Subgroups — C₃×#10618368 #14481500

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66053	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66031	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66022	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65994	C₂	1	4	yes	maximal, complemented
7	C₃×#65983	C₂	1	4	yes	maximal, complemented
8	C₃×#65947	C₂	1	4	yes	maximal, complemented
9	C₃×#65940	C₂	1	2	yes	maximal, complemented
10	C₃×#65937	C₂	1	2	yes	maximal, complemented
11	C₃×#65934	C₂	1	4	yes	maximal, complemented
12	C₃×#65895	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#711	C₂	1	2	yes	maximal, complemented
14	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65852	C₂	1	1	yes	maximal, characteristic, complemented
16	#10618368	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#711	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#123	C₂²	1	4	yes	complemented
22	C₃×C₅×#121	C₂²	1	4	yes	—
23	C₃×C₅×#121	C₂²	1	2	yes	—
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×#4085	C₂²	1	4	yes	—
27	C₃×#4084	C₂²	1	2	yes	—
28	C₃×#4084	C₂²	1	4	yes	—
29	C₃×#4083	C₂²	1	4	yes	—
30	C₃×#4082	C₂²	1	4	yes	—
31	C₃×#4082	C₂²	1	2	yes	complemented
32	C₃×#4081	C₂²	1	4	yes	—
33	C₃×#4081	C₂²	1	4	yes	complemented
34	C₃×D₄×Dic₅	C₂²	1	4	yes	—
35	C₃×D₄×Dic₅	C₂²	1	2	yes	complemented
36	C₃×D₄×Dic₅	C₂²	1	4	yes	complemented
37	C₃×#4075	C₂²	1	4	yes	—
38	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
39	C₃×#4072	C₂²	1	1	yes	characteristic
40	C₃×#4070	C₂²	1	2	yes	—
41	C₃×#4070	C₂²	1	4	yes	complemented
42	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	complemented
43	C₃×#4044	C₂²	1	4	yes	—
44	C₃×#4043	C₂²	1	2	yes	—
45	C₃×#4042	C₂²	1	4	yes	—
46	C₃×#4038	C₂²	1	2	yes	—
47	C₃×#4038	C₂²	1	2	yes	—
48	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
49	C₃×#4036	C₂²	1	4	yes	complemented
50	C₃×#4035	C₂²	1	4	yes	complemented
51	C₃×#4034	C₂²	1	2	yes	complemented
52	C₃×#4033	C₂²	1	2	yes	complemented
53	C₃×#4033	C₂²	1	4	yes	complemented
54	C₃×#4031	C₂²	1	4	yes	—
55	C₃×#4029	C₂²	1	4	yes	—
56	C₃×#4027	C₂²	1	4	yes	—
57	C₃×#4027	C₂²	1	4	yes	—
58	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
59	C₃×#4025	C₂²	1	4	yes	—
60	C₃×#4025	C₂²	1	4	yes	complemented
61	C₃×#4025	C₂²	1	4	yes	complemented
62	C₃×#4024	C₂²	1	4	yes	complemented
63	C₃×#4023	C₂²	1	2	yes	—
64	C₃×#4023	C₂²	1	4	yes	complemented
65	C₃×#4018	C₂²	1	1	yes	characteristic
66	C₃×#4018	C₂²	1	1	yes	characteristic
67	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
68	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
69	C₃×#4016	C₂²	1	1	yes	characteristic, complemented
70	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
71	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
72	C₃×#3455	—	5	1	no	maximal, Hall
73	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
74	#66053	C₂×C₃	1	1	yes	characteristic, complemented
75	#66050	C₂×C₃	1	1	yes	characteristic, complemented
76	#66031	C₂×C₃	1	1	yes	characteristic, complemented
77	#66022	C₂×C₃	1	1	yes	characteristic, complemented
78	#65994	C₂×C₃	1	4	yes	complemented
79	#65983	C₂×C₃	1	4	yes	complemented
80	#65947	C₂×C₃	1	4	yes	complemented
81	#65940	C₂×C₃	1	2	yes	complemented
82	#65937	C₂×C₃	1	2	yes	complemented
83	#65934	C₂×C₃	1	4	yes	complemented
84	#65895	C₂×C₃	1	2	yes	complemented
85	C₄×#711	C₂×C₃	1	2	yes	complemented
86	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
87	#65852	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
90	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
91	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
94	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
95	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
96	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
98	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
99	C₃×#711	—	2	8	no	—
100	C₂×C₃×C₄×D₅	—	2	4	no	—
101	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
105	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
106	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
107	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
108	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
111	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
112	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
117	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
118	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
119	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
120	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
121	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
122	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
123	C₃×#685	C₂³	1	4	yes	—
124	C₃×#685	C₂³	1	4	yes	—
125	C₃×#685	C₂³	1	2	yes	—
126	C₃×#685	C₂³	1	2	yes	—
127	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
128	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
129	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
130	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
131	C₃×#683	C₂³	1	4	yes	—
132	C₃×#683	C₂³	1	4	yes	—
133	C₃×#683	C₂³	1	2	yes	—
134	C₃×#683	C₂³	1	4	yes	—
135	C₃×#683	C₂³	1	4	yes	—
136	C₃×#683	C₂³	1	2	yes	—
137	C₃×#683	C₂³	1	4	yes	—
138	C₃×C₄×Dic₅	C₂³	1	4	yes	—
139	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
140	C₃×C₄×Dic₅	C₂³	1	2	yes	—
141	C₃×C₄×Dic₅	C₂³	1	4	yes	—
142	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
143	C₃×C₄×Dic₅	C₂³	1	4	yes	—
144	C₃×C₄×Dic₅	C₂³	1	2	yes	—
145	C₃×#542	—	5	2	no	—
146	C₃×#542	—	5	2	no	—
147	C₃×#541	—	5	1	no	—
148	C₃×#541	—	5	1	no	—
149	C₃×#540	—	5	1	no	—
150	C₃×#540	D₅	1	1	yes	characteristic, complemented
151	C₃×#539	—	5	4	no	—
152	C₃×#538	—	5	4	no	—
153	C₃×#533	—	5	1	no	—
154	C₃×#532	—	5	1	no	—
155	C₃×#529	—	5	4	no	—
156	C₃×#529	—	5	4	no	—
157	C₃×#525	—	5	2	no	—
158	C₃×C₄×#41	—	5	2	no	—
159	C₂×C₃×#117	—	5	1	no	—
160	C₂×#711	C₂²×C₃	1	2	yes	—
161	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
162	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₅×#123	C₂²×C₃	1	4	yes	complemented
165	C₅×#121	C₂²×C₃	1	4	yes	—
166	C₅×#121	C₂²×C₃	1	2	yes	—
167	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
168	C₅×#117	C₂²×C₃	1	1	yes	characteristic
169	#4085	C₂²×C₃	1	4	yes	—
170	#4084	C₂²×C₃	1	4	yes	—
171	#4084	C₂²×C₃	1	2	yes	—
172	#4083	C₂²×C₃	1	4	yes	—
173	#4082	C₂²×C₃	1	4	yes	—
174	#4082	C₂²×C₃	1	2	yes	complemented
175	#4081	C₂²×C₃	1	4	yes	—
176	#4081	C₂²×C₃	1	4	yes	complemented
177	D₄×Dic₅	C₂²×C₃	1	4	yes	—
178	D₄×Dic₅	C₂²×C₃	1	4	yes	complemented
179	D₄×Dic₅	C₂²×C₃	1	2	yes	complemented
180	#4075	C₂²×C₃	1	4	yes	—
181	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
182	#4072	C₂²×C₃	1	1	yes	characteristic
183	#4070	C₂²×C₃	1	2	yes	—
184	#4070	C₂²×C₃	1	4	yes	complemented
185	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	complemented
186	#4044	C₂²×C₃	1	4	yes	—
187	#4043	C₂²×C₃	1	2	yes	—
188	#4042	C₂²×C₃	1	4	yes	—
189	#4038	C₂²×C₃	1	2	yes	—
190	#4038	C₂²×C₃	1	2	yes	—
191	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
192	#4036	C₂²×C₃	1	4	yes	complemented
193	#4035	C₂²×C₃	1	4	yes	complemented
194	#4034	C₂²×C₃	1	2	yes	complemented
195	#4033	C₂²×C₃	1	2	yes	complemented
196	#4033	C₂²×C₃	1	4	yes	complemented
197	#4031	C₂²×C₃	1	4	yes	—
198	#4029	C₂²×C₃	1	4	yes	—
199	#4027	C₂²×C₃	1	4	yes	—
200	#4027	C₂²×C₃	1	4	yes	—
201	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
202	#4025	C₂²×C₃	1	4	yes	—
203	#4025	C₂²×C₃	1	4	yes	complemented
204	#4025	C₂²×C₃	1	4	yes	complemented
205	#4024	C₂²×C₃	1	4	yes	complemented
206	#4023	C₂²×C₃	1	2	yes	—
207	#4023	C₂²×C₃	1	4	yes	complemented
208	#4018	C₂²×C₃	1	1	yes	characteristic
209	#4018	C₂²×C₃	1	1	yes	characteristic
210	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
211	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
212	#4016	C₂²×C₃	1	1	yes	characteristic, complemented
213	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
214	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
215	#3455	—	5	1	no	Sylow
216	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
217	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₃×D₅	—	2	2	no	—
219	C₂²×C₃×D₅	—	4	2	no	—
220	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
221	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
222	C₃×C₅×D₄	—	2	4	no	—
223	C₃×C₅×D₄	—	4	4	no	—
224	C₃×C₅×D₄	—	4	4	no	—
225	C₂×C₃×C₄×C₅	—	2	2	no	—
226	C₂×C₃×C₄×C₅	—	4	4	no	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
229	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₃×C₂²⋊D₅	—	2	8	no	—
233	C₃×C₂²⋊D₅	—	4	4	no	—
234	C₂×C₃×Dic₅	—	2	2	no	—
235	C₂×C₃×Dic₅	—	2	8	no	—
236	C₂×C₃×Dic₅	—	4	4	no	—
237	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
238	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
239	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
240	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
241	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
242	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
243	C₃×C₄×D₅	—	2	2	no	—
244	C₃×C₄×D₅	—	2	2	no	—
245	C₃×C₄×D₅	—	2	2	no	—
246	C₃×C₄×D₅	—	4	2	no	—
247	C₃×C₄×D₅	—	4	2	no	—
248	C₃×C₄×D₅	#41	1	4	yes	—
249	C₃×Dic₁₀	—	2	4	no	—
250	C₃×Dic₁₀	—	4	4	no	—
251	C₂×C₃×#41	—	5	2	no	—
252	C₂³×C₃×C₄	—	5	1	no	—
253	C₃×C₄⋊Q₈	—	5	2	no	—
254	C₃×C₄⋊Q₈	—	5	1	no	—
255	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
256	C₃×#126	—	5	4	no	—
257	C₃×#126	—	5	4	no	—
258	C₃×#126	—	5	4	no	—
259	C₃×#126	—	5	4	no	—
260	C₃×#125	—	5	4	no	—
261	C₃×#125	—	5	4	no	—
262	C₃×#125	—	5	1	no	—
263	C₃×#125	C₂×D₅	1	1	yes	characteristic, complemented
264	C₃×#124	—	5	4	no	—
265	C₃×#124	—	5	2	no	—
266	C₃×#124	—	5	4	no	—
267	C₃×#123	—	5	4	no	—
268	C₃×#123	—	5	4	no	—
269	C₃×#123	—	5	4	no	—
270	C₃×#123	—	5	4	no	—
271	C₃×#123	C₂×D₅	1	4	yes	complemented
272	C₃×C₂²⋊Q₈	—	5	2	no	—
273	C₃×C₂²⋊Q₈	—	5	4	no	—
274	C₃×C₂²⋊Q₈	—	5	4	no	—
275	C₃×C₂²⋊Q₈	—	5	2	no	—
276	C₃×C₂²⋊Q₈	—	5	4	no	—
277	C₃×#121	—	5	2	no	—
278	C₃×#121	—	5	4	no	—
279	C₃×#121	—	5	4	no	—
280	C₃×#121	C₂×D₅	1	2	yes	—
281	C₃×#121	C₂×D₅	1	4	yes	—
282	C₃×#120	—	5	4	no	—
283	C₃×C₄×Q₈	—	5	2	no	—
284	C₃×C₄×Q₈	—	5	4	no	—
285	C₃×C₄×Q₈	—	5	2	no	—
286	C₃×C₄×D₄	—	5	4	no	—
287	C₃×C₄×D₄	—	5	2	no	—
288	C₃×C₄×D₄	—	5	4	no	—
289	C₃×C₄×D₄	—	5	4	no	—
290	C₃×C₄×D₄	—	5	4	no	—
291	C₃×C₄×D₄	—	5	4	no	—
292	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
293	C₃×#117	—	5	1	no	—
294	C₃×#117	—	5	2	no	—
295	C₃×#117	—	5	2	no	—
296	C₃×#117	—	5	2	no	—
297	C₃×#117	—	5	4	no	—
298	C₃×#117	—	5	1	no	—
299	C₃×#117	—	5	1	no	—
300	C₃×#117	C₂×D₅	1	1	yes	characteristic
301	C₂×C₃×C₄⋊C₄	—	5	2	no	—
302	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
303	C₂×C₃×C₄²	—	5	4	no	—
304	C₂×C₃×C₄²	—	5	1	no	—
305	C₂×C₃×C₄²	—	5	1	no	—
306	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
308	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
309	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
310	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
312	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
313	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
314	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
315	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
316	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
317	#711	—	2	8	no	—
318	C₂×C₄×D₅	—	2	4	no	—
319	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
321	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
323	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
324	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
325	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
326	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
327	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
328	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
329	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
330	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
331	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
333	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
334	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
335	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
336	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
337	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
338	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
339	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
340	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
341	#685	C₂³×C₃	1	2	yes	—
342	#685	C₂³×C₃	1	2	yes	—
343	#685	C₂³×C₃	1	4	yes	—
344	#685	C₂³×C₃	1	4	yes	—
345	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
346	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
347	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
348	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
349	#683	C₂³×C₃	1	4	yes	—
350	#683	C₂³×C₃	1	4	yes	—
351	#683	C₂³×C₃	1	2	yes	—
352	#683	C₂³×C₃	1	2	yes	—
353	#683	C₂³×C₃	1	4	yes	—
354	#683	C₂³×C₃	1	4	yes	—
355	#683	C₂³×C₃	1	4	yes	—
356	C₄×Dic₅	C₂³×C₃	1	4	yes	—
357	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
358	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
359	C₄×Dic₅	C₂³×C₃	1	2	yes	—
360	C₄×Dic₅	C₂³×C₃	1	2	yes	—
361	C₄×Dic₅	C₂³×C₃	1	4	yes	—
362	C₄×Dic₅	C₂³×C₃	1	4	yes	—
363	#542	—	5	2	no	—
364	#542	—	5	2	no	—
365	#541	—	5	1	no	—
366	#541	—	5	1	no	—
367	#540	—	5	1	no	—
368	#540	C₃×D₅	1	1	yes	characteristic, complemented
369	#539	—	5	4	no	—
370	#538	—	5	4	no	—
371	#533	—	5	1	no	—
372	#532	—	5	1	no	—
373	#529	—	5	4	no	—
374	#529	—	5	4	no	—
375	#525	—	5	2	no	—
376	C₄×#41	—	5	2	no	—
377	C₂×#117	—	5	1	no	—
378	C₂²×C₃×C₅	—	2	4	no	—
379	C₂²×C₃×C₅	—	2	1	no	—
380	C₂²×C₃×C₅	—	2	4	no	—
381	C₂²×C₃×C₅	—	2	4	no	—
382	C₂²×C₃×C₅	—	2	2	no	—
383	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
384	C₂×C₃×D₅	—	2	2	no	—
385	C₂×C₃×D₅	—	2	1	no	—
386	C₂×C₃×D₅	—	2	2	no	—
387	C₂×C₃×D₅	—	4	4	no	—
388	C₂×C₃×D₅	C₂×#41	1	2	yes	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	4	no	—
391	C₃×C₄×C₅	—	2	2	no	—
392	C₃×C₄×C₅	—	2	2	no	—
393	C₃×C₄×C₅	C₂×#41	1	2	yes	—
394	C₃×Dic₅	—	2	4	no	—
395	C₃×Dic₅	—	2	1	no	—
396	C₃×Dic₅	—	2	2	no	—
397	C₃×Dic₅	—	2	4	no	—
398	C₃×Dic₅	—	2	2	no	—
399	C₃×Dic₅	C₂×#41	1	2	yes	—
400	C₂⁴×C₃	—	5	1	no	—
401	C₃×#41	—	10	8	no	—
402	C₂×C₃×Q₈	—	5	2	no	—
403	C₂×C₃×Q₈	—	5	4	no	—
404	C₂×C₃×D₄	—	5	4	no	—
405	C₂×C₃×D₄	—	5	4	no	—
406	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
407	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
408	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	4	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	—	5	4	no	—
413	C₂²×C₃×C₄	—	5	1	no	—
414	C₂²×C₃×C₄	—	5	1	no	—
415	C₂²×C₃×C₄	—	5	1	no	—
416	C₂²×C₃×C₄	—	5	2	no	—
417	C₂²×C₃×C₄	—	5	2	no	—
418	C₂²×C₃×C₄	—	10	4	no	—
419	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
421	C₃×C₄⋊C₄	—	5	2	no	—
422	C₃×C₄⋊C₄	—	5	2	no	—
423	C₃×C₄⋊C₄	—	5	4	no	—
424	C₃×C₄⋊C₄	—	5	4	no	—
425	C₃×C₄⋊C₄	—	5	4	no	—
426	C₃×C₄⋊C₄	—	5	4	no	—
427	C₃×C₄⋊C₄	—	5	4	no	—
428	C₃×C₄⋊C₄	—	5	2	no	—
429	C₃×C₄⋊C₄	—	5	2	no	—
430	C₃×C₄⋊C₄	—	5	4	no	—
431	C₃×C₄⋊C₄	—	5	4	no	—
432	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
433	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
434	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
435	C₃×C₂²⋊C₄	—	5	2	no	—
436	C₃×C₂²⋊C₄	—	5	4	no	—
437	C₃×C₂²⋊C₄	—	5	4	no	—
438	C₃×C₂²⋊C₄	—	5	4	no	—
439	C₃×C₂²⋊C₄	—	5	4	no	—
440	C₃×C₂²⋊C₄	—	5	4	no	—
441	C₃×C₂²⋊C₄	—	5	2	no	—
442	C₃×C₂²⋊C₄	—	5	2	no	—
443	C₃×C₂²⋊C₄	—	5	4	no	—
444	C₃×C₂²⋊C₄	—	5	4	no	—
445	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
446	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
447	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
448	C₃×C₄²	—	5	2	no	—
449	C₃×C₄²	—	5	2	no	—
450	C₃×C₄²	—	5	4	no	—
451	C₃×C₄²	—	5	1	no	—
452	C₃×C₄²	—	5	1	no	—
453	C₃×C₄²	—	5	4	no	—
454	C₃×C₄²	—	5	4	no	—
455	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
456	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
457	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
458	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
459	C₂²×D₅	—	2	2	no	—
460	C₂²×D₅	—	4	2	no	—
461	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
462	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
463	C₅×D₄	—	2	4	no	—
464	C₅×D₄	—	4	4	no	—
465	C₅×D₄	—	4	4	no	—
466	C₂×C₄×C₅	—	2	2	no	—
467	C₂×C₄×C₅	—	4	4	no	—
468	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
469	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
470	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
471	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
472	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
473	C₂²⋊D₅	—	2	8	no	—
474	C₂²⋊D₅	—	4	4	no	—
475	C₂×Dic₅	—	2	2	no	—
476	C₂×Dic₅	—	2	8	no	—
477	C₂×Dic₅	—	4	4	no	—
478	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
479	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
480	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
481	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
482	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
483	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
484	C₄×D₅	—	2	2	no	—
485	C₄×D₅	—	2	2	no	—
486	C₄×D₅	—	2	2	no	—
487	C₄×D₅	—	4	2	no	—
488	C₄×D₅	—	4	2	no	—
489	C₄×D₅	C₃×#41	1	4	yes	—
490	Dic₁₀	—	2	4	no	—
491	Dic₁₀	—	4	4	no	—
492	C₂×#41	—	5	2	no	—
493	C₂³×C₄	—	5	1	no	—
494	C₄⋊Q₈	—	5	2	no	—
495	C₄⋊Q₈	—	5	1	no	—
496	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
497	#126	—	5	4	no	—
498	#126	—	5	4	no	—
499	#126	—	5	4	no	—
500	#126	—	5	4	no	—
501	#125	—	5	4	no	—
502	#125	—	5	4	no	—
503	#125	—	5	1	no	—
504	#125	C₂×C₃×D₅	1	1	yes	characteristic, complemented
505	#124	—	5	4	no	—
506	#124	—	5	2	no	—
507	#124	—	5	4	no	—
508	#123	—	5	4	no	—
509	#123	—	5	4	no	—
510	#123	—	5	4	no	—
511	#123	—	5	4	no	—
512	#123	C₂×C₃×D₅	1	4	yes	complemented
513	C₂²⋊Q₈	—	5	2	no	—
514	C₂²⋊Q₈	—	5	4	no	—
515	C₂²⋊Q₈	—	5	2	no	—
516	C₂²⋊Q₈	—	5	4	no	—
517	C₂²⋊Q₈	—	5	4	no	—
518	#121	—	5	2	no	—
519	#121	—	5	4	no	—
520	#121	—	5	4	no	—
521	#121	C₂×C₃×D₅	1	2	yes	—
522	#121	C₂×C₃×D₅	1	4	yes	—
523	#120	—	5	4	no	—
524	C₄×Q₈	—	5	2	no	—
525	C₄×Q₈	—	5	4	no	—
526	C₄×Q₈	—	5	2	no	—
527	C₄×D₄	—	5	2	no	—
528	C₄×D₄	—	5	4	no	—
529	C₄×D₄	—	5	4	no	—
530	C₄×D₄	—	5	4	no	—
531	C₄×D₄	—	5	4	no	—
532	C₄×D₄	—	5	4	no	—
533	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
534	#117	—	5	1	no	—
535	#117	—	5	2	no	—
536	#117	—	5	2	no	—
537	#117	—	5	2	no	—
538	#117	—	5	4	no	—
539	#117	—	5	1	no	—
540	#117	—	5	1	no	—
541	#117	C₂×C₃×D₅	1	1	yes	characteristic
542	C₂×C₄⋊C₄	—	5	2	no	—
543	C₂×C₂²⋊C₄	—	5	2	no	—
544	C₂×C₄²	—	5	4	no	—
545	C₂×C₄²	—	5	1	no	—
546	C₂×C₄²	—	5	1	no	—
547	C₂×C₃×C₅	—	4	1	no	—
548	C₂×C₃×C₅	—	4	4	no	—
549	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
550	C₂×C₃×C₅	#585	1	2	yes	—
551	C₃×D₅	—	2	2	no	—
552	C₃×D₅	—	4	1	no	—
553	C₂³×C₃	—	5	1	no	—
554	C₂³×C₃	—	5	1	no	—
555	C₂³×C₃	—	10	2	no	—
556	C₂³×C₃	—	20	2	no	—
557	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
558	C₂³×C₃	C₂³×D₅	1	4	yes	—
559	C₃×Q₈	—	10	4	no	—
560	C₃×Q₈	—	20	4	no	—
561	C₃×D₄	—	2	4	no	—
562	C₃×D₄	—	4	4	no	—
563	C₃×D₄	—	4	4	no	—
564	C₃×D₄	—	10	8	no	—
565	C₃×D₄	—	20	4	no	—
566	C₂×C₃×C₄	—	2	2	no	—
567	C₂×C₃×C₄	—	4	4	no	—
568	C₂×C₃×C₄	—	5	1	no	—
569	C₂×C₃×C₄	—	5	4	no	—
570	C₂×C₃×C₄	—	5	2	no	—
571	C₂×C₃×C₄	—	5	2	no	—
572	C₂×C₃×C₄	—	5	4	no	—
573	C₂×C₃×C₄	—	5	4	no	—
574	C₂×C₃×C₄	—	5	1	no	—
575	C₂×C₃×C₄	—	10	2	no	—
576	C₂×C₃×C₄	—	10	2	no	—
577	C₂×C₃×C₄	—	10	2	no	—
578	C₂×C₃×C₄	—	10	8	no	—
579	C₂×C₃×C₄	—	10	2	no	—
580	C₂×C₃×C₄	—	20	2	no	—
581	C₂×C₃×C₄	—	20	2	no	—
582	C₂×C₃×C₄	—	20	4	no	—
583	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
584	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
585	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
586	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
588	C₂²×C₅	—	2	4	no	—
589	C₂²×C₅	—	2	1	no	—
590	C₂²×C₅	—	2	4	no	—
591	C₂²×C₅	—	2	4	no	—
592	C₂²×C₅	—	2	2	no	—
593	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
594	C₂×D₅	—	2	2	no	—
595	C₂×D₅	—	2	1	no	—
596	C₂×D₅	—	2	2	no	—
597	C₂×D₅	—	4	4	no	—
598	C₂×D₅	C₂×C₃×#41	1	2	yes	—
599	C₄×C₅	—	2	1	no	—
600	C₄×C₅	—	2	4	no	—
601	C₄×C₅	—	2	2	no	—
602	C₄×C₅	—	2	2	no	—
603	C₄×C₅	C₂×C₃×#41	1	2	yes	—
604	Dic₅	—	2	4	no	—
605	Dic₅	—	2	1	no	—
606	Dic₅	—	2	2	no	—
607	Dic₅	—	2	4	no	—
608	Dic₅	—	2	2	no	—
609	Dic₅	C₂×C₃×#41	1	2	yes	—
610	C₂⁴	—	5	1	no	—
611	#41	—	10	8	no	—
612	C₂×Q₈	—	5	2	no	—
613	C₂×Q₈	—	5	4	no	—
614	C₂×D₄	—	5	4	no	—
615	C₂×D₄	—	5	4	no	—
616	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
617	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
618	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
619	C₂²×C₄	—	5	1	no	—
620	C₂²×C₄	—	5	4	no	—
621	C₂²×C₄	—	5	1	no	—
622	C₂²×C₄	—	5	4	no	—
623	C₂²×C₄	—	5	1	no	—
624	C₂²×C₄	—	5	1	no	—
625	C₂²×C₄	—	5	1	no	—
626	C₂²×C₄	—	5	2	no	—
627	C₂²×C₄	—	5	2	no	—
628	C₂²×C₄	—	10	4	no	—
629	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
630	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
631	C₄⋊C₄	—	5	2	no	—
632	C₄⋊C₄	—	5	2	no	—
633	C₄⋊C₄	—	5	2	no	—
634	C₄⋊C₄	—	5	2	no	—
635	C₄⋊C₄	—	5	4	no	—
636	C₄⋊C₄	—	5	4	no	—
637	C₄⋊C₄	—	5	4	no	—
638	C₄⋊C₄	—	5	4	no	—
639	C₄⋊C₄	—	5	4	no	—
640	C₄⋊C₄	—	5	4	no	—
641	C₄⋊C₄	—	5	4	no	—
642	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
643	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
644	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
645	C₂²⋊C₄	—	5	2	no	—
646	C₂²⋊C₄	—	5	4	no	—
647	C₂²⋊C₄	—	5	4	no	—
648	C₂²⋊C₄	—	5	4	no	—
649	C₂²⋊C₄	—	5	4	no	—
650	C₂²⋊C₄	—	5	4	no	—
651	C₂²⋊C₄	—	5	2	no	—
652	C₂²⋊C₄	—	5	2	no	—
653	C₂²⋊C₄	—	5	4	no	—
654	C₂²⋊C₄	—	5	4	no	—
655	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
656	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
657	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
658	C₄²	—	5	2	no	—
659	C₄²	—	5	2	no	—
660	C₄²	—	5	4	no	—
661	C₄²	—	5	1	no	—
662	C₄²	—	5	1	no	—
663	C₄²	—	5	4	no	—
664	C₄²	—	5	4	no	—
665	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
666	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
667	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
668	C₂²×C₃	—	2	1	no	—
669	C₂²×C₃	—	2	4	no	—
670	C₂²×C₃	—	2	4	no	—
671	C₂²×C₃	—	2	4	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	5	2	no	—
674	C₂²×C₃	—	10	2	no	—
675	C₂²×C₃	—	10	1	no	—
676	C₂²×C₃	—	10	2	no	—
677	C₂²×C₃	—	20	4	no	—
678	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	2	no	—
681	C₃×C₄	—	2	4	no	—
682	C₃×C₄	—	2	2	no	—
683	C₃×C₄	—	5	2	no	—
684	C₃×C₄	—	10	1	no	—
685	C₃×C₄	—	10	4	no	—
686	C₃×C₄	—	10	2	no	—
687	C₃×C₄	—	10	4	no	—
688	C₃×C₄	—	10	2	no	—
689	C₃×C₄	D₅×#41	1	2	yes	—
690	C₂×C₅	—	4	1	no	—
691	C₂×C₅	—	4	4	no	—
692	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
693	C₂×C₅	C₃×#585	1	2	yes	—
694	D₅	—	2	2	no	—
695	D₅	—	4	1	no	—
696	C₂³	—	5	1	no	—
697	C₂³	—	5	1	no	—
698	C₂³	—	10	2	no	—
699	C₂³	—	20	2	no	—
700	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
701	C₂³	C₂³×C₃×D₅	1	4	yes	—
702	Q₈	—	10	4	no	—
703	Q₈	—	20	4	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	10	8	no	—
708	D₄	—	20	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	5	1	no	—
712	C₂×C₄	—	5	4	no	—
713	C₂×C₄	—	5	2	no	—
714	C₂×C₄	—	5	2	no	—
715	C₂×C₄	—	5	4	no	—
716	C₂×C₄	—	5	4	no	—
717	C₂×C₄	—	5	1	no	—
718	C₂×C₄	—	10	2	no	—
719	C₂×C₄	—	10	2	no	—
720	C₂×C₄	—	10	2	no	—
721	C₂×C₄	—	10	8	no	—
722	C₂×C₄	—	10	2	no	—
723	C₂×C₄	—	20	2	no	—
724	C₂×C₄	—	20	2	no	—
725	C₂×C₄	—	20	4	no	—
726	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
727	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
728	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
729	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
730	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
731	C₂×C₃	—	4	1	no	—
732	C₂×C₃	—	4	4	no	—
733	C₂×C₃	—	10	2	no	—
734	C₂×C₃	—	20	1	no	—
735	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
736	C₂×C₃	#66285	1	2	yes	—
737	C₅	C₃×#3455	1	1	yes	characteristic, complemented, Sylow
738	C₂²	—	2	1	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	5	2	no	—
744	C₂²	—	10	2	no	—
745	C₂²	—	10	1	no	—
746	C₂²	—	10	2	no	—
747	C₂²	—	20	4	no	—
748	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	5	2	no	—
754	C₄	—	10	1	no	—
755	C₄	—	10	4	no	—
756	C₄	—	10	2	no	—
757	C₄	—	10	4	no	—
758	C₄	—	10	2	no	—
759	C₄	C₃×D₅×#41	1	2	yes	—
760	C₃	#10618368	1	1	yes	characteristic, direct product factor, Sylow
761	C₂	—	4	1	no	—
762	C₂	—	4	4	no	—
763	C₂	—	10	2	no	—
764	C₂	—	20	1	no	—
765	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
766	C₂	C₃×#66285	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#540	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#540	D₅
hypocenter	C₅	C₃×#3455
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#540

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₃×#66053	C₂	semidirect
3. C₃×#66050	C₂	semidirect
4. C₃×#66031	C₂	semidirect
5. C₃×#66022	C₂	semidirect
6. C₃×#65994	C₂	semidirect
7. C₃×#65983	C₂	semidirect
8. C₃×#65947	C₂	semidirect
9. C₃×#65940	C₂	semidirect
10. C₃×#65937	C₂	semidirect
11. C₃×#65934	C₂	semidirect
12. C₃×#65895	C₂	semidirect
13. C₃×C₄×#711	C₂	semidirect
14. C₃×D₅×#117	C₂	semidirect
15. C₃×#65852	C₂	semidirect
16. #10618368	C₃	direct (N × H)
19. C₃×C₅×#127	C₂²	semidirect
20. C₃×C₅×#125	C₂²	semidirect
21. C₃×C₅×#123	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
31. C₃×#4082	C₂²	semidirect
33. C₃×#4081	C₂²	semidirect
35. C₃×D₄×Dic₅	C₂²	semidirect
36. C₃×D₄×Dic₅	C₂²	semidirect
41. C₃×#4070	C₂²	semidirect
42. C₂×C₃×C₄×Dic₅	C₂²	semidirect
49. C₃×#4036	C₂²	semidirect
50. C₃×#4035	C₂²	semidirect
51. C₃×#4034	C₂²	semidirect
52. C₃×#4033	C₂²	semidirect
53. C₃×#4033	C₂²	semidirect
60. C₃×#4025	C₂²	semidirect
61. C₃×#4025	C₂²	semidirect
62. C₃×#4024	C₂²	semidirect
64. C₃×#4023	C₂²	semidirect
69. C₃×#4016	C₂²	semidirect
70. C₃×#4015	C₂²	semidirect
71. C₃×C₄×Dic₁₀	C₂²	semidirect
73. C₅×#540	C₂×C₃	semidirect
74. #66053	C₂×C₃	semidirect
75. #66050	C₂×C₃	semidirect
76. #66031	C₂×C₃	semidirect
77. #66022	C₂×C₃	semidirect
78. #65994	C₂×C₃	semidirect
79. #65983	C₂×C₃	semidirect
80. #65947	C₂×C₃	semidirect
81. #65940	C₂×C₃	semidirect
82. #65937	C₂×C₃	semidirect
83. #65934	C₂×C₃	semidirect
84. #65895	C₂×C₃	semidirect
85. C₄×#711	C₂×C₃	semidirect
86. D₅×#117	C₂×C₃	semidirect
87. #65852	C₂×C₃	semidirect
150. C₃×#540	D₅	semidirect
162. C₅×#127	C₂²×C₃	semidirect
163. C₅×#125	C₂²×C₃	semidirect
164. C₅×#123	C₂²×C₃	semidirect
167. C₄×C₅×D₄	C₂²×C₃	semidirect
174. #4082	C₂²×C₃	semidirect
176. #4081	C₂²×C₃	semidirect
178. D₄×Dic₅	C₂²×C₃	semidirect
179. D₄×Dic₅	C₂²×C₃	semidirect
184. #4070	C₂²×C₃	semidirect
185. C₂×C₄×Dic₅	C₂²×C₃	semidirect
192. #4036	C₂²×C₃	semidirect
193. #4035	C₂²×C₃	semidirect
194. #4034	C₂²×C₃	semidirect
195. #4033	C₂²×C₃	semidirect
196. #4033	C₂²×C₃	semidirect
203. #4025	C₂²×C₃	semidirect
204. #4025	C₂²×C₃	semidirect
205. #4024	C₂²×C₃	semidirect
207. #4023	C₂²×C₃	semidirect
212. #4016	C₂²×C₃	semidirect
213. #4015	C₂²×C₃	semidirect
214. C₄×Dic₁₀	C₂²×C₃	semidirect
255. C₃×#127	C₂×D₅	semidirect
263. C₃×#125	C₂×D₅	semidirect
271. C₃×#123	C₂×D₅	semidirect
292. C₃×C₄×D₄	C₂×D₅	semidirect
368. #540	C₃×D₅	semidirect
496. #127	C₂×C₃×D₅	semidirect
504. #125	C₂×C₃×D₅	semidirect
512. #123	C₂×C₃×D₅	semidirect
533. C₄×D₄	C₂×C₃×D₅	semidirect
667. C₃×C₅	#3455	semidirect
737. C₅	C₃×#3455	semidirect
760. C₃	#10618368	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×C₅×#540	2
C₃×#66053	2
C₃×#66050	2
C₃×#66031	2
C₃×#66022	2
C₃×#65994	2
C₃×#65983	2
C₃×#65947	2
C₃×#65940	2
C₃×#65937	2
C₃×#65934	2
C₃×#65895	2
C₃×C₄×#711	2
C₃×D₅×#117	2
C₃×#65852	2
#10618368	3
C₃×#3455	5

Subgroups — C3×#10618368 #14481500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618368 #14481500