Subgroups — C₅×#78956 #14412543

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4804	C₂	1	4	yes	maximal, complemented
9	C₅×#4803	C₂	1	4	yes	maximal, complemented
10	C₅×#2896	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#239	—	2	4	no	—
13	C₂×C₅×#239	—	2	1	no	—
14	C₂×C₅×#239	—	2	1	no	—
15	C₂×C₅×#239	C₄	1	8	yes	complemented
16	C₂×C₅×#239	C₂²	1	2	yes	—
17	C₂×C₅×#239	C₂²	1	2	yes	—
18	C₂²×C₅×D₁₂	—	2	1	no	—
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	—	2	1	no	—
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₅×#926	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₅×D₃×M₁₆	—	2	4	no	—
27	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
28	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
29	C₅×#892	C₂²	1	2	yes	complemented
30	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
32	C₅×#877	—	2	1	no	—
33	C₅×#872	—	2	1	no	—
34	C₄²×C₅×D₃	—	2	1	no	—
35	C₃×C₅×#103	C₂²	1	4	yes	complemented
36	C₅×#835	C₂²	1	4	yes	complemented
37	C₅×#821	C₂²	1	4	yes	complemented
38	C₅×#809	C₂²	1	4	yes	complemented
39	#78956	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₅×#41	—	3	1	no	—
41	C₂²×C₅×M₁₆	—	3	1	no	—
42	C₂×C₅×#117	—	3	1	no	—
43	C₅×#419	—	3	1	no	—
44	C₅×#419	D₃	1	1	yes	characteristic, complemented
45	C₅×#418	—	3	1	no	—
46	C₅×#418	—	3	1	no	—
47	C₅×#417	—	3	4	no	—
48	C₅×#416	—	3	4	no	—
49	C₂³×C₅×D₃	—	2	1	no	—
50	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
51	C₂×C₃×C₅×Q₈	—	2	2	no	—
52	C₂×C₃×C₅×Q₈	—	2	1	no	—
53	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	1	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₅×#239	—	2	8	no	—
59	C₅×#239	—	2	8	no	—
60	C₅×#239	—	2	4	no	—
61	C₅×#239	—	2	4	no	—
62	C₅×#239	C₂×C₄	1	8	yes	—
63	C₅×#239	C₂×C₄	1	8	yes	complemented
64	C₂×C₅×D₁₂	—	2	8	no	—
65	C₂×C₅×D₁₂	—	2	2	no	—
66	C₂×C₅×D₁₂	—	2	2	no	—
67	C₂×C₅×D₁₂	—	2	1	no	—
68	C₂×C₅×D₁₂	—	2	2	no	—
69	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₄×C₅×D₃	—	2	8	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	—	2	2	no	—
74	C₂×C₄×C₅×D₃	—	2	2	no	—
75	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
76	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
77	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
79	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
81	C₃×C₅×M₁₆	—	2	2	no	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₅×#217	—	2	1	no	—
87	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
88	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
89	C₅×Dic₃⋊C₄	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	1	no	—
91	C₄×C₅×Dic₃	—	2	2	no	—
92	C₅×#208	—	2	2	no	—
93	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
94	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
95	C₅×D₃×C₈	—	2	4	no	—
96	C₂²×#239	C₂×C₅	1	1	yes	characteristic
97	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
98	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
100	#5225	C₂×C₅	1	1	yes	characteristic, complemented
101	#5131	C₂×C₅	1	1	yes	characteristic, complemented
102	#5001	C₂×C₅	1	1	yes	characteristic, complemented
103	#4804	C₂×C₅	1	4	yes	complemented
104	#4803	C₂×C₅	1	4	yes	complemented
105	C₂×C₅×#41	—	3	8	no	—
106	C₂×C₅×#41	—	3	2	no	—
107	C₂×C₅×#41	—	3	2	no	—
108	C₂×C₅×#41	—	6	1	no	—
109	C₂×C₅×#41	—	6	1	no	—
110	C₂×C₅×#41	—	6	4	no	—
111	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₅×D₄	—	3	1	no	—
113	C₂²×C₅×D₄	—	6	1	no	—
114	C₂³×C₄×C₅	—	3	1	no	—
115	C₂³×C₄×C₅	—	6	1	no	—
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂×C₅×M₁₆	—	3	2	no	—
118	C₂×C₅×M₁₆	—	6	4	no	—
119	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
120	C₂²×C₅×C₈	—	3	2	no	—
121	C₅×#117	—	3	1	no	—
122	C₅×#117	—	3	2	no	—
123	C₅×#117	—	6	1	no	—
124	C₅×#117	—	6	1	no	—
125	C₅×#117	C₂×D₃	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	—	3	2	no	—
127	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
128	C₂×C₄²×C₅	—	6	1	no	—
129	C₅×#103	—	3	4	no	—
130	C₅×#103	C₂×D₃	1	4	yes	complemented
131	C₅×#102	—	3	4	no	—
132	C₅×#102	—	3	4	no	—
133	#2896	—	3	1	no	Sylow
134	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₅×D₃	—	2	4	no	—
136	C₂²×C₅×D₃	—	2	2	no	—
137	C₂²×C₅×D₃	—	4	2	no	—
138	C₂²×C₅×D₃	—	4	4	no	—
139	C₂²×C₅×D₃	C₂²⋊C₄	1	4	yes	—
140	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×Q₈	—	2	4	no	—
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
154	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
156	C₅×D₁₂	—	2	8	no	—
157	C₅×D₁₂	—	2	8	no	—
158	C₅×D₁₂	—	2	4	no	—
159	C₅×D₁₂	—	2	2	no	—
160	C₅×D₁₂	C₂²×C₄	1	4	yes	—
161	C₄×C₅×D₃	—	2	8	no	—
162	C₄×C₅×D₃	—	2	8	no	—
163	C₄×C₅×D₃	—	4	4	no	—
164	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
165	C₄×C₅×D₃	C₂²⋊C₄	1	4	yes	—
166	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
167	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
168	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
169	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
170	C₃×C₅×C₈	—	2	2	no	—
171	C₅×C₃⋊C₈	—	2	2	no	—
172	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×#239	—	2	4	no	—
174	C₂×#239	—	2	1	no	—
175	C₂×#239	—	2	1	no	—
176	C₂×#239	C₄×C₅	1	8	yes	complemented
177	C₂×#239	C₂²×C₅	1	2	yes	—
178	C₂×#239	C₂²×C₅	1	2	yes	—
179	C₂²×D₁₂	—	2	1	no	—
180	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
181	C₂²×C₄×D₃	—	2	1	no	—
182	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
184	C₃×#117	C₂²×C₅	1	1	yes	characteristic
185	#926	C₂²×C₅	1	1	yes	characteristic
186	C₂×#208	C₂²×C₅	1	1	yes	characteristic
187	D₃×M₁₆	—	2	4	no	—
188	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
189	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
190	#892	C₂²×C₅	1	2	yes	complemented
191	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
192	D₃×C₂²⋊C₄	—	2	1	no	—
193	#877	—	2	1	no	—
194	#872	—	2	1	no	—
195	C₄²×D₃	—	2	1	no	—
196	C₃×#103	C₂²×C₅	1	4	yes	complemented
197	#835	C₂²×C₅	1	4	yes	complemented
198	#821	C₂²×C₅	1	4	yes	complemented
199	#809	C₂²×C₅	1	4	yes	complemented
200	C₂⁴×C₅	—	3	1	no	—
201	C₂⁴×C₅	—	6	1	no	—
202	C₅×#41	—	3	8	no	—
203	C₅×#41	—	3	8	no	—
204	C₅×#41	—	6	8	no	—
205	C₅×#41	—	6	8	no	—
206	C₅×#41	—	6	4	no	—
207	C₅×#41	—	6	4	no	—
208	C₂×C₅×Q₈	—	2	2	no	—
209	C₂×C₅×Q₈	—	2	1	no	—
210	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
211	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
212	C₂×C₅×D₄	—	3	4	no	—
213	C₂×C₅×D₄	—	3	2	no	—
214	C₂×C₅×D₄	—	6	8	no	—
215	C₂×C₅×D₄	—	6	2	no	—
216	C₂×C₅×D₄	—	6	2	no	—
217	C₂×C₅×D₄	—	6	1	no	—
218	C₂×C₅×D₄	—	6	2	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	4	no	—
222	C₂²×C₄×C₅	—	3	1	no	—
223	C₂²×C₄×C₅	—	3	1	no	—
224	C₂²×C₄×C₅	—	3	4	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	6	8	no	—
228	C₂²×C₄×C₅	—	6	2	no	—
229	C₂²×C₄×C₅	—	6	2	no	—
230	C₂²×C₄×C₅	—	6	2	no	—
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₅×M₁₆	—	2	2	no	—
233	C₅×M₁₆	—	6	4	no	—
234	C₅×M₁₆	—	6	2	no	—
235	C₂×C₅×C₈	—	3	2	no	—
236	C₂×C₅×C₈	—	6	4	no	—
237	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
238	C₅×C₄⋊C₄	—	3	2	no	—
239	C₅×C₄⋊C₄	—	6	2	no	—
240	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
241	C₅×C₂²⋊C₄	—	2	1	no	—
242	C₅×C₂²⋊C₄	—	6	2	no	—
243	C₅×C₂²⋊C₄	—	6	1	no	—
244	C₄²×C₅	—	2	1	no	—
245	C₄²×C₅	—	6	2	no	—
246	C₄²×C₅	—	6	1	no	—
247	C₂²×#41	—	3	1	no	—
248	C₂²×M₁₆	—	3	1	no	—
249	C₂×#117	—	3	1	no	—
250	#419	—	3	1	no	—
251	#419	C₅×D₃	1	1	yes	characteristic, complemented
252	#418	—	3	1	no	—
253	#418	—	3	1	no	—
254	#417	—	3	4	no	—
255	#416	—	3	4	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₅×D₃	—	2	2	no	—
260	C₂×C₅×D₃	—	2	2	no	—
261	C₂×C₅×D₃	—	2	4	no	—
262	C₂×C₅×D₃	—	4	4	no	—
263	C₂×C₅×D₃	—	4	8	no	—
264	C₂×C₅×D₃	—	4	4	no	—
265	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	2	yes	—
267	C₃×C₄×C₅	—	2	4	no	—
268	C₃×C₄×C₅	—	4	2	no	—
269	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
270	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
271	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₅×Dic₃	—	4	2	no	—
273	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
274	C₅×Dic₃	C₂×C₂²⋊C₄	1	2	yes	—
275	C₂³×D₃	—	2	1	no	—
276	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
277	C₂×C₃×Q₈	—	2	2	no	—
278	C₂×C₃×Q₈	—	2	1	no	—
279	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
280	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	—	2	1	no	—
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
284	#239	—	2	8	no	—
285	#239	—	2	8	no	—
286	#239	—	2	4	no	—
287	#239	—	2	4	no	—
288	#239	C₂×C₄×C₅	1	8	yes	—
289	#239	C₂×C₄×C₅	1	8	yes	complemented
290	C₂×D₁₂	—	2	8	no	—
291	C₂×D₁₂	—	2	2	no	—
292	C₂×D₁₂	—	2	2	no	—
293	C₂×D₁₂	—	2	1	no	—
294	C₂×D₁₂	—	2	2	no	—
295	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
296	C₂×D₁₂	C₂³×C₅	1	2	yes	—
297	C₂×C₄×D₃	—	2	8	no	—
298	C₂×C₄×D₃	—	2	2	no	—
299	C₂×C₄×D₃	—	2	2	no	—
300	C₂×C₄×D₃	—	2	2	no	—
301	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
302	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
303	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
304	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
305	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
307	C₃×M₁₆	—	2	2	no	—
308	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
309	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₄²	—	2	1	no	—
312	#217	—	2	1	no	—
313	(C₂×D₃)⋊C₄	—	2	2	no	—
314	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
315	Dic₃⋊C₄	—	2	2	no	—
316	C₄×Dic₃	—	2	1	no	—
317	C₄×Dic₃	—	2	2	no	—
318	#208	—	2	2	no	—
319	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
320	ΓL(1,𝔽₂₅)	—	2	4	no	—
321	D₃×C₈	—	2	4	no	—
322	C₂³×C₅	—	3	1	no	—
323	C₂³×C₅	—	3	1	no	—
324	C₂³×C₅	—	3	4	no	—
325	C₂³×C₅	—	6	4	no	—
326	C₂³×C₅	—	6	2	no	—
327	C₂³×C₅	—	12	2	no	—
328	C₂³×C₅	—	12	4	no	—
329	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
330	C₅×Q₈	—	2	4	no	—
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
333	C₅×D₄	—	3	4	no	—
334	C₅×D₄	—	6	8	no	—
335	C₅×D₄	—	6	8	no	—
336	C₅×D₄	—	6	4	no	—
337	C₅×D₄	—	6	2	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	3	4	no	—
342	C₂×C₄×C₅	—	3	1	no	—
343	C₂×C₄×C₅	—	3	1	no	—
344	C₂×C₄×C₅	—	3	4	no	—
345	C₂×C₄×C₅	—	3	4	no	—
346	C₂×C₄×C₅	—	3	2	no	—
347	C₂×C₄×C₅	—	3	2	no	—
348	C₂×C₄×C₅	—	3	2	no	—
349	C₂×C₄×C₅	—	3	2	no	—
350	C₂×C₄×C₅	—	6	8	no	—
351	C₂×C₄×C₅	—	6	8	no	—
352	C₂×C₄×C₅	—	6	2	no	—
353	C₂×C₄×C₅	—	12	4	no	—
354	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
355	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
356	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
357	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
358	C₅×C₈	—	2	2	no	—
359	C₅×C₈	—	6	2	no	—
360	C₂×#41	—	3	8	no	—
361	C₂×#41	—	3	2	no	—
362	C₂×#41	—	3	2	no	—
363	C₂×#41	—	6	1	no	—
364	C₂×#41	—	6	1	no	—
365	C₂×#41	—	6	4	no	—
366	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
367	C₂²×D₄	—	3	1	no	—
368	C₂²×D₄	—	6	1	no	—
369	C₂³×C₄	—	3	1	no	—
370	C₂³×C₄	—	6	1	no	—
371	C₂×M₁₆	—	3	1	no	—
372	C₂×M₁₆	—	3	2	no	—
373	C₂×M₁₆	—	6	4	no	—
374	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
375	C₂²×C₈	—	3	2	no	—
376	#117	—	3	1	no	—
377	#117	—	3	2	no	—
378	#117	—	6	1	no	—
379	#117	—	6	1	no	—
380	#117	C₂×C₅×D₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	3	2	no	—
382	C₂×C₂²⋊C₄	—	6	1	no	—
383	C₂×C₄²	—	6	1	no	—
384	#103	—	3	4	no	—
385	#103	C₂×C₅×D₃	1	4	yes	complemented
386	#102	—	3	4	no	—
387	#102	—	3	4	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₃×C₅	#575	1	2	yes	—
391	C₅×D₃	—	2	2	no	—
392	C₅×D₃	—	2	2	no	—
393	C₅×D₃	—	4	4	no	—
394	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂²×D₃	—	2	4	no	—
396	C₂²×D₃	—	2	2	no	—
397	C₂²×D₃	—	4	2	no	—
398	C₂²×D₃	—	4	4	no	—
399	C₂²×D₃	C₅×C₂²⋊C₄	1	4	yes	—
400	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
402	C₃×Q₈	—	2	4	no	—
403	C₃×Q₈	—	2	2	no	—
404	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
409	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
411	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
412	C₂×Dic₃	—	2	2	no	—
413	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
414	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
415	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
416	D₁₂	—	2	8	no	—
417	D₁₂	—	2	8	no	—
418	D₁₂	—	2	4	no	—
419	D₁₂	—	2	2	no	—
420	D₁₂	C₂²×C₄×C₅	1	4	yes	—
421	C₄×D₃	—	2	8	no	—
422	C₄×D₃	—	2	8	no	—
423	C₄×D₃	—	4	4	no	—
424	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
425	C₄×D₃	C₅×C₂²⋊C₄	1	4	yes	—
426	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
427	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
428	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
429	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
430	C₃×C₈	—	2	2	no	—
431	C₃⋊C₈	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	3	2	no	—
434	C₂²×C₅	—	3	2	no	—
435	C₂²×C₅	—	6	2	no	—
436	C₂²×C₅	—	6	2	no	—
437	C₂²×C₅	—	6	4	no	—
438	C₂²×C₅	—	12	4	no	—
439	C₂²×C₅	—	12	8	no	—
440	C₂²×C₅	—	12	4	no	—
441	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
442	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
443	C₄×C₅	—	2	4	no	—
444	C₄×C₅	—	3	2	no	—
445	C₄×C₅	—	3	2	no	—
446	C₄×C₅	—	4	2	no	—
447	C₄×C₅	—	12	2	no	—
448	C₄×C₅	D₃×C₂²⋊C₄	1	2	yes	—
449	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
450	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
451	C₂⁴	—	3	1	no	—
452	C₂⁴	—	6	1	no	—
453	#41	—	3	8	no	—
454	#41	—	3	8	no	—
455	#41	—	6	8	no	—
456	#41	—	6	8	no	—
457	#41	—	6	4	no	—
458	#41	—	6	4	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	C₄×C₅×D₃	1	4	yes	complemented
462	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
463	C₂×D₄	—	3	4	no	—
464	C₂×D₄	—	3	2	no	—
465	C₂×D₄	—	6	8	no	—
466	C₂×D₄	—	6	2	no	—
467	C₂×D₄	—	6	2	no	—
468	C₂×D₄	—	6	1	no	—
469	C₂×D₄	—	6	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	3	1	no	—
472	C₂²×C₄	—	3	4	no	—
473	C₂²×C₄	—	3	1	no	—
474	C₂²×C₄	—	3	1	no	—
475	C₂²×C₄	—	3	4	no	—
476	C₂²×C₄	—	3	1	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	6	8	no	—
479	C₂²×C₄	—	6	2	no	—
480	C₂²×C₄	—	6	2	no	—
481	C₂²×C₄	—	6	2	no	—
482	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
483	M₁₆	—	2	2	no	—
484	M₁₆	—	6	4	no	—
485	M₁₆	—	6	2	no	—
486	C₂×C₈	—	3	2	no	—
487	C₂×C₈	—	6	4	no	—
488	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	6	2	no	—
491	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	6	2	no	—
494	C₂²⋊C₄	—	6	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	6	2	no	—
497	C₄²	—	6	1	no	—
498	C₃×C₅	#2896	1	1	yes	characteristic, complemented, Hall
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
501	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
502	C₂×D₃	—	2	2	no	—
503	C₂×D₃	—	2	2	no	—
504	C₂×D₃	—	2	4	no	—
505	C₂×D₃	—	4	4	no	—
506	C₂×D₃	—	4	8	no	—
507	C₂×D₃	—	4	4	no	—
508	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
509	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
510	C₃×C₄	—	2	4	no	—
511	C₃×C₄	—	4	2	no	—
512	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
513	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
514	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
515	Dic₃	—	4	2	no	—
516	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
517	Dic₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	6	2	no	—
520	C₂×C₅	—	6	2	no	—
521	C₂×C₅	—	12	4	no	—
522	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
523	C₂×C₅	#5777	1	2	yes	—
524	C₂³	—	3	1	no	—
525	C₂³	—	3	1	no	—
526	C₂³	—	3	4	no	—
527	C₂³	—	6	4	no	—
528	C₂³	—	6	2	no	—
529	C₂³	—	12	2	no	—
530	C₂³	—	12	4	no	—
531	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
532	Q₈	—	2	4	no	—
533	Q₈	—	2	2	no	—
534	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
535	D₄	—	3	4	no	—
536	D₄	—	6	8	no	—
537	D₄	—	6	8	no	—
538	D₄	—	6	4	no	—
539	D₄	—	6	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	3	4	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	3	1	no	—
546	C₂×C₄	—	3	4	no	—
547	C₂×C₄	—	3	4	no	—
548	C₂×C₄	—	3	2	no	—
549	C₂×C₄	—	3	2	no	—
550	C₂×C₄	—	3	2	no	—
551	C₂×C₄	—	3	2	no	—
552	C₂×C₄	—	6	8	no	—
553	C₂×C₄	—	6	8	no	—
554	C₂×C₄	—	6	2	no	—
555	C₂×C₄	—	12	4	no	—
556	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
557	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
558	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
559	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
560	C₈	—	2	2	no	—
561	C₈	—	6	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₃	C₅×#575	1	2	yes	—
565	D₃	—	2	2	no	—
566	D₃	—	2	2	no	—
567	D₃	—	4	4	no	—
568	C₅	#78956	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	2	no	—
570	C₂²	—	3	2	no	—
571	C₂²	—	3	2	no	—
572	C₂²	—	6	2	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	6	4	no	—
575	C₂²	—	12	4	no	—
576	C₂²	—	12	8	no	—
577	C₂²	—	12	4	no	—
578	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
579	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	3	2	no	—
582	C₄	—	3	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	12	2	no	—
585	C₄	C₅×D₃×C₂²⋊C₄	1	2	yes	—
586	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
587	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
588	C₃	C₅×#2896	1	1	yes	characteristic, complemented, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	6	2	no	—
591	C₂	—	6	2	no	—
592	C₂	—	12	4	no	—
593	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
594	C₂	C₅×#5777	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#419	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×#239	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#419	D₃
hypocenter	C₃	C₅×#2896
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#419

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₅×D₃×#117	C₂	semidirect
4. C₃×C₅×#419	C₂	semidirect
5. C₅×#5225	C₂	semidirect
6. C₅×#5131	C₂	semidirect
7. C₅×#5001	C₂	semidirect
8. C₅×#4804	C₂	semidirect
9. C₅×#4803	C₂	semidirect
15. C₂×C₅×#239	C₄	semidirect
27. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
28. C₂×C₅×D₃×C₈	C₂²	semidirect
29. C₅×#892	C₂²	semidirect
30. C₅×D₃×C₄⋊C₄	C₂²	semidirect
35. C₃×C₅×#103	C₂²	semidirect
36. C₅×#835	C₂²	semidirect
37. C₅×#821	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. #78956	C₅	direct (N × H)
44. C₅×#419	D₃	semidirect
53. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. C₅×#239	C₂×C₄	semidirect
69. C₂×C₅×D₁₂	C₂×C₄	semidirect
97. C₂×D₃×M₁₆	C₂×C₅	semidirect
98. D₃×#117	C₂×C₅	semidirect
99. C₃×#419	C₂×C₅	semidirect
100. #5225	C₂×C₅	semidirect
101. #5131	C₂×C₅	semidirect
102. #5001	C₂×C₅	semidirect
103. #4804	C₂×C₅	semidirect
104. #4803	C₂×C₅	semidirect
130. C₅×#103	C₂×D₃	semidirect
176. C₂×#239	C₄×C₅	semidirect
188. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
189. C₂×D₃×C₈	C₂²×C₅	semidirect
190. #892	C₂²×C₅	semidirect
191. D₃×C₄⋊C₄	C₂²×C₅	semidirect
196. C₃×#103	C₂²×C₅	semidirect
197. #835	C₂²×C₅	semidirect
198. #821	C₂²×C₅	semidirect
199. #809	C₂²×C₅	semidirect
210. C₂×C₅×Q₈	C₄×D₃	semidirect
251. #419	C₅×D₃	semidirect
279. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
289. #239	C₂×C₄×C₅	semidirect
295. C₂×D₁₂	C₂×C₄×C₅	semidirect
385. #103	C₂×C₅×D₃	semidirect
461. C₂×Q₈	C₄×C₅×D₃	semidirect
498. C₃×C₅	#2896	semidirect
568. C₅	#78956	direct (N × H)
588. C₃	C₅×#2896	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#239	2
C₂×C₅×D₃×M₁₆	2
C₅×D₃×#117	2
C₃×C₅×#419	2
C₅×#5225	2
C₅×#5131	2
C₅×#5001	2
C₅×#4804	2
C₅×#4803	2
C₅×#2896	3
#78956	5

Subgroups — C5×#78956 #14412543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78956 #14412543