Subgroups — C₅×#79778 #14417617

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 728 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
2	C₅×#5574	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4790	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4756	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4710	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2951	—	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×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×#216	C₂²	1	1	yes	characteristic
24	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×#213	C₂²	1	1	yes	characteristic
26	C₄×C₅×#67	—	2	1	no	—
27	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
28	C₅×#916	C₄	1	8	yes	complemented
29	C₂×C₅×#204	C₂²	1	1	yes	characteristic
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₅×#893	—	2	1	no	—
33	C₅×#893	C₂²	1	1	yes	characteristic
34	C₅×D₃×C₄⋊C₄	—	2	1	no	—
35	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×#887	C₂²	1	1	yes	characteristic
38	C₅×#67⋊C₄	—	2	1	no	—
39	C₅×#877	—	2	1	no	—
40	C₄×C₅×D₁₂	—	2	1	no	—
41	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
42	C₅×#872	—	2	1	no	—
43	C₅×#872	C₂²	1	1	yes	characteristic
44	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic
48	C₃×C₅×#97	C₂²	1	1	yes	characteristic
49	C₅×#835	C₂²	1	1	yes	characteristic
50	C₅×#832	C₂²	1	1	yes	characteristic
51	C₅×#821	C₂²	1	1	yes	characteristic
52	C₅×#818	C₂²	1	1	yes	characteristic
53	C₅×#816	C₂²	1	1	yes	characteristic
54	C₅×#815	C₂²	1	1	yes	characteristic
55	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₅×#810	C₂²	1	1	yes	characteristic
57	C₅×#809	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×#807	C₂²	1	1	yes	characteristic
60	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	#79778	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
62	C₂×C₅×#135	—	3	1	no	—
63	C₅×#520	—	3	1	no	—
64	C₅×#520	—	3	1	no	—
65	C₅×#440	—	3	1	no	—
66	C₅×#440	—	3	1	no	—
67	C₅×#440	—	3	1	no	—
68	C₅×#440	D₃	1	1	yes	characteristic, complemented
69	C₄×C₅×Q₁₆	—	3	1	no	—
70	C₄×C₅×Q₁₆	—	3	1	no	—
71	C₄×C₅×D₈	—	3	1	no	—
72	C₄×C₅×D₈	—	3	1	no	—
73	C₂×C₅×#107	—	3	1	no	—
74	C₅×#417	—	3	1	no	—
75	C₅×#417	—	3	1	no	—
76	C₅×#405	—	3	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₅×#67	—	2	1	no	—
81	C₂²×C₅×Dic₃	—	2	1	no	—
82	C₂²×C₅×Dic₃	—	2	1	no	—
83	C₅×#239	—	2	2	no	—
84	C₅×#239	C₂×C₄	1	4	yes	complemented
85	C₅×#237	—	2	2	no	—
86	C₅×#237	C₂×C₄	1	4	yes	complemented
87	C₂×C₅×D₁₂	—	2	1	no	—
88	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	—	2	1	no	—
90	C₂×C₄×C₅×D₃	—	2	1	no	—
91	C₂×C₄×C₅×D₃	—	2	1	no	—
92	C₂×C₄×C₅×D₃	—	2	1	no	—
93	C₂×C₄×C₅×D₃	—	2	1	no	—
94	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
95	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
96	C₃×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₃×C₅×C₄⋊C₄	—	2	1	no	—
100	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₃×C₄²×C₅	—	2	1	no	—
104	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#217	—	2	1	no	—
106	C₅×#216	C₂×C₄	1	4	yes	complemented
107	C₅×#213	C₂×C₄	1	4	yes	complemented
108	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
111	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
112	C₅×C₄⋊Dic₃	—	2	1	no	—
113	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	—	2	1	no	—
117	C₅×Dic₃⋊C₄	—	2	1	no	—
118	C₅×Dic₃⋊C₄	—	2	1	no	—
119	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
120	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	—	2	1	no	—
123	C₄×C₅×Dic₃	—	2	1	no	—
124	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×#204	C₂×C₄	1	4	yes	complemented
128	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
129	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
130	C₂×#916	C₂×C₅	1	1	yes	characteristic
131	#5574	C₂×C₅	1	1	yes	characteristic, complemented
132	#5546	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
134	#5164	C₂×C₅	1	1	yes	characteristic, complemented
135	C₄×#216	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×#213	C₂×C₅	1	1	yes	characteristic, complemented
137	#4889	C₂×C₅	1	1	yes	characteristic, complemented
138	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
139	#4803	C₂×C₅	1	1	yes	characteristic, complemented
140	#4790	C₂×C₅	1	1	yes	characteristic, complemented
141	#4771	C₂×C₅	1	1	yes	characteristic, complemented
142	#4756	C₂×C₅	1	1	yes	characteristic, complemented
143	#4710	C₂×C₅	1	1	yes	characteristic, complemented
144	#4708	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×C₅×#41	—	3	1	no	—
146	C₂×C₅×#41	—	3	1	no	—
147	C₅×#135	—	3	8	no	—
148	C₂×C₅×Q₁₆	—	3	1	no	—
149	C₂×C₅×SD₁₆	—	3	1	no	—
150	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
151	C₂×C₅×D₈	—	3	1	no	—
152	C₂×C₅×M₁₆	—	3	1	no	—
153	C₂²×C₅×C₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	3	1	no	—
160	C₄×C₅×D₄	—	3	1	no	—
161	C₄×C₅×D₄	—	6	1	no	—
162	C₄×C₅×D₄	—	6	1	no	—
163	C₄×C₅×D₄	—	6	1	no	—
164	C₄×C₅×D₄	—	6	1	no	—
165	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
166	C₅×#117	—	3	1	no	—
167	C₅×#117	—	6	1	no	—
168	C₅×#117	—	6	1	no	—
169	C₂×C₅×C₄⋊C₄	—	3	1	no	—
170	C₂×C₅×C₄⋊C₄	—	3	1	no	—
171	C₂×C₅×C₄⋊C₄	—	6	1	no	—
172	C₂×C₅×C₄⋊C₄	—	6	1	no	—
173	C₅×#107	—	3	1	no	—
174	C₅×#107	—	3	1	no	—
175	C₅×#107	—	3	1	no	—
176	C₅×#107	C₂×D₃	1	1	yes	characteristic
177	C₅×#103	—	3	1	no	—
178	C₅×#103	—	3	1	no	—
179	C₅×#103	—	3	1	no	—
180	C₅×#103	C₂×D₃	1	1	yes	characteristic
181	C₅×#102	—	3	1	no	—
182	C₅×#102	—	3	1	no	—
183	C₅×#102	—	3	1	no	—
184	C₅×#102	C₂×D₃	1	1	yes	characteristic
185	C₅×#97	—	3	1	no	—
186	C₅×#97	C₂×D₃	1	1	yes	characteristic
187	C₄×C₅×C₈	—	3	1	no	—
188	C₄×C₅×C₈	—	3	1	no	—
189	#2951	—	3	1	no	Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂²×C₅×D₃	—	2	1	no	—
192	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	8	1	no	—
201	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
202	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
203	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
204	C₅×#67	—	2	4	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	4	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	2	1	no	—
209	C₂×C₅×Dic₃	—	8	1	no	—
210	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
213	C₅×D₁₂	—	2	4	no	—
214	C₅×D₁₂	—	2	1	no	—
215	C₅×D₁₂	C₂²×C₄	1	2	yes	—
216	C₄×C₅×D₃	—	2	4	no	—
217	C₄×C₅×D₃	—	8	1	no	—
218	C₄×C₅×D₃	—	8	1	no	—
219	C₄×C₅×D₃	—	8	1	no	—
220	C₄×C₅×D₃	—	8	1	no	—
221	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
222	C₄×C₅×D₃	#41	1	2	yes	—
223	C₅×Dic₆	—	2	1	no	—
224	C₅×Dic₆	C₂²×C₄	1	2	yes	—
225	C₃×C₅×C₈	—	2	1	no	—
226	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
227	C₅×C₃⋊C₈	—	2	1	no	—
228	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
229	C₂×#239	C₂²×C₅	1	1	yes	characteristic
230	C₂×#237	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
234	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
235	C₂×#216	C₂²×C₅	1	1	yes	characteristic
236	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
237	C₂×#213	C₂²×C₅	1	1	yes	characteristic
238	C₄×#67	—	2	1	no	—
239	C₂×Dic₃⋊C₄	—	2	1	no	—
240	#916	C₄×C₅	1	8	yes	complemented
241	C₂×#204	C₂²×C₅	1	1	yes	characteristic
242	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
243	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
244	#893	—	2	1	no	—
245	#893	C₂²×C₅	1	1	yes	characteristic
246	D₃×C₄⋊C₄	—	2	1	no	—
247	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	#887	C₂²×C₅	1	1	yes	characteristic
250	#67⋊C₄	—	2	1	no	—
251	#877	—	2	1	no	—
252	C₄×D₁₂	—	2	1	no	—
253	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
254	#872	—	2	1	no	—
255	#872	C₂²×C₅	1	1	yes	characteristic
256	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
257	C₃×#107	C₂²×C₅	1	1	yes	characteristic
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic
259	C₃×#102	C₂²×C₅	1	1	yes	characteristic
260	C₃×#97	C₂²×C₅	1	1	yes	characteristic
261	#835	C₂²×C₅	1	1	yes	characteristic
262	#832	C₂²×C₅	1	1	yes	characteristic
263	#821	C₂²×C₅	1	1	yes	characteristic
264	#818	C₂²×C₅	1	1	yes	characteristic
265	#816	C₂²×C₅	1	1	yes	characteristic
266	#815	C₂²×C₅	1	1	yes	characteristic
267	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
268	#810	C₂²×C₅	1	1	yes	characteristic
269	#809	C₂²×C₅	1	1	yes	characteristic
270	#807	C₂²×C₅	1	1	yes	characteristic
271	#807	C₂²×C₅	1	1	yes	characteristic
272	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	C₅×#41	—	3	4	no	—
274	C₅×#41	—	3	4	no	—
275	C₅×#41	—	6	2	no	—
276	C₅×#41	—	6	2	no	—
277	C₂×C₅×Q₈	—	3	1	no	—
278	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
279	C₂×C₅×D₄	—	3	1	no	—
280	C₂×C₅×D₄	—	6	1	no	—
281	C₂×C₅×D₄	—	6	1	no	—
282	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	—	3	1	no	—
285	C₂²×C₄×C₅	—	6	1	no	—
286	C₂²×C₄×C₅	—	6	1	no	—
287	C₂²×C₄×C₅	—	6	1	no	—
288	C₂²×C₄×C₅	—	6	1	no	—
289	C₂²×C₄×C₅	—	6	1	no	—
290	C₂²×C₄×C₅	—	6	1	no	—
291	C₂²×C₄×C₅	—	6	1	no	—
292	C₅×Q₁₆	—	3	4	no	—
293	C₅×SD₁₆	—	3	4	no	—
294	C₅×SD₁₆	C₄×D₃	1	4	yes	complemented
295	C₅×D₈	—	3	4	no	—
296	C₅×M₁₆	—	6	2	no	—
297	C₂×C₅×C₈	—	3	1	no	—
298	C₂×C₅×C₈	—	3	4	no	—
299	C₂×C₅×C₈	—	3	1	no	—
300	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
301	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	—	3	1	no	—
304	C₅×C₄⋊C₄	—	3	1	no	—
305	C₅×C₄⋊C₄	—	3	1	no	—
306	C₅×C₄⋊C₄	—	3	1	no	—
307	C₅×C₄⋊C₄	—	6	1	no	—
308	C₅×C₄⋊C₄	—	6	1	no	—
309	C₅×C₄⋊C₄	—	6	1	no	—
310	C₅×C₄⋊C₄	—	6	1	no	—
311	C₅×C₄⋊C₄	—	6	1	no	—
312	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	3	1	no	—
316	C₅×C₂²⋊C₄	—	3	1	no	—
317	C₅×C₂²⋊C₄	—	6	1	no	—
318	C₅×C₂²⋊C₄	—	6	1	no	—
319	C₅×C₂²⋊C₄	—	6	1	no	—
320	C₄²×C₅	—	2	1	no	—
321	C₄²×C₅	—	3	1	no	—
322	C₄²×C₅	—	6	1	no	—
323	C₄²×C₅	—	6	1	no	—
324	C₄²×C₅	—	6	1	no	—
325	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
326	C₂×#135	—	3	1	no	—
327	#520	—	3	1	no	—
328	#520	—	3	1	no	—
329	#440	—	3	1	no	—
330	#440	—	3	1	no	—
331	#440	—	3	1	no	—
332	#440	C₅×D₃	1	1	yes	characteristic, complemented
333	C₄×Q₁₆	—	3	1	no	—
334	C₄×Q₁₆	—	3	1	no	—
335	C₄×D₈	—	3	1	no	—
336	C₄×D₈	—	3	1	no	—
337	C₂×#107	—	3	1	no	—
338	#417	—	3	1	no	—
339	#417	—	3	1	no	—
340	#405	—	3	1	no	—
341	C₂²×C₃×C₅	—	2	2	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₅×D₃	—	2	1	no	—
346	C₂×C₅×D₃	—	2	1	no	—
347	C₂×C₅×D₃	—	2	2	no	—
348	C₂×C₅×D₃	—	4	1	no	—
349	C₂×C₅×D₃	—	4	1	no	—
350	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
351	C₃×C₄×C₅	—	2	2	no	—
352	C₃×C₄×C₅	—	2	1	no	—
353	C₃×C₄×C₅	—	2	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	—	4	1	no	—
356	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
357	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
358	C₅×Dic₃	—	2	2	no	—
359	C₅×Dic₃	—	2	1	no	—
360	C₅×Dic₃	—	2	1	no	—
361	C₅×Dic₃	—	4	1	no	—
362	C₅×Dic₃	—	4	1	no	—
363	C₅×Dic₃	C₄×D₄	1	2	yes	—
364	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₃×C₄	—	2	1	no	—
367	C₂×#67	—	2	1	no	—
368	C₂²×Dic₃	—	2	1	no	—
369	C₂²×Dic₃	—	2	1	no	—
370	#239	—	2	2	no	—
371	#239	C₂×C₄×C₅	1	4	yes	complemented
372	#237	—	2	2	no	—
373	#237	C₂×C₄×C₅	1	4	yes	complemented
374	C₂×D₁₂	—	2	1	no	—
375	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄×D₃	—	2	1	no	—
377	C₂×C₄×D₃	—	2	1	no	—
378	C₂×C₄×D₃	—	2	1	no	—
379	C₂×C₄×D₃	—	2	1	no	—
380	C₂×C₄×D₃	—	2	1	no	—
381	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
382	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
383	C₃×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
384	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₃×C₂²⋊C₄	—	2	1	no	—
390	C₃×C₄²	—	2	1	no	—
391	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
392	#217	—	2	1	no	—
393	#216	C₂×C₄×C₅	1	4	yes	complemented
394	#213	C₂×C₄×C₅	1	4	yes	complemented
395	(C₂×D₃)⋊C₄	—	2	1	no	—
396	(C₂×D₃)⋊C₄	—	2	1	no	—
397	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
398	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
399	C₄⋊Dic₃	—	2	1	no	—
400	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
401	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
402	Dic₃⋊C₄	—	2	1	no	—
403	Dic₃⋊C₄	—	2	1	no	—
404	Dic₃⋊C₄	—	2	1	no	—
405	Dic₃⋊C₄	—	2	1	no	—
406	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
407	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
408	C₄×Dic₃	—	2	1	no	—
409	C₄×Dic₃	—	2	1	no	—
410	C₄×Dic₃	—	2	1	no	—
411	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
414	#204	C₂×C₄×C₅	1	4	yes	complemented
415	ΓL(1,𝔽₂₅)	—	2	2	no	—
416	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
417	C₂³×C₅	—	2	1	no	—
418	C₂³×C₅	—	3	1	no	—
419	C₂³×C₅	—	6	1	no	—
420	C₅×Q₈	—	2	1	no	—
421	C₅×Q₈	—	3	2	no	—
422	C₅×Q₈	—	6	1	no	—
423	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
424	C₅×D₄	—	2	1	no	—
425	C₅×D₄	—	3	2	no	—
426	C₅×D₄	—	6	4	no	—
427	C₅×D₄	—	6	4	no	—
428	C₅×D₄	—	6	1	no	—
429	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	3	1	no	—
434	C₂×C₄×C₅	—	3	2	no	—
435	C₂×C₄×C₅	—	3	2	no	—
436	C₂×C₄×C₅	—	3	1	no	—
437	C₂×C₄×C₅	—	3	1	no	—
438	C₂×C₄×C₅	—	6	4	no	—
439	C₂×C₄×C₅	—	6	4	no	—
440	C₂×C₄×C₅	—	6	1	no	—
441	C₂×C₄×C₅	—	6	1	no	—
442	C₂×C₄×C₅	—	6	1	no	—
443	C₂×C₄×C₅	—	8	1	no	—
444	C₂×C₄×C₅	—	24	1	no	—
445	C₂×C₄×C₅	—	24	1	no	—
446	C₂×C₄×C₅	—	24	1	no	—
447	C₂×C₄×C₅	—	24	1	no	—
448	C₂×C₄×C₅	—	24	1	no	—
449	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
450	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
451	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
452	C₅×C₈	—	2	1	no	—
453	C₅×C₈	—	3	2	no	—
454	C₅×C₈	—	6	1	no	—
455	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
456	C₂×#41	—	3	1	no	—
457	C₂×#41	—	3	1	no	—
458	#135	—	3	8	no	—
459	C₂×Q₁₆	—	3	1	no	—
460	C₂×SD₁₆	—	3	1	no	—
461	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
462	C₂×D₈	—	3	1	no	—
463	C₂×M₁₆	—	3	1	no	—
464	C₂²×C₈	—	3	1	no	—
465	C₄×Q₈	—	3	1	no	—
466	C₄×Q₈	—	3	1	no	—
467	C₄×Q₈	—	3	1	no	—
468	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
469	C₄×D₄	—	3	1	no	—
470	C₄×D₄	—	3	1	no	—
471	C₄×D₄	—	3	1	no	—
472	C₄×D₄	—	6	1	no	—
473	C₄×D₄	—	6	1	no	—
474	C₄×D₄	—	6	1	no	—
475	C₄×D₄	—	6	1	no	—
476	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
477	#117	—	3	1	no	—
478	#117	—	6	1	no	—
479	#117	—	6	1	no	—
480	C₂×C₄⋊C₄	—	3	1	no	—
481	C₂×C₄⋊C₄	—	3	1	no	—
482	C₂×C₄⋊C₄	—	6	1	no	—
483	C₂×C₄⋊C₄	—	6	1	no	—
484	#107	—	3	1	no	—
485	#107	—	3	1	no	—
486	#107	—	3	1	no	—
487	#107	C₂×C₅×D₃	1	1	yes	characteristic
488	#103	—	3	1	no	—
489	#103	—	3	1	no	—
490	#103	—	3	1	no	—
491	#103	C₂×C₅×D₃	1	1	yes	characteristic
492	#102	—	3	1	no	—
493	#102	—	3	1	no	—
494	#102	—	3	1	no	—
495	#102	C₂×C₅×D₃	1	1	yes	characteristic
496	#97	—	3	1	no	—
497	#97	C₂×C₅×D₃	1	1	yes	characteristic
498	C₄×C₈	—	3	1	no	—
499	C₄×C₈	—	3	1	no	—
500	C₂×C₃×C₅	—	4	2	no	—
501	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
502	C₂×C₃×C₅	#576	1	1	yes	characteristic
503	C₂×C₃×C₅	#578	1	1	yes	characteristic
504	C₅×D₃	—	2	2	no	—
505	C₅×D₃	—	4	2	no	—
506	C₂³×C₃	—	2	1	no	—
507	C₂²×D₃	—	2	1	no	—
508	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
509	C₃×Q₈	—	2	1	no	—
510	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
511	C₃×D₄	—	2	1	no	—
512	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	8	1	no	—
517	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
519	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
520	#67	—	2	4	no	—
521	C₂×Dic₃	—	2	1	no	—
522	C₂×Dic₃	—	2	4	no	—
523	C₂×Dic₃	—	2	1	no	—
524	C₂×Dic₃	—	2	1	no	—
525	C₂×Dic₃	—	8	1	no	—
526	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
528	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
529	D₁₂	—	2	4	no	—
530	D₁₂	—	2	1	no	—
531	D₁₂	C₂²×C₄×C₅	1	2	yes	—
532	C₄×D₃	—	2	4	no	—
533	C₄×D₃	—	8	1	no	—
534	C₄×D₃	—	8	1	no	—
535	C₄×D₃	—	8	1	no	—
536	C₄×D₃	—	8	1	no	—
537	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
538	C₄×D₃	C₅×#41	1	2	yes	—
539	Dic₆	—	2	1	no	—
540	Dic₆	C₂²×C₄×C₅	1	2	yes	—
541	C₃×C₈	—	2	1	no	—
542	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
543	C₃⋊C₈	—	2	1	no	—
544	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
545	C₂²×C₅	—	2	2	no	—
546	C₂²×C₅	—	3	2	no	—
547	C₂²×C₅	—	4	1	no	—
548	C₂²×C₅	—	4	1	no	—
549	C₂²×C₅	—	6	1	no	—
550	C₂²×C₅	—	6	1	no	—
551	C₂²×C₅	—	6	2	no	—
552	C₂²×C₅	—	12	1	no	—
553	C₂²×C₅	—	12	1	no	—
554	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
555	C₄×C₅	—	2	1	no	—
556	C₄×C₅	—	2	1	no	—
557	C₄×C₅	—	2	2	no	—
558	C₄×C₅	—	3	2	no	—
559	C₄×C₅	—	4	1	no	—
560	C₄×C₅	—	4	1	no	—
561	C₄×C₅	—	6	1	no	—
562	C₄×C₅	—	6	1	no	—
563	C₄×C₅	—	6	2	no	—
564	C₄×C₅	—	12	1	no	—
565	C₄×C₅	—	12	1	no	—
566	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
567	C₄×C₅	D₃×#41	1	1	yes	characteristic
568	#41	—	3	4	no	—
569	#41	—	3	4	no	—
570	#41	—	6	2	no	—
571	#41	—	6	2	no	—
572	C₂×Q₈	—	3	1	no	—
573	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
574	C₂×D₄	—	3	1	no	—
575	C₂×D₄	—	6	1	no	—
576	C₂×D₄	—	6	1	no	—
577	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	3	1	no	—
580	C₂²×C₄	—	6	1	no	—
581	C₂²×C₄	—	6	1	no	—
582	C₂²×C₄	—	6	1	no	—
583	C₂²×C₄	—	6	1	no	—
584	C₂²×C₄	—	6	1	no	—
585	C₂²×C₄	—	6	1	no	—
586	C₂²×C₄	—	6	1	no	—
587	Q₁₆	—	3	4	no	—
588	SD₁₆	—	3	4	no	—
589	SD₁₆	C₄×C₅×D₃	1	4	yes	complemented
590	D₈	—	3	4	no	—
591	M₁₆	—	6	2	no	—
592	C₂×C₈	—	3	1	no	—
593	C₂×C₈	—	3	4	no	—
594	C₂×C₈	—	3	1	no	—
595	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
596	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	3	1	no	—
599	C₄⋊C₄	—	3	1	no	—
600	C₄⋊C₄	—	3	1	no	—
601	C₄⋊C₄	—	3	1	no	—
602	C₄⋊C₄	—	6	1	no	—
603	C₄⋊C₄	—	6	1	no	—
604	C₄⋊C₄	—	6	1	no	—
605	C₄⋊C₄	—	6	1	no	—
606	C₄⋊C₄	—	6	1	no	—
607	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
608	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	3	1	no	—
611	C₂²⋊C₄	—	3	1	no	—
612	C₂²⋊C₄	—	6	1	no	—
613	C₂²⋊C₄	—	6	1	no	—
614	C₂²⋊C₄	—	6	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	3	1	no	—
617	C₄²	—	6	1	no	—
618	C₄²	—	6	1	no	—
619	C₄²	—	6	1	no	—
620	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
621	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
622	C₂²×C₃	—	2	2	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
626	C₂×D₃	—	2	1	no	—
627	C₂×D₃	—	2	1	no	—
628	C₂×D₃	—	2	2	no	—
629	C₂×D₃	—	4	1	no	—
630	C₂×D₃	—	4	1	no	—
631	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
632	C₃×C₄	—	2	2	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
638	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
639	Dic₃	—	2	2	no	—
640	Dic₃	—	2	1	no	—
641	Dic₃	—	2	1	no	—
642	Dic₃	—	4	1	no	—
643	Dic₃	—	4	1	no	—
644	Dic₃	C₄×C₅×D₄	1	2	yes	—
645	C₂×C₅	—	4	2	no	—
646	C₂×C₅	—	6	2	no	—
647	C₂×C₅	—	12	2	no	—
648	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
649	C₂×C₅	#5774	1	1	yes	characteristic
650	C₂×C₅	#5779	1	1	yes	characteristic
651	C₂³	—	2	1	no	—
652	C₂³	—	3	1	no	—
653	C₂³	—	6	1	no	—
654	Q₈	—	2	1	no	—
655	Q₈	—	3	2	no	—
656	Q₈	—	6	1	no	—
657	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
658	D₄	—	2	1	no	—
659	D₄	—	3	2	no	—
660	D₄	—	6	4	no	—
661	D₄	—	6	4	no	—
662	D₄	—	6	1	no	—
663	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	3	2	no	—
669	C₂×C₄	—	3	2	no	—
670	C₂×C₄	—	3	1	no	—
671	C₂×C₄	—	3	1	no	—
672	C₂×C₄	—	6	4	no	—
673	C₂×C₄	—	6	4	no	—
674	C₂×C₄	—	6	1	no	—
675	C₂×C₄	—	6	1	no	—
676	C₂×C₄	—	6	1	no	—
677	C₂×C₄	—	8	1	no	—
678	C₂×C₄	—	24	1	no	—
679	C₂×C₄	—	24	1	no	—
680	C₂×C₄	—	24	1	no	—
681	C₂×C₄	—	24	1	no	—
682	C₂×C₄	—	24	1	no	—
683	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
684	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
685	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
686	C₈	—	2	1	no	—
687	C₈	—	3	2	no	—
688	C₈	—	6	1	no	—
689	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
690	C₂×C₃	—	4	2	no	—
691	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
692	C₂×C₃	C₅×#576	1	1	yes	characteristic
693	C₂×C₃	C₅×#578	1	1	yes	characteristic
694	D₃	—	2	2	no	—
695	D₃	—	4	2	no	—
696	C₅	#79778	1	1	yes	characteristic, direct product factor, Sylow
697	C₂²	—	2	2	no	—
698	C₂²	—	3	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	6	1	no	—
702	C₂²	—	6	1	no	—
703	C₂²	—	6	2	no	—
704	C₂²	—	12	1	no	—
705	C₂²	—	12	1	no	—
706	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	2	no	—
710	C₄	—	3	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	6	1	no	—
714	C₄	—	6	1	no	—
715	C₄	—	6	2	no	—
716	C₄	—	12	1	no	—
717	C₄	—	12	1	no	—
718	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
719	C₄	C₅×D₃×#41	1	1	yes	characteristic
720	C₃	C₅×#2951	1	1	yes	characteristic, complemented, Sylow
721	C₂	—	4	2	no	—
722	C₂	—	6	2	no	—
723	C₂	—	12	2	no	—
724	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
725	C₂	C₅×#5774	1	1	yes	characteristic
726	C₂	C₅×#5779	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#440	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#916	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#440	D₃
hypocenter	C₃	C₅×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#440

Complements

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

N	H ≅ G/N	type
2. C₅×#5574	C₂	semidirect
3. C₅×#5546	C₂	semidirect
4. C₃×C₅×#440	C₂	semidirect
5. C₅×#5164	C₂	semidirect
6. C₄×C₅×#216	C₂	semidirect
7. C₄×C₅×#213	C₂	semidirect
8. C₅×#4889	C₂	semidirect
9. C₅×D₃×#107	C₂	semidirect
10. C₅×#4803	C₂	semidirect
11. C₅×#4790	C₂	semidirect
12. C₅×#4771	C₂	semidirect
13. C₅×#4756	C₂	semidirect
14. C₅×#4710	C₂	semidirect
15. C₅×#4708	C₂	semidirect
28. C₅×#916	C₄	semidirect
61. #79778	C₅	direct (N × H)
68. C₅×#440	D₃	semidirect
84. C₅×#239	C₂×C₄	semidirect
86. C₅×#237	C₂×C₄	semidirect
96. C₃×C₅×SD₁₆	C₂×C₄	semidirect
106. C₅×#216	C₂×C₄	semidirect
107. C₅×#213	C₂×C₄	semidirect
127. C₅×#204	C₂×C₄	semidirect
129. C₅×D₃×C₈	C₂×C₄	semidirect
131. #5574	C₂×C₅	semidirect
132. #5546	C₂×C₅	semidirect
133. C₃×#440	C₂×C₅	semidirect
134. #5164	C₂×C₅	semidirect
135. C₄×#216	C₂×C₅	semidirect
136. C₄×#213	C₂×C₅	semidirect
137. #4889	C₂×C₅	semidirect
138. D₃×#107	C₂×C₅	semidirect
139. #4803	C₂×C₅	semidirect
140. #4790	C₂×C₅	semidirect
141. #4771	C₂×C₅	semidirect
142. #4756	C₂×C₅	semidirect
143. #4710	C₂×C₅	semidirect
144. #4708	C₂×C₅	semidirect
240. #916	C₄×C₅	semidirect
294. C₅×SD₁₆	C₄×D₃	semidirect
332. #440	C₅×D₃	semidirect
371. #239	C₂×C₄×C₅	semidirect
373. #237	C₂×C₄×C₅	semidirect
383. C₃×SD₁₆	C₂×C₄×C₅	semidirect
393. #216	C₂×C₄×C₅	semidirect
394. #213	C₂×C₄×C₅	semidirect
414. #204	C₂×C₄×C₅	semidirect
416. D₃×C₈	C₂×C₄×C₅	semidirect
589. SD₁₆	C₄×C₅×D₃	semidirect
621. C₃×C₅	#2951	semidirect
696. C₅	#79778	direct (N × H)
720. C₃	C₅×#2951	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
C₅×#5574	2
C₅×#5546	2
C₃×C₅×#440	2
C₅×#5164	2
C₄×C₅×#216	2
C₄×C₅×#213	2
C₅×#4889	2
C₅×D₃×#107	2
C₅×#4803	2
C₅×#4790	2
C₅×#4771	2
C₅×#4756	2
C₅×#4710	2
C₅×#4708	2
C₅×#2951	3
#79778	5

Subgroups — C5×#79778 #14417617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79778 #14417617