Subgroups — C₅×#80122 #14453937

Order 1920.

1000 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×#5824	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5612	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5167	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5041	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4785	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4733	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4730	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3267	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×#235	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₅×#950	—	2	4	no	—
25	C₅×#946	C₂²	1	1	yes	characteristic
26	C₅×#944	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#215	C₂²	1	1	yes	characteristic
29	C₅×#939	—	2	1	no	—
30	C₅×#938	—	2	1	no	—
31	C₅×#937	—	2	1	no	—
32	C₅×#936	C₂²	1	1	yes	characteristic
33	C₅×#935	—	2	1	no	—
34	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#214	C₂²	1	1	yes	characteristic
36	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#213	C₂²	1	1	yes	characteristic
38	C₅×#929	—	2	1	no	—
39	C₄×C₅×#67	C₂²	1	1	yes	characteristic
40	C₅×#924	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
42	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₅×#911	—	2	4	no	—
44	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×#204	C₂²	1	1	yes	characteristic
46	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
47	C₅×#897	C₂²	1	1	yes	characteristic
48	C₅×#893	C₂²	1	1	yes	characteristic
49	C₅×#883	—	2	1	no	—
50	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×#832	C₂²	1	1	yes	characteristic
55	C₅×#821	C₂²	1	1	yes	characteristic
56	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×#816	C₂²	1	1	yes	characteristic, complemented
58	C₅×#815	C₂²	1	1	yes	characteristic, complemented
59	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×#810	C₂²	1	1	yes	characteristic, complemented
61	C₅×#808	C₂²	1	1	yes	characteristic, complemented
62	#80122	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×#547	—	3	1	no	—
66	C₅×#546	—	3	1	no	—
67	C₅×#497	—	3	1	no	—
68	C₅×#470	—	3	1	no	—
69	C₅×#465	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#461	—	3	1	no	—
72	C₅×#452	—	3	1	no	—
73	C₅×#452	—	3	1	no	—
74	C₅×#450	—	3	1	no	—
75	C₅×#449	D₃	1	1	yes	characteristic, complemented
76	C₅×#442	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	4	1	no	—
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₅×#67	—	2	1	no	—
89	C₂×C₅×#67	—	2	1	no	—
90	C₂×C₅×#67	—	2	1	no	—
91	C₂×C₅×#67	D₄	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	—	2	1	no	—
93	C₂²×C₅×Dic₃	—	2	1	no	—
94	C₅×#237	—	2	2	no	—
95	C₅×#237	—	4	1	no	—
96	C₅×D₃×D₄	—	2	2	no	—
97	C₅×D₃×D₄	—	4	1	no	—
98	C₅×#235	—	2	2	no	—
99	C₅×#235	—	4	1	no	—
100	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	—	2	1	no	—
102	C₂×C₄×C₅×D₃	—	2	1	no	—
103	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
104	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
105	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
106	C₃×C₅×SD₁₆	—	4	1	no	—
107	C₃×C₅×D₈	—	2	2	no	—
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₅×#217	—	2	1	no	—
113	C₅×#217	—	2	1	no	—
114	C₅×#217	—	2	1	no	—
115	C₅×#217	—	2	1	no	—
116	C₅×#217	D₄	1	1	yes	characteristic
117	C₅×#216	—	2	2	no	—
118	C₅×#215	—	2	2	no	—
119	C₅×#214	—	2	2	no	—
120	C₅×#214	—	2	2	no	—
121	C₅×#213	D₄	1	4	yes	complemented
122	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
125	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
126	C₅×C₄⋊Dic₃	—	2	1	no	—
127	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
128	C₅×Dic₃⋊C₄	—	2	1	no	—
129	C₅×Dic₃⋊C₄	—	2	1	no	—
130	C₅×Dic₃⋊C₄	—	2	1	no	—
131	C₅×Dic₃⋊C₄	—	2	1	no	—
132	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
133	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₃⋊C₈	—	2	2	no	—
135	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₅×Dic₁₂	—	4	1	no	—
138	C₅×#204	—	2	2	no	—
139	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
140	#5824	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
143	#5612	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
145	#5169	C₂×C₅	1	1	yes	characteristic, complemented
146	#5167	C₂×C₅	1	1	yes	characteristic, complemented
147	#5153	C₂×C₅	1	1	yes	characteristic, complemented
148	#5041	C₂×C₅	1	1	yes	characteristic, complemented
149	#4818	C₂×C₅	1	1	yes	characteristic, complemented
150	#4816	C₂×C₅	1	1	yes	characteristic, complemented
151	#4785	C₂×C₅	1	1	yes	characteristic, complemented
152	#4783	C₂×C₅	1	1	yes	characteristic, complemented
153	#4733	C₂×C₅	1	1	yes	characteristic, complemented
154	#4730	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	C₂×D₃	1	1	yes	characteristic, complemented
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×Q₁₆	—	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	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
172	C₅×C₄⋊Q₈	—	3	1	no	—
173	C₅×#124	—	3	1	no	—
174	C₅×#123	—	6	1	no	—
175	C₅×#123	—	6	1	no	—
176	C₅×#123	—	6	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	3	1	no	—
179	C₅×C₂²⋊Q₈	—	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×#120	—	6	1	no	—
184	C₄×C₅×D₄	—	3	1	no	—
185	C₄×C₅×D₄	—	3	1	no	—
186	C₄×C₅×D₄	—	3	1	no	—
187	C₂×C₅×C₄⋊C₄	—	6	1	no	—
188	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
189	C₅×#106	—	3	1	no	—
190	C₅×C₄⋊C₈	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
197	C₅×C₂²⋊C₈	—	3	1	no	—
198	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
199	C₅×#97	—	3	1	no	—
200	#3267	—	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	—	4	2	no	—
206	C₂²×C₅×D₃	—	4	2	no	—
207	C₂²×C₅×D₃	—	8	1	no	—
208	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	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	—	4	2	no	—
215	C₃×C₅×D₄	—	8	1	no	—
216	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	4	2	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
224	C₅×#67	—	4	1	no	—
225	C₅×#67	—	4	2	no	—
226	C₅×#67	—	4	2	no	—
227	C₅×#67	—	4	2	no	—
228	C₂×C₅×Dic₃	—	2	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	—	4	2	no	—
233	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
235	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
236	C₅×D₁₂	—	2	1	no	—
237	C₅×D₁₂	C₂×D₄	1	2	yes	—
238	C₄×C₅×D₃	—	2	1	no	—
239	C₄×C₅×D₃	—	2	1	no	—
240	C₄×C₅×D₃	—	4	2	no	—
241	C₄×C₅×D₃	—	8	1	no	—
242	C₅×Dic₆	—	2	1	no	—
243	C₅×Dic₆	—	2	1	no	—
244	C₅×Dic₆	—	2	1	no	—
245	C₅×Dic₆	—	2	1	no	—
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×C₅×C₈	—	2	1	no	—
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
250	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×#237	C₂²×C₅	1	1	yes	characteristic
252	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×#235	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
256	C₃×#121	C₂²×C₅	1	1	yes	characteristic
257	#950	—	2	4	no	—
258	#946	C₂²×C₅	1	1	yes	characteristic
259	#944	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂×#215	C₂²×C₅	1	1	yes	characteristic
262	#939	—	2	1	no	—
263	#938	—	2	1	no	—
264	#937	—	2	1	no	—
265	#936	C₂²×C₅	1	1	yes	characteristic
266	#935	—	2	1	no	—
267	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×#214	C₂²×C₅	1	1	yes	characteristic
269	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×#213	C₂²×C₅	1	1	yes	characteristic
271	#929	—	2	1	no	—
272	C₄×#67	C₂²×C₅	1	1	yes	characteristic
273	#924	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂×Dic₃⋊C₄	—	2	1	no	—
275	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	#911	—	2	4	no	—
277	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×#204	C₂²×C₅	1	1	yes	characteristic
279	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
280	#897	C₂²×C₅	1	1	yes	characteristic
281	#893	C₂²×C₅	1	1	yes	characteristic
282	#883	—	2	1	no	—
283	D₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	#832	C₂²×C₅	1	1	yes	characteristic
288	#821	C₂²×C₅	1	1	yes	characteristic
289	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
290	#816	C₂²×C₅	1	1	yes	characteristic, complemented
291	#815	C₂²×C₅	1	1	yes	characteristic, complemented
292	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
293	#810	C₂²×C₅	1	1	yes	characteristic, complemented
294	#808	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂⁴×C₅	—	6	1	no	—
296	C₅×#41	—	2	2	no	—
297	C₅×#41	—	4	1	no	—
298	C₅×#41	—	6	2	no	—
299	C₅×#41	—	6	2	no	—
300	C₅×#41	—	12	1	no	—
301	C₅×#41	—	12	1	no	—
302	C₂×C₅×Q₈	—	3	1	no	—
303	C₂×C₅×Q₈	—	3	1	no	—
304	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₅×D₄	—	2	1	no	—
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	3	1	no	—
308	C₂×C₅×D₄	—	3	1	no	—
309	C₂×C₅×D₄	—	6	1	no	—
310	C₂×C₅×D₄	—	6	2	no	—
311	C₂×C₅×D₄	—	6	1	no	—
312	C₂×C₅×D₄	—	6	1	no	—
313	C₂×C₅×D₄	—	12	1	no	—
314	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
315	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
316	C₂²×C₄×C₅	—	2	1	no	—
317	C₂²×C₄×C₅	—	3	1	no	—
318	C₂²×C₄×C₅	—	6	1	no	—
319	C₂²×C₄×C₅	—	6	1	no	—
320	C₂²×C₄×C₅	—	6	1	no	—
321	C₂²×C₄×C₅	—	6	1	no	—
322	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₅×Q₁₆	—	6	2	no	—
324	C₅×Q₁₆	—	12	1	no	—
325	C₅×SD₁₆	—	4	1	no	—
326	C₅×SD₁₆	—	6	2	no	—
327	C₅×SD₁₆	—	6	2	no	—
328	C₅×SD₁₆	—	6	2	no	—
329	C₅×SD₁₆	—	6	2	no	—
330	C₅×D₈	—	2	2	no	—
331	C₅×D₈	—	3	4	no	—
332	C₅×M₁₆	—	6	2	no	—
333	C₂×C₅×C₈	—	3	1	no	—
334	C₂×C₅×C₈	—	3	1	no	—
335	C₂×C₅×C₈	—	6	2	no	—
336	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
337	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
338	C₅×C₄⋊C₄	—	3	1	no	—
339	C₅×C₄⋊C₄	—	3	1	no	—
340	C₅×C₄⋊C₄	—	6	1	no	—
341	C₅×C₄⋊C₄	—	6	1	no	—
342	C₅×C₄⋊C₄	—	6	1	no	—
343	C₅×C₄⋊C₄	—	6	1	no	—
344	C₅×C₄⋊C₄	—	6	1	no	—
345	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
346	C₅×C₂²⋊C₄	—	2	1	no	—
347	C₅×C₂²⋊C₄	—	3	1	no	—
348	C₅×C₂²⋊C₄	—	3	1	no	—
349	C₅×C₂²⋊C₄	—	6	1	no	—
350	C₅×C₂²⋊C₄	—	6	1	no	—
351	C₅×C₂²⋊C₄	—	6	1	no	—
352	C₅×C₂²⋊C₄	—	6	1	no	—
353	C₅×C₂²⋊C₄	—	6	1	no	—
354	C₅×C₂²⋊C₄	—	6	1	no	—
355	C₅×C₂²⋊C₄	—	6	1	no	—
356	C₄²×C₅	—	3	1	no	—
357	C₂×AGL(1,ℤ/8)	—	3	1	no	—
358	C₂×#135	—	3	1	no	—
359	#547	—	3	1	no	—
360	#546	—	3	1	no	—
361	#497	—	3	1	no	—
362	#470	—	3	1	no	—
363	#465	—	3	1	no	—
364	#463	—	3	1	no	—
365	#461	—	3	1	no	—
366	#452	—	3	1	no	—
367	#452	—	3	1	no	—
368	#450	—	3	1	no	—
369	#449	C₅×D₃	1	1	yes	characteristic, complemented
370	#442	—	3	1	no	—
371	#435	—	3	1	no	—
372	C₂²×C₃×C₅	—	2	2	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	4	1	no	—
377	C₂²×C₃×C₅	—	4	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	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₅×D₃	—	2	1	no	—
383	C₂×C₅×D₃	—	2	2	no	—
384	C₂×C₅×D₃	—	2	1	no	—
385	C₂×C₅×D₃	—	2	1	no	—
386	C₂×C₅×D₃	—	4	1	no	—
387	C₂×C₅×D₃	—	4	1	no	—
388	C₂×C₅×D₃	—	8	4	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
394	C₅×Dic₃	—	2	1	no	—
395	C₅×Dic₃	—	2	1	no	—
396	C₅×Dic₃	—	2	1	no	—
397	C₅×Dic₃	—	4	1	no	—
398	C₅×Dic₃	—	4	1	no	—
399	C₅×Dic₃	—	4	1	no	—
400	C₂³×D₃	—	2	1	no	—
401	C₃×#41	—	2	2	no	—
402	C₃×#41	—	4	1	no	—
403	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×D₄	—	2	1	no	—
405	C₂×C₃×D₄	—	2	1	no	—
406	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
407	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₃×C₄	—	2	1	no	—
409	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂×#67	—	2	1	no	—
411	C₂×#67	—	2	1	no	—
412	C₂×#67	—	2	1	no	—
413	C₂×#67	C₅×D₄	1	1	yes	characteristic
414	C₂²×Dic₃	—	2	1	no	—
415	C₂²×Dic₃	—	2	1	no	—
416	#237	—	2	2	no	—
417	#237	—	4	1	no	—
418	D₃×D₄	—	2	2	no	—
419	D₃×D₄	—	4	1	no	—
420	#235	—	2	2	no	—
421	#235	—	4	1	no	—
422	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₄×D₃	—	2	1	no	—
424	C₂×C₄×D₃	—	2	1	no	—
425	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
426	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
427	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
428	C₃×SD₁₆	—	4	1	no	—
429	C₃×D₈	—	2	2	no	—
430	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
431	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
432	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
433	C₃×C₂²⋊C₄	—	2	1	no	—
434	#217	—	2	1	no	—
435	#217	—	2	1	no	—
436	#217	—	2	1	no	—
437	#217	—	2	1	no	—
438	#217	C₅×D₄	1	1	yes	characteristic
439	#216	—	2	2	no	—
440	#215	—	2	2	no	—
441	#214	—	2	2	no	—
442	#214	—	2	2	no	—
443	#213	C₅×D₄	1	4	yes	complemented
444	(C₂×D₃)⋊C₄	—	2	1	no	—
445	(C₂×D₃)⋊C₄	—	2	1	no	—
446	(C₂×D₃)⋊C₄	—	2	1	no	—
447	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
448	C₄⋊Dic₃	—	2	1	no	—
449	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
450	Dic₃⋊C₄	—	2	1	no	—
451	Dic₃⋊C₄	—	2	1	no	—
452	Dic₃⋊C₄	—	2	1	no	—
453	Dic₃⋊C₄	—	2	1	no	—
454	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
455	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₃⋊C₈	—	2	2	no	—
457	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
459	Dic₁₂	—	4	1	no	—
460	#204	—	2	2	no	—
461	ΓL(1,𝔽₂₅)	—	2	2	no	—
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	—	3	1	no	—
465	C₂³×C₅	—	6	1	no	—
466	C₂³×C₅	—	12	2	no	—
467	C₂³×C₅	—	12	2	no	—
468	C₂³×C₅	—	24	1	no	—
469	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
470	C₅×Q₈	—	2	1	no	—
471	C₅×Q₈	—	2	1	no	—
472	C₅×Q₈	—	6	1	no	—
473	C₅×Q₈	—	6	1	no	—
474	C₅×Q₈	—	6	1	no	—
475	C₅×Q₈	—	6	1	no	—
476	C₅×D₄	—	2	1	no	—
477	C₅×D₄	—	2	1	no	—
478	C₅×D₄	—	2	1	no	—
479	C₅×D₄	—	3	2	no	—
480	C₅×D₄	—	4	2	no	—
481	C₅×D₄	—	6	1	no	—
482	C₅×D₄	—	8	1	no	—
483	C₅×D₄	—	12	1	no	—
484	C₅×D₄	—	12	2	no	—
485	C₅×D₄	—	12	2	no	—
486	C₅×D₄	—	12	2	no	—
487	C₅×D₄	D₃×D₄	1	2	yes	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	3	1	no	—
493	C₂×C₄×C₅	—	3	1	no	—
494	C₂×C₄×C₅	—	3	1	no	—
495	C₂×C₄×C₅	—	4	2	no	—
496	C₂×C₄×C₅	—	6	1	no	—
497	C₂×C₄×C₅	—	6	1	no	—
498	C₂×C₄×C₅	—	6	1	no	—
499	C₂×C₄×C₅	—	6	1	no	—
500	C₂×C₄×C₅	—	6	1	no	—
501	C₂×C₄×C₅	—	12	2	no	—
502	C₂×C₄×C₅	—	12	2	no	—
503	C₂×C₄×C₅	—	12	2	no	—
504	C₂×C₄×C₅	—	24	1	no	—
505	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
507	C₅×C₈	—	2	1	no	—
508	C₅×C₈	—	2	1	no	—
509	C₅×C₈	—	3	2	no	—
510	C₅×C₈	—	6	1	no	—
511	C₂×#41	—	3	1	no	—
512	C₂×#41	—	3	1	no	—
513	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
514	C₂²×D₄	—	3	1	no	—
515	AGL(1,ℤ/8)	—	6	4	no	—
516	#135	—	6	4	no	—
517	C₂×Q₁₆	—	3	1	no	—
518	C₂×Q₁₆	—	3	1	no	—
519	C₂×SD₁₆	—	3	1	no	—
520	C₂×SD₁₆	—	3	1	no	—
521	C₂×SD₁₆	—	3	1	no	—
522	C₂×SD₁₆	—	3	1	no	—
523	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
524	C₂×D₈	—	3	1	no	—
525	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
526	C₂×M₁₆	—	3	1	no	—
527	C₂²×C₈	—	3	1	no	—
528	C₄⋊Q₈	—	3	1	no	—
529	#124	—	3	1	no	—
530	#123	—	6	1	no	—
531	#123	—	6	1	no	—
532	#123	—	6	1	no	—
533	C₂²⋊Q₈	—	3	1	no	—
534	C₂²⋊Q₈	—	3	1	no	—
535	C₂²⋊Q₈	—	3	1	no	—
536	#121	—	6	1	no	—
537	#121	—	6	1	no	—
538	#121	C₂×C₅×D₃	1	1	yes	characteristic
539	#120	—	6	1	no	—
540	C₄×D₄	—	3	1	no	—
541	C₄×D₄	—	3	1	no	—
542	C₄×D₄	—	3	1	no	—
543	C₂×C₄⋊C₄	—	6	1	no	—
544	C₂×C₂²⋊C₄	—	6	1	no	—
545	#106	—	3	1	no	—
546	C₄⋊C₈	—	3	1	no	—
547	#103	—	3	1	no	—
548	#103	—	3	1	no	—
549	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
550	#102	—	3	1	no	—
551	#102	—	3	1	no	—
552	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
553	C₂²⋊C₈	—	3	1	no	—
554	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	#97	—	3	1	no	—
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	—	4	2	no	—
558	C₂×C₃×C₅	—	8	1	no	—
559	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
560	C₂×C₃×C₅	#575	1	1	yes	characteristic
561	C₂×C₃×C₅	#577	1	1	yes	characteristic
562	C₅×D₃	—	4	1	no	—
563	C₅×D₃	—	4	2	no	—
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	1	no	—
566	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂²×D₃	—	2	1	no	—
568	C₂²×D₃	—	4	2	no	—
569	C₂²×D₃	—	4	2	no	—
570	C₂²×D₃	—	8	1	no	—
571	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
572	C₃×Q₈	—	2	1	no	—
573	C₃×Q₈	—	2	1	no	—
574	C₃×D₄	—	2	1	no	—
575	C₃×D₄	—	2	1	no	—
576	C₃×D₄	—	2	1	no	—
577	C₃×D₄	—	4	2	no	—
578	C₃×D₄	—	8	1	no	—
579	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	4	2	no	—
585	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
587	#67	—	4	1	no	—
588	#67	—	4	2	no	—
589	#67	—	4	2	no	—
590	#67	—	4	2	no	—
591	C₂×Dic₃	—	2	1	no	—
592	C₂×Dic₃	—	2	1	no	—
593	C₂×Dic₃	—	2	1	no	—
594	C₂×Dic₃	—	4	2	no	—
595	C₂×Dic₃	—	4	2	no	—
596	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
597	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
598	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
599	D₁₂	—	2	1	no	—
600	D₁₂	C₂×C₅×D₄	1	2	yes	—
601	C₄×D₃	—	2	1	no	—
602	C₄×D₃	—	2	1	no	—
603	C₄×D₃	—	4	2	no	—
604	C₄×D₃	—	8	1	no	—
605	Dic₆	—	2	1	no	—
606	Dic₆	—	2	1	no	—
607	Dic₆	—	2	1	no	—
608	Dic₆	—	2	1	no	—
609	C₃×C₈	—	2	1	no	—
610	C₃×C₈	—	2	1	no	—
611	C₃⋊C₈	—	2	1	no	—
612	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	2	no	—
617	C₂²×C₅	—	4	1	no	—
618	C₂²×C₅	—	4	1	no	—
619	C₂²×C₅	—	4	1	no	—
620	C₂²×C₅	—	4	1	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	6	1	no	—
623	C₂²×C₅	—	6	1	no	—
624	C₂²×C₅	—	6	1	no	—
625	C₂²×C₅	—	6	2	no	—
626	C₂²×C₅	—	12	1	no	—
627	C₂²×C₅	—	12	1	no	—
628	C₂²×C₅	—	24	4	no	—
629	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	4	1	no	—
632	C₄×C₅	—	4	1	no	—
633	C₄×C₅	—	6	1	no	—
634	C₄×C₅	—	6	1	no	—
635	C₄×C₅	—	6	1	no	—
636	C₄×C₅	—	12	1	no	—
637	C₄×C₅	—	12	1	no	—
638	C₄×C₅	—	12	1	no	—
639	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
640	C₄×C₅	#1004	1	1	yes	characteristic
641	C₂⁴	—	6	1	no	—
642	#41	—	2	2	no	—
643	#41	—	4	1	no	—
644	#41	—	6	2	no	—
645	#41	—	6	2	no	—
646	#41	—	12	1	no	—
647	#41	—	12	1	no	—
648	C₂×Q₈	—	3	1	no	—
649	C₂×Q₈	—	3	1	no	—
650	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	6	1	no	—
656	C₂×D₄	—	6	2	no	—
657	C₂×D₄	—	6	1	no	—
658	C₂×D₄	—	6	1	no	—
659	C₂×D₄	—	12	1	no	—
660	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
661	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	6	1	no	—
665	C₂²×C₄	—	6	1	no	—
666	C₂²×C₄	—	6	1	no	—
667	C₂²×C₄	—	6	1	no	—
668	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
669	Q₁₆	—	6	2	no	—
670	Q₁₆	—	12	1	no	—
671	SD₁₆	—	4	1	no	—
672	SD₁₆	—	6	2	no	—
673	SD₁₆	—	6	2	no	—
674	SD₁₆	—	6	2	no	—
675	SD₁₆	—	6	2	no	—
676	D₈	—	2	2	no	—
677	D₈	—	3	4	no	—
678	M₁₆	—	6	2	no	—
679	C₂×C₈	—	3	1	no	—
680	C₂×C₈	—	3	1	no	—
681	C₂×C₈	—	6	2	no	—
682	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
683	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
684	C₄⋊C₄	—	3	1	no	—
685	C₄⋊C₄	—	3	1	no	—
686	C₄⋊C₄	—	6	1	no	—
687	C₄⋊C₄	—	6	1	no	—
688	C₄⋊C₄	—	6	1	no	—
689	C₄⋊C₄	—	6	1	no	—
690	C₄⋊C₄	—	6	1	no	—
691	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	6	1	no	—
696	C₂²⋊C₄	—	6	1	no	—
697	C₂²⋊C₄	—	6	1	no	—
698	C₂²⋊C₄	—	6	1	no	—
699	C₂²⋊C₄	—	6	1	no	—
700	C₂²⋊C₄	—	6	1	no	—
701	C₂²⋊C₄	—	6	1	no	—
702	C₄²	—	3	1	no	—
703	C₃×C₅	#3267	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	2	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
714	C₂×D₃	—	2	1	no	—
715	C₂×D₃	—	2	2	no	—
716	C₂×D₃	—	2	1	no	—
717	C₂×D₃	—	2	1	no	—
718	C₂×D₃	—	4	1	no	—
719	C₂×D₃	—	4	1	no	—
720	C₂×D₃	—	8	4	no	—
721	C₃×C₄	—	2	1	no	—
722	C₃×C₄	—	4	1	no	—
723	C₃×C₄	—	4	1	no	—
724	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
725	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
726	Dic₃	—	2	1	no	—
727	Dic₃	—	2	1	no	—
728	Dic₃	—	2	1	no	—
729	Dic₃	—	4	1	no	—
730	Dic₃	—	4	1	no	—
731	Dic₃	—	4	1	no	—
732	C₂×C₅	—	4	1	no	—
733	C₂×C₅	—	4	2	no	—
734	C₂×C₅	—	8	1	no	—
735	C₂×C₅	—	12	1	no	—
736	C₂×C₅	—	12	2	no	—
737	C₂×C₅	#5590	1	1	yes	characteristic
738	C₂×C₅	#5768	1	1	yes	characteristic
739	C₂×C₅	#5775	1	1	yes	characteristic
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	3	1	no	—
743	C₂³	—	6	1	no	—
744	C₂³	—	12	2	no	—
745	C₂³	—	12	2	no	—
746	C₂³	—	24	1	no	—
747	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	6	1	no	—
751	Q₈	—	6	1	no	—
752	Q₈	—	6	1	no	—
753	Q₈	—	6	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	2	1	no	—
757	D₄	—	3	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	6	1	no	—
760	D₄	—	8	1	no	—
761	D₄	—	12	1	no	—
762	D₄	—	12	2	no	—
763	D₄	—	12	2	no	—
764	D₄	—	12	2	no	—
765	D₄	C₅×D₃×D₄	1	2	yes	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	3	1	no	—
771	C₂×C₄	—	3	1	no	—
772	C₂×C₄	—	3	1	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	6	1	no	—
775	C₂×C₄	—	6	1	no	—
776	C₂×C₄	—	6	1	no	—
777	C₂×C₄	—	6	1	no	—
778	C₂×C₄	—	6	1	no	—
779	C₂×C₄	—	12	2	no	—
780	C₂×C₄	—	12	2	no	—
781	C₂×C₄	—	12	2	no	—
782	C₂×C₄	—	24	1	no	—
783	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
785	C₈	—	2	1	no	—
786	C₈	—	2	1	no	—
787	C₈	—	3	2	no	—
788	C₈	—	6	1	no	—
789	C₂×C₃	—	4	1	no	—
790	C₂×C₃	—	4	2	no	—
791	C₂×C₃	—	8	1	no	—
792	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
793	C₂×C₃	C₅×#575	1	1	yes	characteristic
794	C₂×C₃	C₅×#577	1	1	yes	characteristic
795	D₃	—	4	1	no	—
796	D₃	—	4	2	no	—
797	C₅	#80122	1	1	yes	characteristic, direct product factor, Sylow
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	6	1	no	—
808	C₂²	—	6	1	no	—
809	C₂²	—	6	1	no	—
810	C₂²	—	6	2	no	—
811	C₂²	—	12	1	no	—
812	C₂²	—	12	1	no	—
813	C₂²	—	24	4	no	—
814	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
815	C₄	—	2	1	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	6	1	no	—
819	C₄	—	6	1	no	—
820	C₄	—	6	1	no	—
821	C₄	—	12	1	no	—
822	C₄	—	12	1	no	—
823	C₄	—	12	1	no	—
824	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
825	C₄	C₅×#1004	1	1	yes	characteristic
826	C₃	C₅×#3267	1	1	yes	characteristic, complemented, Sylow
827	C₂	—	4	1	no	—
828	C₂	—	4	2	no	—
829	C₂	—	8	1	no	—
830	C₂	—	12	1	no	—
831	C₂	—	12	2	no	—
832	C₂	C₅×#5590	1	1	yes	characteristic
833	C₂	C₅×#5768	1	1	yes	characteristic
834	C₂	C₅×#5775	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×#449	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#449	D₃
hypocenter	C₃	C₅×#3267
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#449

Complements

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

N	H ≅ G/N	type
1. C₅×#5824	C₂	semidirect
2. C₂×C₅×#950	C₂	semidirect
3. C₂×C₅×#911	C₂	semidirect
4. C₅×#5612	C₂	semidirect
5. C₃×C₅×#449	C₂	semidirect
6. C₅×#5169	C₂	semidirect
7. C₅×#5167	C₂	semidirect
8. C₅×#5153	C₂	semidirect
9. C₅×#5041	C₂	semidirect
10. C₅×#4818	C₂	semidirect
11. C₅×#4816	C₂	semidirect
12. C₅×#4785	C₂	semidirect
13. C₅×#4783	C₂	semidirect
14. C₅×#4733	C₂	semidirect
15. C₅×#4730	C₂	semidirect
17. C₂×C₃×C₅×#41	C₂²	semidirect
26. C₅×#944	C₂²	semidirect
27. C₂×C₅×#216	C₂²	semidirect
34. C₅×D₄×Dic₃	C₂²	semidirect
36. C₂×C₅×#214	C₂²	semidirect
40. C₅×#924	C₂²	semidirect
42. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
44. C₂×C₅×Dic₁₂	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
57. C₅×#816	C₂²	semidirect
58. C₅×#815	C₂²	semidirect
59. C₅×Dic₃⋊C₈	C₂²	semidirect
60. C₅×#810	C₂²	semidirect
61. C₅×#808	C₂²	semidirect
62. #80122	C₅	direct (N × H)
75. C₅×#449	D₃	semidirect
121. C₅×#213	D₄	semidirect
140. #5824	C₂×C₅	semidirect
141. C₂×#950	C₂×C₅	semidirect
142. C₂×#911	C₂×C₅	semidirect
143. #5612	C₂×C₅	semidirect
144. C₃×#449	C₂×C₅	semidirect
145. #5169	C₂×C₅	semidirect
146. #5167	C₂×C₅	semidirect
147. #5153	C₂×C₅	semidirect
148. #5041	C₂×C₅	semidirect
149. #4818	C₂×C₅	semidirect
150. #4816	C₂×C₅	semidirect
151. #4785	C₂×C₅	semidirect
152. #4783	C₂×C₅	semidirect
153. #4733	C₂×C₅	semidirect
154. #4730	C₂×C₅	semidirect
157. C₂×C₅×#41	C₂×D₃	semidirect
193. C₅×#103	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
198. C₅×C₂²⋊C₈	C₂×D₃	semidirect
250. C₂×C₃×#41	C₂²×C₅	semidirect
259. #944	C₂²×C₅	semidirect
260. C₂×#216	C₂²×C₅	semidirect
267. D₄×Dic₃	C₂²×C₅	semidirect
269. C₂×#214	C₂²×C₅	semidirect
273. #924	C₂²×C₅	semidirect
275. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
277. C₂×Dic₁₂	C₂²×C₅	semidirect
284. C₃×#103	C₂²×C₅	semidirect
285. C₃×#102	C₂²×C₅	semidirect
286. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
290. #816	C₂²×C₅	semidirect
291. #815	C₂²×C₅	semidirect
292. Dic₃⋊C₈	C₂²×C₅	semidirect
293. #810	C₂²×C₅	semidirect
294. #808	C₂²×C₅	semidirect
369. #449	C₅×D₃	semidirect
443. #213	C₅×D₄	semidirect
513. C₂×#41	C₂×C₅×D₃	semidirect
549. #103	C₂×C₅×D₃	semidirect
552. #102	C₂×C₅×D₃	semidirect
554. C₂²⋊C₈	C₂×C₅×D₃	semidirect
703. C₃×C₅	#3267	semidirect
797. C₅	#80122	direct (N × H)
826. C₃	C₅×#3267	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5824	2
C₂×C₅×#950	2
C₂×C₅×#911	2
C₅×#5612	2
C₃×C₅×#449	2
C₅×#5169	2
C₅×#5167	2
C₅×#5153	2
C₅×#5041	2
C₅×#4818	2
C₅×#4816	2
C₅×#4785	2
C₅×#4783	2
C₅×#4733	2
C₅×#4730	2
C₅×#3267	3
#80122	5

Subgroups — C5×#80122 #14453937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80122 #14453937