Subgroups — C₄×C₅×#942 #14416826

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#942	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
4	C₅×#5225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5030	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#216	C₂	1	2	yes	maximal, complemented
7	C₅×#5026	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#215	C₂	1	2	yes	maximal, complemented
9	C₅×#4966	C₂	1	1	yes	maximal, characteristic
10	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#137	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	—	2	1	no	—
16	C₃×C₄×C₅×Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₅×#216	C₂²	1	2	yes	—
24	C₅×#942	C₄	1	8	yes	direct product factor
25	C₂×C₅×#215	C₂²	1	2	yes	—
26	C₄×C₅×#67	—	2	1	no	—
27	C₄×C₅×#67	—	2	1	no	—
28	C₅×#926	C₂²	1	1	yes	characteristic
29	C₂×C₅×#208	C₂²	1	1	yes	characteristic
30	C₂×C₅×#208	C₂²	1	1	yes	characteristic
31	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₅×#872	—	2	1	no	—
34	C₄²×C₅×D₃	—	2	1	no	—
35	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
36	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
37	C₅×#835	C₂²	1	2	yes	—
38	C₅×#835	C₂²	1	2	yes	—
39	C₅×#810	C₂²	1	2	yes	—
40	C₅×#809	C₂²	1	2	yes	—
41	C₅×#808	C₂²	1	2	yes	—
42	C₅×#807	C₂²	1	2	yes	—
43	C₅×#803	C₂²	1	2	yes	—
44	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
45	C₄×#942	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×#137	—	3	1	no	—
47	C₄×C₅×#41	—	3	1	no	—
48	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
49	C₅×#441	—	3	2	no	—
50	C₅×#440	—	3	2	no	—
51	C₄×C₅×Q₁₆	—	3	2	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₅×#428	—	3	1	no	—
54	C₅×#419	—	3	1	no	—
55	C₅×#417	—	3	1	no	—
56	C₄×C₅×M₁₆	—	3	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₅×#67	—	2	1	no	—
67	C₅×#235	—	2	2	no	—
68	C₅×#235	C₂×C₄	1	4	yes	—
69	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
70	C₂×C₄×C₅×D₃	—	2	1	no	—
71	C₂×C₄×C₅×D₃	—	2	1	no	—
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	2	no	—
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#217	—	2	1	no	—
85	C₅×#216	C₂×C₄	1	8	yes	complemented
86	C₅×#215	C₂×C₄	1	8	yes	complemented
87	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
88	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
89	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₅×Dic₃⋊C₄	—	2	1	no	—
92	C₅×Dic₃⋊C₄	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	—	2	1	no	—
96	C₅×#208	—	2	2	no	—
97	C₅×#208	C₂×C₄	1	4	yes	complemented
98	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
99	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
100	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#942	C₂×C₅	1	1	yes	characteristic
102	C₄×#235	C₂×C₅	1	1	yes	characteristic
103	#5225	C₂×C₅	1	1	yes	characteristic, complemented
104	#5030	C₂×C₅	1	2	yes	complemented
105	C₄×#216	C₂×C₅	1	2	yes	complemented
106	#5026	C₂×C₅	1	2	yes	complemented
107	C₄×#215	C₂×C₅	1	2	yes	complemented
108	#4966	C₂×C₅	1	1	yes	characteristic
109	#4964	C₂×C₅	1	1	yes	characteristic, complemented
110	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₅×#41	—	3	1	no	—
112	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
113	C₅×#137	—	3	8	no	—
114	C₂×C₅×Q₁₆	—	3	2	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂×C₅×M₁₆	—	3	1	no	—
118	C₄×C₅×Q₈	—	2	1	no	—
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	—	3	1	no	—
121	C₄×C₅×Q₈	—	3	1	no	—
122	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
123	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
124	C₄×C₅×D₄	—	3	1	no	—
125	C₄×C₅×D₄	—	3	1	no	—
126	C₄×C₅×D₄	—	6	1	no	—
127	C₄×C₅×D₄	—	6	1	no	—
128	C₅×#117	—	3	1	no	—
129	C₅×#117	—	6	1	no	—
130	C₂×C₅×C₄⋊C₄	—	2	1	no	—
131	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₂×C₄²×C₅	—	2	1	no	—
133	C₂×C₄²×C₅	—	6	1	no	—
134	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
135	C₅×#107	—	3	2	no	—
136	C₅×#106	—	3	2	no	—
137	C₅×#103	—	3	2	no	—
138	C₅×#103	—	3	2	no	—
139	C₅×#103	—	3	2	no	—
140	C₅×#102	—	3	2	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	C₄×#137	—	3	1	no	Sylow
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	—	2	1	no	—
146	C₃×C₅×Q₈	—	2	4	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
149	C₂×C₃×C₄×C₅	—	2	4	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	2	no	—
155	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	#41	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
163	C₅×#67	—	2	4	no	—
164	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	2	1	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₅×D₁₂	—	2	1	no	—
168	C₅×D₁₂	C₂²×C₄	1	2	yes	—
169	C₄×C₅×D₃	—	2	4	no	—
170	C₄×C₅×D₃	—	4	2	no	—
171	C₄×C₅×D₃	—	4	2	no	—
172	C₅×Dic₆	—	2	1	no	—
173	C₅×Dic₆	C₂²×C₄	1	2	yes	—
174	C₅×C₃⋊C₈	—	2	2	no	—
175	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
176	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×#235	C₂²×C₅	1	1	yes	characteristic
178	C₃×C₄×Q₈	—	2	1	no	—
179	C₃×C₄×Q₈	—	2	1	no	—
180	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
181	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄²	—	2	1	no	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₂×#216	C₂²×C₅	1	2	yes	—
187	#942	C₄×C₅	1	8	yes	direct product factor
188	C₂×#215	C₂²×C₅	1	2	yes	—
189	C₄×#67	—	2	1	no	—
190	C₄×#67	—	2	1	no	—
191	#926	C₂²×C₅	1	1	yes	characteristic
192	C₂×#208	C₂²×C₅	1	1	yes	characteristic
193	C₂×#208	C₂²×C₅	1	1	yes	characteristic
194	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
195	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
196	#872	—	2	1	no	—
197	C₄²×D₃	—	2	1	no	—
198	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
199	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
200	#835	C₂²×C₅	1	2	yes	—
201	#835	C₂²×C₅	1	2	yes	—
202	#810	C₂²×C₅	1	2	yes	—
203	#809	C₂²×C₅	1	2	yes	—
204	#808	C₂²×C₅	1	2	yes	—
205	#807	C₂²×C₅	1	2	yes	—
206	#803	C₂²×C₅	1	2	yes	—
207	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
208	C₅×#41	—	3	4	no	—
209	C₅×#41	—	6	2	no	—
210	C₂×C₅×Q₈	—	2	2	no	—
211	C₂×C₅×Q₈	—	2	1	no	—
212	C₂×C₅×Q₈	—	3	1	no	—
213	C₂×C₅×Q₈	C₄×D₃	1	4	yes	complemented
214	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
215	C₂×C₅×D₄	—	3	1	no	—
216	C₂×C₅×D₄	—	6	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	6	1	no	—
220	C₂²×C₄×C₅	—	6	1	no	—
221	C₂²×C₄×C₅	—	6	1	no	—
222	C₂²×C₄×C₅	#67	1	1	yes	characteristic
223	C₂²×C₄×C₅	#67	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₅×Q₁₆	—	3	8	no	—
226	C₅×SD₁₆	—	3	8	no	—
227	C₅×M₁₆	—	3	4	no	—
228	C₅×M₁₆	—	6	2	no	—
229	C₂×C₅×C₈	—	3	2	no	—
230	C₂×C₅×C₈	—	3	2	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	3	1	no	—
235	C₅×C₄⋊C₄	—	3	1	no	—
236	C₅×C₄⋊C₄	—	6	1	no	—
237	C₅×C₄⋊C₄	—	6	1	no	—
238	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₅×C₂²⋊C₄	—	6	1	no	—
241	C₅×C₂²⋊C₄	—	6	1	no	—
242	C₄²×C₅	—	2	2	no	—
243	C₄²×C₅	—	2	2	no	—
244	C₄²×C₅	—	6	1	no	—
245	C₄²×C₅	—	6	1	no	—
246	C₄²×C₅	—	6	1	no	—
247	C₄²×C₅	#67	1	1	yes	characteristic
248	C₄²×C₅	#67	1	1	yes	characteristic
249	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
250	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
251	C₂×#137	—	3	1	no	—
252	C₄×#41	—	3	1	no	—
253	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
254	#441	—	3	2	no	—
255	#440	—	3	2	no	—
256	C₄×Q₁₆	—	3	2	no	—
257	C₄×SD₁₆	—	3	2	no	—
258	#428	—	3	1	no	—
259	#419	—	3	1	no	—
260	#417	—	3	1	no	—
261	C₄×M₁₆	—	3	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
265	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₅×D₃	—	2	2	no	—
267	C₂×C₅×D₃	—	4	1	no	—
268	C₂×C₅×D₃	—	4	1	no	—
269	C₃×C₄×C₅	—	2	4	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	—	2	1	no	—
273	C₃×C₄×C₅	—	4	2	no	—
274	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
275	C₃×C₄×C₅	#137	1	2	yes	complemented
276	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
277	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
278	C₅×Dic₃	—	2	2	no	—
279	C₅×Dic₃	—	4	1	no	—
280	C₅×Dic₃	—	4	1	no	—
281	C₂×C₃×Q₈	—	2	1	no	—
282	C₂×C₃×Q₈	—	2	2	no	—
283	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
284	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
285	C₂²×C₃×C₄	—	2	1	no	—
286	C₂²×C₃×C₄	—	2	1	no	—
287	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
288	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
289	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
290	C₂×#67	—	2	1	no	—
291	#235	—	2	2	no	—
292	#235	C₂×C₄×C₅	1	4	yes	—
293	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₄×D₃	—	2	1	no	—
295	C₂×C₄×D₃	—	2	1	no	—
296	C₂×C₄×D₃	—	2	1	no	—
297	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	—	2	2	no	—
299	C₃×C₄⋊C₄	—	2	2	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
302	C₃×C₄²	—	2	2	no	—
303	C₃×C₄²	—	2	2	no	—
304	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
305	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
306	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
307	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
308	#217	—	2	1	no	—
309	#216	C₂×C₄×C₅	1	8	yes	complemented
310	#215	C₂×C₄×C₅	1	8	yes	complemented
311	(C₂×D₃)⋊C₄	—	2	1	no	—
312	(C₂×D₃)⋊C₄	—	2	1	no	—
313	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
314	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
315	Dic₃⋊C₄	—	2	1	no	—
316	Dic₃⋊C₄	—	2	1	no	—
317	C₄×Dic₃	—	2	1	no	—
318	C₄×Dic₃	—	2	1	no	—
319	C₄×Dic₃	—	2	1	no	—
320	#208	—	2	2	no	—
321	#208	C₂×C₄×C₅	1	4	yes	complemented
322	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
323	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
324	C₂³×C₅	—	6	1	no	—
325	C₂³×C₅	C₂×#67	1	1	yes	characteristic
326	C₅×Q₈	—	2	4	no	—
327	C₅×Q₈	—	2	2	no	—
328	C₅×Q₈	—	3	2	no	—
329	C₅×Q₈	—	6	1	no	—
330	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
331	C₅×D₄	—	3	2	no	—
332	C₅×D₄	—	6	4	no	—
333	C₅×D₄	—	6	1	no	—
334	C₂×C₄×C₅	—	2	4	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	4	1	no	—
339	C₂×C₄×C₅	—	4	2	no	—
340	C₂×C₄×C₅	—	6	1	no	—
341	C₂×C₄×C₅	—	6	4	no	—
342	C₂×C₄×C₅	—	6	1	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	—	12	2	no	—
345	C₂×C₄×C₅	—	12	2	no	—
346	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
347	C₂×C₄×C₅	#235	1	2	yes	—
348	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
350	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
351	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
354	C₅×C₈	—	3	4	no	—
355	C₅×C₈	—	6	2	no	—
356	C₂×#41	—	3	1	no	—
357	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
358	#137	—	3	8	no	—
359	C₂×Q₁₆	—	3	2	no	—
360	C₂×SD₁₆	—	3	2	no	—
361	C₂×M₁₆	—	3	1	no	—
362	C₂×M₁₆	—	3	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	3	1	no	—
366	C₄×Q₈	—	3	1	no	—
367	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
368	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
369	C₄×D₄	—	3	1	no	—
370	C₄×D₄	—	3	1	no	—
371	C₄×D₄	—	6	1	no	—
372	C₄×D₄	—	6	1	no	—
373	#117	—	3	1	no	—
374	#117	—	6	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	6	1	no	—
379	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
380	#107	—	3	2	no	—
381	#106	—	3	2	no	—
382	#103	—	3	2	no	—
383	#103	—	3	2	no	—
384	#103	—	3	2	no	—
385	#102	—	3	2	no	—
386	#97	—	3	2	no	—
387	C₄×C₈	—	3	2	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
390	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
391	C₂×C₃×C₅	#575	1	1	yes	characteristic
392	C₅×D₃	—	4	2	no	—
393	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²×D₃	—	2	1	no	—
395	C₃×Q₈	—	2	4	no	—
396	C₃×Q₈	—	2	2	no	—
397	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	4	1	no	—
403	C₂×C₃×C₄	—	4	2	no	—
404	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂×C₃×C₄	C₅×#41	1	2	yes	—
411	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
412	#67	—	2	4	no	—
413	C₂×Dic₃	—	2	1	no	—
414	C₂×Dic₃	—	2	1	no	—
415	C₂×Dic₃	—	2	1	no	—
416	D₁₂	—	2	1	no	—
417	D₁₂	C₂²×C₄×C₅	1	2	yes	—
418	C₄×D₃	—	2	4	no	—
419	C₄×D₃	—	4	2	no	—
420	C₄×D₃	—	4	2	no	—
421	Dic₆	—	2	1	no	—
422	Dic₆	C₂²×C₄×C₅	1	2	yes	—
423	C₃⋊C₈	—	2	2	no	—
424	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	6	2	no	—
428	C₂²×C₅	—	12	1	no	—
429	C₂²×C₅	—	12	1	no	—
430	C₂²×C₅	C₄×#67	1	2	yes	—
431	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
432	C₄×C₅	—	2	4	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	6	2	no	—
438	C₄×C₅	—	12	1	no	—
439	C₄×C₅	—	12	1	no	—
440	C₄×C₅	C₄×#67	1	2	yes	—
441	C₄×C₅	#942	1	2	yes	direct product factor
442	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
443	C₄×C₅	C₂×#235	1	1	yes	characteristic
444	#41	—	3	4	no	—
445	#41	—	6	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	3	1	no	—
449	C₂×Q₈	C₄×C₅×D₃	1	4	yes	complemented
450	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	6	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	6	1	no	—
456	C₂²×C₄	—	6	1	no	—
457	C₂²×C₄	—	6	1	no	—
458	C₂²×C₄	C₅×#67	1	1	yes	characteristic
459	C₂²×C₄	C₅×#67	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
461	Q₁₆	—	3	8	no	—
462	SD₁₆	—	3	8	no	—
463	M₁₆	—	3	4	no	—
464	M₁₆	—	6	2	no	—
465	C₂×C₈	—	3	2	no	—
466	C₂×C₈	—	3	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	3	1	no	—
471	C₄⋊C₄	—	3	1	no	—
472	C₄⋊C₄	—	6	1	no	—
473	C₄⋊C₄	—	6	1	no	—
474	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
475	C₂²⋊C₄	—	6	1	no	—
476	C₂²⋊C₄	—	6	1	no	—
477	C₂²⋊C₄	—	6	1	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	6	1	no	—
481	C₄²	—	6	1	no	—
482	C₄²	—	6	1	no	—
483	C₄²	C₅×#67	1	1	yes	characteristic
484	C₄²	C₅×#67	1	1	yes	characteristic
485	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
486	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
487	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
491	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂×D₃	—	2	2	no	—
493	C₂×D₃	—	4	1	no	—
494	C₂×D₃	—	4	1	no	—
495	C₃×C₄	—	2	4	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	4	2	no	—
500	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
501	C₃×C₄	C₅×#137	1	2	yes	complemented
502	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
503	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
504	Dic₃	—	2	2	no	—
505	Dic₃	—	4	1	no	—
506	Dic₃	—	4	1	no	—
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	12	2	no	—
509	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
510	C₂×C₅	C₂×#942	1	1	yes	characteristic
511	C₂×C₅	#5822	1	1	yes	characteristic
512	C₂³	—	6	1	no	—
513	C₂³	C₂×C₅×#67	1	1	yes	characteristic
514	Q₈	—	2	4	no	—
515	Q₈	—	2	2	no	—
516	Q₈	—	3	2	no	—
517	Q₈	—	6	1	no	—
518	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
519	D₄	—	3	2	no	—
520	D₄	—	6	4	no	—
521	D₄	—	6	1	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	6	1	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	6	1	no	—
531	C₂×C₄	—	6	1	no	—
532	C₂×C₄	—	12	2	no	—
533	C₂×C₄	—	12	2	no	—
534	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
535	C₂×C₄	C₅×#235	1	2	yes	—
536	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
537	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
538	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
539	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
540	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
541	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
542	C₈	—	3	4	no	—
543	C₈	—	6	2	no	—
544	C₂×C₃	—	2	2	no	—
545	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
546	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
547	C₂×C₃	C₅×#575	1	1	yes	characteristic
548	D₃	—	4	2	no	—
549	C₅	C₄×#942	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	6	2	no	—
553	C₂²	—	12	1	no	—
554	C₂²	—	12	1	no	—
555	C₂²	C₄×C₅×#67	1	2	yes	—
556	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
557	C₄	—	2	4	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	2	no	—
562	C₄	—	6	2	no	—
563	C₄	—	12	1	no	—
564	C₄	—	12	1	no	—
565	C₄	C₄×C₅×#67	1	2	yes	—
566	C₄	C₅×#942	1	2	yes	direct product factor
567	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
568	C₄	C₂×C₅×#235	1	1	yes	characteristic
569	C₃	C₄×C₅×#137	1	1	yes	characteristic, complemented, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	12	2	no	—
572	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
573	C₂	C₂×C₅×#942	1	1	yes	characteristic
574	C₂	C₅×#5822	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×Q₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₄×C₅×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₅×#5225	C₂	semidirect
5. C₅×#5030	C₂	semidirect
6. C₄×C₅×#216	C₂	semidirect
7. C₅×#5026	C₂	semidirect
8. C₄×C₅×#215	C₂	semidirect
10. C₅×#4964	C₂	semidirect
11. C₄×C₅×#208	C₂	semidirect
24. C₅×#942	C₄	direct (N × H)
45. C₄×#942	C₅	direct (N × H)
48. C₂×C₄×C₅×Q₈	D₃	semidirect
59. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
85. C₅×#216	C₂×C₄	semidirect
86. C₅×#215	C₂×C₄	semidirect
97. C₅×#208	C₂×C₄	semidirect
100. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
103. #5225	C₂×C₅	semidirect
104. #5030	C₂×C₅	semidirect
105. C₄×#216	C₂×C₅	semidirect
106. #5026	C₂×C₅	semidirect
107. C₄×#215	C₂×C₅	semidirect
109. #4964	C₂×C₅	semidirect
110. C₄×#208	C₂×C₅	semidirect
187. #942	C₄×C₅	direct (N × H)
213. C₂×C₅×Q₈	C₄×D₃	semidirect
253. C₂×C₄×Q₈	C₅×D₃	semidirect
275. C₃×C₄×C₅	#137	semidirect
283. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
309. #216	C₂×C₄×C₅	semidirect
310. #215	C₂×C₄×C₅	semidirect
321. #208	C₂×C₄×C₅	semidirect
441. C₄×C₅	#942	direct (N × H)
449. C₂×Q₈	C₄×C₅×D₃	semidirect
487. C₃×C₅	C₄×#137	semidirect
501. C₃×C₄	C₅×#137	semidirect
549. C₅	C₄×#942	direct (N × H)
566. C₄	C₅×#942	direct (N × H)
569. C₃	C₄×C₅×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×Q₈	2
C₂×C₅×#942	2
C₄×C₅×#235	2
C₅×#5225	2
C₅×#5030	2
C₄×C₅×#216	2
C₅×#5026	2
C₄×C₅×#215	2
C₅×#4966	2
C₅×#4964	2
C₄×C₅×#208	2
C₄×C₅×#137	3
C₄×#942	5

Subgroups — C4×C5×#942 #14416826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#942 #14416826