1	no	—
390	C₂×C₅×D₃	—	2	2	no	—
391	C₂×C₅×D₃	—	2	1	no	—
392	C₂×C₅×D₃	—	2	1	no	—
393	C₂×C₅×D₃	—	4	1	no	—
394	C₂×C₅×D₃	—	4	1	no	—
395	C₂×C₅×D₃	—	4	1	no	—
396	C₂×C₅×D₃	—	4	1	no	—
397	C₂×C₅×D₃	—	4	1	no	—
398	C₂×C₅×D₃	—	8	4	no	—
399	C₂×C₅×D₃	—	8	4	no	—
400	C₃×C₄×C₅	—	2	1	no	—
401	C₃×C₄×C₅	—	4	1	no	—
402	C₃×C₄×C₅	—	4	1	no	—
403	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
404	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
405	C₅×Dic₃	—	2	2	no	—
406	C₅×Dic₃	—	2	1	no	—
407	C₅×Dic₃	—	2	1	no	—
408	C₅×Dic₃	—	2	1	no	—
409	C₅×Dic₃	—	4	1	no	—
410	C₂³×D₃	—	2	1	no	—
411	C₂³×D₃	—	2	1	no	—
412	C₂×C₃×D₄	—	2	1	no	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂×#67	—	2	1	no	—
418	C₂×#67	—	2	1	no	—
419	C₂×#67	—	2	1	no	—
420	C₂×#67	—	2	1	no	—
421	C₂×#67	C₅×D₄	1	1	yes	characteristic
422	C₂²×Dic₃	—	2	1	no	—
423	C₂²×Dic₃	—	2	1	no	—
424	#237	—	2	2	no	—
425	#237	—	4	1	no	—
426	D₃×D₄	—	2	2	no	—
427	D₃×D₄	—	4	1	no	—
428	D₃×D₄	—	4	4	no	—
429	C₂×D₁₂	—	2	2	no	—
430	C₂×D₁₂	—	2	1	no	—
431	C₂×D₁₂	—	2	1	no	—
432	C₂×D₁₂	—	4	1	no	—
433	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
434	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄×D₃	—	2	1	no	—
436	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
437	C₂×Dic₆	—	2	2	no	—
438	C₂×Dic₆	—	2	1	no	—
439	C₂×Dic₆	—	4	1	no	—
440	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
441	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
442	C₃×D₈	—	2	2	no	—
443	C₂×C₃×C₈	—	2	2	no	—
444	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
446	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
447	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
448	C₃×C₂²⋊C₄	—	2	1	no	—
449	C₃×C₂²⋊C₄	—	2	1	no	—
450	#217	—	2	1	no	—
451	#217	—	2	1	no	—
452	#217	C₅×D₄	1	1	yes	characteristic
453	#214	—	2	2	no	—
454	#214	—	4	1	no	—
455	#213	—	2	2	no	—
456	#213	—	4	1	no	—
457	(C₂×D₃)⋊C₄	—	2	1	no	—
458	(C₂×D₃)⋊C₄	—	2	1	no	—
459	(C₂×D₃)⋊C₄	—	2	1	no	—
460	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
461	C₄⋊Dic₃	—	2	1	no	—
462	Dic₃⋊C₄	—	2	1	no	—
463	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
464	C₄×Dic₃	—	2	1	no	—
465	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
466	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
467	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
468	#204	—	2	2	no	—
469	#204	—	2	2	no	—
470	#204	—	2	2	no	—
471	#204	C₅×D₄	1	4	yes	complemented
472	ΓL(1,𝔽₂₅)	—	2	2	no	—
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	3	1	no	—
476	C₂³×C₅	—	6	1	no	—
477	C₂³×C₅	—	6	1	no	—
478	C₂³×C₅	—	12	2	no	—
479	C₂³×C₅	—	12	2	no	—
480	C₂³×C₅	—	12	2	no	—
481	C₂³×C₅	—	12	2	no	—
482	C₂³×C₅	—	24	1	no	—
483	C₂³×C₅	—	24	1	no	—
484	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
485	C₅×Q₈	—	3	2	no	—
486	C₅×Q₈	—	6	1	no	—
487	C₅×Q₈	—	6	1	no	—
488	C₅×Q₈	—	6	1	no	—
489	C₅×Q₈	—	12	2	no	—
490	C₅×D₄	—	2	1	no	—
491	C₅×D₄	—	2	1	no	—
492	C₅×D₄	—	2	1	no	—
493	C₅×D₄	—	2	1	no	—
494	C₅×D₄	—	3	2	no	—
495	C₅×D₄	—	4	2	no	—
496	C₅×D₄	—	4	2	no	—
497	C₅×D₄	—	6	2	no	—
498	C₅×D₄	—	6	1	no	—
499	C₅×D₄	—	6	1	no	—
500	C₅×D₄	—	6	1	no	—
501	C₅×D₄	—	12	2	no	—
502	C₅×D₄	—	12	2	no	—
503	C₅×D₄	—	12	2	no	—
504	C₅×D₄	—	12	2	no	—
505	C₅×D₄	—	12	2	no	—
506	C₅×D₄	—	24	1	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	—	3	1	no	—
512	C₂×C₄×C₅	—	3	1	no	—
513	C₂×C₄×C₅	—	3	1	no	—
514	C₂×C₄×C₅	—	6	1	no	—
515	C₂×C₄×C₅	—	6	1	no	—
516	C₂×C₄×C₅	—	6	1	no	—
517	C₂×C₄×C₅	—	6	1	no	—
518	C₂×C₄×C₅	—	12	2	no	—
519	C₂×C₄×C₅	—	12	2	no	—
520	C₂×C₄×C₅	—	12	2	no	—
521	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
523	C₅×C₈	—	2	1	no	—
524	C₅×C₈	—	6	1	no	—
525	C₅×C₈	—	6	1	no	—
526	C₅×C₈	D₃×D₄	1	2	yes	complemented
527	C₂×#41	—	3	1	no	—
528	C₂²×Q₈	—	3	1	no	—
529	C₂²×D₄	—	3	1	no	—
530	C₂²×D₄	—	3	1	no	—
531	C₂²×D₄	—	6	1	no	—
532	AGL(1,ℤ/8)	—	6	4	no	—
533	C₂×SD₁₆	—	3	1	no	—
534	C₂×SD₁₆	—	3	1	no	—
535	C₂×SD₁₆	—	3	1	no	—
536	C₂×SD₁₆	—	3	1	no	—
537	C₂×SD₁₆	—	3	1	no	—
538	C₂×SD₁₆	—	3	1	no	—
539	C₂×SD₁₆	—	6	4	no	—
540	C₂×D₈	—	3	1	no	—
541	C₂×D₈	—	3	1	no	—
542	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
543	C₂×M₁₆	—	3	1	no	—
544	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
545	#127	—	3	1	no	—
546	#124	—	3	1	no	—
547	#124	—	6	1	no	—
548	C₂²⋊Q₈	—	3	1	no	—
549	C₂²⋊Q₈	—	6	1	no	—
550	#121	—	3	1	no	—
551	#121	—	6	1	no	—
552	#121	—	6	1	no	—
553	#121	C₂×C₅×D₃	1	1	yes	characteristic
554	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	#120	—	6	1	no	—
556	#120	—	6	1	no	—
557	C₄×Q₈	—	3	1	no	—
558	C₄×D₄	—	3	1	no	—
559	C₄×D₄	—	3	1	no	—
560	C₄×D₄	—	6	1	no	—
561	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
562	C₄⋊C₈	—	3	1	no	—
563	#103	—	3	1	no	—
564	#103	—	3	1	no	—
565	#102	—	3	1	no	—
566	#102	—	3	1	no	—
567	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
568	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂²⋊C₈	—	3	1	no	—
570	C₂²⋊C₈	—	3	1	no	—
571	#97	—	3	1	no	—
572	C₂×C₃×C₅	—	2	2	no	—
573	C₂×C₃×C₅	—	8	1	no	—
574	C₂×C₃×C₅	—	8	1	no	—
575	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
576	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
577	C₂×C₃×C₅	#577	1	1	yes	characteristic
578	C₅×D₃	—	4	1	no	—
579	C₅×D₃	—	4	2	no	—
580	C₅×D₃	—	8	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
584	C₂²×D₃	—	2	1	no	—
585	C₂²×D₃	—	2	1	no	—
586	C₂²×D₃	—	4	2	no	—
587	C₂²×D₃	—	4	2	no	—
588	C₂²×D₃	—	4	2	no	—
589	C₂²×D₃	—	4	2	no	—
590	C₂²×D₃	—	8	1	no	—
591	C₂²×D₃	—	8	1	no	—
592	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
593	C₃×D₄	—	2	1	no	—
594	C₃×D₄	—	2	1	no	—
595	C₃×D₄	—	2	1	no	—
596	C₃×D₄	—	2	1	no	—
597	C₃×D₄	—	4	2	no	—
598	C₃×D₄	—	4	2	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
605	#67	—	2	2	no	—
606	#67	—	4	2	no	—
607	#67	—	4	2	no	—
608	#67	—	4	2	no	—
609	#67	—	8	1	no	—
610	C₂×Dic₃	—	2	1	no	—
611	C₂×Dic₃	—	2	1	no	—
612	C₂×Dic₃	—	4	2	no	—
613	C₂×Dic₃	—	4	2	no	—
614	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
615	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
616	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
617	D₁₂	—	2	1	no	—
618	D₁₂	—	2	1	no	—
619	D₁₂	—	2	1	no	—
620	D₁₂	—	4	2	no	—
621	D₁₂	—	4	2	no	—
622	D₁₂	C₂×C₅×D₄	1	2	yes	—
623	C₄×D₃	—	2	1	no	—
624	C₄×D₃	—	2	1	no	—
625	C₄×D₃	—	4	2	no	—
626	Dic₆	—	2	1	no	—
627	Dic₆	—	2	1	no	—
628	Dic₆	—	2	1	no	—
629	Dic₆	—	4	2	no	—
630	Dic₆	C₂×C₅×D₄	1	2	yes	complemented
631	C₃×C₈	—	2	1	no	—
632	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
633	C₃⋊C₈	—	2	1	no	—
634	C₃⋊C₈	—	2	1	no	—
635	C₂²×C₅	—	2	1	no	—
636	C₂²×C₅	—	2	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	—	4	1	no	—
642	C₂²×C₅	—	4	1	no	—
643	C₂²×C₅	—	6	1	no	—
644	C₂²×C₅	—	6	1	no	—
645	C₂²×C₅	—	6	1	no	—
646	C₂²×C₅	—	6	2	no	—
647	C₂²×C₅	—	12	1	no	—
648	C₂²×C₅	—	12	1	no	—
649	C₂²×C₅	—	12	1	no	—
650	C₂²×C₅	—	12	1	no	—
651	C₂²×C₅	—	12	1	no	—
652	C₂²×C₅	—	24	4	no	—
653	C₂²×C₅	—	24	4	no	—
654	C₂²×C₅	#911	1	2	yes	complemented
655	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
656	C₄×C₅	—	2	1	no	—
657	C₄×C₅	—	4	1	no	—
658	C₄×C₅	—	4	1	no	—
659	C₄×C₅	—	6	1	no	—
660	C₄×C₅	—	6	1	no	—
661	C₄×C₅	—	6	1	no	—
662	C₄×C₅	—	6	2	no	—
663	C₄×C₅	—	12	1	no	—
664	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
665	C₄×C₅	#1009	1	1	yes	characteristic
666	C₂⁴	—	6	1	no	—
667	C₂⁴	—	6	1	no	—
668	#41	—	6	2	no	—
669	#41	—	12	1	no	—
670	C₂×Q₈	—	3	1	no	—
671	C₂×Q₈	—	3	1	no	—
672	C₂×Q₈	—	6	2	no	—
673	C₂×Q₈	—	6	1	no	—
674	C₂×Q₈	—	12	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	6	2	no	—
681	C₂×D₄	—	6	1	no	—
682	C₂×D₄	—	6	1	no	—
683	C₂×D₄	—	6	1	no	—
684	C₂×D₄	—	6	1	no	—
685	C₂×D₄	—	6	2	no	—
686	C₂×D₄	—	6	1	no	—
687	C₂×D₄	—	6	1	no	—
688	C₂×D₄	—	12	1	no	—
689	C₂×D₄	—	12	1	no	—
690	C₂×D₄	—	12	4	no	—
691	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
692	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	6	1	no	—
695	C₂²×C₄	—	6	1	no	—
696	C₂²×C₄	—	6	1	no	—
697	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
698	SD₁₆	—	3	4	no	—
699	SD₁₆	—	6	2	no	—
700	SD₁₆	—	6	2	no	—
701	SD₁₆	—	6	2	no	—
702	SD₁₆	—	6	2	no	—
703	SD₁₆	—	12	1	no	—
704	D₈	—	2	2	no	—
705	D₈	—	6	2	no	—
706	D₈	—	12	1	no	—
707	M₁₆	—	6	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	3	1	no	—
710	C₂×C₈	—	3	1	no	—
711	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₄⋊C₄	—	3	1	no	—
714	C₄⋊C₄	—	6	1	no	—
715	C₄⋊C₄	—	6	1	no	—
716	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	3	1	no	—
721	C₂²⋊C₄	—	3	1	no	—
722	C₂²⋊C₄	—	6	1	no	—
723	C₂²⋊C₄	—	6	1	no	—
724	C₂²⋊C₄	—	6	1	no	—
725	C₂²⋊C₄	—	6	1	no	—
726	C₂²⋊C₄	—	6	1	no	—
727	C₄²	—	3	1	no	—
728	C₄²	—	6	1	no	—
729	C₃×C₅	#3265	1	1	yes	characteristic, complemented, Hall
730	C₂²×C₃	—	2	1	no	—
731	C₂²×C₃	—	2	1	no	—
732	C₂²×C₃	—	4	1	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
739	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
740	C₂×D₃	—	2	1	no	—
741	C₂×D₃	—	2	2	no	—
742	C₂×D₃	—	2	1	no	—
743	C₂×D₃	—	2	1	no	—
744	C₂×D₃	—	4	1	no	—
745	C₂×D₃	—	4	1	no	—
746	C₂×D₃	—	4	1	no	—
747	C₂×D₃	—	4	1	no	—
748	C₂×D₃	—	4	1	no	—
749	C₂×D₃	—	8	4	no	—
750	C₂×D₃	—	8	4	no	—
751	C₃×C₄	—	2	1	no	—
752	C₃×C₄	—	4	1	no	—
753	C₃×C₄	—	4	1	no	—
754	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
755	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
756	Dic₃	—	2	2	no	—
757	Dic₃	—	2	1	no	—
758	Dic₃	—	2	1	no	—
759	Dic₃	—	2	1	no	—
760	Dic₃	—	4	1	no	—
761	C₂×C₅	—	2	2	no	—
762	C₂×C₅	—	8	1	no	—
763	C₂×C₅	—	8	1	no	—
764	C₂×C₅	—	12	1	no	—
765	C₂×C₅	—	12	2	no	—
766	C₂×C₅	—	24	1	no	—
767	C₂×C₅	#5609	1	1	yes	characteristic
768	C₂×C₅	C₂×#911	1	1	yes	characteristic
769	C₂×C₅	#5770	1	1	yes	characteristic
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	3	1	no	—
773	C₂³	—	6	1	no	—
774	C₂³	—	6	1	no	—
775	C₂³	—	12	2	no	—
776	C₂³	—	12	2	no	—
777	C₂³	—	12	2	no	—
778	C₂³	—	12	2	no	—
779	C₂³	—	24	1	no	—
780	C₂³	—	24	1	no	—
781	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
782	Q₈	—	3	2	no	—
783	Q₈	—	6	1	no	—
784	Q₈	—	6	1	no	—
785	Q₈	—	6	1	no	—
786	Q₈	—	12	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	3	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	2	no	—
794	D₄	—	6	2	no	—
795	D₄	—	6	1	no	—
796	D₄	—	6	1	no	—
797	D₄	—	6	1	no	—
798	D₄	—	12	2	no	—
799	D₄	—	12	2	no	—
800	D₄	—	12	2	no	—
801	D₄	—	12	2	no	—
802	D₄	—	12	2	no	—
803	D₄	—	24	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	3	1	no	—
809	C₂×C₄	—	3	1	no	—
810	C₂×C₄	—	3	1	no	—
811	C₂×C₄	—	6	1	no	—
812	C₂×C₄	—	6	1	no	—
813	C₂×C₄	—	6	1	no	—
814	C₂×C₄	—	6	1	no	—
815	C₂×C₄	—	12	2	no	—
816	C₂×C₄	—	12	2	no	—
817	C₂×C₄	—	12	2	no	—
818	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
820	C₈	—	2	1	no	—
821	C₈	—	6	1	no	—
822	C₈	—	6	1	no	—
823	C₈	C₅×D₃×D₄	1	2	yes	complemented
824	C₂×C₃	—	2	2	no	—
825	C₂×C₃	—	8	1	no	—
826	C₂×C₃	—	8	1	no	—
827	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
828	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
829	C₂×C₃	C₅×#577	1	1	yes	characteristic
830	D₃	—	4	1	no	—
831	D₃	—	4	2	no	—
832	D₃	—	8	1	no	—
833	C₅	#80727	1	1	yes	characteristic, direct product factor, Sylow
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	6	1	no	—
843	C₂²	—	6	1	no	—
844	C₂²	—	6	1	no	—
845	C₂²	—	6	2	no	—
846	C₂²	—	12	1	no	—
847	C₂²	—	12	1	no	—
848	C₂²	—	12	1	no	—
849	C₂²	—	12	1	no	—
850	C₂²	—	12	1	no	—
851	C₂²	—	24	4	no	—
852	C₂²	—	24	4	no	—
853	C₂²	C₅×#911	1	2	yes	complemented
854	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	6	1	no	—
859	C₄	—	6	1	no	—
860	C₄	—	6	1	no	—
861	C₄	—	6	2	no	—
862	C₄	—	12	1	no	—
863	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
864	C₄	C₅×#1009	1	1	yes	characteristic
865	C₃	C₅×#3265	1	1	yes	characteristic, complemented, Sylow
866	C₂	—	2	2	no	—
867	C₂	—	8	1	no	—
868	C₂	—	8	1	no	—
869	C₂	—	12	1	no	—
870	C₂	—	12	2	no	—
871	C₂	—	24	1	no	—
872	C₂	C₅×#5609	1	1	yes	characteristic
873	C₂	C₂×C₅×#911	1	1	yes	characteristic
874	C₂	C₅×#5770	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#466	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#466	D₃
hypocenter	C₃	C₅×#3265
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#466

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#911	C₂	semidirect
2. C₂²×C₅×#204	C₂	semidirect
3. C₅×#5609	C₂	semidirect
4. C₅×#5598	C₂	semidirect
5. C₃×C₅×#466	C₂	semidirect
6. C₅×#5154	C₂	semidirect
7. C₅×#5111	C₂	semidirect
8. C₅×#5040	C₂	semidirect
9. C₅×#5036	C₂	semidirect
10. C₅×#4889	C₂	semidirect
11. C₅×#4886	C₂	semidirect
12. C₅×#4787	C₂	semidirect
13. C₅×#4781	C₂	semidirect
14. C₅×#4776	C₂	semidirect
15. C₅×#4762	C₂	semidirect
17. C₂×C₅×#237	C₂²	semidirect
21. C₂²×C₅×Dic₆	C₂²	semidirect
22. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₃×C₅×#121	C₂²	semidirect
29. C₅×#936	C₂²	semidirect
31. C₂×C₅×#214	C₂²	semidirect
32. C₂×C₅×#214	C₂²	semidirect
34. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×#204	C₂²	semidirect
41. C₂×C₅×#204	C₂²	semidirect
42. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
43. C₅×#897	C₂²	semidirect
46. C₅×#887	C₂²	semidirect
51. C₃×C₅×#107	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₅×#830	C₂²	semidirect
55. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
56. C₅×#815	C₂²	semidirect
57. C₅×Dic₃⋊C₈	C₂²	semidirect
58. C₅×#810	C₂²	semidirect
59. C₅×#810	C₂²	semidirect
61. C₅×#809	C₂²	semidirect
62. #80727	C₅	direct (N × H)
69. C₅×#466	D₃	semidirect
139. C₅×#204	D₄	semidirect
141. C₂×#911	C₂×C₅	semidirect
142. C₂²×#204	C₂×C₅	semidirect
143. #5609	C₂×C₅	semidirect
144. #5598	C₂×C₅	semidirect
145. C₃×#466	C₂×C₅	semidirect
146. #5154	C₂×C₅	semidirect
147. #5111	C₂×C₅	semidirect
148. #5040	C₂×C₅	semidirect
149. #5036	C₂×C₅	semidirect
150. #4889	C₂×C₅	semidirect
151. #4886	C₂×C₅	semidirect
152. #4787	C₂×C₅	semidirect
153. #4781	C₂×C₅	semidirect
154. #4776	C₂×C₅	semidirect
155. #4762	C₂×C₅	semidirect
171. C₂×C₅×D₈	C₂×D₃	semidirect
173. C₂²×C₅×C₈	C₂×D₃	semidirect
183. C₅×#121	C₂×D₃	semidirect
190. C₅×#107	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
197. C₅×#102	C₂×D₃	semidirect
251. C₅×Dic₆	C₂×D₄	semidirect
253. C₃×C₅×C₈	C₂×D₄	semidirect
256. C₂×#237	C₂²×C₅	semidirect
260. C₂²×Dic₆	C₂²×C₅	semidirect
261. C₂×C₃×D₈	C₂²×C₅	semidirect
262. C₂²×C₃×C₈	C₂²×C₅	semidirect
264. C₃×#121	C₂²×C₅	semidirect
268. #936	C₂²×C₅	semidirect
270. C₂×#214	C₂²×C₅	semidirect
271. C₂×#214	C₂²×C₅	semidirect
273. C₂×#213	C₂²×C₅	semidirect
279. C₂×#204	C₂²×C₅	semidirect
280. C₂×#204	C₂²×C₅	semidirect
281. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
282. #897	C₂²×C₅	semidirect
285. #887	C₂²×C₅	semidirect
290. C₃×#107	C₂²×C₅	semidirect
291. C₃×#102	C₂²×C₅	semidirect
292. C₃×#102	C₂²×C₅	semidirect
293. #830	C₂²×C₅	semidirect
294. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
295. #815	C₂²×C₅	semidirect
296. Dic₃⋊C₈	C₂²×C₅	semidirect
297. #810	C₂²×C₅	semidirect
298. #810	C₂²×C₅	semidirect
300. #809	C₂²×C₅	semidirect
370. #466	C₅×D₃	semidirect
387. C₂²×C₃×C₅	AGL(1,ℤ/8)	semidirect
471. #204	C₅×D₄	semidirect
526. C₅×C₈	D₃×D₄	semidirect
542. C₂×D₈	C₂×C₅×D₃	semidirect
544. C₂²×C₈	C₂×C₅×D₃	semidirect
554. #121	C₂×C₅×D₃	semidirect
561. #107	C₂×C₅×D₃	semidirect
567. #102	C₂×C₅×D₃	semidirect
568. #102	C₂×C₅×D₃	semidirect
630. Dic₆	C₂×C₅×D₄	semidirect
632. C₃×C₈	C₂×C₅×D₄	semidirect
654. C₂²×C₅	#911	semidirect
729. C₃×C₅	#3265	semidirect
738. C₂²×C₃	C₅×AGL(1,ℤ/8)	semidirect
823. C₈	C₅×D₃×D₄	semidirect
833. C₅	#80727	direct (N × H)
853. C₂²	C₅×#911	semidirect
865. C₃	C₅×#3265	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#911	2
C₂²×C₅×#204	2
C₅×#5609	2
C₅×#5598	2
C₃×C₅×#466	2
C₅×#5154	2
C₅×#5111	2
C₅×#5040	2
C₅×#5036	2
C₅×#4889	2
C₅×#4886	2
C₅×#4787	2
C₅×#4781	2
C₅×#4776	2
C₅×#4762	2
C₅×#3265	3
#80727	5

Subgroups — C5×#80727 #14453439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80727 #14453439