Subgroups — C₃×#10602390 #14281687

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄⋊#168	C₂	1	4	yes	maximal, complemented
5	#10602390	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
7	C₂³×C₃×C₄×C₅	—	2	1	no	—
8	C₃×C₄×C₅×D₄	—	2	1	no	—
9	C₃×C₄×C₅×D₄	—	2	1	no	—
10	C₃×C₄×C₅×D₄	C₄	1	2	yes	—
11	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₂²⋊#168	—	2	1	no	—
16	C₃×C₂²⋊#168	—	2	1	no	—
17	C₃×C₄⋊#168	—	2	1	no	—
18	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
19	C₃×C₄×#168	—	2	1	no	—
20	C₃×C₄×#168	C₂²	1	2	yes	complemented
21	C₃×#1478	—	5	1	no	maximal, Hall
22	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
23	#65214	C₂×C₃	1	1	yes	characteristic, complemented
24	#65214	C₂×C₃	1	1	yes	characteristic, complemented
25	D₄⋊#168	C₂×C₃	1	4	yes	complemented
26	C₂⁴×C₃×C₅	—	2	1	no	—
27	C₂×C₃×C₅×D₄	—	2	1	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	C₈	1	4	yes	complemented
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	4	4	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
41	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×#168	—	2	2	no	—
47	C₂×C₃×#168	—	2	2	no	—
48	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
49	C₃×#431	—	5	1	no	—
50	C₃×#431	—	5	1	no	—
51	C₃×D₄⋊C₈	—	5	4	no	—
52	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₅	—	2	1	no	—
54	C₄×C₅×D₄	—	2	1	no	—
55	C₄×C₅×D₄	—	2	1	no	—
56	C₄×C₅×D₄	C₃×C₄	1	2	yes	—
57	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
59	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂²⋊#168	—	2	1	no	—
62	C₂²⋊#168	—	2	1	no	—
63	C₄⋊#168	—	2	1	no	—
64	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
65	C₄×#168	—	2	1	no	—
66	C₄×#168	C₂²×C₃	1	2	yes	complemented
67	#1478	—	5	1	no	Sylow
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	—	4	2	no	—
71	C₂³×C₃×C₅	—	4	2	no	—
72	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
73	C₃×C₅×D₄	—	2	4	no	—
74	C₃×C₅×D₄	—	2	2	no	—
75	C₃×C₅×D₄	C₂×C₈	1	4	yes	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	4	1	no	—
79	C₂×C₃×C₄×C₅	—	4	4	no	—
80	C₂×C₃×C₄×C₅	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	4	4	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
86	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₃×#168	—	4	2	no	—
91	C₃×#168	—	4	2	no	—
92	C₂²×C₃×D₄	Dic₅	1	1	yes	characteristic
93	C₂³×C₃×C₄	—	2	1	no	—
94	C₃×C₄×D₄	—	2	1	no	—
95	C₃×C₄×D₄	—	2	1	no	—
96	C₃×C₄×D₄	Dic₅	1	2	yes	—
97	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
99	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
101	C₃×C₄⋊C₈	—	5	2	no	—
102	C₃×C₄⋊C₈	—	10	1	no	—
103	C₃×C₂²⋊C₈	—	10	1	no	—
104	C₃×C₂²⋊C₈	—	10	1	no	—
105	C₃×C₄×C₈	—	5	2	no	—
106	C₃×C₄×C₈	—	10	1	no	—
107	C₂⁴×C₅	—	2	1	no	—
108	C₂×C₅×D₄	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	C₃×C₈	1	4	yes	complemented
111	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	2	2	no	—
115	C₂²×C₄×C₅	—	4	4	no	—
116	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
119	C₅×C₄⋊C₄	—	2	1	no	—
120	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
121	C₅×C₂²⋊C₄	—	2	2	no	—
122	C₅×C₂²⋊C₄	—	2	2	no	—
123	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
125	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
126	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₂×#168	—	2	2	no	—
128	C₂×#168	—	2	2	no	—
129	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
130	#431	—	5	1	no	—
131	#431	—	5	1	no	—
132	D₄⋊C₈	—	5	4	no	—
133	C₂²×C₃×C₅	—	2	1	no	—
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	—	2	4	no	—
136	C₂²×C₃×C₅	—	4	8	no	—
137	C₂²×C₃×C₅	—	4	2	no	—
138	C₂²×C₃×C₅	—	4	2	no	—
139	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	—	4	2	no	—
145	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
146	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
147	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
148	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
149	C₂⁴×C₃	—	2	1	no	—
150	C₂×C₃×D₄	—	2	2	no	—
151	C₂×C₃×D₄	—	2	1	no	—
152	C₂×C₃×D₄	#168	1	4	yes	complemented
153	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
154	C₂²×C₃×C₄	—	2	1	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	—	4	4	no	—
158	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
161	C₂×C₃×C₈	—	10	2	no	—
162	C₂×C₃×C₈	—	10	2	no	—
163	C₃×C₄⋊C₄	—	2	1	no	—
164	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
165	C₃×C₂²⋊C₄	—	2	2	no	—
166	C₃×C₂²⋊C₄	—	2	2	no	—
167	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
168	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
169	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
170	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
171	C₂³×C₅	—	2	4	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
176	C₅×D₄	—	2	4	no	—
177	C₅×D₄	—	2	2	no	—
178	C₅×D₄	C₂×C₃×C₈	1	4	yes	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	4	1	no	—
182	C₂×C₄×C₅	—	4	4	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	—	4	4	no	—
185	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
189	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	#168	—	4	2	no	—
194	#168	—	4	2	no	—
195	C₂²×D₄	C₃×Dic₅	1	1	yes	characteristic
196	C₂³×C₄	—	2	1	no	—
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	—	2	1	no	—
199	C₄×D₄	C₃×Dic₅	1	2	yes	—
200	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
201	C₂×C₄⋊C₄	C₃×Dic₅	1	1	yes	characteristic
202	C₂×C₂²⋊C₄	—	2	1	no	—
203	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
204	C₄⋊C₈	—	5	2	no	—
205	C₄⋊C₈	—	10	1	no	—
206	C₂²⋊C₈	—	10	1	no	—
207	C₂²⋊C₈	—	10	1	no	—
208	C₄×C₈	—	5	2	no	—
209	C₄×C₈	—	10	1	no	—
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	—	4	4	no	—
212	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
213	C₂×C₃×C₅	#418	1	1	yes	characteristic
214	C₂×C₃×C₅	#421	1	1	yes	characteristic
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	4	no	—
217	C₂³×C₃	—	4	2	no	—
218	C₂³×C₃	—	4	2	no	—
219	C₂³×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
220	C₃×D₄	—	2	4	no	—
221	C₃×D₄	—	2	2	no	—
222	C₃×D₄	C₂×#168	1	4	yes	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	4	no	—
227	C₂×C₃×C₄	—	4	2	no	—
228	C₂×C₃×C₄	—	4	4	no	—
229	C₂×C₃×C₄	C₂×#168	1	2	yes	—
230	C₂×C₃×C₄	#681	1	2	yes	—
231	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
237	C₃×C₈	—	20	2	no	—
238	C₃×C₈	—	20	2	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	—	2	1	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	8	no	—
243	C₂²×C₅	—	4	2	no	—
244	C₂²×C₅	—	4	2	no	—
245	C₂²×C₅	C₃×C₂²⋊C₈	1	2	yes	—
246	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	4	2	no	—
251	C₄×C₅	C₃×C₂²⋊C₈	1	2	yes	—
252	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
253	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
254	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
255	C₂⁴	—	2	1	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	C₃×#168	1	4	yes	complemented
259	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
265	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
266	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
267	C₂×C₈	—	10	2	no	—
268	C₂×C₈	—	10	2	no	—
269	C₄⋊C₄	—	2	1	no	—
270	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
271	C₂²⋊C₄	—	2	2	no	—
272	C₂²⋊C₄	—	2	2	no	—
273	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
274	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
275	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
276	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
277	C₃×C₅	#1478	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	2	1	no	—
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	4	no	—
281	C₂²×C₃	—	4	8	no	—
282	C₂²×C₃	—	4	2	no	—
283	C₂²×C₃	—	4	2	no	—
284	C₂²×C₃	C₂²⋊#168	1	2	yes	—
285	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
286	C₃×C₄	—	2	1	no	—
287	C₃×C₄	—	2	1	no	—
288	C₃×C₄	—	2	1	no	—
289	C₃×C₄	—	4	2	no	—
290	C₃×C₄	C₂²⋊#168	1	2	yes	—
291	C₃×C₄	C₂²×#168	1	1	yes	characteristic
292	C₃×C₄	C₂×#681	1	1	yes	characteristic
293	C₃×C₄	#4078	1	2	yes	—
294	C₂×C₅	—	2	2	no	—
295	C₂×C₅	—	4	4	no	—
296	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
297	C₂×C₅	C₃×#418	1	1	yes	characteristic
298	C₂×C₅	C₃×#421	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	4	2	no	—
302	C₂³	—	4	2	no	—
303	C₂³	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
304	D₄	—	2	4	no	—
305	D₄	—	2	2	no	—
306	D₄	C₂×C₃×#168	1	4	yes	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	C₂×C₃×#168	1	2	yes	—
314	C₂×C₄	C₃×#681	1	2	yes	—
315	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
316	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
317	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
318	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
319	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
320	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
321	C₈	—	20	2	no	—
322	C₈	—	20	2	no	—
323	C₂×C₃	—	2	2	no	—
324	C₂×C₃	—	4	4	no	—
325	C₂×C₃	C₂×C₂²⋊#168	1	1	yes	characteristic
326	C₂×C₃	#65504	1	1	yes	characteristic
327	C₂×C₃	#65525	1	1	yes	characteristic
328	C₅	C₃×#1478	1	1	yes	characteristic, complemented, Sylow
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	8	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	C₃×C₂²⋊#168	1	2	yes	—
336	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	1	no	—
340	C₄	—	4	2	no	—
341	C₄	C₃×C₂²⋊#168	1	2	yes	—
342	C₄	C₂²×C₃×#168	1	1	yes	characteristic
343	C₄	C₂×C₃×#681	1	1	yes	characteristic
344	C₄	C₃×#4078	1	2	yes	—
345	C₃	#10602390	1	1	yes	characteristic, direct product factor, Sylow
346	C₂	—	2	2	no	—
347	C₂	—	4	4	no	—
348	C₂	C₂×C₃×C₂²⋊#168	1	1	yes	characteristic
349	C₂	C₃×#65504	1	1	yes	characteristic
350	C₂	C₃×#65525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₄²	C₂²×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₄²×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₃×#1478
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×#65214	C₂	semidirect
3. C₃×#65214	C₂	semidirect
4. C₃×D₄⋊#168	C₂	semidirect
5. #10602390	C₃	direct (N × H)
18. C₃×C₄⋊#168	C₂²	semidirect
20. C₃×C₄×#168	C₂²	semidirect
23. #65214	C₂×C₃	semidirect
24. #65214	C₂×C₃	semidirect
25. D₄⋊#168	C₂×C₃	semidirect
29. C₂×C₃×C₅×D₄	C₈	semidirect
64. C₄⋊#168	C₂²×C₃	semidirect
66. C₄×#168	C₂²×C₃	semidirect
110. C₂×C₅×D₄	C₃×C₈	semidirect
152. C₂×C₃×D₄	#168	semidirect
258. C₂×D₄	C₃×#168	semidirect
277. C₃×C₅	#1478	semidirect
328. C₅	C₃×#1478	semidirect
345. C₃	#10602390	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×C₄×C₅×D₄	2
C₃×#65214	2
C₃×D₄⋊#168	2
#10602390	3
C₃×#1478	5

Subgroups — C3×#10602390 #14281687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602390 #14281687