Subgroups — C₃×#10610425 #14411969

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 484 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	C₃×#65855	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65529	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65295	C₂	1	2	yes	maximal, complemented
6	C₃×D₅×#99	C₂	1	8	yes	maximal, complemented
7	#10610425	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₃×#4149	—	2	4	no	—
10	C₃×#4149	—	2	4	no	—
11	C₂×C₃×#713	C₄	1	2	yes	complemented
12	C₂×C₃×D₄×D₅	C₄	1	2	yes	complemented
13	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
14	C₂×C₃×#709	C₄	1	2	yes	complemented
15	C₂×C₃×#709	C₂²	1	1	yes	characteristic
16	C₂²×C₃×D₂₀	C₄	1	2	yes	complemented
17	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
18	C₃×C₅×#117	C₂²	1	2	yes	complemented
19	C₃×#4072	C₂²	1	2	yes	complemented
20	C₃×#4039	—	2	4	no	—
21	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
22	C₃×C₄×D₂₀	—	2	4	no	—
23	C₃×C₅×#99	C₂²	1	4	yes	complemented
24	C₃×#3966	C₂²	1	4	yes	complemented
25	C₃×#3938	C₂²	1	8	yes	complemented
26	C₃×#2883	—	5	1	no	maximal, Hall
27	C₂×#4149	C₂×C₃	1	1	yes	characteristic
28	#65855	C₂×C₃	1	2	yes	complemented
29	C₅×#410	C₂×C₃	1	1	yes	characteristic, complemented
30	#65529	C₂×C₃	1	1	yes	characteristic, complemented
31	#65295	C₂×C₃	1	2	yes	complemented
32	D₅×#99	C₂×C₃	1	8	yes	complemented
33	C₂³×C₃×D₅	C₂×C₄	1	4	yes	complemented
34	C₂³×C₃×D₅	C₂³	1	2	yes	—
35	C₃×C₅×#41	—	2	2	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
38	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
39	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	complemented
43	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
44	C₃×#713	—	2	8	no	—
45	C₃×D₄×D₅	—	2	16	no	—
46	C₃×D₄×D₅	—	2	8	no	—
47	C₃×#709	—	2	2	no	—
48	C₃×#709	—	2	2	no	—
49	C₃×#709	—	2	4	no	—
50	C₃×#709	—	2	4	no	—
51	C₂×C₃×D₂₀	—	2	4	no	—
52	C₂×C₃×D₂₀	—	2	4	no	—
53	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
54	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
55	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×D₂₀	D₄	1	4	yes	—
58	C₂×C₃×D₂₀	D₄	1	4	yes	—
59	C₂×C₃×C₄×D₅	—	2	8	no	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	complemented
61	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	complemented
62	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
67	C₃×#685	—	2	8	no	—
68	C₃×C₄⋊Dic₅	—	2	2	no	—
69	C₃×C₄×Dic₅	—	2	2	no	—
70	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
71	C₃×#518	—	5	2	no	—
72	C₃×#410	—	5	1	no	—
73	C₃×#410	—	5	2	no	—
74	C₃×#410	D₅	1	1	yes	characteristic, complemented
75	C₂×C₃×#99	—	5	8	no	—
76	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
77	#4149	—	2	4	no	—
78	#4149	—	2	4	no	—
79	C₂×#713	C₃×C₄	1	2	yes	complemented
80	C₂×D₄×D₅	C₃×C₄	1	2	yes	complemented
81	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
82	C₂×#709	C₃×C₄	1	2	yes	complemented
83	C₂×#709	C₂²×C₃	1	1	yes	characteristic
84	C₂²×D₂₀	C₃×C₄	1	2	yes	complemented
85	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
86	C₅×#117	C₂²×C₃	1	2	yes	complemented
87	#4072	C₂²×C₃	1	2	yes	complemented
88	#4039	—	2	4	no	—
89	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
90	C₄×D₂₀	—	2	4	no	—
91	C₅×#99	C₂²×C₃	1	4	yes	complemented
92	#3966	C₂²×C₃	1	4	yes	complemented
93	#3938	C₂²×C₃	1	8	yes	complemented
94	#2883	—	5	1	no	Sylow
95	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	8	no	—
98	C₂²×C₃×D₅	—	8	2	no	—
99	C₂²×C₃×D₅	—	8	4	no	—
100	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
102	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₃×C₂²⋊D₅	—	2	4	no	—
115	C₃×C₂²⋊D₅	—	2	8	no	—
116	C₂×C₃×Dic₅	—	2	4	no	—
117	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
118	C₃×D₂₀	—	2	8	no	—
119	C₃×D₂₀	—	2	1	no	—
120	C₃×D₂₀	—	2	1	no	—
121	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
122	C₃×D₂₀	C₂²⋊C₄	1	4	yes	—
123	C₃×D₂₀	C₂²⋊C₄	1	8	yes	—
124	C₃×C₄×D₅	—	2	8	no	—
125	C₃×C₄×D₅	—	2	4	no	—
126	C₃×C₄×D₅	—	8	8	no	—
127	C₃×Dic₁₀	—	2	1	no	—
128	C₃×Dic₁₀	—	2	1	no	—
129	C₃×H(5,𝔽₂)	—	10	4	no	—
130	C₃×H(5,𝔽₂)	—	10	4	no	—
131	C₂×C₃×#41	—	5	2	no	—
132	C₂×C₃×#41	—	5	2	no	—
133	C₂×C₃×#41	—	5	1	no	—
134	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
135	C₂²×C₃×D₄	—	5	2	no	—
136	C₂²×C₃×D₄	—	5	4	no	—
137	C₂²×C₃×D₄	—	5	2	no	—
138	C₂²×C₃×D₄	—	5	1	no	—
139	C₃×C₄×D₄	—	10	4	no	—
140	C₃×C₄×D₄	—	10	4	no	—
141	C₃×#117	—	5	2	no	—
142	C₃×#117	C₂×D₅	1	2	yes	complemented
143	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
144	C₃×#99	—	5	4	no	—
145	C₃×#99	—	5	8	no	—
146	C₃×#99	C₂×D₅	1	4	yes	complemented
147	C₂³×D₅	C₂×C₃×C₄	1	4	yes	complemented
148	C₂³×D₅	C₂³×C₃	1	2	yes	—
149	C₅×#41	—	2	2	no	—
150	C₅×#41	—	2	2	no	—
151	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
152	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
153	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	complemented
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	complemented
157	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
158	#713	—	2	8	no	—
159	D₄×D₅	—	2	16	no	—
160	D₄×D₅	—	2	8	no	—
161	#709	—	2	2	no	—
162	#709	—	2	2	no	—
163	#709	—	2	4	no	—
164	#709	—	2	4	no	—
165	C₂×D₂₀	—	2	4	no	—
166	C₂×D₂₀	—	2	4	no	—
167	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
168	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
169	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
170	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
171	C₂×D₂₀	C₃×D₄	1	4	yes	—
172	C₂×D₂₀	C₃×D₄	1	4	yes	—
173	C₂×C₄×D₅	—	2	8	no	—
174	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	complemented
175	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	complemented
176	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic, complemented
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
179	C₄²×C₅	—	2	2	no	—
180	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
181	#685	—	2	8	no	—
182	C₄⋊Dic₅	—	2	2	no	—
183	C₄×Dic₅	—	2	2	no	—
184	C₂×H(5,𝔽₂)	—	5	1	no	—
185	#518	—	5	2	no	—
186	#410	—	5	1	no	—
187	#410	—	5	2	no	—
188	#410	C₃×D₅	1	1	yes	characteristic, complemented
189	C₂×#99	—	5	8	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	—	4	1	no	—
192	C₂²×C₃×C₅	—	4	2	no	—
193	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
195	C₂×C₃×D₅	—	2	2	no	—
196	C₂×C₃×D₅	—	4	8	no	—
197	C₂×C₃×D₅	—	4	4	no	—
198	C₂×C₃×D₅	—	4	2	no	—
199	C₂×C₃×D₅	—	8	8	no	—
200	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	8	yes	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	4	4	no	—
203	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
206	C₃×Dic₅	—	2	2	no	—
207	C₃×Dic₅	—	4	4	no	—
208	C₂⁴×C₃	—	5	2	no	—
209	C₂⁴×C₃	—	5	4	no	—
210	C₃×#41	—	2	2	no	—
211	C₃×#41	—	2	2	no	—
212	C₃×#41	—	10	4	no	—
213	C₃×#41	—	10	4	no	—
214	C₃×#41	—	10	8	no	—
215	C₃×#41	—	10	2	no	—
216	C₃×#41	—	10	2	no	—
217	C₂×C₃×Q₈	—	5	1	no	—
218	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic, complemented
219	C₂×C₃×D₄	—	5	4	no	—
220	C₂×C₃×D₄	—	5	2	no	—
221	C₂×C₃×D₄	—	5	2	no	—
222	C₂×C₃×D₄	—	5	2	no	—
223	C₂×C₃×D₄	—	5	4	no	—
224	C₂×C₃×D₄	—	5	1	no	—
225	C₂×C₃×D₄	—	5	4	no	—
226	C₂×C₃×D₄	—	5	4	no	—
227	C₂×C₃×D₄	—	10	4	no	—
228	C₂×C₃×D₄	—	10	4	no	—
229	C₂×C₃×D₄	—	10	8	no	—
230	C₂×C₃×D₄	—	10	16	no	—
231	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic, complemented
232	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
233	C₂²×C₃×C₄	—	5	4	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	10	8	no	—
236	C₂²×C₃×C₄	C₄×D₅	1	2	yes	complemented
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₃×C₄⋊C₄	—	2	2	no	—
239	C₃×C₄⋊C₄	—	10	2	no	—
240	C₃×C₂²⋊C₄	—	5	4	no	—
241	C₃×C₂²⋊C₄	—	10	8	no	—
242	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
243	C₃×C₄²	—	2	2	no	—
244	C₃×C₄²	—	10	2	no	—
245	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
247	C₂²×D₅	—	2	8	no	—
248	C₂²×D₅	—	8	2	no	—
249	C₂²×D₅	—	8	4	no	—
250	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
251	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
252	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
253	C₅×Q₈	—	2	2	no	—
254	C₅×D₄	—	2	4	no	—
255	C₅×D₄	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
263	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
264	C₂²⋊D₅	—	2	4	no	—
265	C₂²⋊D₅	—	2	8	no	—
266	C₂×Dic₅	—	2	4	no	—
267	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
268	D₂₀	—	2	8	no	—
269	D₂₀	—	2	1	no	—
270	D₂₀	—	2	1	no	—
271	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
272	D₂₀	C₃×C₂²⋊C₄	1	4	yes	—
273	D₂₀	C₃×C₂²⋊C₄	1	8	yes	—
274	C₄×D₅	—	2	8	no	—
275	C₄×D₅	—	2	4	no	—
276	C₄×D₅	—	8	8	no	—
277	Dic₁₀	—	2	1	no	—
278	Dic₁₀	—	2	1	no	—
279	H(5,𝔽₂)	—	10	4	no	—
280	H(5,𝔽₂)	—	10	4	no	—
281	C₂×#41	—	5	2	no	—
282	C₂×#41	—	5	2	no	—
283	C₂×#41	—	5	1	no	—
284	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
285	C₂²×D₄	—	5	2	no	—
286	C₂²×D₄	—	5	4	no	—
287	C₂²×D₄	—	5	2	no	—
288	C₂²×D₄	—	5	1	no	—
289	C₄×D₄	—	10	4	no	—
290	C₄×D₄	—	10	4	no	—
291	#117	—	5	2	no	—
292	#117	C₂×C₃×D₅	1	2	yes	complemented
293	C₂×C₂²⋊C₄	—	5	8	no	—
294	#99	—	5	4	no	—
295	#99	—	5	8	no	—
296	#99	C₂×C₃×D₅	1	4	yes	complemented
297	C₂×C₃×C₅	—	2	2	no	—
298	C₂×C₃×C₅	—	2	1	no	—
299	C₂×C₃×C₅	—	4	2	no	—
300	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₃×D₅	—	2	8	no	—
302	C₃×D₅	—	4	2	no	—
303	C₂³×C₃	—	5	4	no	—
304	C₂³×C₃	—	5	8	no	—
305	C₂³×C₃	—	5	2	no	—
306	C₂³×C₃	—	10	8	no	—
307	C₂³×C₃	—	40	2	no	—
308	C₂³×C₃	—	40	4	no	—
309	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
310	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	10	1	no	—
313	C₃×Q₈	—	10	1	no	—
314	C₃×D₄	—	2	4	no	—
315	C₃×D₄	—	2	2	no	—
316	C₃×D₄	—	5	4	no	—
317	C₃×D₄	—	5	4	no	—
318	C₃×D₄	—	5	8	no	—
319	C₃×D₄	—	10	8	no	—
320	C₃×D₄	—	10	8	no	—
321	C₃×D₄	—	10	4	no	—
322	C₃×D₄	—	10	1	no	—
323	C₃×D₄	—	10	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	5	2	no	—
328	C₂×C₃×C₄	—	10	8	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	—	10	4	no	—
331	C₂×C₃×C₄	—	40	8	no	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
333	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
335	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
336	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	4	1	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
342	C₂×D₅	—	2	2	no	—
343	C₂×D₅	—	4	8	no	—
344	C₂×D₅	—	4	4	no	—
345	C₂×D₅	—	4	2	no	—
346	C₂×D₅	—	8	8	no	—
347	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	8	yes	—
348	C₄×C₅	—	2	2	no	—
349	C₄×C₅	—	4	4	no	—
350	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
352	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
353	Dic₅	—	2	2	no	—
354	Dic₅	—	4	4	no	—
355	C₂⁴	—	5	2	no	—
356	C₂⁴	—	5	4	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	10	4	no	—
360	#41	—	10	4	no	—
361	#41	—	10	8	no	—
362	#41	—	10	2	no	—
363	#41	—	10	2	no	—
364	C₂×Q₈	—	5	1	no	—
365	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic, complemented
366	C₂×D₄	—	5	4	no	—
367	C₂×D₄	—	5	2	no	—
368	C₂×D₄	—	5	2	no	—
369	C₂×D₄	—	5	2	no	—
370	C₂×D₄	—	5	4	no	—
371	C₂×D₄	—	5	1	no	—
372	C₂×D₄	—	5	4	no	—
373	C₂×D₄	—	5	4	no	—
374	C₂×D₄	—	10	4	no	—
375	C₂×D₄	—	10	4	no	—
376	C₂×D₄	—	10	8	no	—
377	C₂×D₄	—	10	16	no	—
378	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic, complemented
379	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
380	C₂²×C₄	—	5	4	no	—
381	C₂²×C₄	—	5	2	no	—
382	C₂²×C₄	—	10	8	no	—
383	C₂²×C₄	C₃×C₄×D₅	1	2	yes	complemented
384	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	10	2	no	—
387	C₂²⋊C₄	—	5	4	no	—
388	C₂²⋊C₄	—	10	8	no	—
389	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
390	C₄²	—	2	2	no	—
391	C₄²	—	10	2	no	—
392	C₃×C₅	#2883	1	1	yes	characteristic, complemented, Hall
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	4	1	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	—	5	8	no	—
397	C₂²×C₃	—	10	2	no	—
398	C₂²×C₃	—	20	8	no	—
399	C₂²×C₃	—	20	4	no	—
400	C₂²×C₃	—	20	2	no	—
401	C₂²×C₃	—	40	8	no	—
402	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
403	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	4	4	no	—
406	C₃×C₄	—	10	2	no	—
407	C₃×C₄	—	20	4	no	—
408	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
409	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
410	C₃×C₄	D₅×C₂²⋊C₄	1	2	yes	—
411	C₂×C₅	—	2	2	no	—
412	C₂×C₅	—	2	1	no	—
413	C₂×C₅	—	4	2	no	—
414	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
415	D₅	—	2	8	no	—
416	D₅	—	4	2	no	—
417	C₂³	—	5	4	no	—
418	C₂³	—	5	8	no	—
419	C₂³	—	5	2	no	—
420	C₂³	—	10	8	no	—
421	C₂³	—	40	2	no	—
422	C₂³	—	40	4	no	—
423	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
424	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
425	Q₈	—	2	2	no	—
426	Q₈	—	10	1	no	—
427	Q₈	—	10	1	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	2	no	—
430	D₄	—	5	4	no	—
431	D₄	—	5	4	no	—
432	D₄	—	5	8	no	—
433	D₄	—	10	8	no	—
434	D₄	—	10	8	no	—
435	D₄	—	10	4	no	—
436	D₄	—	10	1	no	—
437	D₄	—	10	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	5	2	no	—
442	C₂×C₄	—	10	8	no	—
443	C₂×C₄	—	10	4	no	—
444	C₂×C₄	—	10	4	no	—
445	C₂×C₄	—	40	8	no	—
446	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
447	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
448	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
449	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
450	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
451	C₂×C₃	—	2	2	no	—
452	C₂×C₃	—	2	1	no	—
453	C₂×C₃	—	4	2	no	—
454	C₂×C₃	—	10	8	no	—
455	C₂×C₃	—	20	2	no	—
456	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
457	C₅	C₃×#2883	1	1	yes	characteristic, complemented, Sylow
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	5	8	no	—
462	C₂²	—	10	2	no	—
463	C₂²	—	20	8	no	—
464	C₂²	—	20	4	no	—
465	C₂²	—	20	2	no	—
466	C₂²	—	40	8	no	—
467	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
468	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
469	C₄	—	2	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	10	2	no	—
472	C₄	—	20	4	no	—
473	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
475	C₄	C₃×D₅×C₂²⋊C₄	1	2	yes	—
476	C₃	#10610425	1	1	yes	characteristic, direct product factor, Sylow
477	C₂	—	2	2	no	—
478	C₂	—	2	1	no	—
479	C₂	—	4	2	no	—
480	C₂	—	10	8	no	—
481	C₂	—	20	2	no	—
482	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₅×C₂²⋊C₄
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#410	C₂
socle	C₂×C₃×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₃×#4149	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#410	D₅
hypocenter	C₅	C₃×#2883
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#410

Complements

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

N	H ≅ G/N	type
2. C₃×#65855	C₂	semidirect
3. C₃×C₅×#410	C₂	semidirect
4. C₃×#65529	C₂	semidirect
5. C₃×#65295	C₂	semidirect
6. C₃×D₅×#99	C₂	semidirect
7. #10610425	C₃	direct (N × H)
11. C₂×C₃×#713	C₄	semidirect
12. C₂×C₃×D₄×D₅	C₄	semidirect
14. C₂×C₃×#709	C₄	semidirect
16. C₂²×C₃×D₂₀	C₄	semidirect
18. C₃×C₅×#117	C₂²	semidirect
19. C₃×#4072	C₂²	semidirect
21. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
23. C₃×C₅×#99	C₂²	semidirect
24. C₃×#3966	C₂²	semidirect
25. C₃×#3938	C₂²	semidirect
28. #65855	C₂×C₃	semidirect
29. C₅×#410	C₂×C₃	semidirect
30. #65529	C₂×C₃	semidirect
31. #65295	C₂×C₃	semidirect
32. D₅×#99	C₂×C₃	semidirect
33. C₂³×C₃×D₅	C₂×C₄	semidirect
37. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
38. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
40. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
42. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
55. C₂×C₃×D₂₀	C₂×C₄	semidirect
56. C₂×C₃×D₂₀	C₂×C₄	semidirect
60. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
61. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
62. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
74. C₃×#410	D₅	semidirect
79. C₂×#713	C₃×C₄	semidirect
80. C₂×D₄×D₅	C₃×C₄	semidirect
82. C₂×#709	C₃×C₄	semidirect
84. C₂²×D₂₀	C₃×C₄	semidirect
86. C₅×#117	C₂²×C₃	semidirect
87. #4072	C₂²×C₃	semidirect
89. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
91. C₅×#99	C₂²×C₃	semidirect
92. #3966	C₂²×C₃	semidirect
93. #3938	C₂²×C₃	semidirect
142. C₃×#117	C₂×D₅	semidirect
146. C₃×#99	C₂×D₅	semidirect
147. C₂³×D₅	C₂×C₃×C₄	semidirect
151. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
152. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
154. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
156. C₂×C₂²⋊D₅	C₂×C₃×C₄	semidirect
169. C₂×D₂₀	C₂×C₃×C₄	semidirect
170. C₂×D₂₀	C₂×C₃×C₄	semidirect
174. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
175. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
176. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
188. #410	C₃×D₅	semidirect
218. C₂×C₃×Q₈	C₄×D₅	semidirect
231. C₂×C₃×D₄	C₄×D₅	semidirect
236. C₂²×C₃×C₄	C₄×D₅	semidirect
292. #117	C₂×C₃×D₅	semidirect
296. #99	C₂×C₃×D₅	semidirect
365. C₂×Q₈	C₃×C₄×D₅	semidirect
378. C₂×D₄	C₃×C₄×D₅	semidirect
383. C₂²×C₄	C₃×C₄×D₅	semidirect
392. C₃×C₅	#2883	semidirect
457. C₅	C₃×#2883	semidirect
476. C₃	#10610425	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
C₃×#65855	2
C₃×C₅×#410	2
C₃×#65529	2
C₃×#65295	2
C₃×D₅×#99	2
#10610425	3
C₃×#2883	5

Subgroups — C3×#10610425 #14411969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610425 #14411969