Subgroups — C₅×#80444 #14453721

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5727	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5554	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5173	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5086	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5018	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4813	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4812	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4809	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3266	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×#237	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
25	C₅×#946	C₂²	1	1	yes	characteristic
26	C₅×#946	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#215	C₂²	1	1	yes	characteristic
30	C₂×C₅×#215	C₂²	1	1	yes	characteristic
31	C₂×C₅×#214	C₂²	1	1	yes	characteristic
32	C₅×#930	—	2	1	no	—
33	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
34	C₅×#915	—	2	4	no	—
35	C₅×D₃×SD₁₆	—	2	4	no	—
36	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#204	C₂²	1	1	yes	characteristic
38	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
40	C₅×#897	C₂²	1	1	yes	characteristic
41	C₅×#896	—	2	1	no	—
42	C₅×#896	—	2	1	no	—
43	C₅×#895	C₂²	1	1	yes	characteristic
44	C₅×#893	—	2	1	no	—
45	C₅×#888	—	2	1	no	—
46	C₅×#886	—	2	1	no	—
47	C₅×#882	—	2	1	no	—
48	C₅×#875	C₂²	1	1	yes	characteristic
49	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
50	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#103	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×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₅×#816	C₂²	1	1	yes	characteristic, complemented
59	C₅×#810	C₂²	1	1	yes	characteristic, complemented
60	C₅×#807	C₂²	1	1	yes	characteristic, complemented
61	C₅×#803	C₂²	1	1	yes	characteristic, complemented
62	#80444	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#137	—	3	1	no	—
64	C₂²×C₅×SD₁₆	—	3	1	no	—
65	C₅×D₄×Q₈	—	3	1	no	—
66	C₅×#546	—	3	1	no	—
67	C₅×#497	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#467	—	3	1	no	—
70	C₅×#464	—	3	1	no	—
71	C₅×#461	D₃	1	1	yes	characteristic, complemented
72	C₅×#452	—	3	1	no	—
73	C₅×#451	—	3	1	no	—
74	C₅×#450	—	3	1	no	—
75	C₅×#448	—	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×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₅×#67	—	2	1	no	—
84	C₂×C₅×#67	—	2	1	no	—
85	C₂²×C₅×Dic₃	—	2	1	no	—
86	C₅×D₃×Q₈	—	2	2	no	—
87	C₅×D₃×Q₈	—	2	2	no	—
88	C₅×D₃×Q₈	—	4	1	no	—
89	C₅×D₃×Q₈	—	4	1	no	—
90	C₅×#237	—	2	2	no	—
91	C₅×#237	—	4	1	no	—
92	C₅×D₃×D₄	—	2	2	no	—
93	C₅×D₃×D₄	—	4	1	no	—
94	C₂×C₅×D₁₂	—	2	1	no	—
95	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
96	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	—	2	1	no	—
99	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₅×Dic₆	—	2	1	no	—
102	C₂×C₅×Dic₆	—	2	1	no	—
103	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
104	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×SD₁₆	—	2	2	no	—
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₅×#216	—	2	2	no	—
115	C₅×#216	—	4	1	no	—
116	C₅×#215	—	2	2	no	—
117	C₅×#215	—	4	1	no	—
118	C₅×#214	D₄	1	4	yes	complemented
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
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×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
127	C₅×C₄⋊Dic₃	—	2	1	no	—
128	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
129	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
130	C₅×Dic₃⋊C₄	—	2	1	no	—
131	C₅×Dic₃⋊C₄	—	2	1	no	—
132	C₅×Dic₃⋊C₄	—	2	1	no	—
133	C₄×C₅×Dic₃	—	2	1	no	—
134	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₅×Dic₁₂	—	2	2	no	—
137	C₅×#204	—	2	2	no	—
138	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
139	C₅×D₃×C₈	—	2	2	no	—
140	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
142	#5727	C₂×C₅	1	1	yes	characteristic, complemented
143	#5554	C₂×C₅	1	1	yes	characteristic
144	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
145	#5173	C₂×C₅	1	1	yes	characteristic, complemented
146	#5169	C₂×C₅	1	1	yes	characteristic, complemented
147	#5086	C₂×C₅	1	1	yes	characteristic, complemented
148	#5018	C₂×C₅	1	1	yes	characteristic, complemented
149	#4845	C₂×C₅	1	1	yes	characteristic, complemented
150	#4836	C₂×C₅	1	1	yes	characteristic, complemented
151	#4813	C₂×C₅	1	1	yes	characteristic, complemented
152	#4812	C₂×C₅	1	1	yes	characteristic, complemented
153	#4809	C₂×C₅	1	1	yes	characteristic, complemented
154	#4806	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	—	3	1	no	—
156	C₂²×C₅×Q₈	—	3	1	no	—
157	C₂²×C₅×Q₈	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₅×#137	—	6	4	no	—
160	C₂×C₅×Q₁₆	—	3	1	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	—	6	4	no	—
168	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
169	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
170	C₂×C₅×M₁₆	—	3	1	no	—
171	C₂²×C₅×C₈	—	3	1	no	—
172	C₅×C₄⋊Q₈	—	6	1	no	—
173	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
174	C₅×#124	—	3	1	no	—
175	C₅×#123	—	6	1	no	—
176	C₅×C₂²⋊Q₈	—	3	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	3	1	no	—
179	C₅×C₂²⋊Q₈	—	6	1	no	—
180	C₅×C₂²⋊Q₈	—	6	1	no	—
181	C₅×#121	—	3	1	no	—
182	C₅×#121	—	6	1	no	—
183	C₅×#120	—	6	1	no	—
184	C₄×C₅×Q₈	—	3	1	no	—
185	C₄×C₅×D₄	—	3	1	no	—
186	C₄×C₅×D₄	—	6	1	no	—
187	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
189	C₅×#107	—	3	1	no	—
190	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
194	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	C₅×C₂²⋊C₈	—	3	1	no	—
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×#97	—	3	1	no	—
200	#3266	—	3	1	no	Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂²×C₅×D₃	—	2	1	no	—
203	C₂²×C₅×D₃	—	4	2	no	—
204	C₂²×C₅×D₃	—	4	2	no	—
205	C₂²×C₅×D₃	—	8	1	no	—
206	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
208	C₃×C₅×Q₈	—	2	1	no	—
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	8	1	no	—
218	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₅×#67	—	4	2	no	—
222	C₅×#67	—	4	2	no	—
223	C₂×C₅×Dic₃	—	2	1	no	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	4	2	no	—
227	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
228	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
229	C₅×D₁₂	—	2	2	no	—
230	C₅×D₁₂	—	2	1	no	—
231	C₅×D₁₂	—	2	1	no	—
232	C₅×D₁₂	—	8	1	no	—
233	C₄×C₅×D₃	—	2	1	no	—
234	C₄×C₅×D₃	—	2	1	no	—
235	C₄×C₅×D₃	—	2	1	no	—
236	C₄×C₅×D₃	—	2	1	no	—
237	C₄×C₅×D₃	—	4	2	no	—
238	C₄×C₅×D₃	—	4	2	no	—
239	C₅×Dic₆	—	2	1	no	—
240	C₅×Dic₆	—	2	1	no	—
241	C₅×Dic₆	—	2	1	no	—
242	C₅×Dic₆	—	4	2	no	—
243	C₅×Dic₆	—	4	2	no	—
244	C₅×Dic₆	C₂×D₄	1	2	yes	—
245	C₃×C₅×C₈	—	2	1	no	—
246	C₃×C₅×C₈	—	2	1	no	—
247	C₅×C₃⋊C₈	—	2	1	no	—
248	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
249	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×D₃×Q₈	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×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
255	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
257	#946	C₂²×C₅	1	1	yes	characteristic
258	#946	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₂×#216	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	C₂×#215	C₂²×C₅	1	1	yes	characteristic
263	C₂×#214	C₂²×C₅	1	1	yes	characteristic
264	#930	—	2	1	no	—
265	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
266	#915	—	2	4	no	—
267	D₃×SD₁₆	—	2	4	no	—
268	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₂×#204	C₂²×C₅	1	1	yes	characteristic
270	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
272	#897	C₂²×C₅	1	1	yes	characteristic
273	#896	—	2	1	no	—
274	#896	—	2	1	no	—
275	#895	C₂²×C₅	1	1	yes	characteristic
276	#893	—	2	1	no	—
277	#888	—	2	1	no	—
278	#886	—	2	1	no	—
279	#882	—	2	1	no	—
280	#875	C₂²×C₅	1	1	yes	characteristic
281	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
282	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
286	#832	C₂²×C₅	1	1	yes	characteristic
287	#821	C₂²×C₅	1	1	yes	characteristic
288	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
289	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
290	#816	C₂²×C₅	1	1	yes	characteristic, complemented
291	#810	C₂²×C₅	1	1	yes	characteristic, complemented
292	#807	C₂²×C₅	1	1	yes	characteristic, complemented
293	#803	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₂⁴×C₅	—	6	1	no	—
295	C₅×#41	—	6	2	no	—
296	C₅×#41	—	12	1	no	—
297	C₂×C₅×Q₈	—	3	1	no	—
298	C₂×C₅×Q₈	—	3	1	no	—
299	C₂×C₅×Q₈	—	6	1	no	—
300	C₂×C₅×Q₈	—	6	1	no	—
301	C₂×C₅×Q₈	—	6	2	no	—
302	C₂×C₅×Q₈	—	6	2	no	—
303	C₂×C₅×Q₈	—	12	1	no	—
304	C₂×C₅×Q₈	—	12	1	no	—
305	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
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	1	no	—
311	C₂×C₅×D₄	—	6	2	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	C₂²×C₄×C₅	—	2	1	no	—
316	C₂²×C₄×C₅	—	3	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	C₅×Q₁₆	—	6	2	no	—
322	C₅×Q₁₆	—	6	2	no	—
323	C₅×Q₁₆	—	12	1	no	—
324	C₅×SD₁₆	—	2	2	no	—
325	C₅×SD₁₆	—	2	2	no	—
326	C₅×SD₁₆	—	3	4	no	—
327	C₅×SD₁₆	—	6	2	no	—
328	C₅×SD₁₆	—	6	2	no	—
329	C₅×SD₁₆	—	12	1	no	—
330	C₅×M₁₆	—	6	2	no	—
331	C₂×C₅×C₈	—	3	1	no	—
332	C₂×C₅×C₈	—	3	1	no	—
333	C₂×C₅×C₈	—	6	2	no	—
334	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
335	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
336	C₅×C₄⋊C₄	—	2	1	no	—
337	C₅×C₄⋊C₄	—	2	1	no	—
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	C₂²×D₃	1	1	yes	characteristic
345	C₅×C₂²⋊C₄	—	2	1	no	—
346	C₅×C₂²⋊C₄	—	3	1	no	—
347	C₅×C₂²⋊C₄	—	3	1	no	—
348	C₅×C₂²⋊C₄	—	6	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	C₄²×C₅	—	6	1	no	—
355	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
356	C₂×#137	—	3	1	no	—
357	C₂²×SD₁₆	—	3	1	no	—
358	D₄×Q₈	—	3	1	no	—
359	#546	—	3	1	no	—
360	#497	—	3	1	no	—
361	#468	—	3	1	no	—
362	#467	—	3	1	no	—
363	#464	—	3	1	no	—
364	#461	C₅×D₃	1	1	yes	characteristic, complemented
365	#452	—	3	1	no	—
366	#451	—	3	1	no	—
367	#450	—	3	1	no	—
368	#448	—	3	1	no	—
369	#440	—	3	1	no	—
370	#435	—	3	1	no	—
371	C₂²×C₃×C₅	—	2	2	no	—
372	C₂²×C₃×C₅	—	4	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₅×D₃	—	2	1	no	—
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	2	1	no	—
380	C₂×C₅×D₃	—	4	1	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₂×C₅×D₃	—	4	1	no	—
383	C₂×C₅×D₃	—	8	4	no	—
384	C₂×C₅×D₃	#137	1	2	yes	complemented
385	C₃×C₄×C₅	—	2	1	no	—
386	C₃×C₄×C₅	—	2	1	no	—
387	C₃×C₄×C₅	—	4	1	no	—
388	C₃×C₄×C₅	—	4	1	no	—
389	C₃×C₄×C₅	—	4	1	no	—
390	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
391	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
392	C₅×Dic₃	—	2	2	no	—
393	C₅×Dic₃	—	2	1	no	—
394	C₅×Dic₃	—	2	1	no	—
395	C₅×Dic₃	—	4	1	no	—
396	C₅×Dic₃	—	4	1	no	—
397	C₂³×D₃	—	2	1	no	—
398	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
399	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	—	2	1	no	—
402	C₂×#67	—	2	1	no	—
403	C₂×#67	—	2	1	no	—
404	C₂²×Dic₃	—	2	1	no	—
405	D₃×Q₈	—	2	2	no	—
406	D₃×Q₈	—	2	2	no	—
407	D₃×Q₈	—	4	1	no	—
408	D₃×Q₈	—	4	1	no	—
409	#237	—	2	2	no	—
410	#237	—	4	1	no	—
411	D₃×D₄	—	2	2	no	—
412	D₃×D₄	—	4	1	no	—
413	C₂×D₁₂	—	2	1	no	—
414	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
415	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄×D₃	—	2	1	no	—
417	C₂×C₄×D₃	—	2	1	no	—
418	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
420	C₂×Dic₆	—	2	1	no	—
421	C₂×Dic₆	—	2	1	no	—
422	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
423	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
424	C₃×SD₁₆	—	2	2	no	—
425	C₃×SD₁₆	—	2	2	no	—
426	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
428	C₃×C₄⋊C₄	—	2	1	no	—
429	C₃×C₄⋊C₄	—	2	1	no	—
430	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
431	C₃×C₂²⋊C₄	—	2	1	no	—
432	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
433	#216	—	2	2	no	—
434	#216	—	4	1	no	—
435	#215	—	2	2	no	—
436	#215	—	4	1	no	—
437	#214	C₅×D₄	1	4	yes	complemented
438	(C₂×D₃)⋊C₄	—	2	1	no	—
439	(C₂×D₃)⋊C₄	—	2	1	no	—
440	(C₂×D₃)⋊C₄	—	2	1	no	—
441	(C₂×D₃)⋊C₄	—	2	1	no	—
442	(C₂×D₃)⋊C₄	—	2	1	no	—
443	(C₂×D₃)⋊C₄	—	2	1	no	—
444	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
445	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
446	C₄⋊Dic₃	—	2	1	no	—
447	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
448	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
449	Dic₃⋊C₄	—	2	1	no	—
450	Dic₃⋊C₄	—	2	1	no	—
451	Dic₃⋊C₄	—	2	1	no	—
452	C₄×Dic₃	—	2	1	no	—
453	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
455	Dic₁₂	—	2	2	no	—
456	#204	—	2	2	no	—
457	ΓL(1,𝔽₂₅)	—	2	2	no	—
458	D₃×C₈	—	2	2	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	3	1	no	—
461	C₂³×C₅	—	3	1	no	—
462	C₂³×C₅	—	6	1	no	—
463	C₂³×C₅	—	12	2	no	—
464	C₂³×C₅	—	12	2	no	—
465	C₂³×C₅	—	24	1	no	—
466	C₅×Q₈	—	2	1	no	—
467	C₅×Q₈	—	2	1	no	—
468	C₅×Q₈	—	2	1	no	—
469	C₅×Q₈	—	2	1	no	—
470	C₅×Q₈	—	3	2	no	—
471	C₅×Q₈	—	6	1	no	—
472	C₅×Q₈	—	6	1	no	—
473	C₅×Q₈	—	6	1	no	—
474	C₅×Q₈	—	12	2	no	—
475	C₅×Q₈	—	12	2	no	—
476	C₅×D₄	—	2	1	no	—
477	C₅×D₄	—	6	2	no	—
478	C₅×D₄	—	6	1	no	—
479	C₅×D₄	—	6	1	no	—
480	C₅×D₄	—	12	2	no	—
481	C₅×D₄	—	12	2	no	—
482	C₅×D₄	—	24	1	no	—
483	C₅×D₄	D₃×D₄	1	2	yes	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	3	1	no	—
488	C₂×C₄×C₅	—	3	1	no	—
489	C₂×C₄×C₅	—	6	1	no	—
490	C₂×C₄×C₅	—	6	1	no	—
491	C₂×C₄×C₅	—	6	1	no	—
492	C₂×C₄×C₅	—	6	1	no	—
493	C₂×C₄×C₅	—	6	1	no	—
494	C₂×C₄×C₅	—	6	1	no	—
495	C₂×C₄×C₅	—	6	1	no	—
496	C₂×C₄×C₅	—	8	1	no	—
497	C₂×C₄×C₅	—	12	2	no	—
498	C₂×C₄×C₅	—	12	2	no	—
499	C₂×C₄×C₅	—	12	2	no	—
500	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
503	C₅×C₈	—	2	1	no	—
504	C₅×C₈	—	2	1	no	—
505	C₅×C₈	—	3	2	no	—
506	C₅×C₈	—	6	1	no	—
507	C₂×#41	—	3	1	no	—
508	C₂²×Q₈	—	3	1	no	—
509	C₂²×Q₈	—	3	1	no	—
510	C₂²×D₄	—	3	1	no	—
511	#137	—	6	4	no	—
512	C₂×Q₁₆	—	3	1	no	—
513	C₂×Q₁₆	—	3	1	no	—
514	C₂×Q₁₆	—	3	1	no	—
515	C₂×SD₁₆	—	3	1	no	—
516	C₂×SD₁₆	—	3	1	no	—
517	C₂×SD₁₆	—	3	1	no	—
518	C₂×SD₁₆	—	3	1	no	—
519	C₂×SD₁₆	—	6	4	no	—
520	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
521	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
522	C₂×M₁₆	—	3	1	no	—
523	C₂²×C₈	—	3	1	no	—
524	C₄⋊Q₈	—	6	1	no	—
525	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
526	#124	—	3	1	no	—
527	#123	—	6	1	no	—
528	C₂²⋊Q₈	—	3	1	no	—
529	C₂²⋊Q₈	—	3	1	no	—
530	C₂²⋊Q₈	—	3	1	no	—
531	C₂²⋊Q₈	—	6	1	no	—
532	C₂²⋊Q₈	—	6	1	no	—
533	#121	—	3	1	no	—
534	#121	—	6	1	no	—
535	#120	—	6	1	no	—
536	C₄×Q₈	—	3	1	no	—
537	C₄×D₄	—	3	1	no	—
538	C₄×D₄	—	6	1	no	—
539	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	6	1	no	—
541	#107	—	3	1	no	—
542	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
543	#103	—	3	1	no	—
544	#103	—	3	1	no	—
545	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
546	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
547	#102	—	3	1	no	—
548	#102	—	3	1	no	—
549	C₂²⋊C₈	—	3	1	no	—
550	C₂²⋊C₈	—	3	1	no	—
551	#97	—	3	1	no	—
552	C₂×C₃×C₅	—	4	2	no	—
553	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
554	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
555	C₂×C₃×C₅	#577	1	1	yes	characteristic
556	C₅×D₃	—	2	2	no	—
557	C₅×D₃	—	4	1	no	—
558	C₅×D₃	—	8	1	no	—
559	C₂³×C₃	—	2	1	no	—
560	C₂²×D₃	—	2	1	no	—
561	C₂²×D₃	—	4	2	no	—
562	C₂²×D₃	—	4	2	no	—
563	C₂²×D₃	—	8	1	no	—
564	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
566	C₃×Q₈	—	2	1	no	—
567	C₃×Q₈	—	2	1	no	—
568	C₃×Q₈	—	2	1	no	—
569	C₃×Q₈	—	2	1	no	—
570	C₃×D₄	—	2	1	no	—
571	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	8	1	no	—
576	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
579	#67	—	4	2	no	—
580	#67	—	4	2	no	—
581	C₂×Dic₃	—	2	1	no	—
582	C₂×Dic₃	—	2	1	no	—
583	C₂×Dic₃	—	2	1	no	—
584	C₂×Dic₃	—	4	2	no	—
585	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
587	D₁₂	—	2	2	no	—
588	D₁₂	—	2	1	no	—
589	D₁₂	—	2	1	no	—
590	D₁₂	—	8	1	no	—
591	C₄×D₃	—	2	1	no	—
592	C₄×D₃	—	2	1	no	—
593	C₄×D₃	—	2	1	no	—
594	C₄×D₃	—	2	1	no	—
595	C₄×D₃	—	4	2	no	—
596	C₄×D₃	—	4	2	no	—
597	Dic₆	—	2	1	no	—
598	Dic₆	—	2	1	no	—
599	Dic₆	—	2	1	no	—
600	Dic₆	—	4	2	no	—
601	Dic₆	—	4	2	no	—
602	Dic₆	C₂×C₅×D₄	1	2	yes	—
603	C₃×C₈	—	2	1	no	—
604	C₃×C₈	—	2	1	no	—
605	C₃⋊C₈	—	2	1	no	—
606	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
607	C₂²×C₅	—	2	2	no	—
608	C₂²×C₅	—	3	2	no	—
609	C₂²×C₅	—	4	1	no	—
610	C₂²×C₅	—	4	1	no	—
611	C₂²×C₅	—	6	1	no	—
612	C₂²×C₅	—	6	1	no	—
613	C₂²×C₅	—	6	1	no	—
614	C₂²×C₅	—	6	1	no	—
615	C₂²×C₅	—	6	1	no	—
616	C₂²×C₅	—	12	1	no	—
617	C₂²×C₅	—	12	1	no	—
618	C₂²×C₅	—	12	1	no	—
619	C₂²×C₅	—	24	4	no	—
620	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
621	C₄×C₅	—	2	1	no	—
622	C₄×C₅	—	2	1	no	—
623	C₄×C₅	—	4	1	no	—
624	C₄×C₅	—	4	1	no	—
625	C₄×C₅	—	4	1	no	—
626	C₄×C₅	—	6	1	no	—
627	C₄×C₅	—	6	1	no	—
628	C₄×C₅	—	6	2	no	—
629	C₄×C₅	—	12	1	no	—
630	C₄×C₅	—	12	1	no	—
631	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
632	C₄×C₅	#1009	1	1	yes	characteristic
633	C₂⁴	—	6	1	no	—
634	#41	—	6	2	no	—
635	#41	—	12	1	no	—
636	C₂×Q₈	—	3	1	no	—
637	C₂×Q₈	—	3	1	no	—
638	C₂×Q₈	—	6	1	no	—
639	C₂×Q₈	—	6	1	no	—
640	C₂×Q₈	—	6	2	no	—
641	C₂×Q₈	—	6	2	no	—
642	C₂×Q₈	—	12	1	no	—
643	C₂×Q₈	—	12	1	no	—
644	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
645	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	6	1	no	—
649	C₂×D₄	—	6	1	no	—
650	C₂×D₄	—	6	2	no	—
651	C₂×D₄	—	6	1	no	—
652	C₂×D₄	—	12	1	no	—
653	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	1	no	—
657	C₂²×C₄	—	6	1	no	—
658	C₂²×C₄	—	6	1	no	—
659	C₂²×C₄	—	6	1	no	—
660	Q₁₆	—	6	2	no	—
661	Q₁₆	—	6	2	no	—
662	Q₁₆	—	12	1	no	—
663	SD₁₆	—	2	2	no	—
664	SD₁₆	—	2	2	no	—
665	SD₁₆	—	3	4	no	—
666	SD₁₆	—	6	2	no	—
667	SD₁₆	—	6	2	no	—
668	SD₁₆	—	12	1	no	—
669	M₁₆	—	6	2	no	—
670	C₂×C₈	—	3	1	no	—
671	C₂×C₈	—	3	1	no	—
672	C₂×C₈	—	6	2	no	—
673	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
674	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	3	1	no	—
678	C₄⋊C₄	—	3	1	no	—
679	C₄⋊C₄	—	6	1	no	—
680	C₄⋊C₄	—	6	1	no	—
681	C₄⋊C₄	—	6	1	no	—
682	C₄⋊C₄	—	6	1	no	—
683	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	3	1	no	—
686	C₂²⋊C₄	—	3	1	no	—
687	C₂²⋊C₄	—	6	1	no	—
688	C₂²⋊C₄	—	6	1	no	—
689	C₂²⋊C₄	—	6	1	no	—
690	C₂²⋊C₄	—	6	1	no	—
691	C₂²⋊C₄	—	6	1	no	—
692	C₂²⋊C₄	—	6	1	no	—
693	C₄²	—	6	1	no	—
694	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
695	C₃×C₅	#3266	1	1	yes	characteristic, complemented, Hall
696	C₂²×C₃	—	2	2	no	—
697	C₂²×C₃	—	4	1	no	—
698	C₂²×C₃	—	4	1	no	—
699	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
700	C₂×D₃	—	2	1	no	—
701	C₂×D₃	—	2	1	no	—
702	C₂×D₃	—	2	1	no	—
703	C₂×D₃	—	2	1	no	—
704	C₂×D₃	—	2	1	no	—
705	C₂×D₃	—	4	1	no	—
706	C₂×D₃	—	4	1	no	—
707	C₂×D₃	—	4	1	no	—
708	C₂×D₃	—	8	4	no	—
709	C₂×D₃	C₅×#137	1	2	yes	complemented
710	C₃×C₄	—	2	1	no	—
711	C₃×C₄	—	2	1	no	—
712	C₃×C₄	—	4	1	no	—
713	C₃×C₄	—	4	1	no	—
714	C₃×C₄	—	4	1	no	—
715	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
716	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
717	Dic₃	—	2	2	no	—
718	Dic₃	—	2	1	no	—
719	Dic₃	—	2	1	no	—
720	Dic₃	—	4	1	no	—
721	Dic₃	—	4	1	no	—
722	C₂×C₅	—	4	2	no	—
723	C₂×C₅	—	6	2	no	—
724	C₂×C₅	—	12	1	no	—
725	C₂×C₅	—	24	1	no	—
726	C₂×C₅	#5609	1	1	yes	characteristic
727	C₂×C₅	#5762	1	1	yes	characteristic
728	C₂×C₅	D₃×#137	1	1	yes	characteristic
729	C₂³	—	2	1	no	—
730	C₂³	—	3	1	no	—
731	C₂³	—	3	1	no	—
732	C₂³	—	6	1	no	—
733	C₂³	—	12	2	no	—
734	C₂³	—	12	2	no	—
735	C₂³	—	24	1	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	1	no	—
739	Q₈	—	2	1	no	—
740	Q₈	—	3	2	no	—
741	Q₈	—	6	1	no	—
742	Q₈	—	6	1	no	—
743	Q₈	—	6	1	no	—
744	Q₈	—	12	2	no	—
745	Q₈	—	12	2	no	—
746	D₄	—	2	1	no	—
747	D₄	—	6	2	no	—
748	D₄	—	6	1	no	—
749	D₄	—	6	1	no	—
750	D₄	—	12	2	no	—
751	D₄	—	12	2	no	—
752	D₄	—	24	1	no	—
753	D₄	C₅×D₃×D₄	1	2	yes	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	3	1	no	—
758	C₂×C₄	—	3	1	no	—
759	C₂×C₄	—	6	1	no	—
760	C₂×C₄	—	6	1	no	—
761	C₂×C₄	—	6	1	no	—
762	C₂×C₄	—	6	1	no	—
763	C₂×C₄	—	6	1	no	—
764	C₂×C₄	—	6	1	no	—
765	C₂×C₄	—	6	1	no	—
766	C₂×C₄	—	8	1	no	—
767	C₂×C₄	—	12	2	no	—
768	C₂×C₄	—	12	2	no	—
769	C₂×C₄	—	12	2	no	—
770	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
771	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
772	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
773	C₈	—	2	1	no	—
774	C₈	—	2	1	no	—
775	C₈	—	3	2	no	—
776	C₈	—	6	1	no	—
777	C₂×C₃	—	4	2	no	—
778	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
779	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
780	C₂×C₃	C₅×#577	1	1	yes	characteristic
781	D₃	—	2	2	no	—
782	D₃	—	4	1	no	—
783	D₃	—	8	1	no	—
784	C₅	#80444	1	1	yes	characteristic, direct product factor, Sylow
785	C₂²	—	2	2	no	—
786	C₂²	—	3	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	6	1	no	—
790	C₂²	—	6	1	no	—
791	C₂²	—	6	1	no	—
792	C₂²	—	6	1	no	—
793	C₂²	—	6	1	no	—
794	C₂²	—	12	1	no	—
795	C₂²	—	12	1	no	—
796	C₂²	—	12	1	no	—
797	C₂²	—	24	4	no	—
798	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
799	C₄	—	2	1	no	—
800	C₄	—	2	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	6	1	no	—
805	C₄	—	6	1	no	—
806	C₄	—	6	2	no	—
807	C₄	—	12	1	no	—
808	C₄	—	12	1	no	—
809	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
810	C₄	C₅×#1009	1	1	yes	characteristic
811	C₃	C₅×#3266	1	1	yes	characteristic, complemented, Sylow
812	C₂	—	4	2	no	—
813	C₂	—	6	2	no	—
814	C₂	—	12	1	no	—
815	C₂	—	24	1	no	—
816	C₂	C₅×#5609	1	1	yes	characteristic
817	C₂	C₅×#5762	1	1	yes	characteristic
818	C₂	C₅×D₃×#137	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×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5554	C₂
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₅×#3266
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#915	C₂	semidirect
2. C₂×C₅×D₃×SD₁₆	C₂	semidirect
3. C₅×#5727	C₂	semidirect
5. C₃×C₅×#461	C₂	semidirect
6. C₅×#5173	C₂	semidirect
7. C₅×#5169	C₂	semidirect
8. C₅×#5086	C₂	semidirect
9. C₅×#5018	C₂	semidirect
10. C₅×#4845	C₂	semidirect
11. C₅×#4836	C₂	semidirect
12. C₅×#4813	C₂	semidirect
13. C₅×#4812	C₂	semidirect
14. C₅×#4809	C₂	semidirect
15. C₅×#4806	C₂	semidirect
18. C₂×C₅×D₃×Q₈	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
26. C₅×#946	C₂²	semidirect
27. C₂×C₅×#216	C₂²	semidirect
28. C₂×C₅×#216	C₂²	semidirect
36. C₂×C₅×Dic₁₂	C₂²	semidirect
38. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
50. C₄×C₅×Dic₆	C₂²	semidirect
51. C₃×C₅×C₄⋊C₈	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#103	C₂²	semidirect
57. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
58. C₅×#816	C₂²	semidirect
59. C₅×#810	C₂²	semidirect
60. C₅×#807	C₂²	semidirect
61. C₅×#803	C₂²	semidirect
62. #80444	C₅	direct (N × H)
71. C₅×#461	D₃	semidirect
118. C₅×#214	D₄	semidirect
140. C₂×#915	C₂×C₅	semidirect
141. C₂×D₃×SD₁₆	C₂×C₅	semidirect
142. #5727	C₂×C₅	semidirect
144. C₃×#461	C₂×C₅	semidirect
145. #5173	C₂×C₅	semidirect
146. #5169	C₂×C₅	semidirect
147. #5086	C₂×C₅	semidirect
148. #5018	C₂×C₅	semidirect
149. #4845	C₂×C₅	semidirect
150. #4836	C₂×C₅	semidirect
151. #4813	C₂×C₅	semidirect
152. #4812	C₂×C₅	semidirect
153. #4809	C₂×C₅	semidirect
154. #4806	C₂×C₅	semidirect
173. C₅×C₄⋊Q₈	C₂×D₃	semidirect
190. C₅×C₄⋊C₈	C₂×D₃	semidirect
193. C₅×#103	C₂×D₃	semidirect
194. C₅×#103	C₂×D₃	semidirect
250. C₂×D₃×Q₈	C₂²×C₅	semidirect
255. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
258. #946	C₂²×C₅	semidirect
259. C₂×#216	C₂²×C₅	semidirect
260. C₂×#216	C₂²×C₅	semidirect
268. C₂×Dic₁₂	C₂²×C₅	semidirect
270. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
282. C₄×Dic₆	C₂²×C₅	semidirect
283. C₃×C₄⋊C₈	C₂²×C₅	semidirect
284. C₃×#103	C₂²×C₅	semidirect
285. C₃×#103	C₂²×C₅	semidirect
289. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
290. #816	C₂²×C₅	semidirect
291. #810	C₂²×C₅	semidirect
292. #807	C₂²×C₅	semidirect
293. #803	C₂²×C₅	semidirect
364. #461	C₅×D₃	semidirect
384. C₂×C₅×D₃	#137	semidirect
437. #214	C₅×D₄	semidirect
525. C₄⋊Q₈	C₂×C₅×D₃	semidirect
542. C₄⋊C₈	C₂×C₅×D₃	semidirect
545. #103	C₂×C₅×D₃	semidirect
546. #103	C₂×C₅×D₃	semidirect
695. C₃×C₅	#3266	semidirect
709. C₂×D₃	C₅×#137	semidirect
784. C₅	#80444	direct (N × H)
811. C₃	C₅×#3266	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#915	2
C₂×C₅×D₃×SD₁₆	2
C₅×#5727	2
C₅×#5554	2
C₃×C₅×#461	2
C₅×#5173	2
C₅×#5169	2
C₅×#5086	2
C₅×#5018	2
C₅×#4845	2
C₅×#4836	2
C₅×#4813	2
C₅×#4812	2
C₅×#4809	2
C₅×#4806	2
C₅×#3266	3
#80444	5

Subgroups — C5×#80444 #14453721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80444 #14453721