Subgroups — C₃×#10614238 #14430226

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65522	C₂	1	2	yes	maximal
4	C₃×#65311	C₂	1	2	yes	maximal, complemented
5	C₃×#65310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65298	C₂	1	2	yes	maximal, complemented
8	C₃×#65297	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65287	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#10614238	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	—	2	1	no	—
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄²×C₅	—	2	1	no	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×#4072	C₂²	1	2	yes	—
25	C₃×#4070	—	2	1	no	—
26	C₃×#4070	—	2	1	no	—
27	C₂²×C₃×#168	C₂²	1	2	yes	—
28	C₃×#4016	C₂²	1	2	yes	—
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×#4015	C₂²	1	1	yes	characteristic
31	C₃×C₄×Dic₁₀	—	2	1	no	—
32	C₃×C₄×Dic₁₀	—	2	1	no	—
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	2	yes	—
35	C₃×#3964	C₂²	1	2	yes	—
36	C₃×#3964	C₂²	1	2	yes	—
37	C₃×#3940	C₂²	1	2	yes	—
38	C₃×#3940	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×#3939	C₂²	1	2	yes	—
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
43	C₃×C₄⋊#168	C₂²	1	2	yes	—
44	C₃×#3076	—	5	1	no	maximal, Hall
45	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
46	#65804	C₂×C₃	1	1	yes	characteristic, complemented
47	#65522	C₂×C₃	1	2	yes	—
48	#65311	C₂×C₃	1	2	yes	complemented
49	#65310	C₂×C₃	1	1	yes	characteristic, complemented
50	#65309	C₂×C₃	1	1	yes	characteristic, complemented
51	#65298	C₂×C₃	1	2	yes	complemented
52	#65297	C₂×C₃	1	1	yes	characteristic, complemented
53	#65296	C₂×C₃	1	1	yes	characteristic, complemented
54	#65287	C₂×C₃	1	2	yes	complemented
55	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	—	2	1	no	—
68	C₂×C₃×Dic₁₀	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	—	2	1	no	—
78	C₃×C₄²×C₅	—	2	1	no	—
79	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₂²⋊Dic₅	—	2	2	no	—
84	C₃×C₄⋊Dic₅	—	2	1	no	—
85	C₃×C₄⋊Dic₅	—	2	1	no	—
86	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
87	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
88	C₃×#683	—	2	2	no	—
89	C₃×#683	—	2	2	no	—
90	C₃×C₄×Dic₅	—	2	2	no	—
91	C₂×C₃×#168	—	2	4	no	—
92	C₂×C₃×#168	C₂³	1	2	yes	—
93	C₂×C₃×#168	C₂³	1	2	yes	—
94	C₃×#533	—	5	1	no	—
95	C₃×C₄×#41	D₅	1	1	yes	characteristic
96	C₃×#479	—	5	2	no	—
97	C₃×#478	—	5	2	no	—
98	C₃×#477	—	5	1	no	—
99	C₃×#476	—	5	1	no	—
100	C₃×#475	—	5	1	no	—
101	C₃×#474	—	5	1	no	—
102	C₃×#427	—	5	2	no	—
103	C₂×C₃×C₄⋊C₈	—	5	1	no	—
104	C₃×#416	—	5	2	no	—
105	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₄×C₅×D₄	—	2	1	no	—
109	C₄×C₅×D₄	—	2	1	no	—
110	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
111	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₅×#117	—	2	1	no	—
113	C₅×#117	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄²×C₅	—	2	1	no	—
115	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
116	#4072	C₂²×C₃	1	2	yes	—
117	#4070	—	2	1	no	—
118	#4070	—	2	1	no	—
119	C₂²×#168	C₂²×C₃	1	2	yes	—
120	#4016	C₂²×C₃	1	2	yes	—
121	#4015	C₂²×C₃	1	1	yes	characteristic
122	#4015	C₂²×C₃	1	1	yes	characteristic
123	C₄×Dic₁₀	—	2	1	no	—
124	C₄×Dic₁₀	—	2	1	no	—
125	#3967	C₂²×C₃	1	2	yes	—
126	#3967	C₂²×C₃	1	2	yes	—
127	#3964	C₂²×C₃	1	2	yes	—
128	#3964	C₂²×C₃	1	2	yes	—
129	#3940	C₂²×C₃	1	2	yes	—
130	#3940	C₂²×C₃	1	2	yes	—
131	#3939	C₂²×C₃	1	2	yes	—
132	#3939	C₂²×C₃	1	2	yes	—
133	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
134	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
135	C₄⋊#168	C₂²×C₃	1	2	yes	—
136	#3076	—	5	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
141	C₃×C₅×D₄	—	2	4	no	—
142	C₃×C₅×D₄	—	2	1	no	—
143	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	4	1	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	—	4	2	no	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
158	C₂×C₃×C₄×C₅	#41	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₂×C₃×Dic₅	—	2	2	no	—
161	C₂×C₃×Dic₅	—	2	2	no	—
162	C₃×Dic₁₀	—	4	2	no	—
163	C₃×Dic₁₀	—	4	2	no	—
164	C₃×#168	—	2	2	no	—
165	C₃×#168	—	2	2	no	—
166	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
167	C₂²×C₃×C₈	—	5	2	no	—
168	C₃×C₄⋊Q₈	—	5	1	no	—
169	C₃×C₄⋊Q₈	—	5	1	no	—
170	C₃×#125	—	5	2	no	—
171	C₃×C₂²⋊Q₈	—	10	1	no	—
172	C₃×C₂²⋊Q₈	—	10	1	no	—
173	C₃×C₄×Q₈	—	10	1	no	—
174	C₃×C₄×Q₈	—	10	1	no	—
175	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
176	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
177	C₃×C₄×D₄	—	2	1	no	—
178	C₃×C₄×D₄	—	2	1	no	—
179	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
180	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
181	C₃×#117	—	2	1	no	—
182	C₃×#117	—	5	2	no	—
183	C₃×#117	C₂×D₅	1	1	yes	characteristic
184	C₂×C₃×C₄²	—	2	1	no	—
185	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
186	C₃×#107	—	5	2	no	—
187	C₃×#107	—	5	2	no	—
188	C₃×#106	—	5	2	no	—
189	C₃×#106	—	5	2	no	—
190	C₃×C₄⋊C₈	—	5	1	no	—
191	C₃×C₄⋊C₈	—	5	1	no	—
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×#103	—	5	2	no	—
194	C₃×#103	—	5	2	no	—
195	C₃×#102	—	5	2	no	—
196	C₃×#102	—	5	2	no	—
197	C₅×#41	—	2	2	no	—
198	C₅×#41	C₃×Q₈	1	4	yes	complemented
199	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₁₀	—	2	1	no	—
209	C₂×Dic₁₀	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
221	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
222	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
223	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂²⋊Dic₅	—	2	2	no	—
225	C₄⋊Dic₅	—	2	1	no	—
226	C₄⋊Dic₅	—	2	1	no	—
227	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
228	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
229	#683	—	2	2	no	—
230	#683	—	2	2	no	—
231	C₄×Dic₅	—	2	2	no	—
232	C₂×#168	—	2	4	no	—
233	C₂×#168	C₂³×C₃	1	2	yes	—
234	C₂×#168	C₂³×C₃	1	2	yes	—
235	#533	—	5	1	no	—
236	C₄×#41	C₃×D₅	1	1	yes	characteristic
237	#479	—	5	2	no	—
238	#478	—	5	2	no	—
239	#477	—	5	1	no	—
240	#476	—	5	1	no	—
241	#475	—	5	1	no	—
242	#474	—	5	1	no	—
243	#427	—	5	2	no	—
244	C₂×C₄⋊C₈	—	5	1	no	—
245	#416	—	5	2	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	—	4	1	no	—
258	C₃×C₄×C₅	—	4	1	no	—
259	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
260	C₃×C₄×C₅	#135	1	2	yes	—
261	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
262	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
263	C₃×Dic₅	—	4	2	no	—
264	C₃×Dic₅	—	4	2	no	—
265	C₃×#41	—	2	2	no	—
266	C₃×#41	Dic₁₀	1	4	yes	complemented
267	C₂×C₃×Q₈	—	10	1	no	—
268	C₂×C₃×Q₈	—	10	1	no	—
269	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	—	2	1	no	—
275	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
278	C₂×C₃×C₈	—	5	2	no	—
279	C₂×C₃×C₈	—	5	2	no	—
280	C₂×C₃×C₈	—	10	4	no	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	5	2	no	—
284	C₃×C₄⋊C₄	—	5	2	no	—
285	C₃×C₄⋊C₄	—	10	2	no	—
286	C₃×C₄⋊C₄	—	10	2	no	—
287	C₃×C₄⋊C₄	—	10	1	no	—
288	C₃×C₄⋊C₄	—	10	1	no	—
289	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
290	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₂²⋊C₄	—	2	1	no	—
294	C₃×C₂²⋊C₄	—	10	2	no	—
295	C₃×C₄²	—	2	1	no	—
296	C₃×C₄²	—	2	1	no	—
297	C₃×C₄²	—	2	1	no	—
298	C₃×C₄²	—	10	2	no	—
299	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
300	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
301	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
302	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	—
307	C₅×D₄	—	2	4	no	—
308	C₅×D₄	—	2	1	no	—
309	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	4	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	2	no	—
317	C₂×C₄×C₅	—	4	2	no	—
318	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
324	C₂×C₄×C₅	C₃×#41	1	2	yes	—
325	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
326	C₂×Dic₅	—	2	2	no	—
327	C₂×Dic₅	—	2	2	no	—
328	Dic₁₀	—	4	2	no	—
329	Dic₁₀	—	4	2	no	—
330	#168	—	2	2	no	—
331	#168	—	2	2	no	—
332	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
333	C₂²×C₈	—	5	2	no	—
334	C₄⋊Q₈	—	5	1	no	—
335	C₄⋊Q₈	—	5	1	no	—
336	#125	—	5	2	no	—
337	C₂²⋊Q₈	—	10	1	no	—
338	C₂²⋊Q₈	—	10	1	no	—
339	C₄×Q₈	—	10	1	no	—
340	C₄×Q₈	—	10	1	no	—
341	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
342	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
346	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	—	5	2	no	—
349	#117	C₂×C₃×D₅	1	1	yes	characteristic
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
352	#107	—	5	2	no	—
353	#107	—	5	2	no	—
354	#106	—	5	2	no	—
355	#106	—	5	2	no	—
356	C₄⋊C₈	—	5	1	no	—
357	C₄⋊C₈	—	5	1	no	—
358	C₄⋊C₈	—	5	2	no	—
359	#103	—	5	2	no	—
360	#103	—	5	2	no	—
361	#102	—	5	2	no	—
362	#102	—	5	2	no	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	—	4	2	no	—
365	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
367	C₂×C₃×C₅	#575	1	1	yes	characteristic
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	—	20	2	no	—
372	C₃×Q₈	—	20	2	no	—
373	C₃×Q₈	C₂×Dic₁₀	1	2	yes	—
374	C₃×D₄	—	2	4	no	—
375	C₃×D₄	—	2	1	no	—
376	C₃×D₄	C₂×Dic₁₀	1	2	yes	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	—	4	2	no	—
384	C₂×C₃×C₄	—	4	2	no	—
385	C₂×C₃×C₄	—	10	2	no	—
386	C₂×C₃×C₄	—	10	2	no	—
387	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
388	C₂×C₃×C₄	#709	1	2	yes	—
389	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
395	C₃×C₈	—	10	2	no	—
396	C₃×C₈	—	10	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
403	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
411	C₄×C₅	C₃×#135	1	2	yes	—
412	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
413	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
414	Dic₅	—	4	2	no	—
415	Dic₅	—	4	2	no	—
416	#41	—	2	2	no	—
417	#41	C₃×Dic₁₀	1	4	yes	complemented
418	C₂×Q₈	—	10	1	no	—
419	C₂×Q₈	—	10	1	no	—
420	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
427	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
428	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₂×C₈	—	5	2	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	—	10	4	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	5	2	no	—
435	C₄⋊C₄	—	5	2	no	—
436	C₄⋊C₄	—	10	2	no	—
437	C₄⋊C₄	—	10	2	no	—
438	C₄⋊C₄	—	10	1	no	—
439	C₄⋊C₄	—	10	1	no	—
440	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	10	2	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	10	2	no	—
450	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
451	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
452	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
453	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	1	no	—
460	C₂²×C₃	#4070	1	2	yes	—
461	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
462	C₃×C₄	—	2	2	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	—	20	2	no	—
469	C₃×C₄	—	20	2	no	—
470	C₃×C₄	#4070	1	2	yes	—
471	C₃×C₄	#4096	1	2	yes	—
472	C₃×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
473	C₃×C₄	C₂×#709	1	1	yes	characteristic
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
477	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
478	C₂×C₅	C₃×#575	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
481	Q₈	—	2	1	no	—
482	Q₈	—	20	2	no	—
483	Q₈	—	20	2	no	—
484	Q₈	C₂×C₃×Dic₁₀	1	2	yes	—
485	D₄	—	2	4	no	—
486	D₄	—	2	1	no	—
487	D₄	C₂×C₃×Dic₁₀	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	10	2	no	—
497	C₂×C₄	—	10	2	no	—
498	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
499	C₂×C₄	C₃×#709	1	2	yes	—
500	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
501	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
502	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
503	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
504	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
505	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
506	C₈	—	10	2	no	—
507	C₈	—	10	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	4	2	no	—
510	C₂×C₃	C₂×#4070	1	1	yes	characteristic
511	C₂×C₃	C₂×#4096	1	1	yes	characteristic
512	C₂×C₃	#66156	1	1	yes	characteristic
513	C₅	C₃×#3076	1	1	yes	characteristic, complemented, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	C₃×#4070	1	2	yes	—
520	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	20	2	no	—
528	C₄	—	20	2	no	—
529	C₄	C₃×#4070	1	2	yes	—
530	C₄	C₃×#4096	1	2	yes	—
531	C₄	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
532	C₄	C₂×C₃×#709	1	1	yes	characteristic
533	C₃	#10614238	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	C₂×C₃×#4070	1	1	yes	characteristic
537	C₂	C₂×C₃×#4096	1	1	yes	characteristic
538	C₂	C₃×#66156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×#3076
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#65804	C₂	semidirect
4. C₃×#65311	C₂	semidirect
5. C₃×#65310	C₂	semidirect
6. C₃×#65309	C₂	semidirect
7. C₃×#65298	C₂	semidirect
8. C₃×#65297	C₂	semidirect
9. C₃×#65296	C₂	semidirect
10. C₃×#65287	C₂	semidirect
11. C₂×C₃×C₄⋊#168	C₂	semidirect
12. #10614238	C₃	direct (N × H)
46. #65804	C₂×C₃	semidirect
48. #65311	C₂×C₃	semidirect
49. #65310	C₂×C₃	semidirect
50. #65309	C₂×C₃	semidirect
51. #65298	C₂×C₃	semidirect
52. #65297	C₂×C₃	semidirect
53. #65296	C₂×C₃	semidirect
54. #65287	C₂×C₃	semidirect
55. C₂×C₄⋊#168	C₂×C₃	semidirect
57. C₃×C₅×#41	Q₈	semidirect
198. C₅×#41	C₃×Q₈	semidirect
266. C₃×#41	Dic₁₀	semidirect
417. #41	C₃×Dic₁₀	semidirect
454. C₃×C₅	#3076	semidirect
513. C₅	C₃×#3076	semidirect
533. C₃	#10614238	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₃×#65804	2
C₃×#65522	2
C₃×#65311	2
C₃×#65310	2
C₃×#65309	2
C₃×#65298	2
C₃×#65297	2
C₃×#65296	2
C₃×#65287	2
C₂×C₃×C₄⋊#168	2
#10614238	3
C₃×#3076	5

Subgroups — C3×#10614238 #14430226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614238 #14430226