Subgroups — C₃×#10604722 #14297879

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#65765	C₂	1	2	yes	maximal
3	C₂×C₃×#3993	C₂	1	2	yes	maximal, complemented
4	C₃×#64893	C₂	1	2	yes	maximal, complemented
5	#10604722	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
8	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
9	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
10	C₂²×C₃×#168	C₄	1	1	yes	characteristic, complemented
11	C₂×C₃×C₈×D₅	—	2	4	no	—
12	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	—	2	2	no	—
17	C₃×#3993	—	2	4	no	—
18	C₃×#1807	—	5	1	no	maximal, Hall
19	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
20	#65765	C₂×C₃	1	2	yes	—
21	C₂×#3993	C₂×C₃	1	2	yes	complemented
22	#64893	C₂×C₃	1	2	yes	complemented
23	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
24	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×Dic₅	Q₈	1	1	yes	characteristic
27	C₂×C₃×C₄×D₅	—	2	2	no	—
28	C₂×C₃×C₄×D₅	—	2	2	no	—
29	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
33	C₃×C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
34	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
35	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×#168	—	2	2	no	—
40	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
42	C₃×C₈×D₅	—	2	2	no	—
43	C₃×C₈×D₅	—	2	2	no	—
44	C₃×C₈×D₅	—	2	2	no	—
45	C₃×C₈×D₅	D₄	1	4	yes	—
46	C₂³×C₃×C₈	—	5	1	no	—
47	C₂×C₃×#106	—	5	2	no	—
48	C₃×#380	—	5	2	no	—
49	C₃×#340	—	5	2	no	—
50	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
52	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
53	C₂²×C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
54	C₂²×#168	C₃×C₄	1	1	yes	characteristic, complemented
55	C₂×C₈×D₅	—	2	4	no	—
56	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
57	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
58	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
60	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	2	no	—
61	#3993	—	2	4	no	—
62	#1807	—	5	1	no	Sylow
63	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₃×D₅	—	2	2	no	—
65	C₂²×C₃×D₅	—	2	2	no	—
66	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₃×D₅	SD₁₆	1	4	yes	—
68	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
69	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
70	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
71	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₃×Dic₅	—	2	2	no	—
77	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
79	C₃×C₄×D₅	—	2	2	no	—
80	C₃×C₄×D₅	—	2	1	no	—
81	C₃×C₄×D₅	—	2	1	no	—
82	C₃×C₄×D₅	—	2	2	no	—
83	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
84	C₃×C₄×D₅	#41	1	2	yes	—
85	C₃×C₅×C₈	—	2	1	no	—
86	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	complemented
87	C₃×#168	—	2	1	no	—
88	C₃×#168	C₂²⋊C₄	1	2	yes	complemented
89	C₂³×C₃×C₄	—	5	1	no	—
90	C₂²×C₃×C₈	—	5	1	no	—
91	C₂²×C₃×C₈	—	5	1	no	—
92	C₂²×C₃×C₈	—	5	1	no	—
93	C₂²×C₃×C₈	—	5	1	no	—
94	C₂²×C₃×C₈	—	5	1	no	—
95	C₂²×C₃×C₈	—	10	4	no	—
96	C₂²×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
97	C₂×C₃×C₄⋊C₄	—	5	4	no	—
98	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
99	C₃×#106	—	10	4	no	—
100	C₃×#95	—	10	2	no	—
101	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
102	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
103	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
104	C₂²×Dic₅	C₃×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₅	—	2	2	no	—
106	C₂×C₄×D₅	—	2	2	no	—
107	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
111	C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
112	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
113	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂×#168	—	2	2	no	—
118	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
120	C₈×D₅	—	2	2	no	—
121	C₈×D₅	—	2	2	no	—
122	C₈×D₅	—	2	2	no	—
123	C₈×D₅	C₃×D₄	1	4	yes	—
124	C₂³×C₈	—	5	1	no	—
125	C₂×#106	—	5	2	no	—
126	#380	—	5	2	no	—
127	#340	—	5	2	no	—
128	C₂²×C₃×C₅	—	2	1	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	#106	1	2	yes	complemented
131	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₃×D₅	—	2	1	no	—
133	C₂×C₃×D₅	—	2	1	no	—
134	C₂×C₃×D₅	—	2	8	no	—
135	C₂×C₃×D₅	#106	1	2	yes	complemented
136	C₂×C₃×D₅	#121	1	2	yes	—
137	C₂×C₃×D₅	C₂×SD₁₆	1	2	yes	—
138	C₂×C₃×D₅	#135	1	2	yes	—
139	C₃×AGL(1,𝔽₅)	—	8	4	no	—
140	C₃×C₄×C₅	—	2	1	no	—
141	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₃×C₄×C₅	#117	1	1	yes	characteristic
143	C₃×Dic₅	—	2	1	no	—
144	C₃×Dic₅	C₂²⋊Q₈	1	2	yes	—
145	C₂⁴×C₃	—	5	1	no	—
146	C₂²×C₃×C₄	—	5	1	no	—
147	C₂²×C₃×C₄	—	5	1	no	—
148	C₂²×C₃×C₄	—	5	1	no	—
149	C₂²×C₃×C₄	—	5	1	no	—
150	C₂²×C₃×C₄	—	5	1	no	—
151	C₂²×C₃×C₄	—	10	2	no	—
152	C₂²×C₃×C₄	—	10	2	no	—
153	C₂²×C₃×C₄	—	10	4	no	—
154	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	5	1	no	—
157	C₂×C₃×C₈	—	5	4	no	—
158	C₂×C₃×C₈	—	5	1	no	—
159	C₂×C₃×C₈	—	10	2	no	—
160	C₂×C₃×C₈	—	10	2	no	—
161	C₂×C₃×C₈	—	10	2	no	—
162	C₂×C₃×C₈	—	10	2	no	—
163	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	10	4	no	—
166	C₃×C₄⋊C₄	—	10	4	no	—
167	C₃×C₂²⋊C₄	—	20	4	no	—
168	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×D₅	—	2	2	no	—
170	C₂²×D₅	—	2	2	no	—
171	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×D₅	C₃×SD₁₆	1	4	yes	—
173	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
174	C₂×AGL(1,𝔽₅)	—	4	4	no	—
175	C₂×AGL(1,𝔽₅)	—	4	4	no	—
176	C₂×AGL(1,𝔽₅)	—	4	4	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂×Dic₅	—	2	2	no	—
182	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₅	C₂×C₃×Q₈	1	1	yes	characteristic
184	C₄×D₅	—	2	2	no	—
185	C₄×D₅	—	2	1	no	—
186	C₄×D₅	—	2	1	no	—
187	C₄×D₅	—	2	2	no	—
188	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
189	C₄×D₅	C₃×#41	1	2	yes	—
190	C₅×C₈	—	2	1	no	—
191	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	complemented
192	#168	—	2	1	no	—
193	#168	C₃×C₂²⋊C₄	1	2	yes	complemented
194	C₂³×C₄	—	5	1	no	—
195	C₂²×C₈	—	5	1	no	—
196	C₂²×C₈	—	5	1	no	—
197	C₂²×C₈	—	5	1	no	—
198	C₂²×C₈	—	5	1	no	—
199	C₂²×C₈	—	5	1	no	—
200	C₂²×C₈	—	10	4	no	—
201	C₂²×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
202	C₂×C₄⋊C₄	—	5	4	no	—
203	C₂×C₂²⋊C₄	—	10	2	no	—
204	#106	—	10	4	no	—
205	#95	—	10	2	no	—
206	C₂×C₃×C₅	—	2	2	no	—
207	C₂×C₃×C₅	#380	1	1	yes	characteristic
208	C₂×C₃×C₅	C₂×#106	1	1	yes	characteristic
209	C₂×C₃×C₅	#427	1	1	yes	characteristic
210	C₃×D₅	—	2	2	no	—
211	C₃×D₅	#465	1	4	yes	—
212	C₂³×C₃	—	5	1	no	—
213	C₂³×C₃	—	5	1	no	—
214	C₂³×C₃	—	5	4	no	—
215	C₂³×C₃	—	10	2	no	—
216	C₂³×C₃	—	10	2	no	—
217	C₂³×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	5	1	no	—
221	C₂×C₃×C₄	—	5	2	no	—
222	C₂×C₃×C₄	—	5	2	no	—
223	C₂×C₃×C₄	—	5	1	no	—
224	C₂×C₃×C₄	—	10	2	no	—
225	C₂×C₃×C₄	—	10	2	no	—
226	C₂×C₃×C₄	—	10	2	no	—
227	C₂×C₃×C₄	—	10	1	no	—
228	C₂×C₃×C₄	—	10	1	no	—
229	C₂×C₃×C₄	—	20	4	no	—
230	C₂×C₃×C₄	—	20	4	no	—
231	C₂×C₃×C₄	—	20	4	no	—
232	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
234	C₃×C₈	—	2	1	no	—
235	C₃×C₈	—	5	2	no	—
236	C₃×C₈	—	10	1	no	—
237	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	1	no	—
240	C₂²×C₅	C₃×#106	1	2	yes	complemented
241	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
242	C₂×D₅	—	2	1	no	—
243	C₂×D₅	—	2	1	no	—
244	C₂×D₅	—	2	8	no	—
245	C₂×D₅	C₃×#106	1	2	yes	complemented
246	C₂×D₅	C₃×#121	1	2	yes	—
247	C₂×D₅	C₂×C₃×SD₁₆	1	2	yes	—
248	C₂×D₅	C₃×#135	1	2	yes	—
249	AGL(1,𝔽₅)	—	8	4	no	—
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
252	C₄×C₅	C₃×#117	1	1	yes	characteristic
253	Dic₅	—	2	1	no	—
254	Dic₅	C₃×C₂²⋊Q₈	1	2	yes	—
255	C₂⁴	—	5	1	no	—
256	C₂²×C₄	—	5	1	no	—
257	C₂²×C₄	—	5	1	no	—
258	C₂²×C₄	—	5	1	no	—
259	C₂²×C₄	—	5	1	no	—
260	C₂²×C₄	—	5	1	no	—
261	C₂²×C₄	—	10	2	no	—
262	C₂²×C₄	—	10	2	no	—
263	C₂²×C₄	—	10	4	no	—
264	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	5	1	no	—
267	C₂×C₈	—	5	4	no	—
268	C₂×C₈	—	5	1	no	—
269	C₂×C₈	—	10	2	no	—
270	C₂×C₈	—	10	2	no	—
271	C₂×C₈	—	10	2	no	—
272	C₂×C₈	—	10	2	no	—
273	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
274	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
275	C₄⋊C₄	—	10	4	no	—
276	C₄⋊C₄	—	10	4	no	—
277	C₂²⋊C₄	—	20	4	no	—
278	C₃×C₅	#1807	1	1	yes	characteristic, complemented, Hall
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	2	1	no	—
281	C₂²×C₃	—	5	2	no	—
282	C₂²×C₃	—	5	2	no	—
283	C₂²×C₃	—	5	2	no	—
284	C₂²×C₃	—	5	2	no	—
285	C₂²×C₃	—	10	8	no	—
286	C₂²×C₃	—	10	1	no	—
287	C₂²×C₃	—	10	1	no	—
288	C₂²×C₃	#3993	1	2	yes	complemented
289	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	5	2	no	—
292	C₃×C₄	—	10	1	no	—
293	C₃×C₄	—	40	4	no	—
294	C₃×C₄	#4130	1	1	yes	characteristic
295	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₂×C₅	—	2	2	no	—
297	C₂×C₅	C₃×#380	1	1	yes	characteristic
298	C₂×C₅	C₂×C₃×#106	1	1	yes	characteristic
299	C₂×C₅	C₃×#427	1	1	yes	characteristic
300	D₅	—	2	2	no	—
301	D₅	C₃×#465	1	4	yes	—
302	C₂³	—	5	1	no	—
303	C₂³	—	5	4	no	—
304	C₂³	—	5	1	no	—
305	C₂³	—	10	2	no	—
306	C₂³	—	10	2	no	—
307	C₂³	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	5	1	no	—
311	C₂×C₄	—	5	2	no	—
312	C₂×C₄	—	5	2	no	—
313	C₂×C₄	—	5	1	no	—
314	C₂×C₄	—	10	2	no	—
315	C₂×C₄	—	10	2	no	—
316	C₂×C₄	—	10	2	no	—
317	C₂×C₄	—	10	1	no	—
318	C₂×C₄	—	10	1	no	—
319	C₂×C₄	—	20	4	no	—
320	C₂×C₄	—	20	4	no	—
321	C₂×C₄	—	20	4	no	—
322	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
324	C₈	—	2	1	no	—
325	C₈	—	5	2	no	—
326	C₈	—	10	1	no	—
327	C₈	C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
328	C₂×C₃	—	2	2	no	—
329	C₂×C₃	—	5	4	no	—
330	C₂×C₃	—	10	2	no	—
331	C₂×C₃	C₂×#3993	1	1	yes	characteristic
332	C₂×C₃	#65721	1	1	yes	characteristic
333	C₂×C₃	#65765	1	1	yes	characteristic
334	C₅	C₃×#1807	1	1	yes	characteristic, complemented, Sylow
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	5	2	no	—
338	C₂²	—	5	2	no	—
339	C₂²	—	5	2	no	—
340	C₂²	—	5	2	no	—
341	C₂²	—	10	8	no	—
342	C₂²	—	10	1	no	—
343	C₂²	—	10	1	no	—
344	C₂²	C₃×#3993	1	2	yes	complemented
345	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	5	2	no	—
348	C₄	—	10	1	no	—
349	C₄	—	40	4	no	—
350	C₄	C₃×#4130	1	1	yes	characteristic
351	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
352	C₃	#10604722	1	1	yes	characteristic, direct product factor, Sylow
353	C₂	—	2	2	no	—
354	C₂	—	5	4	no	—
355	C₂	—	10	2	no	—
356	C₂	C₂×C₃×#3993	1	1	yes	characteristic
357	C₂	C₃×#65721	1	1	yes	characteristic
358	C₂	C₃×#65765	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂²×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1807
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#3993	C₂	semidirect
4. C₃×#64893	C₂	semidirect
5. #10604722	C₃	direct (N × H)
9. C₂²×C₃×C₅×C₈	C₄	semidirect
10. C₂²×C₃×#168	C₄	semidirect
12. C₂×C₃×C₈×D₅	C₄	semidirect
13. C₂×C₃×C₈×D₅	C₄	semidirect
21. C₂×#3993	C₂×C₃	semidirect
22. #64893	C₂×C₃	semidirect
53. C₂²×C₅×C₈	C₃×C₄	semidirect
54. C₂²×#168	C₃×C₄	semidirect
56. C₂×C₈×D₅	C₃×C₄	semidirect
57. C₂×C₈×D₅	C₃×C₄	semidirect
86. C₃×C₅×C₈	C₂²⋊C₄	semidirect
88. C₃×#168	C₂²⋊C₄	semidirect
96. C₂²×C₃×C₈	AGL(1,𝔽₅)	semidirect
130. C₂²×C₃×C₅	#106	semidirect
135. C₂×C₃×D₅	#106	semidirect
191. C₅×C₈	C₃×C₂²⋊C₄	semidirect
193. #168	C₃×C₂²⋊C₄	semidirect
201. C₂²×C₈	C₃×AGL(1,𝔽₅)	semidirect
237. C₃×C₈	C₂²⋊AGL(1,𝔽₅)	semidirect
240. C₂²×C₅	C₃×#106	semidirect
245. C₂×D₅	C₃×#106	semidirect
278. C₃×C₅	#1807	semidirect
288. C₂²×C₃	#3993	semidirect
327. C₈	C₃×C₂²⋊AGL(1,𝔽₅)	semidirect
334. C₅	C₃×#1807	semidirect
344. C₂²	C₃×#3993	semidirect
352. C₃	#10604722	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×C₈×D₅	2
C₃×#65765	2
C₂×C₃×#3993	2
C₃×#64893	2
#10604722	3
C₃×#1807	5

Subgroups — C3×#10604722 #14297879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604722 #14297879