Subgroups — C₂×C₃×#66031 #14481209

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66031	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4044	C₂	1	4	yes	maximal
4	C₂×C₃×#4043	C₂	1	2	yes	maximal
5	C₂×C₃×#4036	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4033	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
8	C₂×C₃×#4015	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#66031	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
12	C₃×C₅×#125	C₂²	1	8	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	C₂²	1	4	yes	—
17	C₂×C₃×#685	C₂²	1	2	yes	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
20	C₂×C₃×#683	C₂²	1	4	yes	—
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×#4044	C₂²	1	32	yes	—
25	C₃×#4043	C₂²	1	16	yes	—
26	C₃×#4036	C₂²	1	32	yes	complemented
27	C₃×#4033	C₂²	1	16	yes	complemented
28	C₃×#4018	C₂²	1	8	yes	—
29	C₃×#4015	C₂²	1	8	yes	complemented
30	C₂×C₃×#541	—	5	1	no	maximal, Hall
31	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
32	#66031	C₂×C₃	1	16	yes	direct product factor
33	C₂×#4044	C₂×C₃	1	4	yes	—
34	C₂×#4043	C₂×C₃	1	2	yes	—
35	C₂×#4036	C₂×C₃	1	4	yes	complemented
36	C₂×#4033	C₂×C₃	1	2	yes	complemented
37	C₂×#4018	C₂×C₃	1	1	yes	characteristic
38	C₂×#4015	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
48	C₂×C₃×Dic₁₀	—	2	8	no	—
49	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
50	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
52	C₃×C₄²×C₅	C₂³	1	4	yes	—
53	C₃×#685	C₂³	1	8	yes	—
54	C₃×#685	C₂³	1	16	yes	—
55	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
56	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
57	C₃×#683	C₂³	1	8	yes	—
58	C₃×#683	C₂³	1	16	yes	—
59	C₃×C₄×Dic₅	C₂³	1	4	yes	—
60	C₃×C₄×Dic₅	C₂³	1	16	yes	—
61	C₃×#541	—	5	16	no	—
62	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
63	C₂×C₃×#126	—	5	4	no	—
64	C₂×C₃×#125	—	5	4	no	—
65	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
66	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
67	C₂×C₃×C₄×Q₈	—	5	2	no	—
68	C₂×C₃×#117	—	5	1	no	—
69	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
71	C₅×#125	C₂²×C₃	1	8	yes	complemented
72	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
74	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂×#685	C₂²×C₃	1	2	yes	—
76	C₂×#685	C₂²×C₃	1	4	yes	—
77	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
78	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
79	C₂×#683	C₂²×C₃	1	2	yes	—
80	C₂×#683	C₂²×C₃	1	4	yes	—
81	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
83	#4044	C₂²×C₃	1	32	yes	—
84	#4043	C₂²×C₃	1	16	yes	—
85	#4036	C₂²×C₃	1	32	yes	complemented
86	#4033	C₂²×C₃	1	16	yes	complemented
87	#4018	C₂²×C₃	1	8	yes	—
88	#4015	C₂²×C₃	1	8	yes	complemented
89	C₂×#541	—	5	1	no	Sylow
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂²×C₃×D₅	—	2	2	no	—
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	—	2	8	no	—
96	C₂×C₃×C₄×C₅	#41	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
98	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
100	C₂×C₃×Dic₅	—	2	8	no	—
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	—	2	4	no	—
103	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
104	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
105	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
106	C₃×C₄×D₅	—	2	8	no	—
107	C₃×Dic₁₀	—	2	16	no	—
108	C₂²×C₃×Q₈	—	5	2	no	—
109	C₂³×C₃×C₄	—	5	1	no	—
110	C₃×C₄⋊Q₈	—	5	8	no	—
111	C₃×#126	—	5	32	no	—
112	C₃×#125	—	5	32	no	—
113	C₃×#125	C₂×D₅	1	8	yes	complemented
114	C₃×C₂²⋊Q₈	—	5	16	no	—
115	C₃×C₄×Q₈	—	5	16	no	—
116	C₃×#117	—	5	8	no	—
117	C₂×C₃×C₄⋊C₄	—	5	2	no	—
118	C₂×C₃×C₄⋊C₄	—	5	4	no	—
119	C₂×C₃×C₄⋊C₄	—	5	4	no	—
120	C₂×C₃×C₄⋊C₄	—	5	4	no	—
121	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
122	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	4	no	—
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
133	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
134	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
135	C₂×C₄×D₅	—	2	4	no	—
136	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
137	C₂×Dic₁₀	—	2	8	no	—
138	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
139	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
140	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
141	C₄²×C₅	C₂³×C₃	1	4	yes	—
142	#685	C₂³×C₃	1	8	yes	—
143	#685	C₂³×C₃	1	16	yes	—
144	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
145	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
146	#683	C₂³×C₃	1	8	yes	—
147	#683	C₂³×C₃	1	16	yes	—
148	C₄×Dic₅	C₂³×C₃	1	4	yes	—
149	C₄×Dic₅	C₂³×C₃	1	16	yes	—
150	#541	—	5	16	no	—
151	C₂×C₄⋊Q₈	—	5	1	no	—
152	C₂×#126	—	5	4	no	—
153	C₂×#125	—	5	4	no	—
154	C₂×#125	C₃×D₅	1	1	yes	characteristic, complemented
155	C₂×C₂²⋊Q₈	—	5	2	no	—
156	C₂×C₄×Q₈	—	5	2	no	—
157	C₂×#117	—	5	1	no	—
158	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
159	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
160	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₅	—	2	2	no	—
162	C₂×C₃×D₅	—	2	4	no	—
163	C₂×C₃×D₅	—	4	4	no	—
164	C₃×C₄×C₅	—	2	8	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	C₂×#41	1	4	yes	—
167	C₃×Dic₅	—	2	8	no	—
168	C₃×Dic₅	—	2	2	no	—
169	C₃×Dic₅	—	2	4	no	—
170	C₂⁴×C₃	—	5	1	no	—
171	C₂×C₃×Q₈	—	5	8	no	—
172	C₂×C₃×Q₈	—	10	8	no	—
173	C₂²×C₃×C₄	—	5	2	no	—
174	C₂²×C₃×C₄	—	5	4	no	—
175	C₂²×C₃×C₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	5	4	no	—
177	C₂²×C₃×C₄	—	10	4	no	—
178	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
179	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	5	8	no	—
182	C₃×C₄⋊C₄	—	5	16	no	—
183	C₃×C₄⋊C₄	—	5	16	no	—
184	C₃×C₄⋊C₄	—	5	16	no	—
185	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
186	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
187	C₃×C₂²⋊C₄	—	5	8	no	—
188	C₃×C₂²⋊C₄	—	5	16	no	—
189	C₃×C₄²	—	5	4	no	—
190	C₃×C₄²	—	5	16	no	—
191	C₃×C₄²	C₂²×D₅	1	4	yes	—
192	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	—	2	4	no	—
195	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	2	8	no	—
198	C₂×C₄×C₅	C₃×#41	1	4	yes	—
199	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
200	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
201	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
202	C₂×Dic₅	—	2	8	no	—
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	—	2	4	no	—
205	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
206	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
207	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
208	C₄×D₅	—	2	8	no	—
209	Dic₁₀	—	2	16	no	—
210	C₂²×Q₈	—	5	2	no	—
211	C₂³×C₄	—	5	1	no	—
212	C₄⋊Q₈	—	5	8	no	—
213	#126	—	5	32	no	—
214	#125	—	5	32	no	—
215	#125	C₂×C₃×D₅	1	8	yes	complemented
216	C₂²⋊Q₈	—	5	16	no	—
217	C₄×Q₈	—	5	16	no	—
218	#117	—	5	8	no	—
219	C₂×C₄⋊C₄	—	5	2	no	—
220	C₂×C₄⋊C₄	—	5	4	no	—
221	C₂×C₄⋊C₄	—	5	4	no	—
222	C₂×C₄⋊C₄	—	5	4	no	—
223	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
224	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
225	C₂×C₂²⋊C₄	—	5	2	no	—
226	C₂×C₂²⋊C₄	—	5	4	no	—
227	C₂×C₄²	—	5	1	no	—
228	C₂×C₄²	—	5	4	no	—
229	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
230	C₂×C₃×C₅	#541	1	4	yes	complemented
231	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
233	C₃×D₅	—	4	2	no	—
234	C₂³×C₃	—	5	2	no	—
235	C₂³×C₃	—	10	2	no	—
236	C₂³×C₃	—	10	4	no	—
237	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
238	C₃×Q₈	—	10	16	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	5	4	no	—
242	C₂×C₃×C₄	—	5	8	no	—
243	C₂×C₃×C₄	—	5	2	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	10	8	no	—
246	C₂×C₃×C₄	—	10	4	no	—
247	C₂×C₃×C₄	—	10	8	no	—
248	C₂×C₃×C₄	#713	1	4	yes	—
249	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
250	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
251	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
252	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
253	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
254	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
255	C₂×D₅	—	2	2	no	—
256	C₂×D₅	—	2	4	no	—
257	C₂×D₅	—	4	4	no	—
258	C₄×C₅	—	2	8	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	C₂×C₃×#41	1	4	yes	—
261	Dic₅	—	2	8	no	—
262	Dic₅	—	2	2	no	—
263	Dic₅	—	2	4	no	—
264	C₂⁴	—	5	1	no	—
265	C₂×Q₈	—	5	8	no	—
266	C₂×Q₈	—	10	8	no	—
267	C₂²×C₄	—	5	2	no	—
268	C₂²×C₄	—	5	4	no	—
269	C₂²×C₄	—	5	1	no	—
270	C₂²×C₄	—	5	4	no	—
271	C₂²×C₄	—	10	4	no	—
272	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
273	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
274	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
275	C₄⋊C₄	—	5	8	no	—
276	C₄⋊C₄	—	5	16	no	—
277	C₄⋊C₄	—	5	16	no	—
278	C₄⋊C₄	—	5	16	no	—
279	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
280	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
281	C₂²⋊C₄	—	5	8	no	—
282	C₂²⋊C₄	—	5	16	no	—
283	C₄²	—	5	4	no	—
284	C₄²	—	5	16	no	—
285	C₄²	C₂²×C₃×D₅	1	4	yes	—
286	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	10	2	no	—
288	C₂²×C₃	—	10	4	no	—
289	C₂²×C₃	—	20	4	no	—
290	C₂²×C₃	C₂×#713	1	2	yes	—
291	C₂²×C₃	#4150	1	4	yes	—
292	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	10	2	no	—
296	C₃×C₄	—	10	8	no	—
297	C₃×C₄	—	10	4	no	—
298	C₃×C₄	C₂×#713	1	4	yes	—
299	C₂×C₅	C₃×#541	1	4	yes	complemented
300	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
301	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
302	D₅	—	4	2	no	—
303	C₂³	—	5	2	no	—
304	C₂³	—	10	2	no	—
305	C₂³	—	10	4	no	—
306	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
307	Q₈	—	10	16	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	5	4	no	—
311	C₂×C₄	—	5	8	no	—
312	C₂×C₄	—	5	2	no	—
313	C₂×C₄	—	10	2	no	—
314	C₂×C₄	—	10	8	no	—
315	C₂×C₄	—	10	4	no	—
316	C₂×C₄	—	10	8	no	—
317	C₂×C₄	C₃×#713	1	4	yes	—
318	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
319	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
320	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
321	C₂×C₃	—	20	2	no	—
322	C₂×C₃	#66031	1	4	yes	direct product factor
323	C₂×C₃	C₂²×#713	1	1	yes	characteristic
324	C₂×C₃	C₂×#4150	1	2	yes	—
325	C₅	C₂×C₃×#541	1	1	yes	characteristic, complemented, Sylow
326	C₂²	—	10	2	no	—
327	C₂²	—	10	4	no	—
328	C₂²	—	20	4	no	—
329	C₂²	C₂×C₃×#713	1	2	yes	—
330	C₂²	C₃×#4150	1	4	yes	—
331	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	10	2	no	—
335	C₄	—	10	8	no	—
336	C₄	—	10	4	no	—
337	C₄	C₂×C₃×#713	1	4	yes	—
338	C₃	C₂×#66031	1	1	yes	characteristic, direct product factor, Sylow
339	C₂	—	20	2	no	—
340	C₂	C₃×#66031	1	4	yes	direct product factor
341	C₂	C₂²×C₃×#713	1	1	yes	characteristic
342	C₂	C₂×C₃×#4150	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₂×C₃×#125	D₅
hypocenter	C₅	C₂×C₃×#541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₃×#66031	C₂	direct (N × H)
5. C₂×C₃×#4036	C₂	semidirect
6. C₂×C₃×#4033	C₂	semidirect
8. C₂×C₃×#4015	C₂	semidirect
9. C₂×#66031	C₃	direct (N × H)
12. C₃×C₅×#125	C₂²	semidirect
26. C₃×#4036	C₂²	semidirect
27. C₃×#4033	C₂²	semidirect
29. C₃×#4015	C₂²	semidirect
31. C₂×C₅×#125	C₂×C₃	semidirect
32. #66031	C₂×C₃	direct (N × H)
35. C₂×#4036	C₂×C₃	semidirect
36. C₂×#4033	C₂×C₃	semidirect
38. C₂×#4015	C₂×C₃	semidirect
65. C₂×C₃×#125	D₅	semidirect
71. C₅×#125	C₂²×C₃	semidirect
85. #4036	C₂²×C₃	semidirect
86. #4033	C₂²×C₃	semidirect
88. #4015	C₂²×C₃	semidirect
113. C₃×#125	C₂×D₅	semidirect
154. C₂×#125	C₃×D₅	semidirect
215. #125	C₂×C₃×D₅	semidirect
230. C₂×C₃×C₅	#541	semidirect
286. C₃×C₅	C₂×#541	semidirect
299. C₂×C₅	C₃×#541	semidirect
322. C₂×C₃	#66031	direct (N × H)
325. C₅	C₂×C₃×#541	semidirect
338. C₃	C₂×#66031	direct (N × H)
340. C₂	C₃×#66031	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×#125	2
C₃×#66031	2
C₂×C₃×#4044	2
C₂×C₃×#4043	2
C₂×C₃×#4036	2
C₂×C₃×#4033	2
C₂×C₃×#4018	2
C₂×C₃×#4015	2
C₂×#66031	3
C₂×C₃×#541	5

Subgroups — C2×C3×#66031 #14481209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66031 #14481209