Subgroups — C₅×#80728 #14454204

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 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	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5612	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5599	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×#5037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5037	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×#4786	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4773	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3268	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×#235	C₂²	1	1	yes	characteristic
20	C₂×C₅×#235	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
25	C₅×#940	—	2	1	no	—
26	C₅×#940	C₂²	1	1	yes	characteristic, complemented
27	C₅×#939	—	2	1	no	—
28	C₅×#938	—	2	1	no	—
29	C₅×#937	—	2	1	no	—
30	C₅×#936	C₂²	1	1	yes	characteristic
31	C₂×C₅×#214	C₂²	1	1	yes	characteristic
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
35	C₄×C₅×#67	C₂²	1	1	yes	characteristic
36	C₅×#911	—	2	4	no	—
37	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
38	C₅×#904	—	2	4	no	—
39	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×#204	C₂²	1	1	yes	characteristic
41	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
43	C₅×#897	C₂²	1	1	yes	characteristic
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×#884	—	2	1	no	—
48	C₅×#883	—	2	1	no	—
49	C₅×#67⋊C₄	—	2	1	no	—
50	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
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
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	#80728	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂×C₅×#135	—	3	1	no	—
65	C₅×#550	—	3	1	no	—
66	C₅×#546	—	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×#464	—	3	1	no	—
71	C₅×#459	—	3	1	no	—
72	C₅×#452	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#449	—	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	C₂×C₃×C₅×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₅×#67	—	2	1	no	—
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	—	2	1	no	—
90	C₂×C₅×#67	D₄	1	1	yes	characteristic
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×#235	—	2	2	no	—
97	C₅×#235	—	2	2	no	—
98	C₅×#235	—	4	1	no	—
99	C₅×#235	—	4	1	no	—
100	C₂×C₅×D₁₂	—	2	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	—	2	1	no	—
105	C₂×C₄×C₅×D₃	—	2	1	no	—
106	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
107	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
108	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
109	C₃×C₅×D₈	—	2	2	no	—
110	C₂×C₃×C₅×C₈	—	2	2	no	—
111	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₅×#217	—	2	1	no	—
118	C₅×#217	—	2	1	no	—
119	C₅×#217	D₄	1	1	yes	characteristic
120	C₅×#214	—	2	2	no	—
121	C₅×#214	—	4	1	no	—
122	C₅×#213	—	2	2	no	—
123	C₅×#213	—	4	1	no	—
124	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
125	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
126	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
128	C₅×C₄⋊Dic₃	—	2	1	no	—
129	C₅×Dic₃⋊C₄	—	2	1	no	—
130	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
131	C₄×C₅×Dic₃	—	2	1	no	—
132	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
133	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₅×Dic₁₂	—	2	2	no	—
136	C₅×D₂₄	—	2	2	no	—
137	C₅×#204	—	2	2	no	—
138	C₅×#204	D₄	1	4	yes	complemented
139	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
140	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
142	#5612	C₂×C₅	1	1	yes	characteristic, complemented
143	#5599	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
145	#5154	C₂×C₅	1	1	yes	characteristic, complemented
146	#5111	C₂×C₅	1	1	yes	characteristic, complemented
147	#5037	C₂×C₅	1	1	yes	characteristic, complemented
148	#5037	C₂×C₅	1	1	yes	characteristic, complemented
149	#4889	C₂×C₅	1	1	yes	characteristic, complemented
150	#4886	C₂×C₅	1	1	yes	characteristic, complemented
151	#4786	C₂×C₅	1	1	yes	characteristic, complemented
152	#4783	C₂×C₅	1	1	yes	characteristic, complemented
153	#4773	C₂×C₅	1	1	yes	characteristic, complemented
154	#4767	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	—	3	1	no	—
156	C₂×C₅×#41	—	3	1	no	—
157	C₂×C₅×#41	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₅×AGL(1,ℤ/8)	—	6	4	no	—
160	C₅×#135	—	6	4	no	—
161	C₂×C₅×Q₁₆	—	3	1	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×D₈	—	3	1	no	—
167	C₂×C₅×D₈	—	3	1	no	—
168	C₂×C₅×D₈	—	3	1	no	—
169	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
170	C₂×C₅×M₁₆	—	3	1	no	—
171	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₅×#127	—	3	1	no	—
173	C₅×#127	—	6	1	no	—
174	C₅×#124	—	3	1	no	—
175	C₅×#123	—	6	1	no	—
176	C₅×C₂²⋊Q₈	—	3	1	no	—
177	C₅×#121	—	3	1	no	—
178	C₅×#121	—	6	1	no	—
179	C₅×#121	—	6	1	no	—
180	C₅×#121	—	6	1	no	—
181	C₅×#121	C₂×D₃	1	1	yes	characteristic
182	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
183	C₅×#120	—	6	1	no	—
184	C₄×C₅×Q₈	—	3	1	no	—
185	C₄×C₅×D₄	—	3	1	no	—
186	C₄×C₅×D₄	—	3	1	no	—
187	C₄×C₅×D₄	—	6	1	no	—
188	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
189	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
190	C₅×C₄⋊C₈	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	C₂×D₃	1	1	yes	characteristic
196	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
197	C₅×C₂²⋊C₈	—	3	1	no	—
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×#97	—	3	1	no	—
200	#3268	—	3	1	no	Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	4	2	no	—
207	C₂²×C₅×D₃	—	4	2	no	—
208	C₂²×C₅×D₃	—	8	1	no	—
209	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
210	C₃×C₅×D₄	—	2	1	no	—
211	C₃×C₅×D₄	—	2	1	no	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	2	1	no	—
214	C₃×C₅×D₄	—	8	1	no	—
215	C₃×C₅×D₄	—	8	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₅×#67	—	4	1	no	—
223	C₅×#67	—	4	2	no	—
224	C₅×#67	—	4	2	no	—
225	C₅×#67	—	4	2	no	—
226	C₅×#67	—	4	2	no	—
227	C₅×#67	—	4	2	no	—
228	C₅×#67	—	8	1	no	—
229	C₂×C₅×Dic₃	—	2	1	no	—
230	C₂×C₅×Dic₃	—	2	1	no	—
231	C₂×C₅×Dic₃	—	4	2	no	—
232	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
235	C₅×D₁₂	—	2	1	no	—
236	C₅×D₁₂	—	2	1	no	—
237	C₅×D₁₂	—	2	1	no	—
238	C₅×D₁₂	—	8	1	no	—
239	C₅×D₁₂	C₂×D₄	1	2	yes	—
240	C₄×C₅×D₃	—	2	1	no	—
241	C₄×C₅×D₃	—	2	1	no	—
242	C₄×C₅×D₃	—	4	2	no	—
243	C₄×C₅×D₃	—	4	2	no	—
244	C₄×C₅×D₃	—	8	1	no	—
245	C₅×Dic₆	—	2	1	no	—
246	C₅×Dic₆	—	2	1	no	—
247	C₅×Dic₆	—	2	1	no	—
248	C₅×Dic₆	C₂×D₄	1	2	yes	—
249	C₃×C₅×C₈	—	2	1	no	—
250	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
251	C₅×C₃⋊C₈	—	2	1	no	—
252	C₅×C₃⋊C₈	—	2	1	no	—
253	C₂×#237	C₂²×C₅	1	1	yes	characteristic
254	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×#235	C₂²×C₅	1	1	yes	characteristic
256	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
258	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₃×#121	C₂²×C₅	1	1	yes	characteristic
260	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
261	#940	—	2	1	no	—
262	#940	C₂²×C₅	1	1	yes	characteristic, complemented
263	#939	—	2	1	no	—
264	#938	—	2	1	no	—
265	#937	—	2	1	no	—
266	#936	C₂²×C₅	1	1	yes	characteristic
267	C₂×#214	C₂²×C₅	1	1	yes	characteristic
268	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₂×#213	C₂²×C₅	1	1	yes	characteristic
270	C₂×#213	C₂²×C₅	1	1	yes	characteristic
271	C₄×#67	C₂²×C₅	1	1	yes	characteristic
272	#911	—	2	4	no	—
273	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
274	#904	—	2	4	no	—
275	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×#204	C₂²×C₅	1	1	yes	characteristic
277	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
279	#897	C₂²×C₅	1	1	yes	characteristic
280	#895	C₂²×C₅	1	1	yes	characteristic
281	#893	C₂²×C₅	1	1	yes	characteristic
282	#887	C₂²×C₅	1	1	yes	characteristic, complemented
283	#884	—	2	1	no	—
284	#883	—	2	1	no	—
285	#67⋊C₄	—	2	1	no	—
286	D₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₃×#102	C₂²×C₅	1	1	yes	characteristic
289	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
290	#830	C₂²×C₅	1	1	yes	characteristic, complemented
291	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
292	#815	C₂²×C₅	1	1	yes	characteristic, complemented
293	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
294	#810	C₂²×C₅	1	1	yes	characteristic, complemented
295	#810	C₂²×C₅	1	1	yes	characteristic, complemented
296	#809	C₂²×C₅	1	1	yes	characteristic
297	#809	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂⁴×C₅	—	6	1	no	—
299	C₅×#41	—	6	2	no	—
300	C₅×#41	—	6	2	no	—
301	C₅×#41	—	6	2	no	—
302	C₅×#41	—	12	1	no	—
303	C₅×#41	—	12	1	no	—
304	C₅×#41	—	12	1	no	—
305	C₂×C₅×Q₈	—	3	1	no	—
306	C₂×C₅×Q₈	—	3	1	no	—
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	—	3	1	no	—
310	C₂×C₅×D₄	—	3	1	no	—
311	C₂×C₅×D₄	—	3	1	no	—
312	C₂×C₅×D₄	—	6	1	no	—
313	C₂×C₅×D₄	—	6	1	no	—
314	C₂×C₅×D₄	—	6	1	no	—
315	C₂×C₅×D₄	—	6	1	no	—
316	C₂×C₅×D₄	—	6	2	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	—	12	1	no	—
321	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
322	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
323	C₂²×C₄×C₅	—	3	1	no	—
324	C₂²×C₄×C₅	—	6	1	no	—
325	C₂²×C₄×C₅	—	6	1	no	—
326	C₂²×C₄×C₅	—	6	1	no	—
327	C₂²×C₄×C₅	—	6	1	no	—
328	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
329	C₅×Q₁₆	—	6	2	no	—
330	C₅×SD₁₆	—	3	4	no	—
331	C₅×SD₁₆	—	6	2	no	—
332	C₅×SD₁₆	—	6	2	no	—
333	C₅×SD₁₆	—	12	1	no	—
334	C₅×D₈	—	2	2	no	—
335	C₅×D₈	—	6	2	no	—
336	C₅×D₈	—	6	2	no	—
337	C₅×D₈	—	12	1	no	—
338	C₅×M₁₆	—	6	2	no	—
339	C₂×C₅×C₈	—	2	2	no	—
340	C₂×C₅×C₈	—	3	1	no	—
341	C₂×C₅×C₈	—	3	1	no	—
342	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
343	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
344	C₅×C₄⋊C₄	—	3	1	no	—
345	C₅×C₄⋊C₄	—	6	1	no	—
346	C₅×C₄⋊C₄	—	6	1	no	—
347	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	1	no	—
351	C₅×C₂²⋊C₄	—	3	1	no	—
352	C₅×C₂²⋊C₄	—	3	1	no	—
353	C₅×C₂²⋊C₄	—	6	1	no	—
354	C₅×C₂²⋊C₄	—	6	1	no	—
355	C₅×C₂²⋊C₄	—	6	1	no	—
356	C₅×C₂²⋊C₄	—	6	1	no	—
357	C₅×C₂²⋊C₄	—	6	1	no	—
358	C₄²×C₅	—	3	1	no	—
359	C₄²×C₅	—	6	1	no	—
360	C₂×AGL(1,ℤ/8)	—	3	1	no	—
361	C₂×#135	—	3	1	no	—
362	#550	—	3	1	no	—
363	#546	—	3	1	no	—
364	#496	—	3	1	no	—
365	#468	—	3	1	no	—
366	#466	C₅×D₃	1	1	yes	characteristic, complemented
367	#464	—	3	1	no	—
368	#459	—	3	1	no	—
369	#452	—	3	1	no	—
370	#449	—	3	1	no	—
371	#449	—	3	1	no	—
372	#447	—	3	1	no	—
373	#440	—	3	1	no	—
374	#435	—	3	1	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	2	1	no	—
377	C₂²×C₃×C₅	—	2	1	no	—
378	C₂²×C₃×C₅	—	4	1	no	—
379	C₂²×C₃×C₅	—	4	1	no	—
380	C₂²×C₃×C₅	—	4	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	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₅×D₃	—	2	1	no	—
386	C₂×C₅×D₃	—	2	2	no	—
387	C₂×C₅×D₃	—	2	1	no	—
388	C₂×C₅×D₃	—	2	1	no	—
389	C₂×C₅×D₃	—	4	1	no	—
390	C₂×C₅×D₃	—	4	1	no	—
391	C₂×C₅×D₃	—	4	1	no	—
392	C₂×C₅×D₃	—	4	1	no	—
393	C₂×C₅×D₃	—	4	1	no	—
394	C₂×C₅×D₃	—	8	4	no	—
395	C₃×C₄×C₅	—	2	1	no	—
396	C₃×C₄×C₅	—	4	1	no	—
397	C₃×C₄×C₅	—	4	1	no	—
398	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
399	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
400	C₅×Dic₃	—	2	2	no	—
401	C₅×Dic₃	—	2	1	no	—
402	C₅×Dic₃	—	2	1	no	—
403	C₅×Dic₃	—	2	1	no	—
404	C₅×Dic₃	—	4	1	no	—
405	C₂³×D₃	—	2	1	no	—
406	C₂×C₃×D₄	—	2	1	no	—
407	C₂×C₃×D₄	—	2	1	no	—
408	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂×#67	—	2	1	no	—
412	C₂×#67	—	2	1	no	—
413	C₂×#67	—	2	1	no	—
414	C₂×#67	—	2	1	no	—
415	C₂×#67	—	2	1	no	—
416	C₂×#67	—	2	1	no	—
417	C₂×#67	C₅×D₄	1	1	yes	characteristic
418	C₂²×Dic₃	—	2	1	no	—
419	#237	—	2	2	no	—
420	#237	—	4	1	no	—
421	D₃×D₄	—	2	2	no	—
422	D₃×D₄	—	4	1	no	—
423	#235	—	2	2	no	—
424	#235	—	2	2	no	—
425	#235	—	4	1	no	—
426	#235	—	4	1	no	—
427	C₂×D₁₂	—	2	1	no	—
428	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
429	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₄×D₃	—	2	1	no	—
431	C₂×C₄×D₃	—	2	1	no	—
432	C₂×C₄×D₃	—	2	1	no	—
433	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
434	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
435	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
436	C₃×D₈	—	2	2	no	—
437	C₂×C₃×C₈	—	2	2	no	—
438	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
440	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
441	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
442	C₃×C₂²⋊C₄	—	2	1	no	—
443	C₃×C₂²⋊C₄	—	2	1	no	—
444	#217	—	2	1	no	—
445	#217	—	2	1	no	—
446	#217	C₅×D₄	1	1	yes	characteristic
447	#214	—	2	2	no	—
448	#214	—	4	1	no	—
449	#213	—	2	2	no	—
450	#213	—	4	1	no	—
451	(C₂×D₃)⋊C₄	—	2	1	no	—
452	(C₂×D₃)⋊C₄	—	2	1	no	—
453	(C₂×D₃)⋊C₄	—	2	1	no	—
454	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
455	C₄⋊Dic₃	—	2	1	no	—
456	Dic₃⋊C₄	—	2	1	no	—
457	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
458	C₄×Dic₃	—	2	1	no	—
459	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
460	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
461	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
462	Dic₁₂	—	2	2	no	—
463	D₂₄	—	2	2	no	—
464	#204	—	2	2	no	—
465	#204	C₅×D₄	1	4	yes	complemented
466	ΓL(1,𝔽₂₅)	—	2	2	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	3	1	no	—
470	C₂³×C₅	—	6	1	no	—
471	C₂³×C₅	—	6	1	no	—
472	C₂³×C₅	—	12	2	no	—
473	C₂³×C₅	—	12	2	no	—
474	C₂³×C₅	—	24	1	no	—
475	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
476	C₅×Q₈	—	3	2	no	—
477	C₅×Q₈	—	6	1	no	—
478	C₅×Q₈	—	6	1	no	—
479	C₅×Q₈	—	6	1	no	—
480	C₅×D₄	—	2	1	no	—
481	C₅×D₄	—	2	1	no	—
482	C₅×D₄	—	2	1	no	—
483	C₅×D₄	—	2	1	no	—
484	C₅×D₄	—	3	2	no	—
485	C₅×D₄	—	6	1	no	—
486	C₅×D₄	—	6	1	no	—
487	C₅×D₄	—	6	1	no	—
488	C₅×D₄	—	8	1	no	—
489	C₅×D₄	—	8	1	no	—
490	C₅×D₄	—	12	1	no	—
491	C₅×D₄	—	12	2	no	—
492	C₅×D₄	—	12	2	no	—
493	C₅×D₄	—	12	2	no	—
494	C₅×D₄	—	12	2	no	—
495	C₅×D₄	—	12	2	no	—
496	C₅×D₄	—	24	1	no	—
497	C₅×D₄	—	24	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	3	1	no	—
503	C₂×C₄×C₅	—	3	1	no	—
504	C₂×C₄×C₅	—	3	1	no	—
505	C₂×C₄×C₅	—	6	1	no	—
506	C₂×C₄×C₅	—	6	1	no	—
507	C₂×C₄×C₅	—	6	1	no	—
508	C₂×C₄×C₅	—	6	1	no	—
509	C₂×C₄×C₅	—	12	2	no	—
510	C₂×C₄×C₅	—	12	2	no	—
511	C₂×C₄×C₅	—	12	2	no	—
512	C₂×C₄×C₅	—	24	1	no	—
513	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
515	C₅×C₈	—	2	1	no	—
516	C₅×C₈	—	6	1	no	—
517	C₅×C₈	—	6	1	no	—
518	C₅×C₈	D₃×D₄	1	2	yes	—
519	C₂×#41	—	3	1	no	—
520	C₂×#41	—	3	1	no	—
521	C₂×#41	—	3	1	no	—
522	C₂²×D₄	—	3	1	no	—
523	AGL(1,ℤ/8)	—	6	4	no	—
524	#135	—	6	4	no	—
525	C₂×Q₁₆	—	3	1	no	—
526	C₂×SD₁₆	—	3	1	no	—
527	C₂×SD₁₆	—	3	1	no	—
528	C₂×SD₁₆	—	3	1	no	—
529	C₂×SD₁₆	—	3	1	no	—
530	C₂×D₈	—	3	1	no	—
531	C₂×D₈	—	3	1	no	—
532	C₂×D₈	—	3	1	no	—
533	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
534	C₂×M₁₆	—	3	1	no	—
535	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
536	#127	—	3	1	no	—
537	#127	—	6	1	no	—
538	#124	—	3	1	no	—
539	#123	—	6	1	no	—
540	C₂²⋊Q₈	—	3	1	no	—
541	#121	—	3	1	no	—
542	#121	—	6	1	no	—
543	#121	—	6	1	no	—
544	#121	—	6	1	no	—
545	#121	C₂×C₅×D₃	1	1	yes	characteristic
546	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
547	#120	—	6	1	no	—
548	C₄×Q₈	—	3	1	no	—
549	C₄×D₄	—	3	1	no	—
550	C₄×D₄	—	3	1	no	—
551	C₄×D₄	—	6	1	no	—
552	C₂×C₂²⋊C₄	—	6	1	no	—
553	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
554	C₄⋊C₈	—	3	1	no	—
555	#103	—	3	1	no	—
556	#103	—	3	1	no	—
557	#102	—	3	1	no	—
558	#102	—	3	1	no	—
559	#102	C₂×C₅×D₃	1	1	yes	characteristic
560	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
561	C₂²⋊C₈	—	3	1	no	—
562	C₂²⋊C₈	—	3	1	no	—
563	#97	—	3	1	no	—
564	C₂×C₃×C₅	—	4	1	no	—
565	C₂×C₃×C₅	—	8	1	no	—
566	C₂×C₃×C₅	—	8	1	no	—
567	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
568	C₂×C₃×C₅	#575	1	1	yes	characteristic
569	C₂×C₃×C₅	#576	1	1	yes	characteristic
570	C₅×D₃	—	4	1	no	—
571	C₅×D₃	—	4	2	no	—
572	C₅×D₃	—	8	1	no	—
573	C₂³×C₃	—	2	1	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂²×D₃	—	2	1	no	—
577	C₂²×D₃	—	2	1	no	—
578	C₂²×D₃	—	4	2	no	—
579	C₂²×D₃	—	4	2	no	—
580	C₂²×D₃	—	8	1	no	—
581	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
582	C₃×D₄	—	2	1	no	—
583	C₃×D₄	—	2	1	no	—
584	C₃×D₄	—	2	1	no	—
585	C₃×D₄	—	2	1	no	—
586	C₃×D₄	—	8	1	no	—
587	C₃×D₄	—	8	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
594	#67	—	4	1	no	—
595	#67	—	4	2	no	—
596	#67	—	4	2	no	—
597	#67	—	4	2	no	—
598	#67	—	4	2	no	—
599	#67	—	4	2	no	—
600	#67	—	8	1	no	—
601	C₂×Dic₃	—	2	1	no	—
602	C₂×Dic₃	—	2	1	no	—
603	C₂×Dic₃	—	4	2	no	—
604	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
605	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
607	D₁₂	—	2	1	no	—
608	D₁₂	—	2	1	no	—
609	D₁₂	—	2	1	no	—
610	D₁₂	—	8	1	no	—
611	D₁₂	C₂×C₅×D₄	1	2	yes	—
612	C₄×D₃	—	2	1	no	—
613	C₄×D₃	—	2	1	no	—
614	C₄×D₃	—	4	2	no	—
615	C₄×D₃	—	4	2	no	—
616	C₄×D₃	—	8	1	no	—
617	Dic₆	—	2	1	no	—
618	Dic₆	—	2	1	no	—
619	Dic₆	—	2	1	no	—
620	Dic₆	C₂×C₅×D₄	1	2	yes	—
621	C₃×C₈	—	2	1	no	—
622	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
623	C₃⋊C₈	—	2	1	no	—
624	C₃⋊C₈	—	2	1	no	—
625	C₂²×C₅	—	2	1	no	—
626	C₂²×C₅	—	2	1	no	—
627	C₂²×C₅	—	2	1	no	—
628	C₂²×C₅	—	4	1	no	—
629	C₂²×C₅	—	4	1	no	—
630	C₂²×C₅	—	4	1	no	—
631	C₂²×C₅	—	4	1	no	—
632	C₂²×C₅	—	4	1	no	—
633	C₂²×C₅	—	4	1	no	—
634	C₂²×C₅	—	6	1	no	—
635	C₂²×C₅	—	6	1	no	—
636	C₂²×C₅	—	6	1	no	—
637	C₂²×C₅	—	6	2	no	—
638	C₂²×C₅	—	12	1	no	—
639	C₂²×C₅	—	12	1	no	—
640	C₂²×C₅	—	12	1	no	—
641	C₂²×C₅	—	12	1	no	—
642	C₂²×C₅	—	12	1	no	—
643	C₂²×C₅	—	24	4	no	—
644	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	4	1	no	—
647	C₄×C₅	—	4	1	no	—
648	C₄×C₅	—	6	1	no	—
649	C₄×C₅	—	6	1	no	—
650	C₄×C₅	—	6	1	no	—
651	C₄×C₅	—	6	2	no	—
652	C₄×C₅	—	12	1	no	—
653	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
654	C₄×C₅	#1009	1	1	yes	characteristic
655	C₂⁴	—	6	1	no	—
656	#41	—	6	2	no	—
657	#41	—	6	2	no	—
658	#41	—	6	2	no	—
659	#41	—	12	1	no	—
660	#41	—	12	1	no	—
661	#41	—	12	1	no	—
662	C₂×Q₈	—	3	1	no	—
663	C₂×Q₈	—	3	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	3	1	no	—
667	C₂×D₄	—	3	1	no	—
668	C₂×D₄	—	3	1	no	—
669	C₂×D₄	—	6	1	no	—
670	C₂×D₄	—	6	1	no	—
671	C₂×D₄	—	6	1	no	—
672	C₂×D₄	—	6	1	no	—
673	C₂×D₄	—	6	2	no	—
674	C₂×D₄	—	6	1	no	—
675	C₂×D₄	—	6	1	no	—
676	C₂×D₄	—	6	1	no	—
677	C₂×D₄	—	12	1	no	—
678	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
679	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
680	C₂²×C₄	—	3	1	no	—
681	C₂²×C₄	—	6	1	no	—
682	C₂²×C₄	—	6	1	no	—
683	C₂²×C₄	—	6	1	no	—
684	C₂²×C₄	—	6	1	no	—
685	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
686	Q₁₆	—	6	2	no	—
687	SD₁₆	—	3	4	no	—
688	SD₁₆	—	6	2	no	—
689	SD₁₆	—	6	2	no	—
690	SD₁₆	—	12	1	no	—
691	D₈	—	2	2	no	—
692	D₈	—	6	2	no	—
693	D₈	—	6	2	no	—
694	D₈	—	12	1	no	—
695	M₁₆	—	6	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	3	1	no	—
698	C₂×C₈	—	3	1	no	—
699	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
700	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
701	C₄⋊C₄	—	3	1	no	—
702	C₄⋊C₄	—	6	1	no	—
703	C₄⋊C₄	—	6	1	no	—
704	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	3	1	no	—
709	C₂²⋊C₄	—	3	1	no	—
710	C₂²⋊C₄	—	6	1	no	—
711	C₂²⋊C₄	—	6	1	no	—
712	C₂²⋊C₄	—	6	1	no	—
713	C₂²⋊C₄	—	6	1	no	—
714	C₂²⋊C₄	—	6	1	no	—
715	C₄²	—	3	1	no	—
716	C₄²	—	6	1	no	—
717	C₃×C₅	#3268	1	1	yes	characteristic, complemented, Hall
718	C₂²×C₃	—	2	1	no	—
719	C₂²×C₃	—	2	1	no	—
720	C₂²×C₃	—	2	1	no	—
721	C₂²×C₃	—	4	1	no	—
722	C₂²×C₃	—	4	1	no	—
723	C₂²×C₃	—	4	1	no	—
724	C₂²×C₃	—	4	1	no	—
725	C₂²×C₃	—	4	1	no	—
726	C₂²×C₃	—	4	1	no	—
727	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
728	C₂×D₃	—	2	1	no	—
729	C₂×D₃	—	2	2	no	—
730	C₂×D₃	—	2	1	no	—
731	C₂×D₃	—	2	1	no	—
732	C₂×D₃	—	4	1	no	—
733	C₂×D₃	—	4	1	no	—
734	C₂×D₃	—	4	1	no	—
735	C₂×D₃	—	4	1	no	—
736	C₂×D₃	—	4	1	no	—
737	C₂×D₃	—	8	4	no	—
738	C₃×C₄	—	2	1	no	—
739	C₃×C₄	—	4	1	no	—
740	C₃×C₄	—	4	1	no	—
741	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
742	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
743	Dic₃	—	2	2	no	—
744	Dic₃	—	2	1	no	—
745	Dic₃	—	2	1	no	—
746	Dic₃	—	2	1	no	—
747	Dic₃	—	4	1	no	—
748	C₂×C₅	—	4	1	no	—
749	C₂×C₅	—	8	1	no	—
750	C₂×C₅	—	8	1	no	—
751	C₂×C₅	—	12	1	no	—
752	C₂×C₅	—	12	2	no	—
753	C₂×C₅	—	24	1	no	—
754	C₂×C₅	#5609	1	1	yes	characteristic
755	C₂×C₅	#5757	1	1	yes	characteristic
756	C₂×C₅	#5768	1	1	yes	characteristic
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	3	1	no	—
760	C₂³	—	6	1	no	—
761	C₂³	—	6	1	no	—
762	C₂³	—	12	2	no	—
763	C₂³	—	12	2	no	—
764	C₂³	—	24	1	no	—
765	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
766	Q₈	—	3	2	no	—
767	Q₈	—	6	1	no	—
768	Q₈	—	6	1	no	—
769	Q₈	—	6	1	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	1	no	—
773	D₄	—	2	1	no	—
774	D₄	—	3	2	no	—
775	D₄	—	6	1	no	—
776	D₄	—	6	1	no	—
777	D₄	—	6	1	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	1	no	—
780	D₄	—	12	1	no	—
781	D₄	—	12	2	no	—
782	D₄	—	12	2	no	—
783	D₄	—	12	2	no	—
784	D₄	—	12	2	no	—
785	D₄	—	12	2	no	—
786	D₄	—	24	1	no	—
787	D₄	—	24	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	3	1	no	—
793	C₂×C₄	—	3	1	no	—
794	C₂×C₄	—	3	1	no	—
795	C₂×C₄	—	6	1	no	—
796	C₂×C₄	—	6	1	no	—
797	C₂×C₄	—	6	1	no	—
798	C₂×C₄	—	6	1	no	—
799	C₂×C₄	—	12	2	no	—
800	C₂×C₄	—	12	2	no	—
801	C₂×C₄	—	12	2	no	—
802	C₂×C₄	—	24	1	no	—
803	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
805	C₈	—	2	1	no	—
806	C₈	—	6	1	no	—
807	C₈	—	6	1	no	—
808	C₈	C₅×D₃×D₄	1	2	yes	—
809	C₂×C₃	—	4	1	no	—
810	C₂×C₃	—	8	1	no	—
811	C₂×C₃	—	8	1	no	—
812	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
813	C₂×C₃	C₅×#575	1	1	yes	characteristic
814	C₂×C₃	C₅×#576	1	1	yes	characteristic
815	D₃	—	4	1	no	—
816	D₃	—	4	2	no	—
817	D₃	—	8	1	no	—
818	C₅	#80728	1	1	yes	characteristic, direct product factor, Sylow
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	6	1	no	—
829	C₂²	—	6	1	no	—
830	C₂²	—	6	1	no	—
831	C₂²	—	6	2	no	—
832	C₂²	—	12	1	no	—
833	C₂²	—	12	1	no	—
834	C₂²	—	12	1	no	—
835	C₂²	—	12	1	no	—
836	C₂²	—	12	1	no	—
837	C₂²	—	24	4	no	—
838	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	6	1	no	—
843	C₄	—	6	1	no	—
844	C₄	—	6	1	no	—
845	C₄	—	6	2	no	—
846	C₄	—	12	1	no	—
847	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
848	C₄	C₅×#1009	1	1	yes	characteristic
849	C₃	C₅×#3268	1	1	yes	characteristic, complemented, Sylow
850	C₂	—	4	1	no	—
851	C₂	—	8	1	no	—
852	C₂	—	8	1	no	—
853	C₂	—	12	1	no	—
854	C₂	—	12	2	no	—
855	C₂	—	24	1	no	—
856	C₂	C₅×#5609	1	1	yes	characteristic
857	C₂	C₅×#5757	1	1	yes	characteristic
858	C₂	C₅×#5768	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×#3268
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. C₂×C₅×#904	C₂	semidirect
3. C₅×#5612	C₂	semidirect
4. C₅×#5599	C₂	semidirect
5. C₃×C₅×#466	C₂	semidirect
6. C₅×#5154	C₂	semidirect
7. C₅×#5111	C₂	semidirect
8. C₅×#5037	C₂	semidirect
9. C₅×#5037	C₂	semidirect
10. C₅×#4889	C₂	semidirect
11. C₅×#4886	C₂	semidirect
12. C₅×#4786	C₂	semidirect
13. C₅×#4783	C₂	semidirect
14. C₅×#4773	C₂	semidirect
15. C₅×#4767	C₂	semidirect
20. C₂×C₅×#235	C₂²	semidirect
22. C₂²×C₃×C₅×C₈	C₂²	semidirect
24. C₃×C₅×#121	C₂²	semidirect
26. C₅×#940	C₂²	semidirect
32. C₂×C₅×#214	C₂²	semidirect
37. C₂×C₅×Dic₁₂	C₂²	semidirect
41. C₂×C₅×#204	C₂²	semidirect
46. C₅×#887	C₂²	semidirect
51. C₃×C₅×#107	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₅×#830	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. #80728	C₅	direct (N × H)
69. C₅×#466	D₃	semidirect
138. C₅×#204	D₄	semidirect
140. C₂×#911	C₂×C₅	semidirect
141. C₂×#904	C₂×C₅	semidirect
142. #5612	C₂×C₅	semidirect
143. #5599	C₂×C₅	semidirect
144. C₃×#466	C₂×C₅	semidirect
145. #5154	C₂×C₅	semidirect
146. #5111	C₂×C₅	semidirect
147. #5037	C₂×C₅	semidirect
148. #5037	C₂×C₅	semidirect
149. #4889	C₂×C₅	semidirect
150. #4886	C₂×C₅	semidirect
151. #4786	C₂×C₅	semidirect
152. #4783	C₂×C₅	semidirect
153. #4773	C₂×C₅	semidirect
154. #4767	C₂×C₅	semidirect
171. C₂²×C₅×C₈	C₂×D₃	semidirect
182. C₅×#121	C₂×D₃	semidirect
189. C₅×#107	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
256. C₂×#235	C₂²×C₅	semidirect
258. C₂²×C₃×C₈	C₂²×C₅	semidirect
260. C₃×#121	C₂²×C₅	semidirect
262. #940	C₂²×C₅	semidirect
268. C₂×#214	C₂²×C₅	semidirect
273. C₂×Dic₁₂	C₂²×C₅	semidirect
277. C₂×#204	C₂²×C₅	semidirect
282. #887	C₂²×C₅	semidirect
287. C₃×#107	C₂²×C₅	semidirect
289. C₃×#102	C₂²×C₅	semidirect
290. #830	C₂²×C₅	semidirect
292. #815	C₂²×C₅	semidirect
293. Dic₃⋊C₈	C₂²×C₅	semidirect
294. #810	C₂²×C₅	semidirect
295. #810	C₂²×C₅	semidirect
297. #809	C₂²×C₅	semidirect
366. #466	C₅×D₃	semidirect
465. #204	C₅×D₄	semidirect
535. C₂²×C₈	C₂×C₅×D₃	semidirect
546. #121	C₂×C₅×D₃	semidirect
553. #107	C₂×C₅×D₃	semidirect
560. #102	C₂×C₅×D₃	semidirect
717. C₃×C₅	#3268	semidirect
818. C₅	#80728	direct (N × H)
849. C₃	C₅×#3268	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
C₂×C₅×#904	2
C₅×#5612	2
C₅×#5599	2
C₃×C₅×#466	2
C₅×#5154	2
C₅×#5111	2
C₅×#5037	2
C₅×#4889	2
C₅×#4886	2
C₅×#4786	2
C₅×#4783	2
C₅×#4773	2
C₅×#4767	2
C₅×#3268	3
#80728	5

Subgroups — C5×#80728 #14454204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80728 #14454204