Subgroups — C₃×#10610908 #14413402

Order 1920.

984 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	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅×#117	C₂	1	2	yes	maximal
3	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65395	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65287	C₂	1	2	yes	maximal, complemented
6	C₃×#65170	C₂	1	4	yes	maximal, complemented
7	C₃×#65150	C₂	1	4	yes	maximal, complemented
8	#10610908	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	2	yes	—
12	C₃×#4072	C₂²	1	2	yes	—
13	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
14	C₂×C₃×#676	C₄	1	8	yes	complemented
15	C₂×C₃×#676	C₂²	1	2	yes	—
16	C₂×C₃×#676	C₂²	1	2	yes	—
17	C₃×#4038	C₂²	1	4	yes	—
18	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
19	C₃×D₅×C₂²⋊C₄	—	2	2	no	—
20	C₃×#4023	—	2	2	no	—
21	C₃×#4018	—	2	2	no	—
22	C₃×C₄²×D₅	—	2	2	no	—
23	C₃×C₅×#107	C₂²	1	2	yes	complemented
24	C₃×C₅×#106	C₂²	1	2	yes	complemented
25	C₃×#3950	C₂²	1	2	yes	complemented
26	C₃×#3949	C₂²	1	2	yes	complemented
27	C₃×#3940	C₂²	1	4	yes	complemented
28	C₃×#3939	C₂²	1	4	yes	complemented
29	C₃×#2911	—	5	1	no	maximal, Hall
30	C₂²×#676	C₂×C₃	1	1	yes	characteristic
31	D₅×#117	C₂×C₃	1	2	yes	—
32	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
33	#65395	C₂×C₃	1	1	yes	characteristic, complemented
34	#65287	C₂×C₃	1	2	yes	complemented
35	#65170	C₂×C₃	1	4	yes	complemented
36	#65150	C₂×C₃	1	4	yes	complemented
37	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	—	2	4	no	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
42	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
45	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
49	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
50	C₃×C₄²×C₅	—	2	2	no	—
51	C₃×C₂²⋊Dic₅	—	2	2	no	—
52	C₃×#685	—	2	4	no	—
53	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
54	C₃×#683	—	2	4	no	—
55	C₃×C₄×Dic₅	—	2	2	no	—
56	C₃×C₄×Dic₅	—	2	4	no	—
57	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×#168	C₂³	1	2	yes	—
59	C₃×#676	C₂×C₄	1	8	yes	complemented
60	C₃×#676	C₂×C₄	1	8	yes	complemented
61	C₂²×C₃×M₁₆	—	5	1	no	—
62	C₂×C₃×#117	—	5	2	no	—
63	C₃×#428	—	5	4	no	—
64	C₃×#428	—	5	4	no	—
65	C₃×#427	—	5	1	no	—
66	C₃×#427	—	5	2	no	—
67	C₃×#427	D₅	1	1	yes	characteristic, complemented
68	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
70	C₅×#117	C₂²×C₃	1	2	yes	—
71	#4072	C₂²×C₃	1	2	yes	—
72	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
73	C₂×#676	C₃×C₄	1	8	yes	complemented
74	C₂×#676	C₂²×C₃	1	2	yes	—
75	C₂×#676	C₂²×C₃	1	2	yes	—
76	#4038	C₂²×C₃	1	4	yes	—
77	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
78	D₅×C₂²⋊C₄	—	2	2	no	—
79	#4023	—	2	2	no	—
80	#4018	—	2	2	no	—
81	C₄²×D₅	—	2	2	no	—
82	C₅×#107	C₂²×C₃	1	2	yes	complemented
83	C₅×#106	C₂²×C₃	1	2	yes	complemented
84	#3950	C₂²×C₃	1	2	yes	complemented
85	#3949	C₂²×C₃	1	2	yes	complemented
86	#3940	C₂²×C₃	1	4	yes	complemented
87	#3939	C₂²×C₃	1	4	yes	complemented
88	#2911	—	5	1	no	Sylow
89	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×D₅	—	4	2	no	—
91	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
92	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₂×C₃×Dic₅	—	2	4	no	—
99	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
100	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
101	C₃×C₄×D₅	—	4	8	no	—
102	C₃×C₄×D₅	C₄⋊C₄	1	8	yes	—
103	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
104	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
105	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
106	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
107	C₃×#168	C₂²×C₄	1	4	yes	—
108	C₂³×C₃×C₄	—	5	1	no	—
109	C₂×C₃×M₁₆	—	5	8	no	—
110	C₂×C₃×M₁₆	—	5	2	no	—
111	C₂×C₃×M₁₆	—	5	2	no	—
112	C₂²×C₃×C₈	—	5	1	no	—
113	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
114	C₃×#117	—	5	2	no	—
115	C₃×#117	—	5	4	no	—
116	C₃×#117	—	10	2	no	—
117	C₃×#117	—	10	2	no	—
118	C₃×#117	C₂×D₅	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	—	5	4	no	—
120	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
121	C₂×C₃×C₄²	—	10	2	no	—
122	C₃×#107	—	5	2	no	—
123	C₃×#107	—	5	4	no	—
124	C₃×#107	C₂×D₅	1	2	yes	complemented
125	C₃×#106	—	5	2	no	—
126	C₃×#106	—	5	4	no	—
127	C₃×#106	C₂×D₅	1	2	yes	complemented
128	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
131	C₂×C₄×D₅	—	2	4	no	—
132	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
133	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
134	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
135	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
136	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
137	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
139	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
140	C₅×C₂²⋊C₄	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₂²⋊Dic₅	—	2	2	no	—
143	#685	—	2	4	no	—
144	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
145	#683	—	2	4	no	—
146	C₄×Dic₅	—	2	2	no	—
147	C₄×Dic₅	—	2	4	no	—
148	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
149	C₂×#168	C₂³×C₃	1	2	yes	—
150	#676	C₂×C₃×C₄	1	8	yes	complemented
151	#676	C₂×C₃×C₄	1	8	yes	complemented
152	C₂²×M₁₆	—	5	1	no	—
153	C₂×#117	—	5	2	no	—
154	#428	—	5	4	no	—
155	#428	—	5	4	no	—
156	#427	—	5	1	no	—
157	#427	—	5	2	no	—
158	#427	C₃×D₅	1	1	yes	characteristic, complemented
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
161	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×D₅	—	2	4	no	—
163	C₂×C₃×D₅	—	4	4	no	—
164	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
167	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
169	C₃×Dic₅	—	4	4	no	—
170	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
171	C₂⁴×C₃	—	5	1	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	—	5	4	no	—
174	C₂²×C₃×C₄	—	5	2	no	—
175	C₂²×C₃×C₄	—	5	4	no	—
176	C₂²×C₃×C₄	—	5	2	no	—
177	C₂²×C₃×C₄	—	10	4	no	—
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₃×M₁₆	—	5	8	no	—
180	C₃×M₁₆	—	5	8	no	—
181	C₂×C₃×C₈	—	5	4	no	—
182	C₂×C₃×C₈	—	5	2	no	—
183	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
184	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
185	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
186	C₃×C₄⋊C₄	—	5	4	no	—
187	C₃×C₄⋊C₄	—	10	4	no	—
188	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	10	4	no	—
191	C₃×C₂²⋊C₄	—	10	2	no	—
192	C₃×C₄²	—	2	2	no	—
193	C₃×C₄²	—	10	4	no	—
194	C₃×C₄²	—	10	2	no	—
195	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
196	C₂²×D₅	—	4	2	no	—
197	C₂²×D₅	C₃×C₄⋊C₄	1	4	yes	—
198	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
203	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×Dic₅	—	2	4	no	—
205	C₂×Dic₅	C₃×C₄⋊C₄	1	4	yes	—
206	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
207	C₄×D₅	—	4	8	no	—
208	C₄×D₅	C₃×C₄⋊C₄	1	8	yes	—
209	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
210	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
211	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
212	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
213	#168	C₂²×C₃×C₄	1	4	yes	—
214	C₂³×C₄	—	5	1	no	—
215	C₂×M₁₆	—	5	8	no	—
216	C₂×M₁₆	—	5	2	no	—
217	C₂×M₁₆	—	5	2	no	—
218	C₂²×C₈	—	5	1	no	—
219	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
220	#117	—	5	2	no	—
221	#117	—	5	4	no	—
222	#117	—	10	2	no	—
223	#117	—	10	2	no	—
224	#117	C₂×C₃×D₅	1	2	yes	—
225	C₂×C₄⋊C₄	—	5	4	no	—
226	C₂×C₂²⋊C₄	—	10	2	no	—
227	C₂×C₄²	—	10	2	no	—
228	#107	—	5	2	no	—
229	#107	—	5	4	no	—
230	#107	C₂×C₃×D₅	1	2	yes	complemented
231	#106	—	5	2	no	—
232	#106	—	5	4	no	—
233	#106	C₂×C₃×D₅	1	2	yes	complemented
234	C₂×C₃×C₅	—	2	2	no	—
235	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₅	#575	1	2	yes	—
237	C₃×D₅	—	2	4	no	—
238	C₂³×C₃	—	5	2	no	—
239	C₂³×C₃	—	5	4	no	—
240	C₂³×C₃	—	20	2	no	—
241	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	5	2	no	—
244	C₂×C₃×C₄	—	5	4	no	—
245	C₂×C₃×C₄	—	5	4	no	—
246	C₂×C₃×C₄	—	5	4	no	—
247	C₂×C₃×C₄	—	5	8	no	—
248	C₂×C₃×C₄	—	10	4	no	—
249	C₂×C₃×C₄	—	20	8	no	—
250	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
251	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
252	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
253	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
254	C₃×C₈	—	5	4	no	—
255	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
256	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
259	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
260	C₂×D₅	—	2	4	no	—
261	C₂×D₅	—	4	4	no	—
262	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
265	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
266	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
267	Dic₅	—	4	4	no	—
268	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
269	C₂⁴	—	5	1	no	—
270	C₂²×C₄	—	5	1	no	—
271	C₂²×C₄	—	5	4	no	—
272	C₂²×C₄	—	5	2	no	—
273	C₂²×C₄	—	5	4	no	—
274	C₂²×C₄	—	5	2	no	—
275	C₂²×C₄	—	10	4	no	—
276	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
277	M₁₆	—	5	8	no	—
278	M₁₆	—	5	8	no	—
279	C₂×C₈	—	5	4	no	—
280	C₂×C₈	—	5	2	no	—
281	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
282	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
283	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
284	C₄⋊C₄	—	5	4	no	—
285	C₄⋊C₄	—	10	4	no	—
286	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	10	4	no	—
289	C₂²⋊C₄	—	10	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	10	4	no	—
292	C₄²	—	10	2	no	—
293	C₃×C₅	#2911	1	1	yes	characteristic, complemented, Hall
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	5	4	no	—
296	C₂²×C₃	—	10	4	no	—
297	C₂²×C₃	—	20	4	no	—
298	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
299	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
300	C₃×C₄	—	4	4	no	—
301	C₃×C₄	—	5	4	no	—
302	C₃×C₄	—	20	4	no	—
303	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
304	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
305	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
306	C₂×C₅	—	2	2	no	—
307	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₅	C₃×#575	1	2	yes	—
309	D₅	—	2	4	no	—
310	C₂³	—	5	2	no	—
311	C₂³	—	5	4	no	—
312	C₂³	—	20	2	no	—
313	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	5	2	no	—
316	C₂×C₄	—	5	4	no	—
317	C₂×C₄	—	5	4	no	—
318	C₂×C₄	—	5	4	no	—
319	C₂×C₄	—	5	8	no	—
320	C₂×C₄	—	10	4	no	—
321	C₂×C₄	—	20	8	no	—
322	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
323	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
324	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
325	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
326	C₈	—	5	4	no	—
327	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
328	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
329	C₂×C₃	—	2	2	no	—
330	C₂×C₃	—	10	4	no	—
331	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₃	#66102	1	2	yes	—
333	C₅	C₃×#2911	1	1	yes	characteristic, complemented, Sylow
334	C₂²	—	2	2	no	—
335	C₂²	—	5	4	no	—
336	C₂²	—	10	4	no	—
337	C₂²	—	20	4	no	—
338	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
339	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
340	C₄	—	4	4	no	—
341	C₄	—	5	4	no	—
342	C₄	—	20	4	no	—
343	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
344	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
345	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
346	C₃	#10610908	1	1	yes	characteristic, direct product factor, Sylow
347	C₂	—	2	2	no	—
348	C₂	—	10	4	no	—
349	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
350	C₂	C₃×#66102	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#427	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#427	D₅
hypocenter	C₅	C₃×#2911
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#427

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#427	C₂	semidirect
4. C₃×#65395	C₂	semidirect
5. C₃×#65287	C₂	semidirect
6. C₃×#65170	C₂	semidirect
7. C₃×#65150	C₂	semidirect
8. #10610908	C₃	direct (N × H)
14. C₂×C₃×#676	C₄	semidirect
23. C₃×C₅×#107	C₂²	semidirect
24. C₃×C₅×#106	C₂²	semidirect
25. C₃×#3950	C₂²	semidirect
26. C₃×#3949	C₂²	semidirect
27. C₃×#3940	C₂²	semidirect
28. C₃×#3939	C₂²	semidirect
32. C₅×#427	C₂×C₃	semidirect
33. #65395	C₂×C₃	semidirect
34. #65287	C₂×C₃	semidirect
35. #65170	C₂×C₃	semidirect
36. #65150	C₂×C₃	semidirect
45. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
57. C₂×C₃×#168	C₂×C₄	semidirect
59. C₃×#676	C₂×C₄	semidirect
60. C₃×#676	C₂×C₄	semidirect
67. C₃×#427	D₅	semidirect
73. C₂×#676	C₃×C₄	semidirect
82. C₅×#107	C₂²×C₃	semidirect
83. C₅×#106	C₂²×C₃	semidirect
84. #3950	C₂²×C₃	semidirect
85. #3949	C₂²×C₃	semidirect
86. #3940	C₂²×C₃	semidirect
87. #3939	C₂²×C₃	semidirect
124. C₃×#107	C₂×D₅	semidirect
127. C₃×#106	C₂×D₅	semidirect
136. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
148. C₂×#168	C₂×C₃×C₄	semidirect
150. #676	C₂×C₃×C₄	semidirect
151. #676	C₂×C₃×C₄	semidirect
158. #427	C₃×D₅	semidirect
183. C₂×C₃×C₈	C₄×D₅	semidirect
230. #107	C₂×C₃×D₅	semidirect
233. #106	C₂×C₃×D₅	semidirect
281. C₂×C₈	C₃×C₄×D₅	semidirect
293. C₃×C₅	#2911	semidirect
333. C₅	C₃×#2911	semidirect
346. C₃	#10610908	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×#676	2
C₃×D₅×#117	2
C₃×C₅×#427	2
C₃×#65395	2
C₃×#65287	2
C₃×#65170	2
C₃×#65150	2
#10610908	3
C₃×#2911	5

Subgroups — C3×#10610908 #14413402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610908 #14413402