Subgroups — C₂×C₃×#65347 #14438971

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×#686	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4020	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65347	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65347	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₂₀	—	2	2	no	—
11	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
12	C₃×C₅×#124	—	2	2	no	—
13	C₃×C₅×#124	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#688	—	2	8	no	—
17	C₂×C₃×#688	C₂²	1	8	yes	complemented
18	C₂×C₃×#686	—	2	8	no	—
19	C₂×C₃×#686	C₂²	1	8	yes	complemented
20	C₂²×C₃×#168	C₂²	1	2	yes	—
21	C₃×#4020	—	2	2	no	—
22	C₃×#4020	C₂²	1	4	yes	complemented
23	C₃×#3935	C₂²	1	4	yes	complemented
24	C₂×C₃×#496	—	5	1	no	maximal, Hall
25	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂²×#688	C₂×C₃	1	2	yes	complemented
27	C₂²×#686	C₂×C₃	1	2	yes	complemented
28	C₂×#4020	C₂×C₃	1	1	yes	characteristic, complemented
29	#65347	C₂×C₃	1	8	yes	direct product factor
30	C₂×#3935	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂³×C₃×D₅	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×D₂₀	—	2	4	no	—
43	C₂×C₃×D₂₀	—	2	4	no	—
44	C₂×C₃×D₂₀	—	2	8	no	—
45	C₂×C₃×D₂₀	—	2	2	no	—
46	C₂×C₃×D₂₀	—	4	8	no	—
47	C₂×C₃×D₂₀	C₂³	1	4	yes	—
48	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
49	C₃×C₄²×C₅	D₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	2	yes	—
51	C₃×#688	—	2	16	no	—
52	C₃×#686	—	2	16	no	—
53	C₂×C₃×#168	D₄	1	8	yes	complemented
54	C₂×C₃×#168	C₂³	1	4	yes	—
55	C₂²×C₃×SD₁₆	—	5	2	no	—
56	C₂²×C₃×D₈	—	5	2	no	—
57	C₂×C₃×#127	—	5	1	no	—
58	C₂×C₃×#124	D₅	1	1	yes	characteristic, complemented
59	C₃×#496	—	5	8	no	—
60	C₂×C₃×#97	—	5	1	no	—
61	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
63	C₂²×D₂₀	—	2	2	no	—
64	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
65	C₅×#124	—	2	2	no	—
66	C₅×#124	C₂²×C₃	1	4	yes	complemented
67	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂×#688	—	2	8	no	—
70	C₂×#688	C₂²×C₃	1	8	yes	complemented
71	C₂×#686	—	2	8	no	—
72	C₂×#686	C₂²×C₃	1	8	yes	complemented
73	C₂²×#168	C₂²×C₃	1	2	yes	—
74	#4020	—	2	2	no	—
75	#4020	C₂²×C₃	1	4	yes	complemented
76	#3935	C₂²×C₃	1	4	yes	complemented
77	C₂×#496	—	5	1	no	Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	4	2	no	—
80	C₂³×C₃×C₅	—	4	4	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₃×D₅	—	2	4	no	—
83	C₂²×C₃×D₅	—	4	4	no	—
84	C₂²×C₃×D₅	—	4	8	no	—
85	C₃×C₅×Q₈	—	2	4	no	—
86	C₃×C₅×Q₈	—	4	2	no	—
87	C₃×C₅×D₄	—	2	4	no	—
88	C₃×C₅×D₄	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₃×D₂₀	—	2	4	no	—
97	C₃×D₂₀	—	2	4	no	—
98	C₃×D₂₀	—	4	16	no	—
99	C₃×D₂₀	—	4	4	no	—
100	C₃×#168	C₂×D₄	1	8	yes	complemented
101	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
102	C₂²×C₃×D₄	—	5	2	no	—
103	C₂²×C₃×D₄	—	10	2	no	—
104	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
105	C₂×C₃×SD₁₆	—	5	8	no	—
106	C₂×C₃×SD₁₆	—	10	8	no	—
107	C₂×C₃×D₈	—	5	8	no	—
108	C₂×C₃×D₈	—	10	8	no	—
109	C₂²×C₃×C₈	—	5	2	no	—
110	C₃×#127	—	5	4	no	—
111	C₃×#127	—	10	2	no	—
112	C₃×#124	—	2	2	no	—
113	C₃×#124	C₂×D₅	1	4	yes	complemented
114	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
116	C₃×#97	—	5	4	no	—
117	C₂⁴×C₅	—	2	1	no	—
118	C₂³×D₅	—	2	2	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	4	no	—
121	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂×D₂₀	—	2	4	no	—
129	C₂×D₂₀	—	2	4	no	—
130	C₂×D₂₀	—	2	8	no	—
131	C₂×D₂₀	—	2	2	no	—
132	C₂×D₂₀	—	4	8	no	—
133	C₂×D₂₀	C₂³×C₃	1	4	yes	—
134	C₅×C₂²⋊C₄	—	2	8	no	—
135	C₄²×C₅	C₃×D₄	1	2	yes	—
136	C₄²×C₅	C₂³×C₃	1	2	yes	—
137	#688	—	2	16	no	—
138	#686	—	2	16	no	—
139	C₂×#168	C₃×D₄	1	8	yes	complemented
140	C₂×#168	C₂³×C₃	1	4	yes	—
141	C₂²×SD₁₆	—	5	2	no	—
142	C₂²×D₈	—	5	2	no	—
143	C₂×#127	—	5	1	no	—
144	C₂×#124	C₃×D₅	1	1	yes	characteristic, complemented
145	#496	—	5	8	no	—
146	C₂×#97	—	5	1	no	—
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	8	4	no	—
150	C₂²×C₃×C₅	#127	1	2	yes	—
151	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
152	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₃×D₅	—	4	4	no	—
154	C₂×C₃×D₅	—	4	8	no	—
155	C₂×C₃×D₅	—	8	8	no	—
156	C₃×C₄×C₅	—	2	4	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	#127	1	2	yes	—
159	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
160	C₂⁴×C₃	—	2	1	no	—
161	C₂⁴×C₃	—	10	2	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
165	C₂×C₃×D₄	—	2	4	no	—
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	—	5	4	no	—
168	C₂×C₃×D₄	—	10	4	no	—
169	C₂×C₃×D₄	—	10	4	no	—
170	C₂×C₃×D₄	—	10	8	no	—
171	C₂×C₃×D₄	—	10	2	no	—
172	C₂×C₃×D₄	—	20	8	no	—
173	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
176	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
177	C₃×SD₁₆	—	10	16	no	—
178	C₃×D₈	—	10	16	no	—
179	C₂×C₃×C₈	—	5	8	no	—
180	C₂×C₃×C₈	—	5	4	no	—
181	C₃×C₂²⋊C₄	—	2	8	no	—
182	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
183	C₃×C₄²	C₂²×D₅	1	2	yes	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	4	no	—
187	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
188	C₂²×D₅	—	2	4	no	—
189	C₂²×D₅	—	4	4	no	—
190	C₂²×D₅	—	4	8	no	—
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	D₂₀	—	2	4	no	—
203	D₂₀	—	2	4	no	—
204	D₂₀	—	4	16	no	—
205	D₂₀	—	4	4	no	—
206	#168	C₂×C₃×D₄	1	8	yes	complemented
207	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
208	C₂²×D₄	—	5	2	no	—
209	C₂²×D₄	—	10	2	no	—
210	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
211	C₂×SD₁₆	—	5	8	no	—
212	C₂×SD₁₆	—	10	8	no	—
213	C₂×D₈	—	5	8	no	—
214	C₂×D₈	—	10	8	no	—
215	C₂²×C₈	—	5	2	no	—
216	#127	—	5	4	no	—
217	#127	—	10	2	no	—
218	#124	—	2	2	no	—
219	#124	C₂×C₃×D₅	1	4	yes	complemented
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
222	#97	—	5	4	no	—
223	C₂×C₃×C₅	—	8	2	no	—
224	C₂×C₃×C₅	#496	1	4	yes	complemented
225	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
226	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
227	C₃×D₅	—	8	4	no	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	4	2	no	—
230	C₂³×C₃	—	4	4	no	—
231	C₂³×C₃	—	10	4	no	—
232	C₂³×C₃	—	20	4	no	—
233	C₂³×C₃	—	20	8	no	—
234	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
235	C₃×Q₈	—	2	4	no	—
236	C₃×Q₈	—	4	2	no	—
237	C₃×D₄	—	2	4	no	—
238	C₃×D₄	—	4	2	no	—
239	C₃×D₄	—	10	4	no	—
240	C₃×D₄	—	10	4	no	—
241	C₃×D₄	—	20	16	no	—
242	C₃×D₄	—	20	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
247	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
248	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
250	C₃×C₈	—	5	8	no	—
251	C₂²×C₅	—	4	4	no	—
252	C₂²×C₅	—	4	2	no	—
253	C₂²×C₅	—	8	4	no	—
254	C₂²×C₅	C₃×#127	1	2	yes	—
255	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
256	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
257	C₂×D₅	—	4	8	no	—
258	C₂×D₅	—	4	4	no	—
259	C₂×D₅	—	8	8	no	—
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	C₃×#127	1	2	yes	—
263	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
264	C₂⁴	—	2	1	no	—
265	C₂⁴	—	10	2	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	5	4	no	—
272	C₂×D₄	—	10	4	no	—
273	C₂×D₄	—	10	4	no	—
274	C₂×D₄	—	10	8	no	—
275	C₂×D₄	—	10	2	no	—
276	C₂×D₄	—	20	8	no	—
277	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
280	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
281	SD₁₆	—	10	16	no	—
282	D₈	—	10	16	no	—
283	C₂×C₈	—	5	8	no	—
284	C₂×C₈	—	5	4	no	—
285	C₂²⋊C₄	—	2	8	no	—
286	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
287	C₄²	C₂²×C₃×D₅	1	2	yes	—
288	C₃×C₅	C₂×#496	1	1	yes	characteristic, complemented, Hall
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	—	4	4	no	—
291	C₂²×C₃	—	8	4	no	—
292	C₂²×C₃	—	20	4	no	—
293	C₂²×C₃	—	20	8	no	—
294	C₂²×C₃	—	40	8	no	—
295	C₂²×C₃	#4086	1	2	yes	—
296	C₂²×C₃	#4095	1	4	yes	—
297	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	#4086	1	2	yes	—
301	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
302	C₂×C₅	—	8	2	no	—
303	C₂×C₅	C₃×#496	1	4	yes	complemented
304	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
305	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
306	D₅	—	8	4	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	10	4	no	—
311	C₂³	—	20	4	no	—
312	C₂³	—	20	8	no	—
313	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	4	2	no	—
318	D₄	—	10	4	no	—
319	D₄	—	10	4	no	—
320	D₄	—	20	16	no	—
321	D₄	—	20	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
326	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
327	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
328	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
329	C₈	—	5	8	no	—
330	C₂×C₃	—	8	2	no	—
331	C₂×C₃	—	40	4	no	—
332	C₂×C₃	#65347	1	4	yes	direct product factor
333	C₂×C₃	C₂×#4086	1	1	yes	characteristic
334	C₂×C₃	C₂×#4095	1	2	yes	—
335	C₅	C₂×C₃×#496	1	1	yes	characteristic, complemented, Sylow
336	C₂²	—	4	2	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	20	4	no	—
340	C₂²	—	20	8	no	—
341	C₂²	—	40	8	no	—
342	C₂²	C₃×#4086	1	2	yes	—
343	C₂²	C₃×#4095	1	4	yes	—
344	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
345	C₄	—	2	4	no	—
346	C₄	—	4	2	no	—
347	C₄	C₃×#4086	1	2	yes	—
348	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
349	C₃	C₂×#65347	1	1	yes	characteristic, direct product factor, Sylow
350	C₂	—	8	2	no	—
351	C₂	—	40	4	no	—
352	C₂	C₃×#65347	1	4	yes	direct product factor
353	C₂	C₂×C₃×#4086	1	1	yes	characteristic
354	C₂	C₂×C₃×#4095	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₂×C₃×#496
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂²×C₃×#688	C₂	semidirect
3. C₂²×C₃×#686	C₂	semidirect
4. C₂×C₃×#4020	C₂	semidirect
5. C₃×#65347	C₂	direct (N × H)
6. C₂×C₃×#3935	C₂	semidirect
7. C₂×#65347	C₃	direct (N × H)
13. C₃×C₅×#124	C₂²	semidirect
17. C₂×C₃×#688	C₂²	semidirect
19. C₂×C₃×#686	C₂²	semidirect
22. C₃×#4020	C₂²	semidirect
23. C₃×#3935	C₂²	semidirect
25. C₂×C₅×#124	C₂×C₃	semidirect
26. C₂²×#688	C₂×C₃	semidirect
27. C₂²×#686	C₂×C₃	semidirect
28. C₂×#4020	C₂×C₃	semidirect
29. #65347	C₂×C₃	direct (N × H)
30. C₂×#3935	C₂×C₃	semidirect
53. C₂×C₃×#168	D₄	semidirect
58. C₂×C₃×#124	D₅	semidirect
66. C₅×#124	C₂²×C₃	semidirect
70. C₂×#688	C₂²×C₃	semidirect
72. C₂×#686	C₂²×C₃	semidirect
75. #4020	C₂²×C₃	semidirect
76. #3935	C₂²×C₃	semidirect
100. C₃×#168	C₂×D₄	semidirect
113. C₃×#124	C₂×D₅	semidirect
139. C₂×#168	C₃×D₄	semidirect
144. C₂×#124	C₃×D₅	semidirect
206. #168	C₂×C₃×D₄	semidirect
219. #124	C₂×C₃×D₅	semidirect
224. C₂×C₃×C₅	#496	semidirect
288. C₃×C₅	C₂×#496	semidirect
303. C₂×C₅	C₃×#496	semidirect
332. C₂×C₃	#65347	direct (N × H)
335. C₅	C₂×C₃×#496	semidirect
349. C₃	C₂×#65347	direct (N × H)
352. C₂	C₃×#65347	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×#124	2
C₂²×C₃×#688	2
C₂²×C₃×#686	2
C₂×C₃×#4020	2
C₃×#65347	2
C₂×C₃×#3935	2
C₂×#65347	3
C₂×C₃×#496	5

Subgroups — C2×C3×#65347 #14438971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65347 #14438971