Subgroups — C₅×#78662 #14411743

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5234	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5129	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5110	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4727	C₂	1	4	yes	maximal, complemented
9	C₅×#4726	C₂	1	4	yes	maximal, complemented
10	C₅×#2879	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₅×D₃×#41	—	2	4	no	—
13	C₅×D₃×#41	—	2	4	no	—
14	C₂×C₅×#239	C₄	1	1	yes	characteristic
15	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
16	C₂×C₅×#237	C₄	1	2	yes	—
17	C₂×C₅×#237	C₄	1	1	yes	characteristic
18	C₂×C₅×D₃×D₄	C₄	1	2	yes	—
19	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
20	C₂×C₅×#235	C₂²	1	2	yes	—
21	C₂×C₅×#235	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×D₃×M₁₆	—	2	4	no	—
29	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
32	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
33	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
34	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
35	C₅×#830	C₂²	1	4	yes	complemented
36	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
37	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
38	#78662	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂²×C₅×#41	—	3	1	no	—
40	C₂²×C₅×M₁₆	—	3	1	no	—
41	C₂²×C₅×M₁₆	—	3	1	no	—
42	C₅×#408	—	3	4	no	—
43	C₅×#408	—	3	1	no	—
44	C₅×#408	—	3	1	no	—
45	C₅×#408	—	3	1	no	—
46	C₅×#408	D₃	1	1	yes	characteristic, complemented
47	C₅×#407	—	3	4	no	—
48	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
49	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	C₂×C₄	1	2	yes	—
58	C₂×C₅×#67	C₂×C₄	1	2	yes	—
59	C₂×C₅×#67	C₂×C₄	1	2	yes	—
60	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
61	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₅×#239	—	2	4	no	—
63	C₅×D₃×Q₈	—	2	4	no	—
64	C₅×#237	—	2	8	no	—
65	C₅×#237	—	2	4	no	—
66	C₅×D₃×D₄	—	2	8	no	—
67	C₅×D₃×D₄	—	2	4	no	—
68	C₅×#235	—	2	2	no	—
69	C₅×#235	—	2	2	no	—
70	C₅×#235	—	2	4	no	—
71	C₅×#235	—	2	4	no	—
72	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
73	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	—	2	4	no	—
75	C₂×C₄×C₅×D₃	—	2	4	no	—
76	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
77	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
78	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
81	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
82	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
83	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
87	C₃×C₅×M₁₆	—	2	2	no	—
88	C₂×C₃×C₅×C₈	—	2	2	no	—
89	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
91	C₅×#208	—	2	2	no	—
92	C₂×C₅×C₃⋊C₈	—	2	2	no	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
96	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
97	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
98	C₅×D₃×C₈	—	2	4	no	—
99	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic
100	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
103	#5234	C₂×C₅	1	1	yes	characteristic, complemented
104	#5129	C₂×C₅	1	1	yes	characteristic, complemented
105	#5110	C₂×C₅	1	1	yes	characteristic, complemented
106	#4727	C₂×C₅	1	4	yes	complemented
107	#4726	C₂×C₅	1	4	yes	complemented
108	C₂×C₅×#41	—	3	1	no	—
109	C₂×C₅×#41	—	3	2	no	—
110	C₂×C₅×#41	—	3	1	no	—
111	C₂×C₅×#41	—	3	2	no	—
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	—	6	4	no	—
114	C₂×C₅×#41	—	6	4	no	—
115	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
116	C₂²×C₅×Q₈	—	3	1	no	—
117	C₂²×C₅×D₄	—	3	1	no	—
118	C₂²×C₅×D₄	—	3	2	no	—
119	C₂³×C₄×C₅	—	3	1	no	—
120	C₂³×C₄×C₅	—	3	2	no	—
121	C₂×C₅×M₁₆	—	3	1	no	—
122	C₂×C₅×M₁₆	—	3	2	no	—
123	C₂×C₅×M₁₆	—	3	2	no	—
124	C₂×C₅×M₁₆	—	3	2	no	—
125	C₂×C₅×M₁₆	—	6	4	no	—
126	C₂×C₅×M₁₆	—	6	4	no	—
127	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
128	C₂²×C₅×C₈	—	3	1	no	—
129	C₂²×C₅×C₈	—	3	2	no	—
130	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
131	C₅×C₂²⋊C₈	—	3	4	no	—
132	C₅×C₂²⋊C₈	—	3	4	no	—
133	C₅×C₂²⋊C₈	—	3	4	no	—
134	C₅×C₂²⋊C₈	C₂×D₃	1	4	yes	complemented
135	#2879	—	3	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₅×D₃	—	2	4	no	—
139	C₂²×C₅×D₃	—	4	2	no	—
140	C₂²×C₅×D₃	—	4	4	no	—
141	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
142	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
145	C₃×C₅×Q₈	—	2	2	no	—
146	C₃×C₅×D₄	—	2	4	no	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₅×#67	—	2	4	no	—
156	C₅×#67	—	2	4	no	—
157	C₅×#67	—	2	4	no	—
158	C₂×C₅×Dic₃	—	2	4	no	—
159	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
160	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
161	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
163	C₅×D₁₂	—	2	4	no	—
164	C₅×D₁₂	—	2	2	no	—
165	C₄×C₅×D₃	—	2	4	no	—
166	C₄×C₅×D₃	—	2	2	no	—
167	C₄×C₅×D₃	—	2	2	no	—
168	C₄×C₅×D₃	—	2	4	no	—
169	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
170	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
171	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
172	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
173	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
174	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
175	C₅×Dic₆	—	2	2	no	—
176	C₅×Dic₆	—	2	4	no	—
177	C₃×C₅×C₈	—	2	2	no	—
178	C₃×C₅×C₈	—	2	2	no	—
179	C₅×C₃⋊C₈	—	2	2	no	—
180	C₅×C₃⋊C₈	—	2	2	no	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	D₃×#41	—	2	4	no	—
183	D₃×#41	—	2	4	no	—
184	C₂×#239	C₄×C₅	1	1	yes	characteristic
185	C₂×D₃×Q₈	C₄×C₅	1	1	yes	characteristic
186	C₂×#237	C₄×C₅	1	2	yes	—
187	C₂×#237	C₄×C₅	1	1	yes	characteristic
188	C₂×D₃×D₄	C₄×C₅	1	2	yes	—
189	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
190	C₂×#235	C₂²×C₅	1	1	yes	characteristic
191	C₂×#235	C₂²×C₅	1	2	yes	—
192	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
193	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
198	D₃×M₁₆	—	2	4	no	—
199	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
200	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
201	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
202	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
203	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
204	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
205	#830	C₂²×C₅	1	4	yes	complemented
206	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
207	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
208	C₂⁴×C₅	—	3	1	no	—
209	C₂⁴×C₅	—	3	2	no	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	—	2	2	no	—
212	C₅×#41	—	6	4	no	—
213	C₅×#41	—	6	4	no	—
214	C₅×#41	—	6	8	no	—
215	C₅×#41	—	6	4	no	—
216	C₅×#41	—	6	4	no	—
217	C₅×#41	—	6	2	no	—
218	C₅×#41	—	6	2	no	—
219	C₂×C₅×Q₈	—	3	2	no	—
220	C₂×C₅×Q₈	—	3	1	no	—
221	C₂×C₅×Q₈	—	6	4	no	—
222	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
223	C₂×C₅×D₄	—	3	2	no	—
224	C₂×C₅×D₄	—	3	2	no	—
225	C₂×C₅×D₄	—	3	2	no	—
226	C₂×C₅×D₄	—	3	2	no	—
227	C₂×C₅×D₄	—	3	1	no	—
228	C₂×C₅×D₄	—	6	4	no	—
229	C₂×C₅×D₄	—	6	8	no	—
230	C₂×C₅×D₄	C₄×D₃	1	2	yes	—
231	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	—	3	1	no	—
233	C₂²×C₄×C₅	—	3	1	no	—
234	C₂²×C₄×C₅	—	3	1	no	—
235	C₂²×C₄×C₅	—	3	4	no	—
236	C₂²×C₄×C₅	—	3	4	no	—
237	C₂²×C₄×C₅	—	3	1	no	—
238	C₂²×C₄×C₅	—	3	1	no	—
239	C₂²×C₄×C₅	—	3	2	no	—
240	C₂²×C₄×C₅	—	3	2	no	—
241	C₂²×C₄×C₅	—	3	2	no	—
242	C₂²×C₄×C₅	—	3	2	no	—
243	C₂²×C₄×C₅	—	6	4	no	—
244	C₂²×C₄×C₅	—	6	4	no	—
245	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
246	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
247	C₅×M₁₆	—	2	2	no	—
248	C₅×M₁₆	—	6	4	no	—
249	C₅×M₁₆	—	6	4	no	—
250	C₅×M₁₆	—	6	4	no	—
251	C₅×M₁₆	—	6	2	no	—
252	C₂×C₅×C₈	—	2	2	no	—
253	C₂×C₅×C₈	—	3	2	no	—
254	C₂×C₅×C₈	—	3	2	no	—
255	C₂×C₅×C₈	—	6	4	no	—
256	C₂×C₅×C₈	—	6	2	no	—
257	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
258	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
259	C₂²×#41	—	3	1	no	—
260	C₂²×M₁₆	—	3	1	no	—
261	C₂²×M₁₆	—	3	1	no	—
262	#408	—	3	1	no	—
263	#408	—	3	1	no	—
264	#408	—	3	1	no	—
265	#408	—	3	4	no	—
266	#408	C₅×D₃	1	1	yes	characteristic, complemented
267	#407	—	3	4	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	2	4	no	—
271	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₅×D₃	—	2	2	no	—
274	C₂×C₅×D₃	—	2	2	no	—
275	C₂×C₅×D₃	—	2	2	no	—
276	C₂×C₅×D₃	—	2	4	no	—
277	C₂×C₅×D₃	—	4	4	no	—
278	C₂×C₅×D₃	—	4	8	no	—
279	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
281	C₃×C₄×C₅	—	2	2	no	—
282	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
283	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
285	C₅×Dic₃	—	2	2	no	—
286	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
287	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
289	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
290	C₃×#41	—	2	2	no	—
291	C₃×#41	—	2	2	no	—
292	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
293	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
294	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
297	C₂×#67	C₂×C₄×C₅	1	2	yes	—
298	C₂×#67	C₂×C₄×C₅	1	2	yes	—
299	C₂×#67	C₂×C₄×C₅	1	2	yes	—
300	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
301	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
302	#239	—	2	4	no	—
303	D₃×Q₈	—	2	4	no	—
304	#237	—	2	8	no	—
305	#237	—	2	4	no	—
306	D₃×D₄	—	2	8	no	—
307	D₃×D₄	—	2	4	no	—
308	#235	—	2	2	no	—
309	#235	—	2	2	no	—
310	#235	—	2	4	no	—
311	#235	—	2	4	no	—
312	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
313	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
314	C₂×C₄×D₃	—	2	4	no	—
315	C₂×C₄×D₃	—	2	4	no	—
316	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
317	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
318	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
319	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
320	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
321	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
322	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
323	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
324	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
325	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
326	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
327	C₃×M₁₆	—	2	2	no	—
328	C₂×C₃×C₈	—	2	2	no	—
329	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
330	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
331	#208	—	2	2	no	—
332	C₂×C₃⋊C₈	—	2	2	no	—
333	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
334	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
335	ΓL(1,𝔽₂₅)	—	2	4	no	—
336	ΓL(1,𝔽₂₅)	—	2	4	no	—
337	ΓL(1,𝔽₂₅)	—	2	4	no	—
338	D₃×C₈	—	2	4	no	—
339	C₂³×C₅	—	3	1	no	—
340	C₂³×C₅	—	3	1	no	—
341	C₂³×C₅	—	3	4	no	—
342	C₂³×C₅	—	3	2	no	—
343	C₂³×C₅	—	6	4	no	—
344	C₂³×C₅	—	12	2	no	—
345	C₂³×C₅	—	12	4	no	—
346	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
347	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
348	C₅×Q₈	—	2	2	no	—
349	C₅×Q₈	—	6	4	no	—
350	C₅×Q₈	—	6	2	no	—
351	C₅×D₄	—	2	4	no	—
352	C₅×D₄	—	2	2	no	—
353	C₅×D₄	—	6	4	no	—
354	C₅×D₄	—	6	4	no	—
355	C₅×D₄	—	6	4	no	—
356	C₅×D₄	—	6	4	no	—
357	C₅×D₄	—	6	2	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	3	4	no	—
361	C₂×C₄×C₅	—	3	1	no	—
362	C₂×C₄×C₅	—	3	1	no	—
363	C₂×C₄×C₅	—	3	4	no	—
364	C₂×C₄×C₅	—	3	4	no	—
365	C₂×C₄×C₅	—	3	2	no	—
366	C₂×C₄×C₅	—	3	2	no	—
367	C₂×C₄×C₅	—	3	2	no	—
368	C₂×C₄×C₅	—	3	2	no	—
369	C₂×C₄×C₅	—	3	2	no	—
370	C₂×C₄×C₅	—	6	4	no	—
371	C₂×C₄×C₅	—	6	4	no	—
372	C₂×C₄×C₅	—	6	4	no	—
373	C₂×C₄×C₅	—	6	2	no	—
374	C₂×C₄×C₅	—	6	2	no	—
375	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
376	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
377	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
378	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
379	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
380	C₅×C₈	—	2	2	no	—
381	C₅×C₈	—	2	2	no	—
382	C₅×C₈	—	6	2	no	—
383	C₅×C₈	—	6	2	no	—
384	C₂×#41	—	3	1	no	—
385	C₂×#41	—	3	2	no	—
386	C₂×#41	—	3	1	no	—
387	C₂×#41	—	3	2	no	—
388	C₂×#41	—	3	1	no	—
389	C₂×#41	—	6	4	no	—
390	C₂×#41	—	6	4	no	—
391	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
392	C₂²×Q₈	—	3	1	no	—
393	C₂²×D₄	—	3	1	no	—
394	C₂²×D₄	—	3	2	no	—
395	C₂³×C₄	—	3	1	no	—
396	C₂³×C₄	—	3	2	no	—
397	C₂×M₁₆	—	3	1	no	—
398	C₂×M₁₆	—	3	2	no	—
399	C₂×M₁₆	—	3	2	no	—
400	C₂×M₁₆	—	3	2	no	—
401	C₂×M₁₆	—	6	4	no	—
402	C₂×M₁₆	—	6	4	no	—
403	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
404	C₂²×C₈	—	3	1	no	—
405	C₂²×C₈	—	3	2	no	—
406	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
407	C₂²⋊C₈	—	3	4	no	—
408	C₂²⋊C₈	—	3	4	no	—
409	C₂²⋊C₈	—	3	4	no	—
410	C₂²⋊C₈	C₂×C₅×D₃	1	4	yes	complemented
411	C₂×C₃×C₅	—	2	2	no	—
412	C₂×C₃×C₅	—	4	2	no	—
413	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
414	C₂×C₃×C₅	#568	1	2	yes	—
415	C₅×D₃	—	2	2	no	—
416	C₅×D₃	—	2	2	no	—
417	C₅×D₃	—	4	2	no	—
418	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
419	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
420	C₂²×D₃	—	2	4	no	—
421	C₂²×D₃	—	4	2	no	—
422	C₂²×D₃	—	4	4	no	—
423	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
424	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
425	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
426	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
427	C₃×Q₈	—	2	2	no	—
428	C₃×D₄	—	2	4	no	—
429	C₃×D₄	—	2	2	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
433	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
435	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
436	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
437	#67	—	2	4	no	—
438	#67	—	2	4	no	—
439	#67	—	2	4	no	—
440	C₂×Dic₃	—	2	4	no	—
441	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
442	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
443	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
444	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
445	D₁₂	—	2	4	no	—
446	D₁₂	—	2	2	no	—
447	C₄×D₃	—	2	4	no	—
448	C₄×D₃	—	2	2	no	—
449	C₄×D₃	—	2	2	no	—
450	C₄×D₃	—	2	4	no	—
451	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
452	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
453	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
454	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
455	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
456	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
457	Dic₆	—	2	2	no	—
458	Dic₆	—	2	4	no	—
459	C₃×C₈	—	2	2	no	—
460	C₃×C₈	—	2	2	no	—
461	C₃⋊C₈	—	2	2	no	—
462	C₃⋊C₈	—	2	2	no	—
463	C₂²×C₅	—	2	2	no	—
464	C₂²×C₅	—	2	2	no	—
465	C₂²×C₅	—	2	4	no	—
466	C₂²×C₅	—	3	2	no	—
467	C₂²×C₅	—	3	2	no	—
468	C₂²×C₅	—	6	2	no	—
469	C₂²×C₅	—	6	2	no	—
470	C₂²×C₅	—	6	2	no	—
471	C₂²×C₅	—	6	4	no	—
472	C₂²×C₅	—	12	4	no	—
473	C₂²×C₅	—	12	8	no	—
474	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
475	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	3	2	no	—
478	C₄×C₅	—	3	2	no	—
479	C₄×C₅	—	6	2	no	—
480	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
481	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
482	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
483	C₂⁴	—	3	1	no	—
484	C₂⁴	—	3	2	no	—
485	#41	—	2	2	no	—
486	#41	—	2	2	no	—
487	#41	—	6	4	no	—
488	#41	—	6	4	no	—
489	#41	—	6	8	no	—
490	#41	—	6	4	no	—
491	#41	—	6	4	no	—
492	#41	—	6	2	no	—
493	#41	—	6	2	no	—
494	C₂×Q₈	—	3	2	no	—
495	C₂×Q₈	—	3	1	no	—
496	C₂×Q₈	—	6	4	no	—
497	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
498	C₂×D₄	—	3	2	no	—
499	C₂×D₄	—	3	2	no	—
500	C₂×D₄	—	3	2	no	—
501	C₂×D₄	—	3	2	no	—
502	C₂×D₄	—	3	1	no	—
503	C₂×D₄	—	6	4	no	—
504	C₂×D₄	—	6	8	no	—
505	C₂×D₄	C₄×C₅×D₃	1	2	yes	—
506	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
507	C₂²×C₄	—	3	1	no	—
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	—	3	1	no	—
510	C₂²×C₄	—	3	4	no	—
511	C₂²×C₄	—	3	4	no	—
512	C₂²×C₄	—	3	1	no	—
513	C₂²×C₄	—	3	1	no	—
514	C₂²×C₄	—	3	2	no	—
515	C₂²×C₄	—	3	2	no	—
516	C₂²×C₄	—	3	2	no	—
517	C₂²×C₄	—	3	2	no	—
518	C₂²×C₄	—	6	4	no	—
519	C₂²×C₄	—	6	4	no	—
520	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
521	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
522	M₁₆	—	2	2	no	—
523	M₁₆	—	6	4	no	—
524	M₁₆	—	6	4	no	—
525	M₁₆	—	6	4	no	—
526	M₁₆	—	6	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	3	2	no	—
529	C₂×C₈	—	3	2	no	—
530	C₂×C₈	—	6	4	no	—
531	C₂×C₈	—	6	2	no	—
532	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
533	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
534	C₃×C₅	#2879	1	1	yes	characteristic, complemented, Hall
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	2	4	no	—
538	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
539	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	2	2	no	—
542	C₂×D₃	—	2	2	no	—
543	C₂×D₃	—	2	4	no	—
544	C₂×D₃	—	4	4	no	—
545	C₂×D₃	—	4	8	no	—
546	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
547	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
550	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
551	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
552	Dic₃	—	2	2	no	—
553	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
554	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
555	C₂×C₅	—	2	2	no	—
556	C₂×C₅	—	4	2	no	—
557	C₂×C₅	—	6	2	no	—
558	C₂×C₅	—	6	2	no	—
559	C₂×C₅	—	12	2	no	—
560	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₅	#5750	1	2	yes	—
562	C₂³	—	3	1	no	—
563	C₂³	—	3	1	no	—
564	C₂³	—	3	4	no	—
565	C₂³	—	3	2	no	—
566	C₂³	—	6	4	no	—
567	C₂³	—	12	2	no	—
568	C₂³	—	12	4	no	—
569	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
570	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
571	Q₈	—	2	2	no	—
572	Q₈	—	6	4	no	—
573	Q₈	—	6	2	no	—
574	D₄	—	2	4	no	—
575	D₄	—	2	2	no	—
576	D₄	—	6	4	no	—
577	D₄	—	6	4	no	—
578	D₄	—	6	4	no	—
579	D₄	—	6	4	no	—
580	D₄	—	6	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	3	4	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	3	1	no	—
586	C₂×C₄	—	3	4	no	—
587	C₂×C₄	—	3	4	no	—
588	C₂×C₄	—	3	2	no	—
589	C₂×C₄	—	3	2	no	—
590	C₂×C₄	—	3	2	no	—
591	C₂×C₄	—	3	2	no	—
592	C₂×C₄	—	3	2	no	—
593	C₂×C₄	—	6	4	no	—
594	C₂×C₄	—	6	4	no	—
595	C₂×C₄	—	6	4	no	—
596	C₂×C₄	—	6	2	no	—
597	C₂×C₄	—	6	2	no	—
598	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
599	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
600	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
601	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
602	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	2	2	no	—
605	C₈	—	6	2	no	—
606	C₈	—	6	2	no	—
607	C₂×C₃	—	2	2	no	—
608	C₂×C₃	—	4	2	no	—
609	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
610	C₂×C₃	C₅×#568	1	2	yes	—
611	D₃	—	2	2	no	—
612	D₃	—	2	2	no	—
613	D₃	—	4	2	no	—
614	C₅	#78662	1	1	yes	characteristic, direct product factor, Sylow
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	3	2	no	—
619	C₂²	—	3	2	no	—
620	C₂²	—	6	2	no	—
621	C₂²	—	6	2	no	—
622	C₂²	—	6	2	no	—
623	C₂²	—	6	4	no	—
624	C₂²	—	12	4	no	—
625	C₂²	—	12	8	no	—
626	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
627	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	3	2	no	—
630	C₄	—	3	2	no	—
631	C₄	—	6	2	no	—
632	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
633	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
634	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
635	C₃	C₅×#2879	1	1	yes	characteristic, complemented, Sylow
636	C₂	—	2	2	no	—
637	C₂	—	4	2	no	—
638	C₂	—	6	2	no	—
639	C₂	—	6	2	no	—
640	C₂	—	12	2	no	—
641	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
642	C₂	C₅×#5750	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#408	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×D₃×#41	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#408	D₃
hypocenter	C₃	C₅×#2879
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#408

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₅×#5234	C₂	semidirect
6. C₅×#5129	C₂	semidirect
7. C₅×#5110	C₂	semidirect
8. C₅×#4727	C₂	semidirect
9. C₅×#4726	C₂	semidirect
24. C₂×C₃×C₅×M₁₆	C₂²	semidirect
25. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₂×C₅×#208	C₂²	semidirect
27. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
32. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
33. C₂×C₅×D₃×C₈	C₂²	semidirect
34. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
35. C₅×#830	C₂²	semidirect
36. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
37. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
38. #78662	C₅	direct (N × H)
46. C₅×#408	D₃	semidirect
100. C₂×D₃×M₁₆	C₂×C₅	semidirect
101. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
102. C₃×#408	C₂×C₅	semidirect
103. #5234	C₂×C₅	semidirect
104. #5129	C₂×C₅	semidirect
105. #5110	C₂×C₅	semidirect
106. #4727	C₂×C₅	semidirect
107. #4726	C₂×C₅	semidirect
127. C₂×C₅×M₁₆	C₂×D₃	semidirect
130. C₂²×C₅×C₈	C₂×D₃	semidirect
134. C₅×C₂²⋊C₈	C₂×D₃	semidirect
194. C₂×C₃×M₁₆	C₂²×C₅	semidirect
195. C₂²×C₃×C₈	C₂²×C₅	semidirect
196. C₂×#208	C₂²×C₅	semidirect
197. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
202. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
203. C₂×D₃×C₈	C₂²×C₅	semidirect
204. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
205. #830	C₂²×C₅	semidirect
206. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
207. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
266. #408	C₅×D₃	semidirect
403. C₂×M₁₆	C₂×C₅×D₃	semidirect
406. C₂²×C₈	C₂×C₅×D₃	semidirect
410. C₂²⋊C₈	C₂×C₅×D₃	semidirect
534. C₃×C₅	#2879	semidirect
614. C₅	#78662	direct (N × H)
635. C₃	C₅×#2879	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₂×C₅×D₃×M₁₆	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₃×C₅×#408	2
C₅×#5234	2
C₅×#5129	2
C₅×#5110	2
C₅×#4727	2
C₅×#4726	2
C₅×#2879	3
#78662	5

Subgroups — C5×#78662 #14411743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78662 #14411743