Subgroups — C₅×#81848 #14439543

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#914	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5715	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5176	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5168	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5154	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5151	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5073	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4712	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3155	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic
18	C₂×C₅×#237	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×D₄	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, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
27	C₅×#947	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, complemented
30	C₅×#940	C₂²	1	1	yes	characteristic, complemented
31	C₅×#940	C₂²	1	1	yes	characteristic, complemented
32	C₅×#939	—	2	2	no	—
33	C₅×#937	—	2	2	no	—
34	C₅×#936	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#213	C₂²	1	1	yes	characteristic
37	C₂×C₅×#213	C₂²	1	1	yes	characteristic
38	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
41	C₅×#916	—	2	4	no	—
42	C₅×#914	—	2	4	no	—
43	C₅×#911	—	2	4	no	—
44	C₅×D₃×D₈	—	2	4	no	—
45	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
50	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
51	C₅×#884	—	2	2	no	—
52	C₅×#882	—	2	2	no	—
53	C₅×#875	C₂²	1	1	yes	characteristic, complemented
54	C₅×#874	C₂²	1	1	yes	characteristic, complemented
55	C₅×#872	C₂²	1	1	yes	characteristic
56	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
57	C₅×#815	C₂²	1	1	yes	characteristic, complemented
58	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#81848	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
62	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
63	C₂×C₅×#135	—	3	1	no	—
64	C₂²×C₅×D₈	—	3	1	no	—
65	C₅×#535	—	3	1	no	—
66	C₅×#535	—	3	1	no	—
67	C₅×#496	—	3	1	no	—
68	C₅×#496	—	3	1	no	—
69	C₅×#496	—	3	1	no	—
70	C₅×#496	D₃	1	1	yes	characteristic, complemented
71	C₅×#495	—	3	1	no	—
72	C₅×#495	—	3	1	no	—
73	C₅×#493	—	3	1	no	—
74	C₅×#493	—	3	1	no	—
75	C₅×#405	—	3	1	no	—
76	C₂³×C₅×D₃	—	2	1	no	—
77	C₂³×C₅×D₃	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	—	2	1	no	—
84	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	2	no	—
87	C₂×C₅×#67	—	2	2	no	—
88	C₂²×C₅×Dic₃	—	2	1	no	—
89	C₅×#239	—	2	2	no	—
90	C₅×#239	—	2	2	no	—
91	C₅×#237	—	2	2	no	—
92	C₅×#237	—	2	2	no	—
93	C₅×D₃×D₄	—	2	2	no	—
94	C₅×D₃×D₄	—	2	2	no	—
95	C₅×D₃×D₄	—	2	2	no	—
96	C₅×D₃×D₄	—	2	2	no	—
97	C₂×C₅×D₁₂	—	2	1	no	—
98	C₂×C₅×D₁₂	—	2	2	no	—
99	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
100	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
101	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
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	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×SD₁₆	—	2	2	no	—
107	C₃×C₅×D₈	—	2	2	no	—
108	C₃×C₅×D₈	—	2	2	no	—
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₅×#217	—	2	2	no	—
114	C₅×#216	—	2	2	no	—
115	C₅×#215	—	2	2	no	—
116	C₅×#214	—	2	2	no	—
117	C₅×#213	—	2	2	no	—
118	C₅×#213	—	2	2	no	—
119	C₅×#213	—	2	2	no	—
120	C₅×#213	—	2	2	no	—
121	C₅×#213	—	2	2	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
124	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
125	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
126	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₅×D₂₄	—	2	2	no	—
130	C₅×D₂₄	—	2	2	no	—
131	C₅×#204	—	2	2	no	—
132	C₅×#204	—	2	2	no	—
133	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
134	C₅×D₃×C₈	D₄	1	4	yes	complemented
135	C₂×#916	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×#914	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
139	#5715	C₂×C₅	1	1	yes	characteristic, complemented
140	#5674	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
142	#5176	C₂×C₅	1	1	yes	characteristic, complemented
143	#5168	C₂×C₅	1	1	yes	characteristic, complemented
144	#5154	C₂×C₅	1	1	yes	characteristic, complemented
145	#5151	C₂×C₅	1	1	yes	characteristic, complemented
146	#5073	C₂×C₅	1	1	yes	characteristic, complemented
147	#5059	C₂×C₅	1	1	yes	characteristic, complemented
148	#4712	C₂×C₅	1	1	yes	characteristic, complemented
149	#4708	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×C₅×#41	—	3	1	no	—
151	C₂×C₅×#41	—	3	1	no	—
152	C₂²×C₅×D₄	—	3	1	no	—
153	C₂²×C₅×D₄	—	3	1	no	—
154	C₅×AGL(1,ℤ/8)	—	6	4	no	—
155	C₅×AGL(1,ℤ/8)	—	6	4	no	—
156	C₅×#135	—	6	4	no	—
157	C₂×C₅×Q₁₆	—	3	1	no	—
158	C₂×C₅×SD₁₆	—	3	1	no	—
159	C₂×C₅×SD₁₆	—	3	1	no	—
160	C₂×C₅×SD₁₆	—	3	1	no	—
161	C₂×C₅×SD₁₆	—	3	1	no	—
162	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
163	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂×C₅×D₈	—	3	1	no	—
165	C₂×C₅×D₈	—	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	—	3	1	no	—
170	C₂×C₅×D₈	—	3	1	no	—
171	C₂×C₅×D₈	—	6	4	no	—
172	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
173	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
174	C₂×C₅×M₁₆	—	3	1	no	—
175	C₂²×C₅×C₈	—	3	1	no	—
176	C₅×#127	—	3	1	no	—
177	C₅×#127	—	3	1	no	—
178	C₅×#127	—	3	1	no	—
179	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
180	C₅×#124	—	3	1	no	—
181	C₅×#124	—	3	1	no	—
182	C₅×#124	—	3	1	no	—
183	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
184	C₅×#121	—	6	2	no	—
185	C₅×#121	—	6	2	no	—
186	C₅×#120	—	6	2	no	—
187	C₅×#120	—	6	2	no	—
188	C₅×#117	—	3	1	no	—
189	C₅×#97	—	3	1	no	—
190	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
191	C₄×C₅×C₈	—	3	1	no	—
192	C₄×C₅×C₈	—	3	1	no	—
193	#3155	—	3	1	no	Sylow
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂²×C₅×D₃	—	2	1	no	—
198	C₂²×C₅×D₃	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	4	2	no	—
201	C₂²×C₅×D₃	—	4	2	no	—
202	C₂²×C₅×D₃	—	8	2	no	—
203	C₂²×C₅×D₃	—	8	2	no	—
204	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
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	—	8	2	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
216	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₅×#67	—	4	2	no	—
218	C₅×#67	—	4	2	no	—
219	C₅×#67	—	4	2	no	—
220	C₅×#67	—	8	2	no	—
221	C₅×#67	—	8	2	no	—
222	C₂×C₅×Dic₃	—	2	1	no	—
223	C₂×C₅×Dic₃	—	4	2	no	—
224	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
225	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
226	C₅×D₁₂	—	2	1	no	—
227	C₅×D₁₂	—	2	1	no	—
228	C₅×D₁₂	—	2	1	no	—
229	C₅×D₁₂	—	2	1	no	—
230	C₅×D₁₂	—	2	1	no	—
231	C₅×D₁₂	—	2	1	no	—
232	C₅×D₁₂	—	4	2	no	—
233	C₅×D₁₂	—	8	2	no	—
234	C₄×C₅×D₃	—	4	2	no	—
235	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
236	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
237	C₅×Dic₆	—	2	1	no	—
238	C₅×Dic₆	—	2	1	no	—
239	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
240	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
241	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
242	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
243	C₂×#239	C₂²×C₅	1	1	yes	characteristic
244	C₂×#237	C₂²×C₅	1	1	yes	characteristic
245	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
253	#947	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
256	#940	C₂²×C₅	1	1	yes	characteristic, complemented
257	#940	C₂²×C₅	1	1	yes	characteristic, complemented
258	#939	—	2	2	no	—
259	#937	—	2	2	no	—
260	#936	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×#213	C₂²×C₅	1	1	yes	characteristic
263	C₂×#213	C₂²×C₅	1	1	yes	characteristic
264	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
267	#916	—	2	4	no	—
268	#914	—	2	4	no	—
269	#911	—	2	4	no	—
270	D₃×D₈	—	2	4	no	—
271	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
276	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
277	#884	—	2	2	no	—
278	#882	—	2	2	no	—
279	#875	C₂²×C₅	1	1	yes	characteristic, complemented
280	#874	C₂²×C₅	1	1	yes	characteristic, complemented
281	#872	C₂²×C₅	1	1	yes	characteristic
282	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
283	#815	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂⁴×C₅	—	6	1	no	—
287	C₂⁴×C₅	—	6	1	no	—
288	C₅×#41	—	6	2	no	—
289	C₅×#41	—	6	2	no	—
290	C₅×#41	—	6	2	no	—
291	C₅×#41	—	6	2	no	—
292	C₂×C₅×Q₈	—	3	1	no	—
293	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₅×D₄	—	2	2	no	—
295	C₂×C₅×D₄	—	3	1	no	—
296	C₂×C₅×D₄	—	3	1	no	—
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂×C₅×D₄	—	6	1	no	—
299	C₂×C₅×D₄	—	6	2	no	—
300	C₂×C₅×D₄	—	6	2	no	—
301	C₂×C₅×D₄	—	6	2	no	—
302	C₂×C₅×D₄	—	6	2	no	—
303	C₂×C₅×D₄	—	6	1	no	—
304	C₂×C₅×D₄	—	6	1	no	—
305	C₂×C₅×D₄	—	6	2	no	—
306	C₂×C₅×D₄	—	6	2	no	—
307	C₂×C₅×D₄	—	6	1	no	—
308	C₂×C₅×D₄	—	6	2	no	—
309	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	6	1	no	—
314	C₂²×C₄×C₅	—	6	1	no	—
315	C₅×Q₁₆	—	6	2	no	—
316	C₅×SD₁₆	—	2	2	no	—
317	C₅×SD₁₆	—	2	2	no	—
318	C₅×SD₁₆	—	6	2	no	—
319	C₅×SD₁₆	—	6	2	no	—
320	C₅×SD₁₆	—	6	2	no	—
321	C₅×SD₁₆	—	6	2	no	—
322	C₅×D₈	—	2	2	no	—
323	C₅×D₈	—	2	2	no	—
324	C₅×D₈	—	6	2	no	—
325	C₅×D₈	—	6	2	no	—
326	C₅×D₈	—	6	2	no	—
327	C₅×D₈	—	6	2	no	—
328	C₅×D₈	—	6	2	no	—
329	C₅×D₈	—	6	2	no	—
330	C₅×D₈	—	6	2	no	—
331	C₅×M₁₆	—	3	4	no	—
332	C₂×C₅×C₈	—	3	1	no	—
333	C₂×C₅×C₈	—	3	1	no	—
334	C₂×C₅×C₈	—	3	4	no	—
335	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
336	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
337	C₅×C₄⋊C₄	—	3	2	no	—
338	C₅×C₂²⋊C₄	—	2	2	no	—
339	C₅×C₂²⋊C₄	—	3	2	no	—
340	C₅×C₂²⋊C₄	—	6	2	no	—
341	C₅×C₂²⋊C₄	—	6	2	no	—
342	C₅×C₂²⋊C₄	—	6	2	no	—
343	C₄²×C₅	—	3	1	no	—
344	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
345	C₂×AGL(1,ℤ/8)	—	3	1	no	—
346	C₂×AGL(1,ℤ/8)	—	3	1	no	—
347	C₂×#135	—	3	1	no	—
348	C₂²×D₈	—	3	1	no	—
349	#535	—	3	1	no	—
350	#535	—	3	1	no	—
351	#496	—	3	1	no	—
352	#496	—	3	1	no	—
353	#496	—	3	1	no	—
354	#496	C₅×D₃	1	1	yes	characteristic, complemented
355	#495	—	3	1	no	—
356	#495	—	3	1	no	—
357	#493	—	3	1	no	—
358	#493	—	3	1	no	—
359	#405	—	3	1	no	—
360	C₂²×C₃×C₅	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	2	no	—
364	C₂²×C₃×C₅	—	4	2	no	—
365	C₂²×C₃×C₅	—	4	2	no	—
366	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₅×D₃	—	2	2	no	—
368	C₂×C₅×D₃	—	4	1	no	—
369	C₂×C₅×D₃	—	4	1	no	—
370	C₂×C₅×D₃	—	4	1	no	—
371	C₂×C₅×D₃	—	4	2	no	—
372	C₂×C₅×D₃	—	4	2	no	—
373	C₂×C₅×D₃	—	4	2	no	—
374	C₂×C₅×D₃	—	8	4	no	—
375	C₂×C₅×D₃	—	8	4	no	—
376	C₂×C₅×D₃	#127	1	2	yes	—
377	C₃×C₄×C₅	—	2	2	no	—
378	C₃×C₄×C₅	—	4	1	no	—
379	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
381	C₅×Dic₃	—	2	2	no	—
382	C₅×Dic₃	—	4	1	no	—
383	C₅×Dic₃	#127	1	2	yes	—
384	C₂³×D₃	—	2	1	no	—
385	C₂³×D₃	—	2	1	no	—
386	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₃×D₄	—	2	2	no	—
388	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
391	C₂×#67	—	2	1	no	—
392	C₂×#67	—	2	1	no	—
393	C₂×#67	—	2	1	no	—
394	C₂×#67	—	2	2	no	—
395	C₂×#67	—	2	2	no	—
396	C₂²×Dic₃	—	2	1	no	—
397	#239	—	2	2	no	—
398	#239	—	2	2	no	—
399	#237	—	2	2	no	—
400	#237	—	2	2	no	—
401	D₃×D₄	—	2	2	no	—
402	D₃×D₄	—	2	2	no	—
403	D₃×D₄	—	2	2	no	—
404	D₃×D₄	—	2	2	no	—
405	C₂×D₁₂	—	2	1	no	—
406	C₂×D₁₂	—	2	2	no	—
407	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
408	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
409	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	2	1	no	—
411	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
412	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
413	C₃×SD₁₆	—	2	2	no	—
414	C₃×SD₁₆	—	2	2	no	—
415	C₃×D₈	—	2	2	no	—
416	C₃×D₈	—	2	2	no	—
417	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
421	#217	—	2	2	no	—
422	#216	—	2	2	no	—
423	#215	—	2	2	no	—
424	#214	—	2	2	no	—
425	#213	—	2	2	no	—
426	#213	—	2	2	no	—
427	#213	—	2	2	no	—
428	#213	—	2	2	no	—
429	#213	—	2	2	no	—
430	(C₂×D₃)⋊C₄	—	2	2	no	—
431	(C₂×D₃)⋊C₄	—	2	2	no	—
432	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
433	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
434	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
437	D₂₄	—	2	2	no	—
438	D₂₄	—	2	2	no	—
439	#204	—	2	2	no	—
440	#204	—	2	2	no	—
441	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	complemented
442	D₃×C₈	C₅×D₄	1	4	yes	complemented
443	C₂³×C₅	—	2	1	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	2	1	no	—
446	C₂³×C₅	—	3	1	no	—
447	C₂³×C₅	—	6	1	no	—
448	C₂³×C₅	—	6	1	no	—
449	C₂³×C₅	—	6	1	no	—
450	C₂³×C₅	—	12	2	no	—
451	C₂³×C₅	—	12	2	no	—
452	C₂³×C₅	—	24	2	no	—
453	C₂³×C₅	—	24	2	no	—
454	C₅×Q₈	—	2	1	no	—
455	C₅×Q₈	—	2	1	no	—
456	C₅×Q₈	—	6	1	no	—
457	C₅×Q₈	—	6	1	no	—
458	C₅×D₄	—	2	1	no	—
459	C₅×D₄	—	2	1	no	—
460	C₅×D₄	—	2	1	no	—
461	C₅×D₄	—	2	1	no	—
462	C₅×D₄	—	2	1	no	—
463	C₅×D₄	—	2	1	no	—
464	C₅×D₄	—	6	1	no	—
465	C₅×D₄	—	6	1	no	—
466	C₅×D₄	—	6	1	no	—
467	C₅×D₄	—	6	1	no	—
468	C₅×D₄	—	6	1	no	—
469	C₅×D₄	—	6	1	no	—
470	C₅×D₄	—	8	2	no	—
471	C₅×D₄	—	12	2	no	—
472	C₅×D₄	—	12	2	no	—
473	C₅×D₄	—	12	2	no	—
474	C₅×D₄	—	12	2	no	—
475	C₅×D₄	—	24	2	no	—
476	C₅×D₄	—	24	2	no	—
477	C₅×D₄	—	24	2	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	3	1	no	—
480	C₂×C₄×C₅	—	3	2	no	—
481	C₂×C₄×C₅	—	3	2	no	—
482	C₂×C₄×C₅	—	3	2	no	—
483	C₂×C₄×C₅	—	6	1	no	—
484	C₂×C₄×C₅	—	12	2	no	—
485	C₂×C₄×C₅	—	12	2	no	—
486	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
487	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
488	C₅×C₈	—	3	2	no	—
489	C₅×C₈	—	3	2	no	—
490	C₅×C₈	D₃×D₄	1	2	yes	—
491	C₅×C₈	D₃×D₄	1	2	yes	—
492	C₂×#41	—	3	1	no	—
493	C₂×#41	—	3	1	no	—
494	C₂²×D₄	—	3	1	no	—
495	C₂²×D₄	—	3	1	no	—
496	AGL(1,ℤ/8)	—	6	4	no	—
497	AGL(1,ℤ/8)	—	6	4	no	—
498	#135	—	6	4	no	—
499	C₂×Q₁₆	—	3	1	no	—
500	C₂×SD₁₆	—	3	1	no	—
501	C₂×SD₁₆	—	3	1	no	—
502	C₂×SD₁₆	—	3	1	no	—
503	C₂×SD₁₆	—	3	1	no	—
504	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
506	C₂×D₈	—	3	1	no	—
507	C₂×D₈	—	3	1	no	—
508	C₂×D₈	—	3	1	no	—
509	C₂×D₈	—	3	1	no	—
510	C₂×D₈	—	3	1	no	—
511	C₂×D₈	—	3	1	no	—
512	C₂×D₈	—	3	1	no	—
513	C₂×D₈	—	6	4	no	—
514	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
515	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
516	C₂×M₁₆	—	3	1	no	—
517	C₂²×C₈	—	3	1	no	—
518	#127	—	3	1	no	—
519	#127	—	3	1	no	—
520	#127	—	3	1	no	—
521	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
522	#124	—	3	1	no	—
523	#124	—	3	1	no	—
524	#124	—	3	1	no	—
525	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
526	#121	—	6	2	no	—
527	#121	—	6	2	no	—
528	#120	—	6	2	no	—
529	#120	—	6	2	no	—
530	#117	—	3	1	no	—
531	#97	—	3	1	no	—
532	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
533	C₄×C₈	—	3	1	no	—
534	C₄×C₈	—	3	1	no	—
535	C₂×C₃×C₅	—	8	1	no	—
536	C₂×C₃×C₅	—	8	1	no	—
537	C₂×C₃×C₅	—	8	1	no	—
538	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
539	C₂×C₃×C₅	#576	1	2	yes	—
540	C₅×D₃	—	2	2	no	—
541	C₅×D₃	—	8	1	no	—
542	C₅×D₃	—	8	1	no	—
543	C₅×D₃	—	8	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	1	no	—
547	C₂²×D₃	—	2	1	no	—
548	C₂²×D₃	—	2	1	no	—
549	C₂²×D₃	—	2	1	no	—
550	C₂²×D₃	—	4	2	no	—
551	C₂²×D₃	—	4	2	no	—
552	C₂²×D₃	—	8	2	no	—
553	C₂²×D₃	—	8	2	no	—
554	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
555	C₃×Q₈	—	2	1	no	—
556	C₃×Q₈	—	2	1	no	—
557	C₃×D₄	—	2	1	no	—
558	C₃×D₄	—	2	1	no	—
559	C₃×D₄	—	2	1	no	—
560	C₃×D₄	—	2	1	no	—
561	C₃×D₄	—	2	1	no	—
562	C₃×D₄	—	2	1	no	—
563	C₃×D₄	—	8	2	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
566	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
567	#67	—	4	2	no	—
568	#67	—	4	2	no	—
569	#67	—	4	2	no	—
570	#67	—	8	2	no	—
571	#67	—	8	2	no	—
572	C₂×Dic₃	—	2	1	no	—
573	C₂×Dic₃	—	4	2	no	—
574	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
575	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
576	D₁₂	—	2	1	no	—
577	D₁₂	—	2	1	no	—
578	D₁₂	—	2	1	no	—
579	D₁₂	—	2	1	no	—
580	D₁₂	—	2	1	no	—
581	D₁₂	—	2	1	no	—
582	D₁₂	—	4	2	no	—
583	D₁₂	—	8	2	no	—
584	C₄×D₃	—	4	2	no	—
585	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
586	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
587	Dic₆	—	2	1	no	—
588	Dic₆	—	2	1	no	—
589	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
590	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
591	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
592	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
593	C₂²×C₅	—	3	2	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	4	2	no	—
598	C₂²×C₅	—	4	2	no	—
599	C₂²×C₅	—	4	2	no	—
600	C₂²×C₅	—	6	2	no	—
601	C₂²×C₅	—	12	1	no	—
602	C₂²×C₅	—	12	1	no	—
603	C₂²×C₅	—	12	1	no	—
604	C₂²×C₅	—	12	2	no	—
605	C₂²×C₅	—	12	2	no	—
606	C₂²×C₅	—	12	2	no	—
607	C₂²×C₅	—	24	4	no	—
608	C₂²×C₅	—	24	4	no	—
609	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
610	C₄×C₅	—	2	2	no	—
611	C₄×C₅	—	3	2	no	—
612	C₄×C₅	—	4	1	no	—
613	C₄×C₅	—	6	2	no	—
614	C₄×C₅	—	12	1	no	—
615	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
616	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
617	C₂⁴	—	6	1	no	—
618	C₂⁴	—	6	1	no	—
619	#41	—	6	2	no	—
620	#41	—	6	2	no	—
621	#41	—	6	2	no	—
622	#41	—	6	2	no	—
623	C₂×Q₈	—	3	1	no	—
624	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	3	1	no	—
627	C₂×D₄	—	3	1	no	—
628	C₂×D₄	—	3	1	no	—
629	C₂×D₄	—	6	1	no	—
630	C₂×D₄	—	6	2	no	—
631	C₂×D₄	—	6	2	no	—
632	C₂×D₄	—	6	2	no	—
633	C₂×D₄	—	6	2	no	—
634	C₂×D₄	—	6	1	no	—
635	C₂×D₄	—	6	1	no	—
636	C₂×D₄	—	6	2	no	—
637	C₂×D₄	—	6	2	no	—
638	C₂×D₄	—	6	1	no	—
639	C₂×D₄	—	6	2	no	—
640	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
641	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
642	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
643	C₂²×C₄	—	3	1	no	—
644	C₂²×C₄	—	6	1	no	—
645	C₂²×C₄	—	6	1	no	—
646	Q₁₆	—	6	2	no	—
647	SD₁₆	—	2	2	no	—
648	SD₁₆	—	2	2	no	—
649	SD₁₆	—	6	2	no	—
650	SD₁₆	—	6	2	no	—
651	SD₁₆	—	6	2	no	—
652	SD₁₆	—	6	2	no	—
653	D₈	—	2	2	no	—
654	D₈	—	2	2	no	—
655	D₈	—	6	2	no	—
656	D₈	—	6	2	no	—
657	D₈	—	6	2	no	—
658	D₈	—	6	2	no	—
659	D₈	—	6	2	no	—
660	D₈	—	6	2	no	—
661	D₈	—	6	2	no	—
662	M₁₆	—	3	4	no	—
663	C₂×C₈	—	3	1	no	—
664	C₂×C₈	—	3	1	no	—
665	C₂×C₈	—	3	4	no	—
666	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
668	C₄⋊C₄	—	3	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	3	2	no	—
671	C₂²⋊C₄	—	6	2	no	—
672	C₂²⋊C₄	—	6	2	no	—
673	C₂²⋊C₄	—	6	2	no	—
674	C₄²	—	3	1	no	—
675	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
676	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	2	no	—
681	C₂²×C₃	—	4	2	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
684	C₂×D₃	—	2	2	no	—
685	C₂×D₃	—	4	1	no	—
686	C₂×D₃	—	4	1	no	—
687	C₂×D₃	—	4	1	no	—
688	C₂×D₃	—	4	2	no	—
689	C₂×D₃	—	4	2	no	—
690	C₂×D₃	—	4	2	no	—
691	C₂×D₃	—	8	4	no	—
692	C₂×D₃	—	8	4	no	—
693	C₂×D₃	C₅×#127	1	2	yes	—
694	C₃×C₄	—	2	2	no	—
695	C₃×C₄	—	4	1	no	—
696	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
697	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
698	Dic₃	—	2	2	no	—
699	Dic₃	—	4	1	no	—
700	Dic₃	C₅×#127	1	2	yes	—
701	C₂×C₅	—	6	2	no	—
702	C₂×C₅	—	8	1	no	—
703	C₂×C₅	—	8	1	no	—
704	C₂×C₅	—	8	1	no	—
705	C₂×C₅	—	24	1	no	—
706	C₂×C₅	—	24	1	no	—
707	C₂×C₅	—	24	1	no	—
708	C₂×C₅	D₃×#127	1	1	yes	characteristic
709	C₂×C₅	#5774	1	2	yes	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	3	1	no	—
714	C₂³	—	6	1	no	—
715	C₂³	—	6	1	no	—
716	C₂³	—	6	1	no	—
717	C₂³	—	12	2	no	—
718	C₂³	—	12	2	no	—
719	C₂³	—	24	2	no	—
720	C₂³	—	24	2	no	—
721	Q₈	—	2	1	no	—
722	Q₈	—	2	1	no	—
723	Q₈	—	6	1	no	—
724	Q₈	—	6	1	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	1	no	—
727	D₄	—	2	1	no	—
728	D₄	—	2	1	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	1	no	—
731	D₄	—	6	1	no	—
732	D₄	—	6	1	no	—
733	D₄	—	6	1	no	—
734	D₄	—	6	1	no	—
735	D₄	—	6	1	no	—
736	D₄	—	6	1	no	—
737	D₄	—	8	2	no	—
738	D₄	—	12	2	no	—
739	D₄	—	12	2	no	—
740	D₄	—	12	2	no	—
741	D₄	—	12	2	no	—
742	D₄	—	24	2	no	—
743	D₄	—	24	2	no	—
744	D₄	—	24	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	3	1	no	—
747	C₂×C₄	—	3	2	no	—
748	C₂×C₄	—	3	2	no	—
749	C₂×C₄	—	3	2	no	—
750	C₂×C₄	—	6	1	no	—
751	C₂×C₄	—	12	2	no	—
752	C₂×C₄	—	12	2	no	—
753	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
754	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
755	C₈	—	3	2	no	—
756	C₈	—	3	2	no	—
757	C₈	C₅×D₃×D₄	1	2	yes	—
758	C₈	C₅×D₃×D₄	1	2	yes	—
759	C₂×C₃	—	8	1	no	—
760	C₂×C₃	—	8	1	no	—
761	C₂×C₃	—	8	1	no	—
762	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
763	C₂×C₃	C₅×#576	1	2	yes	—
764	D₃	—	2	2	no	—
765	D₃	—	8	1	no	—
766	D₃	—	8	1	no	—
767	D₃	—	8	1	no	—
768	C₅	#81848	1	1	yes	characteristic, direct product factor, Sylow
769	C₂²	—	3	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	6	2	no	—
777	C₂²	—	12	1	no	—
778	C₂²	—	12	1	no	—
779	C₂²	—	12	1	no	—
780	C₂²	—	12	2	no	—
781	C₂²	—	12	2	no	—
782	C₂²	—	12	2	no	—
783	C₂²	—	24	4	no	—
784	C₂²	—	24	4	no	—
785	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	3	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	6	2	no	—
790	C₄	—	12	1	no	—
791	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
792	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
793	C₃	C₅×#3155	1	1	yes	characteristic, complemented, Sylow
794	C₂	—	6	2	no	—
795	C₂	—	8	1	no	—
796	C₂	—	8	1	no	—
797	C₂	—	8	1	no	—
798	C₂	—	24	1	no	—
799	C₂	—	24	1	no	—
800	C₂	—	24	1	no	—
801	C₂	C₅×D₃×#127	1	1	yes	characteristic
802	C₂	C₅×#5774	1	2	yes	—

	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×#496	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#496	D₃
hypocenter	C₃	C₅×#3155
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#496

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#916	C₂	semidirect
2. C₂×C₅×#914	C₂	semidirect
3. C₂×C₅×#911	C₂	semidirect
4. C₂×C₅×D₃×D₈	C₂	semidirect
5. C₅×#5715	C₂	semidirect
6. C₅×#5674	C₂	semidirect
7. C₃×C₅×#496	C₂	semidirect
8. C₅×#5176	C₂	semidirect
9. C₅×#5168	C₂	semidirect
10. C₅×#5154	C₂	semidirect
11. C₅×#5151	C₂	semidirect
12. C₅×#5073	C₂	semidirect
13. C₅×#5059	C₂	semidirect
14. C₅×#4712	C₂	semidirect
15. C₅×#4708	C₂	semidirect
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂×C₃×C₅×D₈	C₂²	semidirect
25. C₃×C₅×#127	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
27. C₅×#947	C₂²	semidirect
28. C₂×C₅×#216	C₂²	semidirect
29. C₂×C₅×#215	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
31. C₅×#940	C₂²	semidirect
34. C₅×#936	C₂²	semidirect
35. C₂×C₅×#214	C₂²	semidirect
38. C₂×C₅×#213	C₂²	semidirect
39. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×#213	C₂²	semidirect
46. C₂×C₅×D₂₄	C₂²	semidirect
47. C₂×C₅×#204	C₂²	semidirect
48. C₂×C₅×#204	C₂²	semidirect
53. C₅×#875	C₂²	semidirect
54. C₅×#874	C₂²	semidirect
56. C₃×C₅×#97	C₂²	semidirect
57. C₅×#815	C₂²	semidirect
58. C₅×C₈×Dic₃	C₂²	semidirect
59. C₄×C₅×C₃⋊C₈	C₂²	semidirect
60. #81848	C₅	direct (N × H)
70. C₅×#496	D₃	semidirect
133. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
134. C₅×D₃×C₈	D₄	semidirect
135. C₂×#916	C₂×C₅	semidirect
136. C₂×#914	C₂×C₅	semidirect
137. C₂×#911	C₂×C₅	semidirect
138. C₂×D₃×D₈	C₂×C₅	semidirect
139. #5715	C₂×C₅	semidirect
140. #5674	C₂×C₅	semidirect
141. C₃×#496	C₂×C₅	semidirect
142. #5176	C₂×C₅	semidirect
143. #5168	C₂×C₅	semidirect
144. #5154	C₂×C₅	semidirect
145. #5151	C₂×C₅	semidirect
146. #5073	C₂×C₅	semidirect
147. #5059	C₂×C₅	semidirect
148. #4712	C₂×C₅	semidirect
149. #4708	C₂×C₅	semidirect
162. C₂×C₅×SD₁₆	C₂×D₃	semidirect
163. C₂×C₅×SD₁₆	C₂×D₃	semidirect
173. C₂×C₅×D₈	C₂×D₃	semidirect
179. C₅×#127	C₂×D₃	semidirect
183. C₅×#124	C₂×D₃	semidirect
190. C₅×#97	C₂×D₃	semidirect
247. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
248. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
250. C₂×C₃×D₈	C₂²×C₅	semidirect
251. C₃×#127	C₂²×C₅	semidirect
252. C₃×#124	C₂²×C₅	semidirect
253. #947	C₂²×C₅	semidirect
254. C₂×#216	C₂²×C₅	semidirect
255. C₂×#215	C₂²×C₅	semidirect
256. #940	C₂²×C₅	semidirect
257. #940	C₂²×C₅	semidirect
260. #936	C₂²×C₅	semidirect
261. C₂×#214	C₂²×C₅	semidirect
264. C₂×#213	C₂²×C₅	semidirect
265. C₂×#213	C₂²×C₅	semidirect
266. C₂×#213	C₂²×C₅	semidirect
272. C₂×D₂₄	C₂²×C₅	semidirect
273. C₂×#204	C₂²×C₅	semidirect
274. C₂×#204	C₂²×C₅	semidirect
279. #875	C₂²×C₅	semidirect
280. #874	C₂²×C₅	semidirect
282. C₃×#97	C₂²×C₅	semidirect
283. #815	C₂²×C₅	semidirect
284. C₈×Dic₃	C₂²×C₅	semidirect
285. C₄×C₃⋊C₈	C₂²×C₅	semidirect
354. #496	C₅×D₃	semidirect
441. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
442. D₃×C₈	C₅×D₄	semidirect
504. C₂×SD₁₆	C₂×C₅×D₃	semidirect
505. C₂×SD₁₆	C₂×C₅×D₃	semidirect
515. C₂×D₈	C₂×C₅×D₃	semidirect
521. #127	C₂×C₅×D₃	semidirect
525. #124	C₂×C₅×D₃	semidirect
532. #97	C₂×C₅×D₃	semidirect
676. C₃×C₅	#3155	semidirect
768. C₅	#81848	direct (N × H)
793. C₃	C₅×#3155	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#916	2
C₂×C₅×#914	2
C₂×C₅×#911	2
C₂×C₅×D₃×D₈	2
C₅×#5715	2
C₅×#5674	2
C₃×C₅×#496	2
C₅×#5176	2
C₅×#5168	2
C₅×#5154	2
C₅×#5151	2
C₅×#5073	2
C₅×#5059	2
C₅×#4712	2
C₅×#4708	2
C₅×#3155	3
#81848	5

Subgroups — C5×#81848 #14439543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81848 #14439543