Subgroups — C₃×#10601268 #14297418

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3952	C₂	1	2	yes	maximal
4	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64770	C₂	1	2	yes	maximal, complemented
6	#10601268	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	2	yes	—
16	C₃×C₄²×D₅	—	2	2	no	—
17	C₃×C₄²×D₅	—	2	2	no	—
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₃×#3952	—	2	4	no	—
20	C₃×C₄⋊#168	—	2	2	no	—
21	C₃×#1797	—	5	1	no	maximal, Hall
22	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×#3952	C₂×C₃	1	2	yes	—
25	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
26	#64770	C₂×C₃	1	2	yes	complemented
27	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	—	2	2	no	—
35	C₂×C₃×C₄×D₅	—	2	2	no	—
36	C₂×C₃×C₄×D₅	—	2	2	no	—
37	C₂×C₃×C₄×D₅	—	2	2	no	—
38	C₂×C₃×C₄×D₅	—	2	1	no	—
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×C₄×D₅	—	2	1	no	—
41	C₂×C₃×C₄×D₅	—	2	1	no	—
42	C₂×C₃×C₄×D₅	—	2	2	no	—
43	C₂×C₃×C₄×D₅	C₈	1	4	yes	complemented
44	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₂×C₃×C₅×C₈	—	2	2	no	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₃×C₄²×C₅	D₄	1	2	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₃×C₄×Dic₅	—	2	2	no	—
52	C₃×C₄×Dic₅	—	2	2	no	—
53	C₃×C₄×Dic₅	—	2	1	no	—
54	C₃×C₄×Dic₅	—	2	1	no	—
55	C₂×C₃×#168	—	2	2	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₂×C₃×#168	—	2	2	no	—
58	C₂²×C₃×C₄²	—	5	1	no	—
59	C₂×C₃×C₄⋊C₈	—	5	1	no	—
60	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
61	C₂×C₃×C₂²⋊C₈	—	5	2	no	—
62	C₃×#336	—	5	2	no	—
63	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
67	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
71	C₂²×#168	C₂²×C₃	1	2	yes	—
72	C₄²×D₅	—	2	2	no	—
73	C₄²×D₅	—	2	2	no	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	#3952	—	2	4	no	—
76	C₄⋊#168	—	2	2	no	—
77	#1797	—	5	1	no	Sylow
78	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₃×D₅	—	2	1	no	—
80	C₂²×C₃×D₅	—	2	1	no	—
81	C₂²×C₃×D₅	—	2	1	no	—
82	C₂²×C₃×D₅	—	2	1	no	—
83	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
84	C₂²×C₃×D₅	C₂×C₈	1	2	yes	—
85	C₂²×C₃×D₅	M₁₆	1	2	yes	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
91	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×Dic₅	—	2	1	no	—
99	C₂×C₃×Dic₅	—	2	1	no	—
100	C₂×C₃×Dic₅	—	2	1	no	—
101	C₂×C₃×Dic₅	—	2	1	no	—
102	C₂×C₃×Dic₅	—	2	1	no	—
103	C₂×C₃×Dic₅	—	2	1	no	—
104	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
105	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
106	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
107	C₃×C₄×D₅	—	2	8	no	—
108	C₃×C₄×D₅	—	2	8	no	—
109	C₃×C₄×D₅	—	2	2	no	—
110	C₃×C₄×D₅	—	2	2	no	—
111	C₃×C₄×D₅	—	2	2	no	—
112	C₃×C₄×D₅	—	2	2	no	—
113	C₃×C₅×C₈	—	4	2	no	—
114	C₃×#168	—	4	2	no	—
115	C₂³×C₃×C₄	—	5	1	no	—
116	C₂³×C₃×C₄	—	5	1	no	—
117	C₂³×C₃×C₄	—	5	1	no	—
118	C₂²×C₃×C₈	—	5	2	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₃×C₄²	—	5	1	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	10	2	no	—
124	C₂×C₃×C₄²	—	10	2	no	—
125	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
126	C₃×C₄⋊C₈	—	2	2	no	—
127	C₃×C₄⋊C₈	—	10	2	no	—
128	C₃×C₂²⋊C₈	—	10	4	no	—
129	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
133	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	—	2	2	no	—
137	C₂×C₄×D₅	—	2	2	no	—
138	C₂×C₄×D₅	—	2	2	no	—
139	C₂×C₄×D₅	—	2	2	no	—
140	C₂×C₄×D₅	—	2	1	no	—
141	C₂×C₄×D₅	—	2	1	no	—
142	C₂×C₄×D₅	—	2	1	no	—
143	C₂×C₄×D₅	—	2	1	no	—
144	C₂×C₄×D₅	—	2	2	no	—
145	C₂×C₄×D₅	C₃×C₈	1	4	yes	complemented
146	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
147	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₄²×C₅	C₃×D₄	1	2	yes	—
152	C₄²×C₅	C₃×D₄	1	2	yes	—
153	C₄×Dic₅	—	2	2	no	—
154	C₄×Dic₅	—	2	2	no	—
155	C₄×Dic₅	—	2	1	no	—
156	C₄×Dic₅	—	2	1	no	—
157	C₂×#168	—	2	2	no	—
158	C₂×#168	—	2	2	no	—
159	C₂×#168	—	2	2	no	—
160	C₂²×C₄²	—	5	1	no	—
161	C₂×C₄⋊C₈	—	5	1	no	—
162	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊C₈	—	5	2	no	—
164	#336	—	5	2	no	—
165	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	#117	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
169	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
172	C₂×C₃×D₅	—	2	2	no	—
173	C₂×C₃×D₅	—	2	2	no	—
174	C₂×C₃×D₅	—	2	2	no	—
175	C₂×C₃×D₅	—	2	2	no	—
176	C₂×C₃×D₅	—	2	2	no	—
177	C₂×C₃×D₅	—	2	2	no	—
178	C₂×C₃×D₅	C₄⋊C₈	1	4	yes	complemented
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	C₂²⋊C₈	1	4	yes	complemented
181	C₃×C₄×C₅	#121	1	1	yes	characteristic
182	C₃×C₄×C₅	#121	1	1	yes	characteristic
183	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
184	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₃×Dic₅	—	2	2	no	—
186	C₃×Dic₅	—	2	2	no	—
187	C₃×Dic₅	—	2	2	no	—
188	C₂⁴×C₃	—	5	1	no	—
189	C₂²×C₃×C₄	—	5	1	no	—
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	4	no	—
193	C₂²×C₃×C₄	—	5	2	no	—
194	C₂²×C₃×C₄	—	5	2	no	—
195	C₂²×C₃×C₄	—	10	2	no	—
196	C₂²×C₃×C₄	—	10	2	no	—
197	C₂²×C₃×C₄	—	10	2	no	—
198	C₂²×C₃×C₄	—	10	2	no	—
199	C₂²×C₃×C₄	—	10	2	no	—
200	C₂²×C₃×C₄	—	10	1	no	—
201	C₂²×C₃×C₄	—	10	1	no	—
202	C₂²×C₃×C₄	—	10	1	no	—
203	C₂²×C₃×C₄	—	10	1	no	—
204	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₂×C₃×C₈	—	2	2	no	—
208	C₂×C₃×C₈	—	2	2	no	—
209	C₂×C₃×C₈	—	2	2	no	—
210	C₂×C₃×C₈	—	10	2	no	—
211	C₂×C₃×C₈	—	10	2	no	—
212	C₂×C₃×C₈	—	10	2	no	—
213	C₃×C₄²	—	10	2	no	—
214	C₃×C₄²	—	10	2	no	—
215	C₃×C₄²	—	10	1	no	—
216	C₃×C₄²	—	10	1	no	—
217	C₃×C₄²	D₂₀	1	2	yes	—
218	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
219	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂²×D₅	—	2	1	no	—
221	C₂²×D₅	—	2	1	no	—
222	C₂²×D₅	—	2	1	no	—
223	C₂²×D₅	—	2	1	no	—
224	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
225	C₂²×D₅	C₂×C₃×C₈	1	2	yes	—
226	C₂²×D₅	C₃×M₁₆	1	2	yes	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
231	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
232	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
239	C₂×Dic₅	—	2	1	no	—
240	C₂×Dic₅	—	2	1	no	—
241	C₂×Dic₅	—	2	1	no	—
242	C₂×Dic₅	—	2	1	no	—
243	C₂×Dic₅	—	2	1	no	—
244	C₂×Dic₅	—	2	1	no	—
245	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
246	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
247	C₂×Dic₅	C₃×M₁₆	1	2	yes	—
248	C₄×D₅	—	2	8	no	—
249	C₄×D₅	—	2	8	no	—
250	C₄×D₅	—	2	2	no	—
251	C₄×D₅	—	2	2	no	—
252	C₄×D₅	—	2	2	no	—
253	C₄×D₅	—	2	2	no	—
254	C₅×C₈	—	4	2	no	—
255	#168	—	4	2	no	—
256	C₂³×C₄	—	5	1	no	—
257	C₂³×C₄	—	5	1	no	—
258	C₂³×C₄	—	5	1	no	—
259	C₂²×C₈	—	5	2	no	—
260	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
261	C₂×C₄²	—	5	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	1	no	—
264	C₂×C₄²	—	10	2	no	—
265	C₂×C₄²	—	10	2	no	—
266	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	10	2	no	—
269	C₂²⋊C₈	—	10	4	no	—
270	C₂×C₃×C₅	#380	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
272	C₂×C₃×C₅	#407	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
274	C₂×C₃×C₅	#423	1	1	yes	characteristic
275	C₂×C₃×C₅	#431	1	1	yes	characteristic
276	C₂×C₃×C₅	#432	1	1	yes	characteristic
277	C₃×D₅	—	2	4	no	—
278	C₂³×C₃	—	5	2	no	—
279	C₂³×C₃	—	5	2	no	—
280	C₂³×C₃	—	5	2	no	—
281	C₂³×C₃	—	10	1	no	—
282	C₂³×C₃	—	10	1	no	—
283	C₂³×C₃	—	10	1	no	—
284	C₂³×C₃	—	10	1	no	—
285	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	5	2	no	—
290	C₂×C₃×C₄	—	5	2	no	—
291	C₂×C₃×C₄	—	10	8	no	—
292	C₂×C₃×C₄	—	10	1	no	—
293	C₂×C₃×C₄	—	10	1	no	—
294	C₂×C₃×C₄	—	10	1	no	—
295	C₂×C₃×C₄	—	10	1	no	—
296	C₂×C₃×C₄	—	10	1	no	—
297	C₂×C₃×C₄	—	10	1	no	—
298	C₂×C₃×C₄	—	10	8	no	—
299	C₂×C₃×C₄	—	10	2	no	—
300	C₂×C₃×C₄	—	10	2	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	10	2	no	—
303	C₂×C₃×C₄	C₈×D₅	1	2	yes	—
304	C₂×C₃×C₄	#676	1	2	yes	—
305	C₂×C₃×C₄	#685	1	2	yes	—
306	C₂×C₃×C₄	#685	1	2	yes	—
307	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
308	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
309	C₂×C₃×C₄	#711	1	1	yes	characteristic
310	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	#713	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
313	C₃×C₈	—	4	2	no	—
314	C₃×C₈	—	20	2	no	—
315	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
317	C₂²×C₅	C₃×#117	1	1	yes	characteristic
318	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
319	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
320	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
321	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
322	C₂×D₅	—	2	2	no	—
323	C₂×D₅	—	2	2	no	—
324	C₂×D₅	—	2	2	no	—
325	C₂×D₅	—	2	2	no	—
326	C₂×D₅	—	2	2	no	—
327	C₂×D₅	—	2	2	no	—
328	C₂×D₅	C₃×C₄⋊C₈	1	4	yes	complemented
329	C₄×C₅	—	2	2	no	—
330	C₄×C₅	C₃×C₂²⋊C₈	1	4	yes	complemented
331	C₄×C₅	C₃×#121	1	1	yes	characteristic
332	C₄×C₅	C₃×#121	1	1	yes	characteristic
333	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
334	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
335	Dic₅	—	2	2	no	—
336	Dic₅	—	2	2	no	—
337	Dic₅	—	2	2	no	—
338	C₂⁴	—	5	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	4	no	—
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	2	no	—
345	C₂²×C₄	—	10	2	no	—
346	C₂²×C₄	—	10	2	no	—
347	C₂²×C₄	—	10	2	no	—
348	C₂²×C₄	—	10	2	no	—
349	C₂²×C₄	—	10	2	no	—
350	C₂²×C₄	—	10	1	no	—
351	C₂²×C₄	—	10	1	no	—
352	C₂²×C₄	—	10	1	no	—
353	C₂²×C₄	—	10	1	no	—
354	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
355	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	10	2	no	—
361	C₂×C₈	—	10	2	no	—
362	C₂×C₈	—	10	2	no	—
363	C₄²	—	10	2	no	—
364	C₄²	—	10	2	no	—
365	C₄²	—	10	1	no	—
366	C₄²	—	10	1	no	—
367	C₄²	C₃×D₂₀	1	2	yes	—
368	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
369	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	—	5	4	no	—
371	C₂²×C₃	—	10	2	no	—
372	C₂²×C₃	—	10	2	no	—
373	C₂²×C₃	—	10	2	no	—
374	C₂²×C₃	—	10	2	no	—
375	C₂²×C₃	—	10	2	no	—
376	C₂²×C₃	—	10	2	no	—
377	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
378	C₂²×C₃	#4038	1	1	yes	characteristic
379	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
380	C₂²×C₃	C₂×#676	1	1	yes	characteristic
381	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
382	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
383	C₂²×C₃	C₂×#685	1	1	yes	characteristic
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	10	2	no	—
386	C₃×C₄	—	10	2	no	—
387	C₃×C₄	—	10	2	no	—
388	C₃×C₄	#3952	1	4	yes	complemented
389	C₃×C₄	#4041	1	1	yes	characteristic
390	C₃×C₄	#4043	1	1	yes	characteristic
391	C₃×C₄	#4084	1	1	yes	characteristic
392	C₃×C₄	#4092	1	1	yes	characteristic
393	C₂×C₅	C₃×#380	1	1	yes	characteristic
394	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
395	C₂×C₅	C₃×#407	1	1	yes	characteristic
396	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
397	C₂×C₅	C₃×#423	1	1	yes	characteristic
398	C₂×C₅	C₃×#431	1	1	yes	characteristic
399	C₂×C₅	C₃×#432	1	1	yes	characteristic
400	D₅	—	2	4	no	—
401	C₂³	—	5	2	no	—
402	C₂³	—	5	2	no	—
403	C₂³	—	5	2	no	—
404	C₂³	—	10	1	no	—
405	C₂³	—	10	1	no	—
406	C₂³	—	10	1	no	—
407	C₂³	—	10	1	no	—
408	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	5	2	no	—
414	C₂×C₄	—	10	8	no	—
415	C₂×C₄	—	10	1	no	—
416	C₂×C₄	—	10	1	no	—
417	C₂×C₄	—	10	1	no	—
418	C₂×C₄	—	10	1	no	—
419	C₂×C₄	—	10	1	no	—
420	C₂×C₄	—	10	1	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	2	no	—
423	C₂×C₄	—	10	8	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	C₃×C₈×D₅	1	2	yes	—
427	C₂×C₄	C₃×#676	1	2	yes	—
428	C₂×C₄	C₃×#685	1	2	yes	—
429	C₂×C₄	C₃×#685	1	2	yes	—
430	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
431	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
432	C₂×C₄	C₃×#711	1	1	yes	characteristic
433	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
434	C₂×C₄	C₃×#713	1	1	yes	characteristic
435	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	20	2	no	—
438	C₂×C₃	—	10	4	no	—
439	C₂×C₃	D₅×C₄⋊C₈	1	1	yes	characteristic
440	C₂×C₃	#65122	1	1	yes	characteristic
441	C₂×C₃	#65124	1	1	yes	characteristic
442	C₂×C₃	#65126	1	1	yes	characteristic
443	C₂×C₃	#65276	1	1	yes	characteristic
444	C₂×C₃	C₂×#3952	1	1	yes	characteristic
445	C₂×C₃	#65415	1	1	yes	characteristic
446	C₅	C₃×#1797	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	5	4	no	—
448	C₂²	—	10	2	no	—
449	C₂²	—	10	2	no	—
450	C₂²	—	10	2	no	—
451	C₂²	—	10	2	no	—
452	C₂²	—	10	2	no	—
453	C₂²	—	10	2	no	—
454	C₂²	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
455	C₂²	C₃×#4038	1	1	yes	characteristic
456	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
457	C₂²	C₂×C₃×#676	1	1	yes	characteristic
458	C₂²	C₃×D₅×M₁₆	1	1	yes	characteristic
459	C₂²	C₃×D₅×M₁₆	1	1	yes	characteristic
460	C₂²	C₂×C₃×#685	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	10	2	no	—
463	C₄	—	10	2	no	—
464	C₄	—	10	2	no	—
465	C₄	C₃×#3952	1	4	yes	complemented
466	C₄	C₃×#4041	1	1	yes	characteristic
467	C₄	C₃×#4043	1	1	yes	characteristic
468	C₄	C₃×#4084	1	1	yes	characteristic
469	C₄	C₃×#4092	1	1	yes	characteristic
470	C₃	#10601268	1	1	yes	characteristic, direct product factor, Sylow
471	C₂	—	10	4	no	—
472	C₂	C₃×D₅×C₄⋊C₈	1	1	yes	characteristic
473	C₂	C₃×#65122	1	1	yes	characteristic
474	C₂	C₃×#65124	1	1	yes	characteristic
475	C₂	C₃×#65126	1	1	yes	characteristic
476	C₂	C₃×#65276	1	1	yes	characteristic
477	C₂	C₂×C₃×#3952	1	1	yes	characteristic
478	C₂	C₃×#65415	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂²×C₃×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#1797
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
4. C₂×C₃×C₄⋊#168	C₂	semidirect
5. C₃×#64770	C₂	semidirect
6. #10601268	C₃	direct (N × H)
23. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
25. C₂×C₄⋊#168	C₂×C₃	semidirect
26. #64770	C₂×C₃	semidirect
43. C₂×C₃×C₄×D₅	C₈	semidirect
60. C₂×C₃×C₄⋊C₈	D₅	semidirect
145. C₂×C₄×D₅	C₃×C₈	semidirect
162. C₂×C₄⋊C₈	C₃×D₅	semidirect
178. C₂×C₃×D₅	C₄⋊C₈	semidirect
180. C₃×C₄×C₅	C₂²⋊C₈	semidirect
328. C₂×D₅	C₃×C₄⋊C₈	semidirect
330. C₄×C₅	C₃×C₂²⋊C₈	semidirect
369. C₃×C₅	#1797	semidirect
388. C₃×C₄	#3952	semidirect
446. C₅	C₃×#1797	semidirect
465. C₄	C₃×#3952	semidirect
470. C₃	#10601268	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₅	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3952	2
C₂×C₃×C₄⋊#168	2
C₃×#64770	2
#10601268	3
C₃×#1797	5

Subgroups — C3×#10601268 #14297418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601268 #14297418