Subgroups — C₃×#10615631 #14426215

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#41×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65471	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65455	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65454	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65439	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65402	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
16	#10615631	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×#709	C₂²	1	1	yes	characteristic
20	C₃×C₅×#135	—	2	4	no	—
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#4096	—	2	4	no	—
27	C₃×#4093	C₂²	1	1	yes	characteristic
28	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
29	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
30	C₃×#4090	C₂²	1	1	yes	characteristic
31	C₂×C₃×#689	C₂²	1	1	yes	characteristic
32	C₂×C₃×#688	C₂²	1	1	yes	characteristic
33	C₃×#4086	C₂²	1	1	yes	characteristic
34	C₃×#4085	—	2	1	no	—
35	C₃×#4085	—	2	1	no	—
36	C₃×#4082	C₂²	1	1	yes	characteristic
37	C₃×D₄×Dic₅	—	2	1	no	—
38	C₃×D₄×Dic₅	—	2	1	no	—
39	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
41	C₂×C₃×#687	C₂²	1	1	yes	characteristic
42	C₂×C₃×#686	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
44	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
45	C₃×#4072	—	2	1	no	—
46	C₃×#4072	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×Dic₅	—	2	1	no	—
48	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
49	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
50	C₃×#3967	C₂²	1	1	yes	characteristic
51	C₃×#3967	C₂²	1	1	yes	characteristic
52	C₃×#3964	C₂²	1	1	yes	characteristic
53	C₃×#3964	C₂²	1	1	yes	characteristic
54	C₃×#3953	C₂²	1	1	yes	characteristic
55	C₃×#3953	C₂²	1	1	yes	characteristic
56	C₃×#3948	C₂²	1	1	yes	characteristic
57	C₃×#3948	C₂²	1	1	yes	characteristic
58	C₃×#3946	C₂²	1	1	yes	characteristic
59	C₃×#3946	C₂²	1	1	yes	characteristic
60	C₃×#3946	C₂²	1	1	yes	characteristic
61	C₃×#3946	C₂²	1	1	yes	characteristic
62	C₃×#3035	—	5	1	no	maximal, Hall
63	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
64	#66166	C₂×C₃	1	1	yes	characteristic, complemented
65	#41×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×#4096	C₂×C₃	1	1	yes	characteristic, complemented
67	#65522	C₂×C₃	1	1	yes	characteristic, complemented
68	#65474	C₂×C₃	1	1	yes	characteristic, complemented
69	#65471	C₂×C₃	1	1	yes	characteristic, complemented
70	#65455	C₂×C₃	1	1	yes	characteristic, complemented
71	#65454	C₂×C₃	1	1	yes	characteristic, complemented
72	#65452	C₂×C₃	1	1	yes	characteristic, complemented
73	#65451	C₂×C₃	1	1	yes	characteristic, complemented
74	#65442	C₂×C₃	1	1	yes	characteristic, complemented
75	#65439	C₂×C₃	1	1	yes	characteristic, complemented
76	#65402	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
78	C₃×C₅×#41	—	2	2	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	D₄	1	4	yes	complemented
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
93	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
94	C₂²×C₃×Dic₅	—	2	1	no	—
95	C₂²×C₃×Dic₅	—	2	1	no	—
96	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
97	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
98	C₃×#709	—	2	2	no	—
99	C₃×#709	—	2	2	no	—
100	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₅	—	2	1	no	—
102	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
103	C₃×C₅×Q₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	2	2	no	—
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×D₈	—	2	2	no	—
107	C₂×C₃×C₅×C₈	—	2	2	no	—
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₂²⋊Dic₅	—	2	1	no	—
111	C₃×C₂²⋊Dic₅	—	2	1	no	—
112	C₃×C₂²⋊Dic₅	—	2	1	no	—
113	C₃×C₂²⋊Dic₅	—	2	1	no	—
114	C₃×C₂²⋊Dic₅	—	2	1	no	—
115	C₃×#689	—	2	2	no	—
116	C₃×#688	—	2	2	no	—
117	C₃×#687	—	2	2	no	—
118	C₃×#686	—	2	2	no	—
119	C₃×#685	—	2	1	no	—
120	C₃×#685	—	2	1	no	—
121	C₃×C₄⋊Dic₅	—	2	1	no	—
122	C₃×C₄⋊Dic₅	—	2	1	no	—
123	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
124	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
125	C₃×#683	—	2	1	no	—
126	C₃×#683	—	2	1	no	—
127	C₃×C₄×Dic₅	—	2	1	no	—
128	C₃×C₄×Dic₅	—	2	1	no	—
129	C₃×C₄×Dic₅	—	2	1	no	—
130	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
131	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
132	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
133	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
134	C₂×C₃×#168	—	2	2	no	—
135	C₂×C₃×#168	C₂³	1	1	yes	characteristic
136	C₂×C₃×#168	C₂³	1	1	yes	characteristic
137	C₂×C₃×#135	—	5	1	no	—
138	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
139	C₃×#532	—	5	1	no	—
140	C₃×C₄×#41	—	5	1	no	—
141	C₃×#464	—	5	1	no	—
142	C₃×#464	—	5	1	no	—
143	C₃×#463	—	5	1	no	—
144	C₃×#463	—	5	1	no	—
145	C₃×#462	—	5	1	no	—
146	C₃×#461	—	5	1	no	—
147	C₃×#460	—	5	1	no	—
148	C₃×#459	—	5	1	no	—
149	C₂×C₃×C₄⋊C₈	—	5	1	no	—
150	C₃×#416	—	5	1	no	—
151	C₃×#416	—	5	1	no	—
152	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
154	C₂×#709	C₂²×C₃	1	1	yes	characteristic
155	C₅×#135	—	2	4	no	—
156	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
160	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
161	#4096	—	2	4	no	—
162	#4093	C₂²×C₃	1	1	yes	characteristic
163	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
164	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
165	#4090	C₂²×C₃	1	1	yes	characteristic
166	C₂×#689	C₂²×C₃	1	1	yes	characteristic
167	C₂×#688	C₂²×C₃	1	1	yes	characteristic
168	#4086	C₂²×C₃	1	1	yes	characteristic
169	#4085	—	2	1	no	—
170	#4085	—	2	1	no	—
171	#4082	C₂²×C₃	1	1	yes	characteristic
172	D₄×Dic₅	—	2	1	no	—
173	D₄×Dic₅	—	2	1	no	—
174	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
175	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
176	C₂×#687	C₂²×C₃	1	1	yes	characteristic
177	C₂×#686	C₂²×C₃	1	1	yes	characteristic
178	C₄×C₂²⋊D₅	—	2	1	no	—
179	C₄×C₂²⋊D₅	—	2	1	no	—
180	#4072	—	2	1	no	—
181	#4072	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₄×Dic₅	—	2	1	no	—
183	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
184	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
185	#3967	C₂²×C₃	1	1	yes	characteristic
186	#3967	C₂²×C₃	1	1	yes	characteristic
187	#3964	C₂²×C₃	1	1	yes	characteristic
188	#3964	C₂²×C₃	1	1	yes	characteristic
189	#3953	C₂²×C₃	1	1	yes	characteristic
190	#3953	C₂²×C₃	1	1	yes	characteristic
191	#3948	C₂²×C₃	1	1	yes	characteristic
192	#3948	C₂²×C₃	1	1	yes	characteristic
193	#3946	C₂²×C₃	1	1	yes	characteristic
194	#3946	C₂²×C₃	1	1	yes	characteristic
195	#3946	C₂²×C₃	1	1	yes	characteristic
196	#3946	C₂²×C₃	1	1	yes	characteristic
197	#3035	—	5	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₃×D₅	—	2	1	no	—
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×Q₈	—	2	1	no	—
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
206	C₃×C₅×D₄	—	2	4	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	4	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	4	2	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂×C₃×C₄×C₅	#41	1	2	yes	—
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₃×C₂²⋊D₅	—	4	2	no	—
221	C₃×C₂²⋊D₅	—	4	2	no	—
222	C₃×C₂²⋊D₅	—	4	2	no	—
223	C₂×C₃×Dic₅	—	2	2	no	—
224	C₂×C₃×Dic₅	—	2	1	no	—
225	C₂×C₃×Dic₅	—	2	1	no	—
226	C₂×C₃×Dic₅	—	2	1	no	—
227	C₂×C₃×Dic₅	—	4	1	no	—
228	C₂×C₃×Dic₅	—	4	2	no	—
229	C₂×C₃×Dic₅	—	4	2	no	—
230	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
231	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
232	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
233	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
234	C₃×D₂₀	—	2	1	no	—
235	C₃×D₂₀	—	2	1	no	—
236	C₃×C₄×D₅	—	4	2	no	—
237	C₃×Dic₁₀	—	2	1	no	—
238	C₃×Dic₁₀	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×C₅×C₈	—	2	1	no	—
241	C₃×#168	—	2	1	no	—
242	C₃×#168	—	2	1	no	—
243	C₂×C₃×#41	—	5	1	no	—
244	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
245	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
246	C₃×#135	—	2	4	no	—
247	C₃×#135	—	10	4	no	—
248	C₂×C₃×Q₁₆	—	5	1	no	—
249	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
250	C₂×C₃×SD₁₆	—	5	1	no	—
251	C₂×C₃×SD₁₆	—	5	1	no	—
252	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
253	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
254	C₂×C₃×D₈	—	5	1	no	—
255	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
256	C₂²×C₃×C₈	—	5	1	no	—
257	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
258	C₃×C₄⋊Q₈	—	5	1	no	—
259	C₃×#127	—	5	1	no	—
260	C₃×#124	—	5	1	no	—
261	C₃×#124	—	5	1	no	—
262	C₃×#121	—	10	1	no	—
263	C₃×#121	—	10	1	no	—
264	C₃×C₄×Q₈	—	5	1	no	—
265	C₃×C₄×Q₈	—	5	1	no	—
266	C₃×C₄×D₄	—	5	1	no	—
267	C₃×C₄×D₄	—	5	1	no	—
268	C₃×C₄×D₄	—	10	1	no	—
269	C₃×C₄×D₄	—	10	1	no	—
270	C₃×C₄×D₄	—	10	1	no	—
271	C₃×C₄×D₄	—	10	1	no	—
272	C₃×#117	—	5	1	no	—
273	C₃×#117	—	10	1	no	—
274	C₂×C₃×C₄²	—	5	1	no	—
275	C₂×C₃×C₄²	—	10	1	no	—
276	C₃×C₄⋊C₈	—	5	1	no	—
277	C₃×C₄⋊C₈	—	5	1	no	—
278	C₃×C₄⋊C₈	—	5	1	no	—
279	C₃×C₄⋊C₈	—	5	1	no	—
280	C₃×#103	—	5	1	no	—
281	C₃×#103	—	5	1	no	—
282	C₃×#103	—	5	1	no	—
283	C₃×#103	—	5	1	no	—
284	C₃×#102	—	5	1	no	—
285	C₃×#102	—	5	1	no	—
286	C₃×#102	—	5	1	no	—
287	C₃×#102	—	5	1	no	—
288	C₅×#41	—	2	2	no	—
289	C₅×#41	—	2	2	no	—
290	C₅×#41	—	2	2	no	—
291	C₅×#41	C₃×D₄	1	4	yes	complemented
292	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₅×D₄	—	2	1	no	—
295	C₂×C₅×D₄	—	2	1	no	—
296	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	—	2	1	no	—
299	C₂²×C₄×C₅	—	2	1	no	—
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₂²⋊D₅	—	2	1	no	—
302	C₂×C₂²⋊D₅	—	2	1	no	—
303	C₂×C₂²⋊D₅	—	2	1	no	—
304	C₂²×Dic₅	—	2	1	no	—
305	C₂²×Dic₅	—	2	1	no	—
306	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
307	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
308	#709	—	2	2	no	—
309	#709	—	2	2	no	—
310	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₄×D₅	—	2	1	no	—
312	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
313	C₅×Q₁₆	—	2	2	no	—
314	C₅×SD₁₆	—	2	2	no	—
315	C₅×SD₁₆	—	2	2	no	—
316	C₅×D₈	—	2	2	no	—
317	C₂×C₅×C₈	—	2	2	no	—
318	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
320	C₂²⋊Dic₅	—	2	1	no	—
321	C₂²⋊Dic₅	—	2	1	no	—
322	C₂²⋊Dic₅	—	2	1	no	—
323	C₂²⋊Dic₅	—	2	1	no	—
324	C₂²⋊Dic₅	—	2	1	no	—
325	#689	—	2	2	no	—
326	#688	—	2	2	no	—
327	#687	—	2	2	no	—
328	#686	—	2	2	no	—
329	#685	—	2	1	no	—
330	#685	—	2	1	no	—
331	C₄⋊Dic₅	—	2	1	no	—
332	C₄⋊Dic₅	—	2	1	no	—
333	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
334	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
335	#683	—	2	1	no	—
336	#683	—	2	1	no	—
337	C₄×Dic₅	—	2	1	no	—
338	C₄×Dic₅	—	2	1	no	—
339	C₄×Dic₅	—	2	1	no	—
340	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
341	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
342	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
343	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
344	C₂×#168	—	2	2	no	—
345	C₂×#168	C₂³×C₃	1	1	yes	characteristic
346	C₂×#168	C₂³×C₃	1	1	yes	characteristic
347	C₂×#135	—	5	1	no	—
348	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
349	#532	—	5	1	no	—
350	C₄×#41	—	5	1	no	—
351	#464	—	5	1	no	—
352	#464	—	5	1	no	—
353	#463	—	5	1	no	—
354	#463	—	5	1	no	—
355	#462	—	5	1	no	—
356	#461	—	5	1	no	—
357	#460	—	5	1	no	—
358	#459	—	5	1	no	—
359	C₂×C₄⋊C₈	—	5	1	no	—
360	#416	—	5	1	no	—
361	#416	—	5	1	no	—
362	C₂²×C₃×C₅	—	2	1	no	—
363	C₂²×C₃×C₅	—	2	1	no	—
364	C₂²×C₃×C₅	—	2	2	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	—	4	1	no	—
370	C₂²×C₃×C₅	#121	1	2	yes	—
371	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₃×D₅	—	4	1	no	—
373	C₂×C₃×D₅	—	4	1	no	—
374	C₂×C₃×D₅	—	4	1	no	—
375	C₃×C₄×C₅	—	2	2	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	#121	1	2	yes	—
378	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
380	C₃×Dic₅	—	2	1	no	—
381	C₃×Dic₅	—	2	1	no	—
382	C₃×Dic₅	—	2	1	no	—
383	C₃×Dic₅	—	4	1	no	—
384	C₃×Dic₅	—	4	1	no	—
385	C₃×Dic₅	—	4	1	no	—
386	C₃×Dic₅	#135	1	2	yes	complemented
387	C₃×#41	—	2	2	no	—
388	C₃×#41	—	2	2	no	—
389	C₃×#41	—	2	2	no	—
390	C₃×#41	—	10	2	no	—
391	C₃×#41	—	10	2	no	—
392	C₃×#41	C₂²⋊D₅	1	4	yes	complemented
393	C₂×C₃×Q₈	—	5	1	no	—
394	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
395	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
396	C₂×C₃×D₄	—	2	1	no	—
397	C₂×C₃×D₄	—	2	1	no	—
398	C₂×C₃×D₄	—	5	1	no	—
399	C₂×C₃×D₄	—	10	1	no	—
400	C₂×C₃×D₄	—	10	1	no	—
401	C₂×C₃×D₄	—	10	1	no	—
402	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
403	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	—	2	1	no	—
405	C₂²×C₃×C₄	—	2	1	no	—
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	10	1	no	—
409	C₂²×C₃×C₄	—	10	1	no	—
410	C₂²×C₃×C₄	—	10	1	no	—
411	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
412	C₃×Q₁₆	—	2	2	no	—
413	C₃×Q₁₆	—	10	2	no	—
414	C₃×SD₁₆	—	2	2	no	—
415	C₃×SD₁₆	—	2	2	no	—
416	C₃×SD₁₆	—	10	2	no	—
417	C₃×SD₁₆	—	10	2	no	—
418	C₃×D₈	—	2	2	no	—
419	C₃×D₈	—	10	2	no	—
420	C₂×C₃×C₈	—	2	2	no	—
421	C₂×C₃×C₈	—	5	1	no	—
422	C₂×C₃×C₈	—	5	1	no	—
423	C₂×C₃×C₈	—	10	2	no	—
424	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
425	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
426	C₃×C₄⋊C₄	—	5	1	no	—
427	C₃×C₄⋊C₄	—	5	1	no	—
428	C₃×C₄⋊C₄	—	10	1	no	—
429	C₃×C₄⋊C₄	—	10	1	no	—
430	C₃×C₄⋊C₄	—	10	1	no	—
431	C₃×C₄⋊C₄	—	10	1	no	—
432	C₃×C₂²⋊C₄	—	10	1	no	—
433	C₃×C₂²⋊C₄	—	10	1	no	—
434	C₃×C₂²⋊C₄	—	10	1	no	—
435	C₃×C₂²⋊C₄	—	10	1	no	—
436	C₃×C₂²⋊C₄	—	10	1	no	—
437	C₃×C₂²⋊C₄	—	10	1	no	—
438	C₃×C₂²⋊C₄	—	10	1	no	—
439	C₃×C₄²	—	5	1	no	—
440	C₃×C₄²	—	5	1	no	—
441	C₃×C₄²	—	5	1	no	—
442	C₃×C₄²	—	5	1	no	—
443	C₃×C₄²	—	10	1	no	—
444	C₃×C₄²	—	10	1	no	—
445	C₃×C₄²	—	10	1	no	—
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	2	1	no	—
448	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
449	C₂²×D₅	—	2	1	no	—
450	C₅×Q₈	—	2	1	no	—
451	C₅×Q₈	—	2	1	no	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
454	C₅×D₄	—	2	4	no	—
455	C₅×D₄	—	2	1	no	—
456	C₅×D₄	—	2	1	no	—
457	C₅×D₄	—	2	1	no	—
458	C₅×D₄	—	4	2	no	—
459	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	4	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	4	2	no	—
464	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
466	C₂×C₄×C₅	C₃×#41	1	2	yes	—
467	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
468	C₂²⋊D₅	—	4	2	no	—
469	C₂²⋊D₅	—	4	2	no	—
470	C₂²⋊D₅	—	4	2	no	—
471	C₂×Dic₅	—	2	2	no	—
472	C₂×Dic₅	—	2	1	no	—
473	C₂×Dic₅	—	2	1	no	—
474	C₂×Dic₅	—	2	1	no	—
475	C₂×Dic₅	—	4	1	no	—
476	C₂×Dic₅	—	4	2	no	—
477	C₂×Dic₅	—	4	2	no	—
478	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
479	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
480	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
481	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
482	D₂₀	—	2	1	no	—
483	D₂₀	—	2	1	no	—
484	C₄×D₅	—	4	2	no	—
485	Dic₁₀	—	2	1	no	—
486	Dic₁₀	—	2	1	no	—
487	C₅×C₈	—	2	1	no	—
488	C₅×C₈	—	2	1	no	—
489	#168	—	2	1	no	—
490	#168	—	2	1	no	—
491	C₂×#41	—	5	1	no	—
492	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
493	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
494	#135	—	2	4	no	—
495	#135	—	10	4	no	—
496	C₂×Q₁₆	—	5	1	no	—
497	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
498	C₂×SD₁₆	—	5	1	no	—
499	C₂×SD₁₆	—	5	1	no	—
500	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
501	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
502	C₂×D₈	—	5	1	no	—
503	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
504	C₂²×C₈	—	5	1	no	—
505	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
506	C₄⋊Q₈	—	5	1	no	—
507	#127	—	5	1	no	—
508	#124	—	5	1	no	—
509	#124	—	5	1	no	—
510	#121	—	10	1	no	—
511	#121	—	10	1	no	—
512	C₄×Q₈	—	5	1	no	—
513	C₄×Q₈	—	5	1	no	—
514	C₄×D₄	—	5	1	no	—
515	C₄×D₄	—	5	1	no	—
516	C₄×D₄	—	10	1	no	—
517	C₄×D₄	—	10	1	no	—
518	C₄×D₄	—	10	1	no	—
519	C₄×D₄	—	10	1	no	—
520	#117	—	5	1	no	—
521	#117	—	10	1	no	—
522	C₂×C₄²	—	5	1	no	—
523	C₂×C₄²	—	10	1	no	—
524	C₄⋊C₈	—	5	1	no	—
525	C₄⋊C₈	—	5	1	no	—
526	C₄⋊C₈	—	5	1	no	—
527	C₄⋊C₈	—	5	1	no	—
528	#103	—	5	1	no	—
529	#103	—	5	1	no	—
530	#103	—	5	1	no	—
531	#103	—	5	1	no	—
532	#102	—	5	1	no	—
533	#102	—	5	1	no	—
534	#102	—	5	1	no	—
535	#102	—	5	1	no	—
536	C₂×C₃×C₅	—	2	2	no	—
537	C₂×C₃×C₅	—	4	2	no	—
538	C₂×C₃×C₅	—	8	1	no	—
539	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
540	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
541	C₂×C₃×C₅	#575	1	1	yes	characteristic
542	C₃×D₅	—	8	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	10	1	no	—
546	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
547	C₃×Q₈	—	2	1	no	—
548	C₃×Q₈	—	2	1	no	—
549	C₃×Q₈	—	2	1	no	—
550	C₃×Q₈	—	10	1	no	—
551	C₃×Q₈	—	10	1	no	—
552	C₃×Q₈	C₂×C₂²⋊D₅	1	2	yes	—
553	C₃×D₄	—	2	4	no	—
554	C₃×D₄	—	2	1	no	—
555	C₃×D₄	—	2	1	no	—
556	C₃×D₄	—	2	1	no	—
557	C₃×D₄	—	4	2	no	—
558	C₃×D₄	—	10	1	no	—
559	C₃×D₄	—	10	1	no	—
560	C₃×D₄	—	20	2	no	—
561	C₃×D₄	—	20	2	no	—
562	C₃×D₄	—	20	2	no	—
563	C₃×D₄	C₂×C₂²⋊D₅	1	2	yes	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	4	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	4	2	no	—
568	C₂×C₃×C₄	—	5	1	no	—
569	C₂×C₃×C₄	—	5	1	no	—
570	C₂×C₃×C₄	—	5	1	no	—
571	C₂×C₃×C₄	—	5	1	no	—
572	C₂×C₃×C₄	—	10	2	no	—
573	C₂×C₃×C₄	—	10	1	no	—
574	C₂×C₃×C₄	—	10	1	no	—
575	C₂×C₃×C₄	—	10	1	no	—
576	C₂×C₃×C₄	—	20	2	no	—
577	C₂×C₃×C₄	—	20	1	no	—
578	C₂×C₃×C₄	—	20	2	no	—
579	C₂×C₃×C₄	—	20	2	no	—
580	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
581	C₂×C₃×C₄	#711	1	2	yes	—
582	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
583	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
584	C₃×C₈	—	2	1	no	—
585	C₃×C₈	—	2	1	no	—
586	C₃×C₈	—	10	1	no	—
587	C₃×C₈	—	10	1	no	—
588	C₂²×C₅	—	2	1	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	2	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	C₃×#121	1	2	yes	—
597	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
598	C₂×D₅	—	4	1	no	—
599	C₂×D₅	—	4	1	no	—
600	C₂×D₅	—	4	1	no	—
601	C₄×C₅	—	2	2	no	—
602	C₄×C₅	—	4	1	no	—
603	C₄×C₅	C₃×#121	1	2	yes	—
604	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
605	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
606	Dic₅	—	2	1	no	—
607	Dic₅	—	2	1	no	—
608	Dic₅	—	2	1	no	—
609	Dic₅	—	4	1	no	—
610	Dic₅	—	4	1	no	—
611	Dic₅	—	4	1	no	—
612	Dic₅	C₃×#135	1	2	yes	complemented
613	#41	—	2	2	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	#41	—	10	2	no	—
617	#41	—	10	2	no	—
618	#41	C₃×C₂²⋊D₅	1	4	yes	complemented
619	C₂×Q₈	—	5	1	no	—
620	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
621	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	5	1	no	—
625	C₂×D₄	—	10	1	no	—
626	C₂×D₄	—	10	1	no	—
627	C₂×D₄	—	10	1	no	—
628	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
629	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	5	1	no	—
633	C₂²×C₄	—	5	1	no	—
634	C₂²×C₄	—	10	1	no	—
635	C₂²×C₄	—	10	1	no	—
636	C₂²×C₄	—	10	1	no	—
637	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
638	Q₁₆	—	2	2	no	—
639	Q₁₆	—	10	2	no	—
640	SD₁₆	—	2	2	no	—
641	SD₁₆	—	2	2	no	—
642	SD₁₆	—	10	2	no	—
643	SD₁₆	—	10	2	no	—
644	D₈	—	2	2	no	—
645	D₈	—	10	2	no	—
646	C₂×C₈	—	2	2	no	—
647	C₂×C₈	—	5	1	no	—
648	C₂×C₈	—	5	1	no	—
649	C₂×C₈	—	10	2	no	—
650	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
651	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
652	C₄⋊C₄	—	5	1	no	—
653	C₄⋊C₄	—	5	1	no	—
654	C₄⋊C₄	—	10	1	no	—
655	C₄⋊C₄	—	10	1	no	—
656	C₄⋊C₄	—	10	1	no	—
657	C₄⋊C₄	—	10	1	no	—
658	C₂²⋊C₄	—	10	1	no	—
659	C₂²⋊C₄	—	10	1	no	—
660	C₂²⋊C₄	—	10	1	no	—
661	C₂²⋊C₄	—	10	1	no	—
662	C₂²⋊C₄	—	10	1	no	—
663	C₂²⋊C₄	—	10	1	no	—
664	C₂²⋊C₄	—	10	1	no	—
665	C₄²	—	5	1	no	—
666	C₄²	—	5	1	no	—
667	C₄²	—	5	1	no	—
668	C₄²	—	5	1	no	—
669	C₄²	—	10	1	no	—
670	C₄²	—	10	1	no	—
671	C₄²	—	10	1	no	—
672	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
673	C₂²×C₃	—	2	1	no	—
674	C₂²×C₃	—	2	1	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	—	20	1	no	—
682	C₂²×C₃	—	20	1	no	—
683	C₂²×C₃	—	20	1	no	—
684	C₂²×C₃	#4085	1	2	yes	—
685	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	4	1	no	—
688	C₃×C₄	—	5	2	no	—
689	C₃×C₄	—	10	1	no	—
690	C₃×C₄	—	10	1	no	—
691	C₃×C₄	—	10	1	no	—
692	C₃×C₄	—	20	1	no	—
693	C₃×C₄	—	20	1	no	—
694	C₃×C₄	—	20	1	no	—
695	C₃×C₄	#4085	1	2	yes	—
696	C₃×C₄	C₂×#711	1	1	yes	characteristic
697	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
698	C₂×C₅	—	2	2	no	—
699	C₂×C₅	—	4	2	no	—
700	C₂×C₅	—	8	1	no	—
701	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
702	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
703	C₂×C₅	C₃×#575	1	1	yes	characteristic
704	D₅	—	8	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	10	1	no	—
708	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
709	Q₈	—	2	1	no	—
710	Q₈	—	2	1	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	10	1	no	—
713	Q₈	—	10	1	no	—
714	Q₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
715	D₄	—	2	4	no	—
716	D₄	—	2	1	no	—
717	D₄	—	2	1	no	—
718	D₄	—	2	1	no	—
719	D₄	—	4	2	no	—
720	D₄	—	10	1	no	—
721	D₄	—	10	1	no	—
722	D₄	—	20	2	no	—
723	D₄	—	20	2	no	—
724	D₄	—	20	2	no	—
725	D₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	5	1	no	—
731	C₂×C₄	—	5	1	no	—
732	C₂×C₄	—	5	1	no	—
733	C₂×C₄	—	5	1	no	—
734	C₂×C₄	—	10	2	no	—
735	C₂×C₄	—	10	1	no	—
736	C₂×C₄	—	10	1	no	—
737	C₂×C₄	—	10	1	no	—
738	C₂×C₄	—	20	2	no	—
739	C₂×C₄	—	20	1	no	—
740	C₂×C₄	—	20	2	no	—
741	C₂×C₄	—	20	2	no	—
742	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
743	C₂×C₄	C₃×#711	1	2	yes	—
744	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
745	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	10	1	no	—
749	C₈	—	10	1	no	—
750	C₂×C₃	—	2	2	no	—
751	C₂×C₃	—	4	2	no	—
752	C₂×C₃	—	8	1	no	—
753	C₂×C₃	—	40	1	no	—
754	C₂×C₃	D₅×#135	1	1	yes	characteristic
755	C₂×C₃	#66102	1	1	yes	characteristic
756	C₂×C₃	C₂×#4085	1	1	yes	characteristic
757	C₅	C₃×#3035	1	1	yes	characteristic, complemented, Sylow
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	20	1	no	—
767	C₂²	—	20	1	no	—
768	C₂²	—	20	1	no	—
769	C₂²	C₃×#4085	1	2	yes	—
770	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
771	C₄	—	2	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	5	2	no	—
774	C₄	—	10	1	no	—
775	C₄	—	10	1	no	—
776	C₄	—	10	1	no	—
777	C₄	—	20	1	no	—
778	C₄	—	20	1	no	—
779	C₄	—	20	1	no	—
780	C₄	C₃×#4085	1	2	yes	—
781	C₄	C₂×C₃×#711	1	1	yes	characteristic
782	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
783	C₃	#10615631	1	1	yes	characteristic, direct product factor, Sylow
784	C₂	—	2	2	no	—
785	C₂	—	4	2	no	—
786	C₂	—	8	1	no	—
787	C₂	—	40	1	no	—
788	C₂	C₃×D₅×#135	1	1	yes	characteristic
789	C₂	C₃×#66102	1	1	yes	characteristic
790	C₂	C₂×C₃×#4085	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#3035
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×#66166	C₂	semidirect
3. C₃×#41×Dic₅	C₂	semidirect
4. C₂×C₃×#4096	C₂	semidirect
5. C₃×#65522	C₂	semidirect
6. C₃×#65474	C₂	semidirect
7. C₃×#65471	C₂	semidirect
8. C₃×#65455	C₂	semidirect
9. C₃×#65454	C₂	semidirect
10. C₃×#65452	C₂	semidirect
11. C₃×#65451	C₂	semidirect
12. C₃×#65442	C₂	semidirect
13. C₃×#65439	C₂	semidirect
14. C₃×#65402	C₂	semidirect
15. C₂×C₃×#3946	C₂	semidirect
16. #10615631	C₃	direct (N × H)
63. C₂×C₅×#135	C₂×C₃	semidirect
64. #66166	C₂×C₃	semidirect
65. #41×Dic₅	C₂×C₃	semidirect
66. C₂×#4096	C₂×C₃	semidirect
67. #65522	C₂×C₃	semidirect
68. #65474	C₂×C₃	semidirect
69. #65471	C₂×C₃	semidirect
70. #65455	C₂×C₃	semidirect
71. #65454	C₂×C₃	semidirect
72. #65452	C₂×C₃	semidirect
73. #65451	C₂×C₃	semidirect
74. #65442	C₂×C₃	semidirect
75. #65439	C₂×C₃	semidirect
76. #65402	C₂×C₃	semidirect
77. C₂×#3946	C₂×C₃	semidirect
81. C₃×C₅×#41	D₄	semidirect
138. C₂×C₃×#135	D₅	semidirect
291. C₅×#41	C₃×D₄	semidirect
348. C₂×#135	C₃×D₅	semidirect
386. C₃×Dic₅	#135	semidirect
392. C₃×#41	C₂²⋊D₅	semidirect
612. Dic₅	C₃×#135	semidirect
618. #41	C₃×C₂²⋊D₅	semidirect
672. C₃×C₅	#3035	semidirect
757. C₅	C₃×#3035	semidirect
783. C₃	#10615631	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×C₅×#135	2
C₃×#66166	2
C₃×#41×Dic₅	2
C₂×C₃×#4096	2
C₃×#65522	2
C₃×#65474	2
C₃×#65471	2
C₃×#65455	2
C₃×#65454	2
C₃×#65452	2
C₃×#65451	2
C₃×#65442	2
C₃×#65439	2
C₃×#65402	2
C₂×C₃×#3946	2
#10615631	3
C₃×#3035	5

Subgroups — C3×#10615631 #14426215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615631 #14426215