Subgroups — C₃×#10610613 #14412624

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65838	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65420	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65093	C₂	1	2	yes	maximal, complemented
9	C₃×#65092	C₂	1	2	yes	maximal, complemented
10	C₃×#65059	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
12	#10610613	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×#4149	—	2	4	no	—
15	C₃×#4149	C₄	1	8	yes	complemented
16	C₂×C₃×#713	C₂²	1	2	yes	—
17	C₂×C₃×D₄×D₅	—	2	2	no	—
18	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
19	C₂×C₃×#709	—	2	1	no	—
20	C₂×C₃×#709	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₂₀	—	2	1	no	—
22	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
26	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4053	—	2	4	no	—
29	C₂×C₃×#676	C₂²	1	2	yes	complemented
30	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
31	C₃×#4039	—	2	1	no	—
32	C₃×#4038	C₂²	1	2	yes	complemented
33	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
34	C₃×#4033	—	2	1	no	—
35	C₃×C₅×#103	C₂²	1	2	yes	complemented
36	C₃×C₅×#102	C₂²	1	2	yes	complemented
37	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3953	C₂²	1	2	yes	complemented
42	C₃×#3953	C₂²	1	2	yes	complemented
43	C₃×#3941	C₂²	1	2	yes	complemented
44	C₃×#3941	C₂²	1	2	yes	complemented
45	C₃×#2897	—	5	1	no	maximal, Hall
46	C₂×#4149	C₂×C₃	1	1	yes	characteristic
47	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
48	#65838	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
50	#65522	C₂×C₃	1	1	yes	characteristic, complemented
51	#65420	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#3941	C₂×C₃	1	1	yes	characteristic, complemented
53	#65093	C₂×C₃	1	2	yes	complemented
54	#65092	C₂×C₃	1	2	yes	complemented
55	#65059	C₂×C₃	1	2	yes	complemented
56	D₅×#102	C₂×C₃	1	2	yes	complemented
57	C₂³×C₃×D₅	—	2	1	no	—
58	C₂³×C₃×D₅	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
68	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
69	C₃×#713	—	2	4	no	—
70	C₃×#713	C₂×C₄	1	8	yes	complemented
71	C₃×D₄×D₅	—	2	16	no	—
72	C₃×D₄×D₅	—	2	4	no	—
73	C₃×D₄×D₅	C₂×C₄	1	8	yes	complemented
74	C₃×#709	—	2	8	no	—
75	C₃×#709	C₂×C₄	1	4	yes	—
76	C₃×#709	D₄	1	4	yes	—
77	C₂×C₃×D₂₀	—	2	2	no	—
78	C₂×C₃×D₂₀	—	2	1	no	—
79	C₂×C₃×D₂₀	—	2	2	no	—
80	C₂×C₃×D₂₀	—	2	8	no	—
81	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
82	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
83	C₂×C₃×D₂₀	C₂³	1	2	yes	—
84	C₂×C₃×C₄×D₅	—	2	2	no	—
85	C₂×C₃×C₄×D₅	—	2	2	no	—
86	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
87	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
88	C₃×C₅×M₁₆	—	2	2	no	—
89	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
90	C₃×C₅×C₄⋊C₄	—	2	1	no	—
91	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
92	C₃×C₂²⋊Dic₅	—	2	1	no	—
93	C₃×#685	—	2	2	no	—
94	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
95	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
96	C₃×#683	—	2	2	no	—
97	C₃×C₄×Dic₅	—	2	1	no	—
98	C₃×C₄×Dic₅	—	2	2	no	—
99	C₂×C₃×#168	—	2	2	no	—
100	C₂×C₃×#168	C₂³	1	1	yes	characteristic
101	C₂×C₃×#168	C₂³	1	1	yes	characteristic
102	C₃×#676	—	2	4	no	—
103	C₃×C₈×D₅	—	2	4	no	—
104	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
105	C₂×C₃×#131	—	5	1	no	—
106	C₃×#520	—	5	1	no	—
107	C₃×#418	—	5	1	no	—
108	C₃×#418	—	5	2	no	—
109	C₃×#417	—	5	2	no	—
110	C₃×#417	D₅	1	1	yes	characteristic, complemented
111	C₃×#416	—	5	1	no	—
112	C₃×#416	—	5	2	no	—
113	C₂×C₃×#102	—	5	1	no	—
114	C₂×C₃×#102	—	5	2	no	—
115	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
116	#4149	—	2	4	no	—
117	#4149	C₃×C₄	1	8	yes	complemented
118	C₂×#713	C₂²×C₃	1	2	yes	—
119	C₂×D₄×D₅	—	2	2	no	—
120	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
121	C₂×#709	—	2	1	no	—
122	C₂×#709	C₂²×C₃	1	1	yes	characteristic
123	C₂²×D₂₀	—	2	1	no	—
124	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₄×C₂²⋊D₅	—	2	2	no	—
128	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
130	#4053	—	2	4	no	—
131	C₂×#676	C₂²×C₃	1	2	yes	complemented
132	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
133	#4039	—	2	1	no	—
134	#4038	C₂²×C₃	1	2	yes	complemented
135	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
136	#4033	—	2	1	no	—
137	C₅×#103	C₂²×C₃	1	2	yes	complemented
138	C₅×#102	C₂²×C₃	1	2	yes	complemented
139	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
140	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
141	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
142	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
143	#3953	C₂²×C₃	1	2	yes	complemented
144	#3953	C₂²×C₃	1	2	yes	complemented
145	#3941	C₂²×C₃	1	2	yes	complemented
146	#3941	C₂²×C₃	1	2	yes	complemented
147	#2897	—	5	1	no	Sylow
148	C₂³×C₃×C₅	—	2	1	no	—
149	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₃×D₅	—	2	2	no	—
151	C₂²×C₃×D₅	—	2	4	no	—
152	C₂²×C₃×D₅	—	2	8	no	—
153	C₂²×C₃×D₅	—	8	2	no	—
154	C₂²×C₃×D₅	—	8	2	no	—
155	C₂²×C₃×D₅	—	8	1	no	—
156	C₂²×C₃×D₅	—	8	1	no	—
157	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
158	C₃×C₅×Q₈	—	2	1	no	—
159	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
160	C₃×C₅×D₄	—	2	4	no	—
161	C₃×C₅×D₄	—	2	1	no	—
162	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	4	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	8	1	no	—
167	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
168	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₃×C₂²⋊D₅	—	2	8	no	—
172	C₃×C₂²⋊D₅	C₂²⋊C₄	1	8	yes	—
173	C₂×C₃×Dic₅	—	2	1	no	—
174	C₂×C₃×Dic₅	—	2	1	no	—
175	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
176	C₃×D₂₀	—	2	8	no	—
177	C₃×D₂₀	—	2	4	no	—
178	C₃×D₂₀	—	2	2	no	—
179	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
180	C₃×D₂₀	C₂²×C₄	1	4	yes	—
181	C₃×C₄×D₅	—	2	8	no	—
182	C₃×C₄×D₅	—	8	2	no	—
183	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
184	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
185	C₃×Dic₁₀	C₂²⋊C₄	1	4	yes	—
186	C₃×C₅×C₈	—	2	2	no	—
187	C₃×#168	—	2	1	no	—
188	C₃×#168	—	2	1	no	—
189	C₃×H(5,𝔽₂)	—	5	8	no	—
190	C₃×H(5,𝔽₂)	—	10	4	no	—
191	C₂×C₃×#41	—	5	1	no	—
192	C₂×C₃×#41	—	5	2	no	—
193	C₂×C₃×#41	—	10	1	no	—
194	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
195	C₂²×C₃×D₄	—	5	2	no	—
196	C₂²×C₃×D₄	—	5	1	no	—
197	C₂²×C₃×D₄	—	10	1	no	—
198	C₂²×C₃×D₄	—	10	2	no	—
199	C₃×#131	—	10	4	no	—
200	C₂×C₃×M₁₆	—	5	2	no	—
201	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₈	—	5	1	no	—
203	C₂²×C₃×C₈	—	5	2	no	—
204	C₃×C₄×Q₈	—	10	1	no	—
205	C₃×C₄×D₄	—	10	1	no	—
206	C₃×C₄×D₄	—	10	2	no	—
207	C₃×#117	—	5	1	no	—
208	C₃×#117	—	5	2	no	—
209	C₂×C₃×C₄⋊C₄	—	5	2	no	—
210	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
211	C₃×#103	—	5	1	no	—
212	C₃×#103	—	5	1	no	—
213	C₃×#103	C₂×D₅	1	2	yes	complemented
214	C₃×#102	—	5	1	no	—
215	C₃×#102	—	5	1	no	—
216	C₃×#102	—	5	2	no	—
217	C₃×#102	—	5	2	no	—
218	C₃×#102	—	5	2	no	—
219	C₃×#102	—	5	2	no	—
220	C₃×#102	C₂×D₅	1	2	yes	complemented
221	C₂³×D₅	—	2	1	no	—
222	C₂³×D₅	—	2	2	no	—
223	C₅×#41	—	2	2	no	—
224	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
225	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₄×C₅	—	2	1	no	—
229	C₂²×C₄×C₅	—	2	1	no	—
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₂²⋊D₅	—	2	2	no	—
232	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
233	#713	—	2	4	no	—
234	#713	C₂×C₃×C₄	1	8	yes	complemented
235	D₄×D₅	—	2	16	no	—
236	D₄×D₅	—	2	4	no	—
237	D₄×D₅	C₂×C₃×C₄	1	8	yes	complemented
238	#709	—	2	8	no	—
239	#709	C₂×C₃×C₄	1	4	yes	—
240	#709	C₃×D₄	1	4	yes	—
241	C₂×D₂₀	—	2	2	no	—
242	C₂×D₂₀	—	2	1	no	—
243	C₂×D₂₀	—	2	2	no	—
244	C₂×D₂₀	—	2	8	no	—
245	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
246	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
247	C₂×D₂₀	C₂³×C₃	1	2	yes	—
248	C₂×C₄×D₅	—	2	2	no	—
249	C₂×C₄×D₅	—	2	2	no	—
250	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
251	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
252	C₅×M₁₆	—	2	2	no	—
253	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
254	C₅×C₄⋊C₄	—	2	1	no	—
255	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
256	C₂²⋊Dic₅	—	2	1	no	—
257	#685	—	2	2	no	—
258	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
259	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
260	#683	—	2	2	no	—
261	C₄×Dic₅	—	2	1	no	—
262	C₄×Dic₅	—	2	2	no	—
263	C₂×#168	—	2	2	no	—
264	C₂×#168	C₂³×C₃	1	1	yes	characteristic
265	C₂×#168	C₂³×C₃	1	1	yes	characteristic
266	#676	—	2	4	no	—
267	C₈×D₅	—	2	4	no	—
268	C₂×H(5,𝔽₂)	—	5	1	no	—
269	C₂×#131	—	5	1	no	—
270	#520	—	5	1	no	—
271	#418	—	5	1	no	—
272	#418	—	5	2	no	—
273	#417	—	5	2	no	—
274	#417	C₃×D₅	1	1	yes	characteristic, complemented
275	#416	—	5	1	no	—
276	#416	—	5	2	no	—
277	C₂×#102	—	5	1	no	—
278	C₂×#102	—	5	2	no	—
279	C₂²×C₃×C₅	—	2	1	no	—
280	C₂²×C₃×C₅	—	2	1	no	—
281	C₂²×C₃×C₅	—	2	2	no	—
282	C₂²×C₃×C₅	—	4	1	no	—
283	C₂²×C₃×C₅	—	4	1	no	—
284	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₃×D₅	—	2	2	no	—
287	C₂×C₃×D₅	—	2	2	no	—
288	C₂×C₃×D₅	—	2	4	no	—
289	C₂×C₃×D₅	—	4	2	no	—
290	C₂×C₃×D₅	—	4	2	no	—
291	C₂×C₃×D₅	—	8	8	no	—
292	C₂×C₃×D₅	—	8	4	no	—
293	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	4	yes	—
294	C₃×C₄×C₅	—	2	2	no	—
295	C₃×C₄×C₅	—	4	2	no	—
296	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
297	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
298	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
299	C₃×Dic₅	—	4	1	no	—
300	C₃×Dic₅	—	4	1	no	—
301	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
302	C₂⁴×C₃	—	10	2	no	—
303	C₂⁴×C₃	—	10	1	no	—
304	C₃×#41	—	2	2	no	—
305	C₃×#41	—	5	4	no	—
306	C₃×#41	—	5	4	no	—
307	C₃×#41	—	5	8	no	—
308	C₃×#41	—	10	8	no	—
309	C₃×#41	—	10	4	no	—
310	C₃×#41	C₄×D₅	1	4	yes	complemented
311	C₂×C₃×Q₈	—	5	1	no	—
312	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
313	C₂×C₃×D₄	—	2	1	no	—
314	C₂×C₃×D₄	—	5	2	no	—
315	C₂×C₃×D₄	—	5	8	no	—
316	C₂×C₃×D₄	—	5	4	no	—
317	C₂×C₃×D₄	—	5	1	no	—
318	C₂×C₃×D₄	—	5	2	no	—
319	C₂×C₃×D₄	—	10	8	no	—
320	C₂×C₃×D₄	—	10	2	no	—
321	C₂×C₃×D₄	—	10	4	no	—
322	C₂×C₃×D₄	—	10	2	no	—
323	C₂×C₃×D₄	—	10	16	no	—
324	C₂×C₃×D₄	—	10	1	no	—
325	C₂×C₃×D₄	—	10	2	no	—
326	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
327	C₂²×C₃×C₄	—	2	1	no	—
328	C₂²×C₃×C₄	—	2	1	no	—
329	C₂²×C₃×C₄	—	5	2	no	—
330	C₂²×C₃×C₄	—	10	2	no	—
331	C₂²×C₃×C₄	—	10	2	no	—
332	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
333	C₃×M₁₆	—	2	2	no	—
334	C₃×M₁₆	—	10	4	no	—
335	C₂×C₃×C₈	—	5	1	no	—
336	C₂×C₃×C₈	—	5	1	no	—
337	C₂×C₃×C₈	—	10	4	no	—
338	C₂×C₃×C₈	—	10	2	no	—
339	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
340	C₃×C₄⋊C₄	—	2	1	no	—
341	C₃×C₄⋊C₄	—	5	1	no	—
342	C₃×C₄⋊C₄	—	5	1	no	—
343	C₃×C₄⋊C₄	—	10	2	no	—
344	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
345	C₃×C₂²⋊C₄	—	10	2	no	—
346	C₃×C₂²⋊C₄	—	10	1	no	—
347	C₃×C₄²	—	10	2	no	—
348	C₃×C₄²	—	10	1	no	—
349	C₂³×C₅	—	2	1	no	—
350	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂²×D₅	—	2	2	no	—
352	C₂²×D₅	—	2	4	no	—
353	C₂²×D₅	—	2	8	no	—
354	C₂²×D₅	—	8	2	no	—
355	C₂²×D₅	—	8	2	no	—
356	C₂²×D₅	—	8	1	no	—
357	C₂²×D₅	—	8	1	no	—
358	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
359	C₅×Q₈	—	2	1	no	—
360	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
361	C₅×D₄	—	2	4	no	—
362	C₅×D₄	—	2	1	no	—
363	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	4	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	8	1	no	—
368	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
369	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
370	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
371	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
372	C₂²⋊D₅	—	2	8	no	—
373	C₂²⋊D₅	C₃×C₂²⋊C₄	1	8	yes	—
374	C₂×Dic₅	—	2	1	no	—
375	C₂×Dic₅	—	2	1	no	—
376	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
377	D₂₀	—	2	8	no	—
378	D₂₀	—	2	4	no	—
379	D₂₀	—	2	2	no	—
380	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
381	D₂₀	C₂²×C₃×C₄	1	4	yes	—
382	C₄×D₅	—	2	8	no	—
383	C₄×D₅	—	8	2	no	—
384	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
385	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
386	Dic₁₀	C₃×C₂²⋊C₄	1	4	yes	—
387	C₅×C₈	—	2	2	no	—
388	#168	—	2	1	no	—
389	#168	—	2	1	no	—
390	H(5,𝔽₂)	—	5	8	no	—
391	H(5,𝔽₂)	—	10	4	no	—
392	C₂×#41	—	5	1	no	—
393	C₂×#41	—	5	2	no	—
394	C₂×#41	—	10	1	no	—
395	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
396	C₂²×D₄	—	5	2	no	—
397	C₂²×D₄	—	5	1	no	—
398	C₂²×D₄	—	10	1	no	—
399	C₂²×D₄	—	10	2	no	—
400	#131	—	10	4	no	—
401	C₂×M₁₆	—	5	2	no	—
402	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
403	C₂²×C₈	—	5	1	no	—
404	C₂²×C₈	—	5	2	no	—
405	C₄×Q₈	—	10	1	no	—
406	C₄×D₄	—	10	1	no	—
407	C₄×D₄	—	10	2	no	—
408	#117	—	5	1	no	—
409	#117	—	5	2	no	—
410	C₂×C₄⋊C₄	—	5	2	no	—
411	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
412	#103	—	5	1	no	—
413	#103	—	5	1	no	—
414	#103	C₂×C₃×D₅	1	2	yes	complemented
415	#102	—	5	1	no	—
416	#102	—	5	1	no	—
417	#102	—	5	2	no	—
418	#102	—	5	2	no	—
419	#102	—	5	2	no	—
420	#102	—	5	2	no	—
421	#102	C₂×C₃×D₅	1	2	yes	complemented
422	C₂×C₃×C₅	—	2	2	no	—
423	C₂×C₃×C₅	—	4	2	no	—
424	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
425	C₂×C₃×C₅	#576	1	1	yes	characteristic
426	C₂×C₃×C₅	#577	1	1	yes	characteristic
427	C₃×D₅	—	2	4	no	—
428	C₃×D₅	—	4	4	no	—
429	C₂³×C₃	—	2	1	no	—
430	C₂³×C₃	—	5	2	no	—
431	C₂³×C₃	—	10	8	no	—
432	C₂³×C₃	—	10	2	no	—
433	C₂³×C₃	—	10	4	no	—
434	C₂³×C₃	—	40	1	no	—
435	C₂³×C₃	—	40	1	no	—
436	C₂³×C₃	—	40	2	no	—
437	C₂³×C₃	—	40	2	no	—
438	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
439	C₃×Q₈	—	2	1	no	—
440	C₃×Q₈	—	5	4	no	—
441	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
442	C₃×D₄	—	2	4	no	—
443	C₃×D₄	—	2	1	no	—
444	C₃×D₄	—	5	8	no	—
445	C₃×D₄	—	5	4	no	—
446	C₃×D₄	—	5	4	no	—
447	C₃×D₄	—	10	8	no	—
448	C₃×D₄	—	10	8	no	—
449	C₃×D₄	—	10	2	no	—
450	C₃×D₄	—	10	4	no	—
451	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	4	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	5	2	no	—
456	C₂×C₃×C₄	—	5	4	no	—
457	C₂×C₃×C₄	—	5	4	no	—
458	C₂×C₃×C₄	—	8	1	no	—
459	C₂×C₃×C₄	—	10	8	no	—
460	C₂×C₃×C₄	—	10	1	no	—
461	C₂×C₃×C₄	—	10	1	no	—
462	C₂×C₃×C₄	—	40	2	no	—
463	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
464	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
465	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
467	C₃×C₈	—	2	2	no	—
468	C₃×C₈	—	10	1	no	—
469	C₃×C₈	—	10	1	no	—
470	C₂²×C₅	—	2	1	no	—
471	C₂²×C₅	—	2	1	no	—
472	C₂²×C₅	—	2	2	no	—
473	C₂²×C₅	—	4	1	no	—
474	C₂²×C₅	—	4	1	no	—
475	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
476	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
477	C₂×D₅	—	2	2	no	—
478	C₂×D₅	—	2	2	no	—
479	C₂×D₅	—	2	4	no	—
480	C₂×D₅	—	4	2	no	—
481	C₂×D₅	—	4	2	no	—
482	C₂×D₅	—	8	8	no	—
483	C₂×D₅	—	8	4	no	—
484	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
485	C₄×C₅	—	2	2	no	—
486	C₄×C₅	—	4	2	no	—
487	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
488	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
489	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
490	Dic₅	—	4	1	no	—
491	Dic₅	—	4	1	no	—
492	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
493	C₂⁴	—	10	2	no	—
494	C₂⁴	—	10	1	no	—
495	#41	—	2	2	no	—
496	#41	—	5	4	no	—
497	#41	—	5	4	no	—
498	#41	—	5	8	no	—
499	#41	—	10	8	no	—
500	#41	—	10	4	no	—
501	#41	C₃×C₄×D₅	1	4	yes	complemented
502	C₂×Q₈	—	5	1	no	—
503	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	5	2	no	—
506	C₂×D₄	—	5	8	no	—
507	C₂×D₄	—	5	4	no	—
508	C₂×D₄	—	5	1	no	—
509	C₂×D₄	—	5	2	no	—
510	C₂×D₄	—	10	8	no	—
511	C₂×D₄	—	10	2	no	—
512	C₂×D₄	—	10	4	no	—
513	C₂×D₄	—	10	2	no	—
514	C₂×D₄	—	10	16	no	—
515	C₂×D₄	—	10	1	no	—
516	C₂×D₄	—	10	2	no	—
517	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	5	2	no	—
521	C₂²×C₄	—	10	2	no	—
522	C₂²×C₄	—	10	2	no	—
523	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
524	M₁₆	—	2	2	no	—
525	M₁₆	—	10	4	no	—
526	C₂×C₈	—	5	1	no	—
527	C₂×C₈	—	5	1	no	—
528	C₂×C₈	—	10	4	no	—
529	C₂×C₈	—	10	2	no	—
530	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	10	2	no	—
535	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
536	C₂²⋊C₄	—	10	2	no	—
537	C₂²⋊C₄	—	10	1	no	—
538	C₄²	—	10	2	no	—
539	C₄²	—	10	1	no	—
540	C₃×C₅	#2897	1	1	yes	characteristic, complemented, Hall
541	C₂²×C₃	—	2	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	2	no	—
544	C₂²×C₃	—	4	1	no	—
545	C₂²×C₃	—	4	1	no	—
546	C₂²×C₃	—	5	4	no	—
547	C₂²×C₃	—	10	2	no	—
548	C₂²×C₃	—	10	2	no	—
549	C₂²×C₃	—	10	4	no	—
550	C₂²×C₃	—	20	2	no	—
551	C₂²×C₃	—	20	2	no	—
552	C₂²×C₃	—	40	4	no	—
553	C₂²×C₃	—	40	8	no	—
554	C₂²×C₃	D₅×C₂²⋊C₄	1	2	yes	—
555	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
556	C₃×C₄	—	2	2	no	—
557	C₃×C₄	—	4	2	no	—
558	C₃×C₄	—	5	4	no	—
559	C₃×C₄	—	20	1	no	—
560	C₃×C₄	—	20	1	no	—
561	C₃×C₄	D₅×C₂²⋊C₄	1	2	yes	—
562	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
563	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
564	C₂×C₅	—	2	2	no	—
565	C₂×C₅	—	4	2	no	—
566	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×C₅	C₃×#576	1	1	yes	characteristic
568	C₂×C₅	C₃×#577	1	1	yes	characteristic
569	D₅	—	2	4	no	—
570	D₅	—	4	4	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	5	2	no	—
573	C₂³	—	10	8	no	—
574	C₂³	—	10	2	no	—
575	C₂³	—	10	4	no	—
576	C₂³	—	40	1	no	—
577	C₂³	—	40	1	no	—
578	C₂³	—	40	2	no	—
579	C₂³	—	40	2	no	—
580	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
581	Q₈	—	2	1	no	—
582	Q₈	—	5	4	no	—
583	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
584	D₄	—	2	4	no	—
585	D₄	—	2	1	no	—
586	D₄	—	5	8	no	—
587	D₄	—	5	4	no	—
588	D₄	—	5	4	no	—
589	D₄	—	10	8	no	—
590	D₄	—	10	8	no	—
591	D₄	—	10	2	no	—
592	D₄	—	10	4	no	—
593	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	5	2	no	—
598	C₂×C₄	—	5	4	no	—
599	C₂×C₄	—	5	4	no	—
600	C₂×C₄	—	8	1	no	—
601	C₂×C₄	—	10	8	no	—
602	C₂×C₄	—	10	1	no	—
603	C₂×C₄	—	10	1	no	—
604	C₂×C₄	—	40	2	no	—
605	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
606	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
607	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
608	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
609	C₈	—	2	2	no	—
610	C₈	—	10	1	no	—
611	C₈	—	10	1	no	—
612	C₂×C₃	—	2	2	no	—
613	C₂×C₃	—	4	2	no	—
614	C₂×C₃	—	10	4	no	—
615	C₂×C₃	—	20	4	no	—
616	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
617	C₂×C₃	#66108	1	1	yes	characteristic
618	C₂×C₃	#66112	1	1	yes	characteristic
619	C₅	C₃×#2897	1	1	yes	characteristic, complemented, Sylow
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	5	4	no	—
626	C₂²	—	10	2	no	—
627	C₂²	—	10	2	no	—
628	C₂²	—	10	4	no	—
629	C₂²	—	20	2	no	—
630	C₂²	—	20	2	no	—
631	C₂²	—	40	4	no	—
632	C₂²	—	40	8	no	—
633	C₂²	C₃×D₅×C₂²⋊C₄	1	2	yes	—
634	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	5	4	no	—
638	C₄	—	20	1	no	—
639	C₄	—	20	1	no	—
640	C₄	C₃×D₅×C₂²⋊C₄	1	2	yes	—
641	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
642	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
643	C₃	#10610613	1	1	yes	characteristic, direct product factor, Sylow
644	C₂	—	2	2	no	—
645	C₂	—	4	2	no	—
646	C₂	—	10	4	no	—
647	C₂	—	20	4	no	—
648	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
649	C₂	C₃×#66108	1	1	yes	characteristic
650	C₂	C₃×#66112	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4149	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#417	D₅
hypocenter	C₅	C₃×#2897
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#417

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4053	C₂	semidirect
3. C₃×#65838	C₂	semidirect
4. C₃×C₅×#417	C₂	semidirect
5. C₃×#65522	C₂	semidirect
6. C₃×#65420	C₂	semidirect
7. C₂×C₃×#3941	C₂	semidirect
8. C₃×#65093	C₂	semidirect
9. C₃×#65092	C₂	semidirect
10. C₃×#65059	C₂	semidirect
11. C₃×D₅×#102	C₂	semidirect
12. #10610613	C₃	direct (N × H)
15. C₃×#4149	C₄	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₃×#4072	C₂²	semidirect
27. C₂²×C₃×#168	C₂²	semidirect
29. C₂×C₃×#676	C₂²	semidirect
30. C₂×C₃×C₈×D₅	C₂²	semidirect
32. C₃×#4038	C₂²	semidirect
33. C₃×D₅×C₄⋊C₄	C₂²	semidirect
35. C₃×C₅×#103	C₂²	semidirect
36. C₃×C₅×#102	C₂²	semidirect
37. C₃×#3967	C₂²	semidirect
38. C₃×#3967	C₂²	semidirect
39. C₃×#3964	C₂²	semidirect
40. C₃×#3964	C₂²	semidirect
41. C₃×#3953	C₂²	semidirect
42. C₃×#3953	C₂²	semidirect
43. C₃×#3941	C₂²	semidirect
44. C₃×#3941	C₂²	semidirect
47. C₂×#4053	C₂×C₃	semidirect
48. #65838	C₂×C₃	semidirect
49. C₅×#417	C₂×C₃	semidirect
50. #65522	C₂×C₃	semidirect
51. #65420	C₂×C₃	semidirect
52. C₂×#3941	C₂×C₃	semidirect
53. #65093	C₂×C₃	semidirect
54. #65092	C₂×C₃	semidirect
55. #65059	C₂×C₃	semidirect
56. D₅×#102	C₂×C₃	semidirect
60. C₃×C₅×#41	C₂×C₄	semidirect
70. C₃×#713	C₂×C₄	semidirect
73. C₃×D₄×D₅	C₂×C₄	semidirect
81. C₂×C₃×D₂₀	C₂×C₄	semidirect
110. C₃×#417	D₅	semidirect
117. #4149	C₃×C₄	semidirect
125. C₂×C₅×M₁₆	C₂²×C₃	semidirect
126. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
128. #4072	C₂²×C₃	semidirect
129. C₂²×#168	C₂²×C₃	semidirect
131. C₂×#676	C₂²×C₃	semidirect
132. C₂×C₈×D₅	C₂²×C₃	semidirect
134. #4038	C₂²×C₃	semidirect
135. D₅×C₄⋊C₄	C₂²×C₃	semidirect
137. C₅×#103	C₂²×C₃	semidirect
138. C₅×#102	C₂²×C₃	semidirect
139. #3967	C₂²×C₃	semidirect
140. #3967	C₂²×C₃	semidirect
141. #3964	C₂²×C₃	semidirect
142. #3964	C₂²×C₃	semidirect
143. #3953	C₂²×C₃	semidirect
144. #3953	C₂²×C₃	semidirect
145. #3941	C₂²×C₃	semidirect
146. #3941	C₂²×C₃	semidirect
201. C₂×C₃×M₁₆	C₂×D₅	semidirect
210. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
213. C₃×#103	C₂×D₅	semidirect
220. C₃×#102	C₂×D₅	semidirect
224. C₅×#41	C₂×C₃×C₄	semidirect
234. #713	C₂×C₃×C₄	semidirect
237. D₄×D₅	C₂×C₃×C₄	semidirect
245. C₂×D₂₀	C₂×C₃×C₄	semidirect
274. #417	C₃×D₅	semidirect
310. C₃×#41	C₄×D₅	semidirect
402. C₂×M₁₆	C₂×C₃×D₅	semidirect
411. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
414. #103	C₂×C₃×D₅	semidirect
421. #102	C₂×C₃×D₅	semidirect
501. #41	C₃×C₄×D₅	semidirect
540. C₃×C₅	#2897	semidirect
619. C₅	C₃×#2897	semidirect
643. C₃	#10610613	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×#4149	2
C₂×C₃×#4053	2
C₃×#65838	2
C₃×C₅×#417	2
C₃×#65522	2
C₃×#65420	2
C₂×C₃×#3941	2
C₃×#65093	2
C₃×#65092	2
C₃×#65059	2
C₃×D₅×#102	2
#10610613	3
C₃×#2897	5

Subgroups — C3×#10610613 #14412624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610613 #14412624