Subgroups — C₂×C₃×#64904 #14313788

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3994	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64904	C₂	1	4	yes	maximal, direct product factor
5	C₂×#64904	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×D₄×D₅	—	2	1	no	—
7	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
8	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
9	C₂×C₃×#686	—	2	1	no	—
10	C₃×D₅×D₈	—	2	1	no	—
11	C₃×D₅×D₈	—	2	1	no	—
12	C₃×D₅×D₈	C₄	1	2	yes	complemented
13	C₃×D₅×D₈	C₂²	1	2	yes	—
14	C₂×C₃×D₄₀	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#674	—	2	1	no	—
17	C₃×#3994	—	2	1	no	—
18	C₃×#3994	C₂²	1	2	yes	complemented
19	C₃×D₅⋊C₁₆	—	2	1	no	—
20	C₃×D₅⋊C₁₆	C₂²	1	2	yes	complemented
21	C₂×C₃×#357	—	5	1	no	maximal, Hall
22	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
23	C₂×#3994	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×D₅⋊C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
25	#64904	C₂×C₃	1	4	yes	direct product factor
26	C₂³×C₃×D₅	—	4	1	no	—
27	C₂²×C₃×AGL(1,𝔽₅)	—	4	1	no	—
28	C₂×C₃×C₅×D₄	—	2	1	no	—
29	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
30	C₃×D₄×D₅	—	2	2	no	—
31	C₃×D₄×D₅	—	2	2	no	—
32	C₃×D₄×D₅	—	4	1	no	—
33	C₃×D₄×D₅	—	4	1	no	—
34	C₂×C₃×D₂₀	—	2	1	no	—
35	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
36	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
37	C₃×C₄⋊AGL(1,𝔽₅)	—	4	1	no	—
38	C₃×C₅×D₈	—	2	1	no	—
39	C₃×C₅×D₈	C₂×C₄	1	2	yes	complemented
40	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
41	C₃×#686	—	2	2	no	—
42	C₃×#686	—	2	2	no	—
43	C₂×C₃×#168	D₄	1	1	yes	characteristic
44	C₃×D₄₀	—	2	1	no	—
45	C₃×D₄₀	C₂×C₄	1	2	yes	complemented
46	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₈×D₅	D₄	1	1	yes	characteristic
48	C₃×C₈×D₅	D₄	1	1	yes	characteristic
49	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
50	C₃×#674	—	2	2	no	—
51	C₂²×C₃×D₈	—	5	1	no	—
52	C₂²×C₃×C₁₆	—	5	1	no	—
53	C₂×C₃×#107	—	5	1	no	—
54	C₃×#357	—	5	4	no	—
55	C₂×D₄×D₅	—	2	1	no	—
56	C₂×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
57	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic, complemented
58	C₂×#686	—	2	1	no	—
59	D₅×D₈	—	2	1	no	—
60	D₅×D₈	—	2	1	no	—
61	D₅×D₈	C₃×C₄	1	2	yes	complemented
62	D₅×D₈	C₂²×C₃	1	2	yes	—
63	C₂×D₄₀	C₃×C₄	1	1	yes	characteristic, complemented
64	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
65	C₂×#674	—	2	1	no	—
66	#3994	—	2	1	no	—
67	#3994	C₂²×C₃	1	2	yes	complemented
68	D₅⋊C₁₆	—	2	1	no	—
69	D₅⋊C₁₆	C₂²×C₃	1	2	yes	complemented
70	C₂×#357	—	5	1	no	Sylow
71	C₂³×C₃×C₅	—	4	1	no	—
72	C₂²×C₃×D₅	—	4	1	no	—
73	C₂²×C₃×D₅	—	4	2	no	—
74	C₂²×C₃×D₅	—	4	2	no	—
75	C₂²×C₃×D₅	—	8	2	no	—
76	C₂²×C₃×D₅	—	8	2	no	—
77	C₂²×C₃×D₅	D₈	1	1	yes	characteristic
78	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
79	C₂×C₃×AGL(1,𝔽₅)	—	8	2	no	—
80	C₃×C₅×D₄	—	2	2	no	—
81	C₃×C₅×D₄	—	4	1	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₃×C₂²⋊D₅	—	4	2	no	—
84	C₃×C₂²⋊D₅	—	4	2	no	—
85	C₂×C₃×Dic₅	SD₁₆	1	1	yes	characteristic
86	C₃×D₂₀	—	2	2	no	—
87	C₃×D₂₀	—	4	1	no	—
88	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₃×C₄×D₅	D₈	1	1	yes	characteristic
90	C₃×C₄×D₅	SD₁₆	1	1	yes	characteristic
91	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
93	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
94	C₃×#168	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×#168	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×D₄	—	10	1	no	—
97	C₂×C₃×D₈	—	5	2	no	—
98	C₂×C₃×D₈	—	5	2	no	—
99	C₂×C₃×D₈	—	5	1	no	—
100	C₂×C₃×D₈	—	10	1	no	—
101	C₂×C₃×D₈	—	10	1	no	—
102	C₂×C₃×D₈	—	10	1	no	—
103	C₂×C₃×D₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
104	C₂²×C₃×C₈	—	5	1	no	—
105	C₂×C₃×C₄⋊C₄	—	10	1	no	—
106	C₂×C₃×C₁₆	—	5	2	no	—
107	C₂×C₃×C₁₆	—	10	1	no	—
108	C₂×C₃×C₁₆	—	10	1	no	—
109	C₃×#107	—	5	2	no	—
110	C₃×#107	—	10	1	no	—
111	C₂³×D₅	—	4	1	no	—
112	C₂²×AGL(1,𝔽₅)	—	4	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₂²⋊D₅	—	4	1	no	—
115	D₄×D₅	—	2	2	no	—
116	D₄×D₅	—	2	2	no	—
117	D₄×D₅	—	4	1	no	—
118	D₄×D₅	—	4	1	no	—
119	C₂×D₂₀	—	2	1	no	—
120	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
121	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
122	C₄⋊AGL(1,𝔽₅)	—	4	1	no	—
123	C₅×D₈	—	2	1	no	—
124	C₅×D₈	C₂×C₃×C₄	1	2	yes	complemented
125	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
126	#686	—	2	2	no	—
127	#686	—	2	2	no	—
128	C₂×#168	C₃×D₄	1	1	yes	characteristic
129	D₄₀	—	2	1	no	—
130	D₄₀	C₂×C₃×C₄	1	2	yes	complemented
131	C₈×D₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₈×D₅	C₃×D₄	1	1	yes	characteristic
133	C₈×D₅	C₃×D₄	1	1	yes	characteristic
134	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
135	#674	—	2	2	no	—
136	C₂²×D₈	—	5	1	no	—
137	C₂²×C₁₆	—	5	1	no	—
138	C₂×#107	—	5	1	no	—
139	#357	—	5	4	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	8	2	no	—
142	C₂²×C₃×C₅	#102	1	1	yes	characteristic
143	C₂×C₃×D₅	—	4	2	no	—
144	C₂×C₃×D₅	—	8	2	no	—
145	C₂×C₃×D₅	—	8	4	no	—
146	C₂×C₃×D₅	—	8	2	no	—
147	C₂×C₃×D₅	—	8	2	no	—
148	C₂×C₃×D₅	#102	1	1	yes	characteristic
149	C₂×C₃×D₅	D₁₆	1	2	yes	—
150	C₂×C₃×D₅	SD₃₂	1	2	yes	—
151	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
152	C₃×AGL(1,𝔽₅)	—	8	2	no	—
153	C₃×C₄×C₅	#102	1	1	yes	characteristic
154	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₃×Dic₅	#102	1	1	yes	characteristic
156	C₃×Dic₅	C₂×SD₁₆	1	1	yes	characteristic
157	C₂⁴×C₃	—	20	1	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	10	2	no	—
160	C₂×C₃×D₄	—	10	2	no	—
161	C₂×C₃×D₄	—	10	1	no	—
162	C₂×C₃×D₄	—	20	1	no	—
163	C₂×C₃×D₄	—	20	1	no	—
164	C₂×C₃×D₄	—	20	1	no	—
165	C₂²×C₃×C₄	—	5	1	no	—
166	C₂²×C₃×C₄	—	20	1	no	—
167	C₃×D₈	—	2	1	no	—
168	C₃×D₈	—	5	2	no	—
169	C₃×D₈	—	10	2	no	—
170	C₃×D₈	—	10	2	no	—
171	C₃×D₈	—	10	1	no	—
172	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
173	C₂×C₃×C₈	—	5	1	no	—
174	C₂×C₃×C₈	—	5	1	no	—
175	C₂×C₃×C₈	—	5	1	no	—
176	C₂×C₃×C₈	—	5	1	no	—
177	C₂×C₃×C₈	—	5	1	no	—
178	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
179	C₃×C₄⋊C₄	—	10	2	no	—
180	C₃×C₄⋊C₄	—	20	1	no	—
181	C₃×C₁₆	—	10	2	no	—
182	C₂³×C₅	—	4	1	no	—
183	C₂²×D₅	—	4	1	no	—
184	C₂²×D₅	—	4	2	no	—
185	C₂²×D₅	—	4	2	no	—
186	C₂²×D₅	—	8	2	no	—
187	C₂²×D₅	—	8	2	no	—
188	C₂²×D₅	C₃×D₈	1	1	yes	characteristic
189	C₂×AGL(1,𝔽₅)	—	4	2	no	—
190	C₂×AGL(1,𝔽₅)	—	8	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	4	1	no	—
193	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²⋊D₅	—	4	2	no	—
195	C₂²⋊D₅	—	4	2	no	—
196	C₂×Dic₅	C₃×SD₁₆	1	1	yes	characteristic
197	D₂₀	—	2	2	no	—
198	D₂₀	—	4	1	no	—
199	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₄×D₅	C₃×D₈	1	1	yes	characteristic
201	C₄×D₅	C₃×SD₁₆	1	1	yes	characteristic
202	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
205	#168	C₃×C₂²⋊C₄	1	1	yes	characteristic
206	#168	C₂×C₃×D₄	1	1	yes	characteristic
207	C₂²×D₄	—	10	1	no	—
208	C₂×D₈	—	5	2	no	—
209	C₂×D₈	—	5	2	no	—
210	C₂×D₈	—	5	1	no	—
211	C₂×D₈	—	10	1	no	—
212	C₂×D₈	—	10	1	no	—
213	C₂×D₈	—	10	1	no	—
214	C₂×D₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
215	C₂²×C₈	—	5	1	no	—
216	C₂×C₄⋊C₄	—	10	1	no	—
217	C₂×C₁₆	—	5	2	no	—
218	C₂×C₁₆	—	10	1	no	—
219	C₂×C₁₆	—	10	1	no	—
220	#107	—	5	2	no	—
221	#107	—	10	1	no	—
222	C₂×C₃×C₅	—	8	2	no	—
223	C₂×C₃×C₅	#357	1	2	yes	complemented
224	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
225	C₃×D₅	—	8	2	no	—
226	C₃×D₅	#357	1	2	yes	complemented
227	C₃×D₅	C₂×D₁₆	1	1	yes	characteristic
228	C₃×D₅	C₂×SD₃₂	1	1	yes	characteristic
229	C₂³×C₃	—	4	1	no	—
230	C₂³×C₃	—	5	1	no	—
231	C₂³×C₃	—	20	2	no	—
232	C₂³×C₃	—	20	2	no	—
233	C₂³×C₃	—	20	1	no	—
234	C₂³×C₃	—	40	2	no	—
235	C₂³×C₃	—	40	2	no	—
236	C₃×D₄	—	2	2	no	—
237	C₃×D₄	—	4	1	no	—
238	C₃×D₄	—	10	2	no	—
239	C₃×D₄	—	20	2	no	—
240	C₃×D₄	—	20	2	no	—
241	C₃×D₄	—	20	1	no	—
242	C₂×C₃×C₄	—	5	1	no	—
243	C₂×C₃×C₄	—	5	1	no	—
244	C₂×C₃×C₄	—	5	1	no	—
245	C₂×C₃×C₄	—	5	1	no	—
246	C₂×C₃×C₄	—	5	1	no	—
247	C₂×C₃×C₄	—	20	2	no	—
248	C₂×C₃×C₄	—	40	2	no	—
249	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₃×C₈	—	5	1	no	—
251	C₃×C₈	—	5	1	no	—
252	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
253	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	8	2	no	—
256	C₂²×C₅	C₃×#102	1	1	yes	characteristic
257	C₂×D₅	—	4	2	no	—
258	C₂×D₅	—	8	2	no	—
259	C₂×D₅	—	8	2	no	—
260	C₂×D₅	—	8	2	no	—
261	C₂×D₅	—	8	4	no	—
262	C₂×D₅	C₃×#102	1	1	yes	characteristic
263	C₂×D₅	C₃×D₁₆	1	2	yes	—
264	C₂×D₅	C₃×SD₃₂	1	2	yes	—
265	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
266	AGL(1,𝔽₅)	—	8	2	no	—
267	C₄×C₅	C₃×#102	1	1	yes	characteristic
268	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
269	Dic₅	C₃×#102	1	1	yes	characteristic
270	Dic₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
271	C₂⁴	—	20	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	10	2	no	—
274	C₂×D₄	—	10	2	no	—
275	C₂×D₄	—	10	1	no	—
276	C₂×D₄	—	20	1	no	—
277	C₂×D₄	—	20	1	no	—
278	C₂×D₄	—	20	1	no	—
279	C₂²×C₄	—	5	1	no	—
280	C₂²×C₄	—	20	1	no	—
281	D₈	—	2	1	no	—
282	D₈	—	5	2	no	—
283	D₈	—	10	2	no	—
284	D₈	—	10	2	no	—
285	D₈	—	10	1	no	—
286	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
287	C₂×C₈	—	5	1	no	—
288	C₂×C₈	—	5	1	no	—
289	C₂×C₈	—	5	1	no	—
290	C₂×C₈	—	5	1	no	—
291	C₂×C₈	—	5	1	no	—
292	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
293	C₄⋊C₄	—	10	2	no	—
294	C₄⋊C₄	—	20	1	no	—
295	C₁₆	—	10	2	no	—
296	C₃×C₅	C₂×#357	1	1	yes	characteristic, complemented, Hall
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	5	2	no	—
299	C₂²×C₃	—	5	2	no	—
300	C₂²×C₃	—	5	1	no	—
301	C₂²×C₃	—	5	1	no	—
302	C₂²×C₃	—	8	2	no	—
303	C₂²×C₃	—	20	2	no	—
304	C₂²×C₃	—	40	2	no	—
305	C₂²×C₃	—	40	4	no	—
306	C₂²×C₃	—	40	2	no	—
307	C₂²×C₃	—	40	2	no	—
308	C₂²×C₃	#4007	1	1	yes	characteristic
309	C₃×C₄	—	5	1	no	—
310	C₃×C₄	—	5	1	no	—
311	C₃×C₄	—	40	2	no	—
312	C₃×C₄	#4007	1	1	yes	characteristic
313	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₂×C₅	—	8	2	no	—
315	C₂×C₅	C₃×#357	1	2	yes	complemented
316	C₂×C₅	C₂×C₃×#102	1	1	yes	characteristic
317	D₅	—	8	2	no	—
318	D₅	C₃×#357	1	2	yes	complemented
319	D₅	C₂×C₃×D₁₆	1	1	yes	characteristic
320	D₅	C₂×C₃×SD₃₂	1	1	yes	characteristic
321	C₂³	—	4	1	no	—
322	C₂³	—	5	1	no	—
323	C₂³	—	20	2	no	—
324	C₂³	—	20	2	no	—
325	C₂³	—	20	1	no	—
326	C₂³	—	40	2	no	—
327	C₂³	—	40	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	4	1	no	—
330	D₄	—	10	2	no	—
331	D₄	—	20	2	no	—
332	D₄	—	20	2	no	—
333	D₄	—	20	1	no	—
334	C₂×C₄	—	5	1	no	—
335	C₂×C₄	—	5	1	no	—
336	C₂×C₄	—	5	1	no	—
337	C₂×C₄	—	5	1	no	—
338	C₂×C₄	—	5	1	no	—
339	C₂×C₄	—	20	2	no	—
340	C₂×C₄	—	40	2	no	—
341	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₈	—	5	1	no	—
343	C₈	—	5	1	no	—
344	C₈	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₂×C₃	—	5	1	no	—
347	C₂×C₃	—	5	2	no	—
348	C₂×C₃	—	5	1	no	—
349	C₂×C₃	—	8	2	no	—
350	C₂×C₃	—	40	2	no	—
351	C₂×C₃	#64904	1	2	yes	direct product factor
352	C₂×C₃	C₂×#4007	1	1	yes	characteristic
353	C₅	C₂×C₃×#357	1	1	yes	characteristic, complemented, Sylow
354	C₂²	—	4	2	no	—
355	C₂²	—	5	1	no	—
356	C₂²	—	5	1	no	—
357	C₂²	—	5	2	no	—
358	C₂²	—	5	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	20	2	no	—
361	C₂²	—	40	2	no	—
362	C₂²	—	40	2	no	—
363	C₂²	—	40	4	no	—
364	C₂²	—	40	2	no	—
365	C₂²	C₃×#4007	1	1	yes	characteristic
366	C₄	—	5	1	no	—
367	C₄	—	5	1	no	—
368	C₄	—	40	2	no	—
369	C₄	C₃×#4007	1	1	yes	characteristic
370	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₃	C₂×#64904	1	1	yes	characteristic, direct product factor, Sylow
372	C₂	—	5	1	no	—
373	C₂	—	5	1	no	—
374	C₂	—	5	2	no	—
375	C₂	—	8	2	no	—
376	C₂	—	40	2	no	—
377	C₂	C₃×#64904	1	2	yes	direct product factor
378	C₂	C₂×C₃×#4007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4007
commutator	C₅×C₈	C₂²×C₃×C₄
Frattini	C₈	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×D₈	C₄
socle	C₂²×C₃×C₅	#102
prime radical	C₂×C₃×D₅×D₈	C₂
cosocle	C₈×D₅	C₂³×C₃
hypercenter	C₂×C₃×D₈	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#357
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#3994	C₂	semidirect
3. C₂×C₃×D₅⋊C₁₆	C₂	semidirect
4. C₃×#64904	C₂	direct (N × H)
5. C₂×#64904	C₃	direct (N × H)
8. C₂×C₃×C₅×D₈	C₄	semidirect
12. C₃×D₅×D₈	C₄	semidirect
14. C₂×C₃×D₄₀	C₄	semidirect
18. C₃×#3994	C₂²	semidirect
20. C₃×D₅⋊C₁₆	C₂²	semidirect
23. C₂×#3994	C₂×C₃	semidirect
24. C₂×D₅⋊C₁₆	C₂×C₃	semidirect
25. #64904	C₂×C₃	direct (N × H)
39. C₃×C₅×D₈	C₂×C₄	semidirect
45. C₃×D₄₀	C₂×C₄	semidirect
57. C₂×C₅×D₈	C₃×C₄	semidirect
61. D₅×D₈	C₃×C₄	semidirect
63. C₂×D₄₀	C₃×C₄	semidirect
67. #3994	C₂²×C₃	semidirect
69. D₅⋊C₁₆	C₂²×C₃	semidirect
103. C₂×C₃×D₈	AGL(1,𝔽₅)	semidirect
124. C₅×D₈	C₂×C₃×C₄	semidirect
130. D₄₀	C₂×C₃×C₄	semidirect
172. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
214. C₂×D₈	C₃×AGL(1,𝔽₅)	semidirect
223. C₂×C₃×C₅	#357	semidirect
226. C₃×D₅	#357	semidirect
286. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
296. C₃×C₅	C₂×#357	semidirect
315. C₂×C₅	C₃×#357	semidirect
318. D₅	C₃×#357	semidirect
351. C₂×C₃	#64904	direct (N × H)
353. C₅	C₂×C₃×#357	semidirect
371. C₃	C₂×#64904	direct (N × H)
377. C₂	C₃×#64904	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×D₅×D₈	2
C₂×C₃×#3994	2
C₂×C₃×D₅⋊C₁₆	2
C₃×#64904	2
C₂×#64904	3
C₂×C₃×#357	5

Subgroups — C2×C3×#64904 #14313788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64904 #14313788