Subgroups — C₃×#10611648 #14418461

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65912	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65128	C₂	1	2	yes	maximal
5	C₃×#65126	C₂	1	1	yes	maximal, characteristic
6	C₃×#65120	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65117	C₂	1	2	yes	maximal, complemented
8	C₃×#64978	C₂	1	2	yes	maximal
9	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
10	C₃×C₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×Dic₁₀	C₂	1	2	yes	maximal, complemented
12	#10611648	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×#4092	C₄	1	1	yes	characteristic
15	C₃×#4090	C₄	1	1	yes	characteristic
16	C₂×C₃×#676	C₂²	1	2	yes	—
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	C₃×#4043	C₄	1	1	yes	characteristic
20	C₃×#4042	C₄	1	2	yes	—
21	C₃×#4035	C₄	1	2	yes	—
22	C₃×#4034	C₄	1	1	yes	characteristic
23	C₃×#4018	C₂²	1	2	yes	—
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
26	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
31	C₃×#3947	C₂²	1	2	yes	—
32	C₃×#3946	C₂²	1	2	yes	—
33	C₃×#3946	C₂²	1	2	yes	—
34	C₃×#3946	C₂²	1	2	yes	—
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₅	C₂²	1	2	yes	—
38	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊#168	C₂²	1	2	yes	—
40	C₃×#3935	C₂²	1	2	yes	—
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#2960	—	5	1	no	maximal, Hall
43	#65912	C₂×C₃	1	1	yes	characteristic
44	C₅×C₈×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
45	#65313	C₂×C₃	1	1	yes	characteristic, complemented
46	#65128	C₂×C₃	1	2	yes	—
47	#65126	C₂×C₃	1	1	yes	characteristic
48	#65120	C₂×C₃	1	1	yes	characteristic, complemented
49	#65117	C₂×C₃	1	2	yes	complemented
50	#64978	C₂×C₃	1	2	yes	—
51	C₄×C₈×D₅	C₂×C₃	1	1	yes	characteristic
52	C₈×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
53	C₈×Dic₁₀	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
71	C₃×#683	C₂×C₄	1	2	yes	—
72	C₃×#683	C₂×C₄	1	2	yes	—
73	C₃×#683	C₂×C₄	1	2	yes	—
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂³	1	2	yes	—
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	2	yes	—
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₃×#676	—	2	4	no	—
84	C₃×C₈×D₅	—	2	2	no	—
85	C₃×C₈×D₅	Q₈	1	4	yes	complemented
86	C₃×#533	—	5	1	no	—
87	C₃×#446	—	5	1	no	—
88	C₃×#446	—	5	2	no	—
89	C₃×#446	—	5	1	no	—
90	C₃×C₈×Q₈	—	5	2	no	—
91	C₃×C₈×Q₈	—	5	1	no	—
92	C₃×C₈×Q₈	D₅	1	1	yes	characteristic, complemented
93	C₃×#424	—	5	2	no	—
94	C₃×#423	—	5	1	no	—
95	C₃×#405	—	5	2	no	—
96	C₂×C₃×C₄×C₈	—	5	1	no	—
97	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
98	#4092	C₃×C₄	1	1	yes	characteristic
99	#4090	C₃×C₄	1	1	yes	characteristic
100	C₂×#676	C₂²×C₃	1	2	yes	—
101	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
103	#4043	C₃×C₄	1	1	yes	characteristic
104	#4042	C₃×C₄	1	2	yes	—
105	#4035	C₃×C₄	1	2	yes	—
106	#4034	C₃×C₄	1	1	yes	characteristic
107	#4018	C₂²×C₃	1	2	yes	—
108	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
109	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
110	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
112	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
115	#3947	C₂²×C₃	1	2	yes	—
116	#3946	C₂²×C₃	1	2	yes	—
117	#3946	C₂²×C₃	1	2	yes	—
118	#3946	C₂²×C₃	1	2	yes	—
119	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
120	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
121	C₈×Dic₅	C₂²×C₃	1	2	yes	—
122	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
123	C₄⋊#168	C₂²×C₃	1	2	yes	—
124	#3935	C₂²×C₃	1	2	yes	—
125	C₄×#168	C₂²×C₃	1	1	yes	characteristic
126	#2960	—	5	1	no	Sylow
127	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₃×C₄×D₅	—	2	2	no	—
140	C₃×C₄×D₅	—	2	2	no	—
141	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
142	C₃×C₄×D₅	#41	1	2	yes	—
143	C₃×Dic₁₀	—	2	2	no	—
144	C₃×Dic₁₀	—	2	4	no	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	—	2	2	no	—
147	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
148	C₃×#168	—	2	1	no	—
149	C₃×#168	—	2	2	no	—
150	C₃×#168	C₂×Q₈	1	2	yes	—
151	C₂×C₃×M₁₆	—	5	2	no	—
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₂²×C₃×C₈	—	5	1	no	—
154	C₃×C₄⋊Q₈	—	5	1	no	—
155	C₃×C₄⋊Q₈	—	5	1	no	—
156	C₃×#125	—	5	2	no	—
157	C₃×C₂²⋊Q₈	—	5	1	no	—
158	C₃×C₂²⋊Q₈	—	5	2	no	—
159	C₃×C₂²⋊Q₈	—	5	1	no	—
160	C₃×C₄×Q₈	—	5	2	no	—
161	C₃×C₄×Q₈	—	5	1	no	—
162	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
163	C₃×#117	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₃×C₄⋊C₈	—	5	2	no	—
166	C₃×C₄⋊C₈	—	5	2	no	—
167	C₃×C₄⋊C₈	—	5	2	no	—
168	C₃×C₄⋊C₈	—	5	1	no	—
169	C₃×C₄⋊C₈	—	5	2	no	—
170	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
171	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
172	C₃×#97	—	5	2	no	—
173	C₃×#97	—	5	2	no	—
174	C₃×C₄×C₈	—	5	1	no	—
175	C₃×C₄×C₈	—	5	1	no	—
176	C₃×C₄×C₈	—	5	2	no	—
177	C₃×C₄×C₈	—	5	1	no	—
178	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
179	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
180	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
185	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
190	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
191	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₄²×C₅	C₂³×C₃	1	2	yes	—
193	#685	C₂×C₃×C₄	1	2	yes	—
194	#685	C₂×C₃×C₄	1	2	yes	—
195	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
196	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
197	#683	C₂×C₃×C₄	1	2	yes	—
198	#683	C₂×C₃×C₄	1	2	yes	—
199	#683	C₂×C₃×C₄	1	2	yes	—
200	#683	C₂×C₃×C₄	1	2	yes	—
201	#683	C₂×C₃×C₄	1	2	yes	—
202	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
203	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
204	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
205	C₄×Dic₅	C₂³×C₃	1	2	yes	—
206	C₂×#168	C₂³×C₃	1	1	yes	characteristic
207	C₂×#168	C₂³×C₃	1	2	yes	—
208	C₂×#168	C₂³×C₃	1	1	yes	characteristic
209	#676	—	2	4	no	—
210	C₈×D₅	—	2	2	no	—
211	C₈×D₅	C₃×Q₈	1	4	yes	complemented
212	#533	—	5	1	no	—
213	#446	—	5	1	no	—
214	#446	—	5	2	no	—
215	#446	—	5	1	no	—
216	C₈×Q₈	—	5	2	no	—
217	C₈×Q₈	—	5	1	no	—
218	C₈×Q₈	C₃×D₅	1	1	yes	characteristic, complemented
219	#424	—	5	2	no	—
220	#423	—	5	1	no	—
221	#405	—	5	2	no	—
222	C₂×C₄×C₈	—	5	1	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₃×D₅	—	2	1	no	—
225	C₂×C₃×D₅	—	2	1	no	—
226	C₂×C₃×D₅	C₄×Q₈	1	2	yes	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	#131	1	2	yes	—
231	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₃×Dic₅	—	2	2	no	—
234	C₃×Dic₅	—	2	2	no	—
235	C₃×Dic₅	—	2	1	no	—
236	C₃×Dic₅	C₄×Q₈	1	2	yes	—
237	C₃×Dic₅	#131	1	2	yes	—
238	C₂×C₃×Q₈	—	5	2	no	—
239	C₂×C₃×Q₈	—	5	1	no	—
240	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₃×M₁₆	—	10	4	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	4	no	—
247	C₂×C₃×C₈	—	5	1	no	—
248	C₂×C₃×C₈	—	5	2	no	—
249	C₂×C₃×C₈	—	10	2	no	—
250	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	5	2	no	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	2	no	—
256	C₃×C₄⋊C₄	—	5	2	no	—
257	C₃×C₄⋊C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	5	2	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
261	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
262	C₃×C₂²⋊C₄	—	5	2	no	—
263	C₃×C₂²⋊C₄	—	5	2	no	—
264	C₃×C₄²	—	5	1	no	—
265	C₃×C₄²	—	5	1	no	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	—	5	2	no	—
268	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
269	C₃×C₄²	C₂²×D₅	1	2	yes	—
270	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₅×Q₈	—	2	2	no	—
272	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
274	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
275	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
277	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
278	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
279	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
280	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
281	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₄×D₅	—	2	2	no	—
283	C₄×D₅	—	2	2	no	—
284	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
285	C₄×D₅	C₃×#41	1	2	yes	—
286	Dic₁₀	—	2	2	no	—
287	Dic₁₀	—	2	4	no	—
288	C₅×C₈	—	2	1	no	—
289	C₅×C₈	—	2	2	no	—
290	C₅×C₈	C₂×C₃×Q₈	1	2	yes	—
291	#168	—	2	1	no	—
292	#168	—	2	2	no	—
293	#168	C₂×C₃×Q₈	1	2	yes	—
294	C₂×M₁₆	—	5	2	no	—
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₄⋊Q₈	—	5	1	no	—
298	C₄⋊Q₈	—	5	1	no	—
299	#125	—	5	2	no	—
300	C₂²⋊Q₈	—	5	1	no	—
301	C₂²⋊Q₈	—	5	2	no	—
302	C₂²⋊Q₈	—	5	1	no	—
303	C₄×Q₈	—	5	2	no	—
304	C₄×Q₈	—	5	1	no	—
305	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
306	#117	—	5	2	no	—
307	C₂×C₄²	—	5	1	no	—
308	C₄⋊C₈	—	5	2	no	—
309	C₄⋊C₈	—	5	2	no	—
310	C₄⋊C₈	—	5	2	no	—
311	C₄⋊C₈	—	5	1	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
315	#97	—	5	2	no	—
316	#97	—	5	2	no	—
317	C₄×C₈	—	5	1	no	—
318	C₄×C₈	—	5	1	no	—
319	C₄×C₈	—	5	2	no	—
320	C₄×C₈	—	5	1	no	—
321	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
322	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
323	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	C₃×D₅	—	2	2	no	—
327	C₂³×C₃	—	5	1	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	10	4	no	—
330	C₃×Q₈	—	10	2	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	1	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	1	no	—
336	C₂×C₃×C₄	—	5	2	no	—
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	10	2	no	—
340	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	—	5	2	no	—
348	C₃×C₈	—	10	1	no	—
349	C₃×C₈	—	10	2	no	—
350	C₃×C₈	Q₈×D₅	1	2	yes	—
351	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
352	C₂×D₅	—	2	1	no	—
353	C₂×D₅	—	2	1	no	—
354	C₂×D₅	C₃×C₄×Q₈	1	2	yes	—
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	C₃×#131	1	2	yes	—
359	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
360	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
361	Dic₅	—	2	2	no	—
362	Dic₅	—	2	2	no	—
363	Dic₅	—	2	1	no	—
364	Dic₅	C₃×C₄×Q₈	1	2	yes	—
365	Dic₅	C₃×#131	1	2	yes	—
366	C₂×Q₈	—	5	2	no	—
367	C₂×Q₈	—	5	1	no	—
368	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	—	5	1	no	—
372	M₁₆	—	10	4	no	—
373	C₂×C₈	—	5	1	no	—
374	C₂×C₈	—	5	4	no	—
375	C₂×C₈	—	5	1	no	—
376	C₂×C₈	—	5	2	no	—
377	C₂×C₈	—	10	2	no	—
378	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
380	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
381	C₄⋊C₄	—	5	2	no	—
382	C₄⋊C₄	—	5	2	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	5	2	no	—
385	C₄⋊C₄	—	5	2	no	—
386	C₄⋊C₄	—	5	2	no	—
387	C₄⋊C₄	—	5	1	no	—
388	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
389	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
390	C₂²⋊C₄	—	5	2	no	—
391	C₂²⋊C₄	—	5	2	no	—
392	C₄²	—	5	1	no	—
393	C₄²	—	5	1	no	—
394	C₄²	—	5	1	no	—
395	C₄²	—	5	2	no	—
396	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₄²	C₂²×C₃×D₅	1	2	yes	—
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	—	5	2	no	—
400	C₂²×C₃	—	10	1	no	—
401	C₂²×C₃	—	10	1	no	—
402	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	5	2	no	—
407	C₃×C₄	—	5	2	no	—
408	C₃×C₄	—	10	1	no	—
409	C₃×C₄	—	10	2	no	—
410	C₃×C₄	—	10	2	no	—
411	C₃×C₄	#4047	1	2	yes	—
412	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
413	C₃×C₄	D₅×#41	1	1	yes	characteristic
414	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
415	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
416	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
417	D₅	—	2	2	no	—
418	C₂³	—	5	1	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	10	4	no	—
421	Q₈	—	10	2	no	—
422	C₂×C₄	—	5	1	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	5	2	no	—
425	C₂×C₄	—	5	2	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	5	2	no	—
428	C₂×C₄	—	5	2	no	—
429	C₂×C₄	—	10	2	no	—
430	C₂×C₄	—	10	2	no	—
431	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
432	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
433	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
434	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
435	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	2	no	—
438	C₈	—	5	2	no	—
439	C₈	—	10	1	no	—
440	C₈	—	10	2	no	—
441	C₈	C₃×Q₈×D₅	1	2	yes	—
442	C₂×C₃	—	10	2	no	—
443	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
444	C₂×C₃	C₂×#4047	1	1	yes	characteristic
445	C₂×C₃	D₅×#131	1	1	yes	characteristic
446	C₅	C₃×#2960	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	5	2	no	—
448	C₂²	—	10	1	no	—
449	C₂²	—	10	1	no	—
450	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	5	2	no	—
455	C₄	—	5	2	no	—
456	C₄	—	10	1	no	—
457	C₄	—	10	2	no	—
458	C₄	—	10	2	no	—
459	C₄	C₃×#4047	1	2	yes	—
460	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
461	C₄	C₃×D₅×#41	1	1	yes	characteristic
462	C₃	#10611648	1	1	yes	characteristic, direct product factor, Sylow
463	C₂	—	10	2	no	—
464	C₂	C₃×C₄×Q₈×D₅	1	1	yes	characteristic
465	C₂	C₂×C₃×#4047	1	1	yes	characteristic
466	C₂	C₃×D₅×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×C₈×Q₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₈×Q₈	D₅
hypocenter	C₅	C₃×#2960
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₈×Q₈	C₂	semidirect
3. C₃×#65313	C₂	semidirect
6. C₃×#65120	C₂	semidirect
7. C₃×#65117	C₂	semidirect
10. C₃×C₈×Dic₁₀	C₂	semidirect
11. C₃×C₈×Dic₁₀	C₂	semidirect
12. #10611648	C₃	direct (N × H)
44. C₅×C₈×Q₈	C₂×C₃	semidirect
45. #65313	C₂×C₃	semidirect
48. #65120	C₂×C₃	semidirect
49. #65117	C₂×C₃	semidirect
52. C₈×Dic₁₀	C₂×C₃	semidirect
53. C₈×Dic₁₀	C₂×C₃	semidirect
85. C₃×C₈×D₅	Q₈	semidirect
92. C₃×C₈×Q₈	D₅	semidirect
211. C₈×D₅	C₃×Q₈	semidirect
218. C₈×Q₈	C₃×D₅	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	C₃×#2960	semidirect
462. C₃	#10611648	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#65912	2
C₃×C₅×C₈×Q₈	2
C₃×#65313	2
C₃×#65128	2
C₃×#65126	2
C₃×#65120	2
C₃×#65117	2
C₃×#64978	2
C₃×C₄×C₈×D₅	2
C₃×C₈×Dic₁₀	2
#10611648	3
C₃×#2960	5

Subgroups — C3×#10611648 #14418461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611648 #14418461