Subgroups — C₃⋊C₈×#709 #14418928

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃⋊C₈×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	C₃⋊C₈×D₂₀	C₂	1	2	yes	maximal, complemented
6	C₄×D₅×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	#11746868	C₂	1	2	yes	maximal, complemented
8	C₃⋊C₈×Dic₁₀	C₂	1	2	yes	maximal, complemented
9	C₈×#709	—	3	1	no	maximal, Hall
10	C₂×C₃×#709	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₃×C₄×C₂²⋊D₅	C₄	1	2	yes	—
14	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
15	C₃×#4072	C₄	1	1	yes	characteristic
16	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
17	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
18	C₃×#4018	C₄	1	2	yes	—
19	C₃×C₄²×D₅	C₂²	1	2	yes	—
20	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
21	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₂×D₅×C₃⋊C₈	C₂²	1	4	yes	—
23	#91114	C₂²	1	2	yes	—
24	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
25	C₄×C₃⋊#168	C₂²	1	2	yes	—
26	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
27	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	#90982	C₂²	1	4	yes	—
30	#90955	C₂²	1	4	yes	—
31	Dic₅×C₃⋊C₈	C₂²	1	4	yes	—
32	#41×C₃⋊C₈	—	5	1	no	maximal, Hall
33	C₄×#709	D₃	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	—	3	1	no	—
35	C₈×C₂²⋊D₅	—	3	4	no	—
36	#65214	—	3	1	no	—
37	C₈×D₂₀	—	3	2	no	—
38	#64974	—	3	2	no	—
39	C₄×C₈×D₅	—	3	2	no	—
40	C₈×Dic₁₀	—	3	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
45	C₃×#709	C₈	1	8	yes	complemented
46	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
50	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃⋊#168	C₂³	1	4	yes	—
56	C₂×C₅×C₃⋊C₈	—	2	4	no	—
57	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
59	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
60	C₃×#685	C₂×C₄	1	2	yes	—
61	C₃×#685	C₂×C₄	1	2	yes	—
62	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
63	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×#683	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
68	C₃×C₄×Dic₅	C₂³	1	2	yes	—
69	D₅×C₃⋊C₈	—	2	8	no	—
70	C₃×C₄×#41	—	5	1	no	—
71	Q₈×C₃⋊C₈	—	5	2	no	—
72	D₄×C₃⋊C₈	—	5	4	no	—
73	D₄×C₃⋊C₈	—	5	2	no	—
74	#4925	—	5	1	no	—
75	#4925	—	5	2	no	—
76	C₂×C₄×C₃⋊C₈	—	5	2	no	—
77	C₂×C₄×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
78	C₂×#709	Dic₃	1	1	yes	characteristic
79	C₂²×C₅×C₈	—	3	2	no	—
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	Dic₃	1	2	yes	—
82	C₄×C₂²⋊D₅	C₂×D₃	1	2	yes	—
83	#4072	Dic₃	1	1	yes	characteristic
84	C₂×C₈×D₅	—	3	4	no	—
85	C₄×D₂₀	Dic₃	1	1	yes	characteristic
86	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
87	#4018	Dic₃	1	2	yes	—
88	C₄²×D₅	C₂×D₃	1	2	yes	—
89	C₄×Dic₁₀	Dic₃	1	1	yes	characteristic
90	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
91	C₄×C₅×C₈	—	3	2	no	—
92	C₄×C₅×C₈	—	3	1	no	—
93	C₄×C₅×C₈	—	3	1	no	—
94	C₂²⋊#168	—	3	2	no	—
95	#3952	—	3	4	no	—
96	#3946	—	3	4	no	—
97	C₈×Dic₅	—	3	4	no	—
98	C₄⋊#168	—	3	2	no	—
99	C₄×#168	—	3	2	no	—
100	C₈×#41	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₂²⋊D₅	C₂×C₈	1	8	yes	complemented
113	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₃×D₂₀	C₂×C₈	1	4	yes	complemented
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×C₄×D₅	C₂×C₈	1	8	yes	complemented
120	C₃×Dic₁₀	C₂×C₈	1	4	yes	complemented
121	C₃⋊#168	—	2	4	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	#41	1	4	yes	complemented
124	C₂×C₃×#41	—	5	1	no	—
125	C₃×C₄×Q₈	—	5	1	no	—
126	C₃×C₄×Q₈	—	5	1	no	—
127	C₃×C₄×D₄	—	5	2	no	—
128	C₃×C₄×D₄	—	5	2	no	—
129	C₃×C₄×D₄	—	5	1	no	—
130	C₃×C₄×D₄	—	5	1	no	—
131	C₃×#117	—	5	1	no	—
132	C₃×#117	—	5	2	no	—
133	C₂×C₃×C₄²	—	5	2	no	—
134	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
135	C₂²×C₃⋊C₈	—	5	4	no	—
136	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
137	#830	—	5	2	no	—
138	#830	—	5	4	no	—
139	C₄⋊(C₃⋊C₈)	—	5	2	no	—
140	C₄⋊(C₃⋊C₈)	—	5	4	no	—
141	C₄×C₃⋊C₈	—	5	2	no	—
142	C₄×C₃⋊C₈	—	5	4	no	—
143	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
144	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
145	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	—
146	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×Dic₃	1	2	yes	—
150	#709	C₃⋊C₈	1	8	yes	direct product factor
151	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
153	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
154	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
155	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
156	C₂×C₅×C₈	—	3	2	no	—
157	C₂×C₅×C₈	—	3	2	no	—
158	C₂×C₅×C₈	—	6	4	no	—
159	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
160	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
161	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
164	#685	C₂×Dic₃	1	2	yes	—
165	#685	C₂×Dic₃	1	2	yes	—
166	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
167	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
168	#683	C₂×Dic₃	1	2	yes	—
169	#683	C₂×Dic₃	1	2	yes	—
170	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
171	C₄×Dic₅	C₂×Dic₃	1	2	yes	—
172	C₄×Dic₅	C₂²×D₃	1	2	yes	—
173	C₂×#168	—	3	4	no	—
174	C₈×D₅	—	6	8	no	—
175	C₄×#41	—	5	1	no	—
176	C₈×Q₈	—	15	2	no	—
177	C₈×D₄	—	15	2	no	—
178	C₈×D₄	—	15	4	no	—
179	#431	—	15	2	no	—
180	#431	—	15	1	no	—
181	C₂×C₄×C₈	—	3	1	no	—
182	C₂×C₄×C₈	—	15	2	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	—	2	2	no	—
189	C₂×C₃×D₅	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	2	yes	—
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	—	2	2	no	—
198	C₃×Dic₅	C₂²×C₈	1	4	yes	—
199	C₃×#41	—	5	8	no	—
200	C₂×C₃×Q₈	—	5	1	no	—
201	C₂×C₃×D₄	—	5	2	no	—
202	C₂×C₃×D₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	2	no	—
206	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₃×C₄⋊C₄	—	5	2	no	—
210	C₃×C₄⋊C₄	—	5	2	no	—
211	C₃×C₄⋊C₄	—	5	1	no	—
212	C₃×C₄⋊C₄	—	5	1	no	—
213	C₃×C₂²⋊C₄	—	5	2	no	—
214	C₃×C₂²⋊C₄	—	5	2	no	—
215	C₃×C₂²⋊C₄	—	5	2	no	—
216	C₃×C₄²	—	5	2	no	—
217	C₃×C₄²	—	5	2	no	—
218	C₃×C₄²	—	5	2	no	—
219	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
220	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
221	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
222	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
223	C₂×C₃⋊C₈	—	2	4	no	—
224	C₂×C₃⋊C₈	—	5	4	no	—
225	C₂×C₃⋊C₈	—	10	8	no	—
226	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
227	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
228	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
229	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	C₂×C₃⋊C₈	1	4	yes	complemented
233	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
239	C₂²⋊D₅	C₂×C₃⋊C₈	1	8	yes	complemented
240	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
241	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
242	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
243	D₂₀	C₂×C₃⋊C₈	1	4	yes	complemented
244	C₄×D₅	—	2	4	no	—
245	C₄×D₅	—	2	4	no	—
246	C₄×D₅	C₂×C₃⋊C₈	1	8	yes	complemented
247	Dic₁₀	C₂×C₃⋊C₈	1	4	yes	complemented
248	C₅×C₈	—	3	4	no	—
249	C₅×C₈	—	6	2	no	—
250	#168	—	6	4	no	—
251	C₂×#41	—	5	1	no	—
252	C₂²×C₈	—	3	2	no	—
253	C₂²×C₈	—	15	4	no	—
254	C₄×Q₈	—	5	1	no	—
255	C₄×Q₈	—	5	1	no	—
256	C₄×D₄	—	5	2	no	—
257	C₄×D₄	—	5	2	no	—
258	C₄×D₄	—	5	1	no	—
259	C₄×D₄	—	5	1	no	—
260	#117	—	5	1	no	—
261	#117	—	5	2	no	—
262	C₂×C₄²	—	5	2	no	—
263	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	15	4	no	—
265	C₄⋊C₈	—	15	2	no	—
266	C₂²⋊C₈	—	15	4	no	—
267	C₂²⋊C₈	—	15	2	no	—
268	C₄×C₈	—	3	2	no	—
269	C₄×C₈	—	3	1	no	—
270	C₄×C₈	—	3	1	no	—
271	C₄×C₈	—	15	4	no	—
272	C₄×C₈	—	15	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₃×D₅	—	2	4	no	—
278	C₂³×C₃	—	5	2	no	—
279	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
280	C₃×Q₈	—	5	4	no	—
281	C₃×D₄	—	5	8	no	—
282	C₃×D₄	—	5	4	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	5	2	no	—
286	C₂×C₃×C₄	—	5	8	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	5	2	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	10	4	no	—
291	C₂×C₃×C₄	C₈×D₅	1	4	yes	complemented
292	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
298	C₃⋊C₈	—	2	2	no	—
299	C₃⋊C₈	—	10	4	no	—
300	C₃⋊C₈	#709	1	4	yes	direct product factor
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	C₂²×C₃⋊C₈	1	2	yes	—
304	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
305	C₂×D₅	—	2	2	no	—
306	C₂×D₅	—	2	2	no	—
307	C₂×D₅	C₂²×C₃⋊C₈	1	4	yes	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₂²×C₃⋊C₈	1	2	yes	—
311	C₄×C₅	C₂²×C₃⋊C₈	1	2	yes	—
312	C₄×C₅	#948	1	2	yes	—
313	C₄×C₅	D₃×#41	1	2	yes	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	2	2	no	—
316	Dic₅	C₂²×C₃⋊C₈	1	4	yes	—
317	#41	—	5	8	no	—
318	C₂×Q₈	—	5	1	no	—
319	C₂×D₄	—	5	2	no	—
320	C₂×D₄	—	5	1	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	—	5	2	no	—
324	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
325	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
327	C₂×C₈	—	3	2	no	—
328	C₂×C₈	—	3	2	no	—
329	C₂×C₈	—	6	4	no	—
330	C₂×C₈	—	15	4	no	—
331	C₂×C₈	—	30	8	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	5	2	no	—
334	C₄⋊C₄	—	5	1	no	—
335	C₄⋊C₄	—	5	1	no	—
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	2	no	—
338	C₂²⋊C₄	—	5	2	no	—
339	C₄²	—	5	2	no	—
340	C₄²	—	5	2	no	—
341	C₄²	—	5	2	no	—
342	C₄²	D₅×Dic₃	1	1	yes	characteristic
343	C₄²	D₅×Dic₃	1	1	yes	characteristic
344	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
345	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	5	4	no	—
350	C₂²×C₃	—	10	2	no	—
351	C₂²×C₃	—	10	2	no	—
352	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
353	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	5	4	no	—
357	C₃×C₄	—	10	2	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
360	C₃×C₄	C₂×C₈×D₅	1	2	yes	—
361	C₃×C₄	#4047	1	2	yes	—
362	C₃×C₄	C₂×#709	1	2	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₂³×C₃⋊C₈	1	1	yes	characteristic
365	C₂×C₅	C₂×#948	1	1	yes	characteristic
366	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
367	D₅	—	2	4	no	—
368	C₂³	—	5	2	no	—
369	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
370	Q₈	—	5	4	no	—
371	D₄	—	5	8	no	—
372	D₄	—	5	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	8	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	10	4	no	—
380	C₂×C₄	—	10	4	no	—
381	C₂×C₄	D₅×C₃⋊C₈	1	4	yes	complemented
382	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
383	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
384	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
385	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
386	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
388	C₈	—	3	4	no	—
389	C₈	—	6	2	no	—
390	C₈	—	30	4	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	10	4	no	—
393	C₂×C₃	C₄×#709	1	1	yes	characteristic
394	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
395	C₂×C₃	C₂×#4047	1	1	yes	characteristic
396	C₅	#41×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	5	4	no	—
400	C₂²	—	10	2	no	—
401	C₂²	—	10	2	no	—
402	C₂²	C₂×D₅×C₃⋊C₈	1	2	yes	—
403	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	5	4	no	—
407	C₄	—	10	2	no	—
408	C₄	—	10	2	no	—
409	C₄	C₂×D₅×C₃⋊C₈	1	2	yes	—
410	C₄	C₂×D₅×C₃⋊C₈	1	2	yes	—
411	C₄	#91283	1	2	yes	—
412	C₄	D₃×#709	1	2	yes	—
413	C₃	C₈×#709	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	10	4	no	—
416	C₂	C₂²×D₅×C₃⋊C₈	1	1	yes	characteristic
417	C₂	C₂×#91283	1	1	yes	characteristic
418	C₂	Dic₃×#709	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #11751026	C₂	semidirect
3. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
4. C₃⋊C₈×C₂²⋊D₅	C₂	semidirect
5. C₃⋊C₈×D₂₀	C₂	semidirect
6. C₄×D₅×C₃⋊C₈	C₂	semidirect
7. #11746868	C₂	semidirect
8. C₃⋊C₈×Dic₁₀	C₂	semidirect
45. C₃×#709	C₈	semidirect
77. C₂×C₄×C₃⋊C₈	D₅	semidirect
105. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
112. C₃×C₂²⋊D₅	C₂×C₈	semidirect
116. C₃×D₂₀	C₂×C₈	semidirect
119. C₃×C₄×D₅	C₂×C₈	semidirect
120. C₃×Dic₁₀	C₂×C₈	semidirect
123. C₅×C₃⋊C₈	#41	semidirect
150. #709	C₃⋊C₈	direct (N × H)
232. C₂×C₄×C₅	C₂×C₃⋊C₈	semidirect
239. C₂²⋊D₅	C₂×C₃⋊C₈	semidirect
243. D₂₀	C₂×C₃⋊C₈	semidirect
246. C₄×D₅	C₂×C₃⋊C₈	semidirect
247. Dic₁₀	C₂×C₃⋊C₈	semidirect
291. C₂×C₃×C₄	C₈×D₅	semidirect
300. C₃⋊C₈	#709	direct (N × H)
346. C₃×C₅	C₈×#41	semidirect
381. C₂×C₄	D₅×C₃⋊C₈	semidirect
396. C₅	#41×C₃⋊C₈	semidirect
413. C₃	C₈×#709	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#709	2
#11751026	2
C₂×C₄×C₅×C₃⋊C₈	2
C₃⋊C₈×C₂²⋊D₅	2
C₃⋊C₈×D₂₀	2
C₄×D₅×C₃⋊C₈	2
#11746868	2
C₃⋊C₈×Dic₁₀	2
C₈×#709	3
#41×C₃⋊C₈	5

Subgroups — C3⋊C8×#709 #14418928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊C₈×#709 #14418928