Subgroups — C₃×#10611598 #14417331

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#65879	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65441	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#686	C₂	1	2	yes	maximal, complemented
6	C₃×#65158	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65149	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65059	C₂	1	2	yes	maximal, complemented
9	C₃×#65045	C₂	1	2	yes	maximal, complemented
10	C₃×#65000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64997	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611598	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
16	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
17	C₂×C₃×#686	C₂²	1	2	yes	—
18	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
19	C₂×C₃×#685	—	2	2	no	—
20	C₃×D₅×D₈	C₄	1	8	yes	complemented
21	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
22	C₂×C₃×#676	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4039	C₂²	1	2	yes	complemented
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×#4027	—	2	2	no	—
27	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
28	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
29	C₃×#4018	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3964	C₂²	1	2	yes	complemented
34	C₃×#3953	C₂²	1	2	yes	complemented
35	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3941	C₂²	1	2	yes	complemented
39	C₃×#3939	C₂²	1	2	yes	complemented
40	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
41	C₃×#2948	—	5	1	no	maximal, Hall
42	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
43	#65879	C₂×C₃	1	2	yes	complemented
44	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
45	#65441	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×#686	C₂×C₃	1	2	yes	complemented
47	#65158	C₂×C₃	1	1	yes	characteristic, complemented
48	#65149	C₂×C₃	1	1	yes	characteristic, complemented
49	#65059	C₂×C₃	1	2	yes	complemented
50	#65045	C₂×C₃	1	2	yes	complemented
51	#65000	C₂×C₃	1	1	yes	characteristic, complemented
52	#64997	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₃×D₄×D₅	—	2	4	no	—
59	C₃×D₄×D₅	C₂×C₄	1	8	yes	complemented
60	C₂×C₃×D₂₀	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₂²⋊Dic₅	—	2	2	no	—
71	C₃×#686	C₂×C₄	1	8	yes	complemented
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×#685	—	2	2	no	—
75	C₃×#685	D₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
77	C₃×#683	D₄	1	2	yes	—
78	C₃×C₄×Dic₅	—	2	2	no	—
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
83	C₃×#676	—	2	2	no	—
84	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
85	C₂²×C₃×D₈	—	5	1	no	—
86	C₃×#518	—	5	2	no	—
87	C₃×#442	—	5	1	no	—
88	C₃×#442	—	5	1	no	—
89	C₃×#442	—	5	1	no	—
90	C₃×#442	D₅	1	1	yes	characteristic, complemented
91	C₃×C₄×D₈	—	5	2	no	—
92	C₃×C₄×D₈	—	5	2	no	—
93	C₃×#427	—	5	1	no	—
94	C₃×#418	—	5	2	no	—
95	C₃×#405	—	5	1	no	—
96	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
97	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
99	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
100	C₂×#686	C₂²×C₃	1	2	yes	—
101	C₄×C₂²⋊D₅	—	2	2	no	—
102	C₂×#685	—	2	2	no	—
103	D₅×D₈	C₃×C₄	1	8	yes	complemented
104	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×#676	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	#4039	C₂²×C₃	1	2	yes	complemented
108	#4038	C₂²×C₃	1	2	yes	—
109	#4027	—	2	2	no	—
110	D₅×C₂²⋊C₄	—	2	2	no	—
111	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
112	#4018	C₂²×C₃	1	1	yes	characteristic
113	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₅×#102	C₂²×C₃	1	2	yes	complemented
115	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
116	#3964	C₂²×C₃	1	2	yes	complemented
117	#3953	C₂²×C₃	1	2	yes	complemented
118	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
119	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
121	#3941	C₂²×C₃	1	2	yes	complemented
122	#3939	C₂²×C₃	1	2	yes	complemented
123	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
124	#2948	—	5	1	no	Sylow
125	C₂³×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×D₅	—	2	2	no	—
127	C₂²×C₃×D₅	—	2	8	no	—
128	C₂²×C₃×D₅	—	8	2	no	—
129	C₂²×C₃×D₅	—	8	2	no	—
130	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	8	2	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₃×C₂²⋊D₅	—	2	8	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	—	8	2	no	—
140	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
142	C₃×D₂₀	—	2	2	no	—
143	C₃×D₂₀	C₂²×C₄	1	4	yes	—
144	C₃×C₄×D₅	—	8	2	no	—
145	C₃×C₄×D₅	—	8	2	no	—
146	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
147	C₃×C₄×D₅	#41	1	2	yes	—
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
150	C₃×#168	—	2	1	no	—
151	C₃×#168	C₂²×C₄	1	2	yes	—
152	C₂²×C₃×D₄	—	5	2	no	—
153	C₂×C₃×D₈	—	5	2	no	—
154	C₂×C₃×D₈	—	5	8	no	—
155	C₂×C₃×D₈	—	5	1	no	—
156	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
157	C₂×C₃×M₁₆	—	5	1	no	—
158	C₂²×C₃×C₈	—	5	1	no	—
159	C₃×C₄×D₄	—	5	2	no	—
160	C₃×C₄×D₄	—	5	2	no	—
161	C₃×C₄×D₄	—	5	2	no	—
162	C₃×C₄×D₄	—	10	2	no	—
163	C₃×C₄×D₄	—	10	2	no	—
164	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
165	C₃×#117	—	5	1	no	—
166	C₃×#117	—	5	2	no	—
167	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
168	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
169	C₃×#107	—	5	2	no	—
170	C₃×#106	—	5	1	no	—
171	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
172	C₃×#102	—	5	2	no	—
173	C₃×#102	—	5	2	no	—
174	C₃×#102	—	5	2	no	—
175	C₃×#102	C₂×D₅	1	2	yes	complemented
176	C₃×#97	—	5	1	no	—
177	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
178	C₃×C₄×C₈	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₂³×D₅	—	2	2	no	—
181	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂×C₂²⋊D₅	—	2	2	no	—
184	C₂²×Dic₅	—	2	2	no	—
185	D₄×D₅	—	2	4	no	—
186	D₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
187	C₂×D₂₀	C₂³×C₃	1	2	yes	—
188	C₂×C₄×D₅	—	2	2	no	—
189	C₂×C₄×D₅	—	2	2	no	—
190	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
191	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
192	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₂²⋊Dic₅	—	2	2	no	—
198	#686	C₂×C₃×C₄	1	8	yes	complemented
199	#685	—	2	2	no	—
200	#685	—	2	2	no	—
201	#685	—	2	2	no	—
202	#685	C₃×D₄	1	2	yes	—
203	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
204	#683	C₃×D₄	1	2	yes	—
205	C₄×Dic₅	—	2	2	no	—
206	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×#168	C₂³×C₃	1	1	yes	characteristic
208	C₂×#168	C₂³×C₃	1	1	yes	characteristic
209	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
210	#676	—	2	2	no	—
211	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
212	C₂²×D₈	—	5	1	no	—
213	#518	—	5	2	no	—
214	#442	—	5	1	no	—
215	#442	—	5	1	no	—
216	#442	—	5	1	no	—
217	#442	C₃×D₅	1	1	yes	characteristic, complemented
218	C₄×D₈	—	5	2	no	—
219	C₄×D₈	—	5	2	no	—
220	#427	—	5	1	no	—
221	#418	—	5	2	no	—
222	#405	—	5	1	no	—
223	C₂²×C₃×C₅	—	2	4	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	—	2	2	no	—
228	C₂×C₃×D₅	—	2	4	no	—
229	C₂×C₃×D₅	—	4	2	no	—
230	C₂×C₃×D₅	—	4	2	no	—
231	C₂×C₃×D₅	—	8	8	no	—
232	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	4	2	no	—
235	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₃×Dic₅	—	2	2	no	—
238	C₃×Dic₅	—	4	2	no	—
239	C₃×Dic₅	C₄×D₄	1	2	yes	—
240	C₂⁴×C₃	—	10	2	no	—
241	C₂×C₃×D₄	—	5	8	no	—
242	C₂×C₃×D₄	—	5	2	no	—
243	C₂×C₃×D₄	—	10	4	no	—
244	C₂×C₃×D₄	—	10	2	no	—
245	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
246	C₂²×C₃×C₄	—	2	2	no	—
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	10	2	no	—
249	C₂²×C₃×C₄	—	10	2	no	—
250	C₂²×C₃×C₄	—	10	2	no	—
251	C₃×D₈	—	5	8	no	—
252	C₃×D₈	—	5	4	no	—
253	C₃×D₈	C₄×D₅	1	4	yes	complemented
254	C₃×M₁₆	—	10	2	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	4	no	—
257	C₂×C₃×C₈	—	5	1	no	—
258	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
259	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
260	C₃×C₄⋊C₄	—	5	2	no	—
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
263	C₃×C₂²⋊C₄	—	2	2	no	—
264	C₃×C₂²⋊C₄	—	5	2	no	—
265	C₃×C₂²⋊C₄	—	10	2	no	—
266	C₃×C₂²⋊C₄	—	10	2	no	—
267	C₃×C₂²⋊C₄	—	10	2	no	—
268	C₃×C₂²⋊C₄	—	10	2	no	—
269	C₃×C₄²	—	5	1	no	—
270	C₃×C₄²	—	10	2	no	—
271	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
272	C₂³×C₅	—	2	2	no	—
273	C₂²×D₅	—	2	2	no	—
274	C₂²×D₅	—	2	8	no	—
275	C₂²×D₅	—	8	2	no	—
276	C₂²×D₅	—	8	2	no	—
277	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	8	2	no	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
284	C₂²⋊D₅	—	2	8	no	—
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	8	2	no	—
287	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
288	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
289	D₂₀	—	2	2	no	—
290	D₂₀	C₂²×C₃×C₄	1	4	yes	—
291	C₄×D₅	—	8	2	no	—
292	C₄×D₅	—	8	2	no	—
293	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
294	C₄×D₅	C₃×#41	1	2	yes	—
295	C₅×C₈	—	2	1	no	—
296	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
297	#168	—	2	1	no	—
298	#168	C₂²×C₃×C₄	1	2	yes	—
299	C₂²×D₄	—	5	2	no	—
300	C₂×D₈	—	5	2	no	—
301	C₂×D₈	—	5	8	no	—
302	C₂×D₈	—	5	1	no	—
303	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
304	C₂×M₁₆	—	5	1	no	—
305	C₂²×C₈	—	5	1	no	—
306	C₄×D₄	—	5	2	no	—
307	C₄×D₄	—	5	2	no	—
308	C₄×D₄	—	5	2	no	—
309	C₄×D₄	—	10	2	no	—
310	C₄×D₄	—	10	2	no	—
311	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
312	#117	—	5	1	no	—
313	#117	—	5	2	no	—
314	C₂×C₂²⋊C₄	—	10	2	no	—
315	C₂×C₂²⋊C₄	—	10	2	no	—
316	#107	—	5	2	no	—
317	#106	—	5	1	no	—
318	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
319	#102	—	5	2	no	—
320	#102	—	5	2	no	—
321	#102	—	5	2	no	—
322	#102	C₂×C₃×D₅	1	2	yes	complemented
323	#97	—	5	1	no	—
324	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
325	C₄×C₈	—	5	1	no	—
326	C₄×C₈	—	5	1	no	—
327	C₂×C₃×C₅	—	4	4	no	—
328	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
329	C₂×C₃×C₅	#576	1	2	yes	—
330	C₃×D₅	—	2	2	no	—
331	C₃×D₅	—	4	4	no	—
332	C₂³×C₃	—	2	2	no	—
333	C₂³×C₃	—	5	1	no	—
334	C₂³×C₃	—	10	8	no	—
335	C₂³×C₃	—	10	2	no	—
336	C₂³×C₃	—	40	2	no	—
337	C₂³×C₃	—	40	2	no	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	5	4	no	—
340	C₃×D₄	—	10	8	no	—
341	C₃×D₄	—	10	2	no	—
342	C₃×D₄	C₂×C₄×D₅	1	4	yes	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	8	2	no	—
349	C₂×C₃×C₄	—	10	2	no	—
350	C₂×C₃×C₄	—	40	2	no	—
351	C₂×C₃×C₄	—	40	2	no	—
352	C₂×C₃×C₄	—	40	2	no	—
353	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
354	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	—	5	2	no	—
357	C₃×C₈	—	10	1	no	—
358	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
359	C₂²×C₅	—	2	4	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	2	no	—
362	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₂×D₅	—	2	2	no	—
364	C₂×D₅	—	2	4	no	—
365	C₂×D₅	—	4	2	no	—
366	C₂×D₅	—	4	2	no	—
367	C₂×D₅	—	8	8	no	—
368	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
369	C₄×C₅	—	2	2	no	—
370	C₄×C₅	—	4	2	no	—
371	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
372	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
373	Dic₅	—	2	2	no	—
374	Dic₅	—	4	2	no	—
375	Dic₅	C₃×C₄×D₄	1	2	yes	—
376	C₂⁴	—	10	2	no	—
377	C₂×D₄	—	5	8	no	—
378	C₂×D₄	—	5	2	no	—
379	C₂×D₄	—	10	4	no	—
380	C₂×D₄	—	10	2	no	—
381	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	10	2	no	—
385	C₂²×C₄	—	10	2	no	—
386	C₂²×C₄	—	10	2	no	—
387	D₈	—	5	8	no	—
388	D₈	—	5	4	no	—
389	D₈	C₃×C₄×D₅	1	4	yes	complemented
390	M₁₆	—	10	2	no	—
391	C₂×C₈	—	5	1	no	—
392	C₂×C₈	—	5	4	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
396	C₄⋊C₄	—	5	2	no	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	5	2	no	—
401	C₂²⋊C₄	—	10	2	no	—
402	C₂²⋊C₄	—	10	2	no	—
403	C₂²⋊C₄	—	10	2	no	—
404	C₂²⋊C₄	—	10	2	no	—
405	C₄²	—	5	1	no	—
406	C₄²	—	10	2	no	—
407	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
408	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	4	2	no	—
411	C₂²×C₃	—	4	2	no	—
412	C₂²×C₃	—	5	2	no	—
413	C₂²×C₃	—	10	2	no	—
414	C₂²×C₃	—	10	4	no	—
415	C₂²×C₃	—	20	2	no	—
416	C₂²×C₃	—	20	2	no	—
417	C₂²×C₃	—	40	8	no	—
418	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	5	2	no	—
422	C₃×C₄	—	10	2	no	—
423	C₃×C₄	—	20	2	no	—
424	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₃×C₄	D₅×#41	1	1	yes	characteristic
426	C₂×C₅	—	4	4	no	—
427	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
428	C₂×C₅	C₃×#576	1	2	yes	—
429	D₅	—	2	2	no	—
430	D₅	—	4	4	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	5	1	no	—
433	C₂³	—	10	8	no	—
434	C₂³	—	10	2	no	—
435	C₂³	—	40	2	no	—
436	C₂³	—	40	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	5	4	no	—
439	D₄	—	10	8	no	—
440	D₄	—	10	2	no	—
441	D₄	C₂×C₃×C₄×D₅	1	4	yes	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	5	2	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	40	2	no	—
450	C₂×C₄	—	40	2	no	—
451	C₂×C₄	—	40	2	no	—
452	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
453	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	5	2	no	—
456	C₈	—	10	1	no	—
457	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
458	C₂×C₃	—	4	4	no	—
459	C₂×C₃	—	10	2	no	—
460	C₂×C₃	—	20	4	no	—
461	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
462	C₂×C₃	#66108	1	2	yes	—
463	C₅	C₃×#2948	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	5	2	no	—
468	C₂²	—	10	2	no	—
469	C₂²	—	10	4	no	—
470	C₂²	—	20	2	no	—
471	C₂²	—	20	2	no	—
472	C₂²	—	40	8	no	—
473	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	5	2	no	—
477	C₄	—	10	2	no	—
478	C₄	—	20	2	no	—
479	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
480	C₄	C₃×D₅×#41	1	1	yes	characteristic
481	C₃	#10611598	1	1	yes	characteristic, direct product factor, Sylow
482	C₂	—	4	4	no	—
483	C₂	—	10	2	no	—
484	C₂	—	20	4	no	—
485	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
486	C₂	C₃×#66108	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#442	D₅
hypocenter	C₅	C₃×#2948
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#442

Complements

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

N	H ≅ G/N	type
2. C₃×#65879	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₃×#65441	C₂	semidirect
5. C₃×C₄×#686	C₂	semidirect
6. C₃×#65158	C₂	semidirect
7. C₃×#65149	C₂	semidirect
8. C₃×#65059	C₂	semidirect
9. C₃×#65045	C₂	semidirect
10. C₃×#65000	C₂	semidirect
11. C₃×#64997	C₂	semidirect
12. #10611598	C₃	direct (N × H)
15. C₃×C₄×C₅×D₄	C₂²	semidirect
16. C₃×D₄×Dic₅	C₂²	semidirect
20. C₃×D₅×D₈	C₄	semidirect
24. C₃×#4039	C₂²	semidirect
28. C₃×C₄×D₂₀	C₂²	semidirect
30. C₃×C₅×#106	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#97	C₂²	semidirect
33. C₃×#3964	C₂²	semidirect
34. C₃×#3953	C₂²	semidirect
35. C₃×#3949	C₂²	semidirect
36. C₃×#3947	C₂²	semidirect
37. C₃×C₈×Dic₅	C₂²	semidirect
38. C₃×#3941	C₂²	semidirect
39. C₃×#3939	C₂²	semidirect
40. C₃×C₄×#168	C₂²	semidirect
43. #65879	C₂×C₃	semidirect
44. C₅×#442	C₂×C₃	semidirect
45. #65441	C₂×C₃	semidirect
46. C₄×#686	C₂×C₃	semidirect
47. #65158	C₂×C₃	semidirect
48. #65149	C₂×C₃	semidirect
49. #65059	C₂×C₃	semidirect
50. #65045	C₂×C₃	semidirect
51. #65000	C₂×C₃	semidirect
52. #64997	C₂×C₃	semidirect
59. C₃×D₄×D₅	C₂×C₄	semidirect
64. C₃×C₅×D₈	C₂×C₄	semidirect
71. C₃×#686	C₂×C₄	semidirect
82. C₃×D₄₀	C₂×C₄	semidirect
84. C₃×C₈×D₅	C₂×C₄	semidirect
90. C₃×#442	D₅	semidirect
98. C₄×C₅×D₄	C₂²×C₃	semidirect
99. D₄×Dic₅	C₂²×C₃	semidirect
103. D₅×D₈	C₃×C₄	semidirect
107. #4039	C₂²×C₃	semidirect
111. C₄×D₂₀	C₂²×C₃	semidirect
113. C₅×#106	C₂²×C₃	semidirect
114. C₅×#102	C₂²×C₃	semidirect
115. C₅×#97	C₂²×C₃	semidirect
116. #3964	C₂²×C₃	semidirect
117. #3953	C₂²×C₃	semidirect
118. #3949	C₂²×C₃	semidirect
119. #3947	C₂²×C₃	semidirect
120. C₈×Dic₅	C₂²×C₃	semidirect
121. #3941	C₂²×C₃	semidirect
122. #3939	C₂²×C₃	semidirect
123. C₄×#168	C₂²×C₃	semidirect
164. C₃×C₄×D₄	C₂×D₅	semidirect
171. C₃×#106	C₂×D₅	semidirect
175. C₃×#102	C₂×D₅	semidirect
177. C₃×#97	C₂×D₅	semidirect
186. D₄×D₅	C₂×C₃×C₄	semidirect
191. C₅×D₈	C₂×C₃×C₄	semidirect
198. #686	C₂×C₃×C₄	semidirect
209. D₄₀	C₂×C₃×C₄	semidirect
211. C₈×D₅	C₂×C₃×C₄	semidirect
217. #442	C₃×D₅	semidirect
253. C₃×D₈	C₄×D₅	semidirect
311. C₄×D₄	C₂×C₃×D₅	semidirect
318. #106	C₂×C₃×D₅	semidirect
322. #102	C₂×C₃×D₅	semidirect
324. #97	C₂×C₃×D₅	semidirect
389. D₈	C₃×C₄×D₅	semidirect
408. C₃×C₅	#2948	semidirect
463. C₅	C₃×#2948	semidirect
481. C₃	#10611598	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×D₅×D₈	2
C₃×#65879	2
C₃×C₅×#442	2
C₃×#65441	2
C₃×C₄×#686	2
C₃×#65158	2
C₃×#65149	2
C₃×#65059	2
C₃×#65045	2
C₃×#65000	2
C₃×#64997	2
#10611598	3
C₃×#2948	5

Subgroups — C3×#10611598 #14417331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611598 #14417331