Subgroups — C₃×#10615008 #14415841

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	2	yes	maximal, complemented
3	C₃×#65523	C₂	1	2	yes	maximal, complemented
4	C₃×#65301	C₂	1	2	yes	maximal, complemented
5	C₃×#65300	C₂	1	4	yes	maximal, complemented
6	C₃×D₄×#168	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615008	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#127	C₄	1	1	yes	characteristic
13	C₃×C₅×#124	C₄	1	2	yes	—
14	C₃×C₅×#121	C₄	1	2	yes	—
15	C₃×C₅×#121	C₄	1	2	yes	—
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×#4094	—	2	8	no	—
20	C₂×C₃×#681	C₂²	1	4	yes	—
21	C₂×C₃×#681	C₂²	1	1	yes	characteristic
22	C₂×C₃×#681	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	4	yes	—
24	C₂²×C₃×#168	C₂²	1	2	yes	—
25	C₃×C₂²⋊#168	C₂²	1	4	yes	—
26	C₃×C₂²⋊#168	C₂²	1	4	yes	—
27	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊#168	C₂²	1	2	yes	—
29	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
30	C₃×#3935	C₂²	1	2	yes	—
31	C₃×C₄×#168	C₂²	1	2	yes	—
32	C₃×#2935	—	5	1	no	maximal, Hall
33	C₅×#532	C₂×C₃	1	1	yes	characteristic
34	C₂×#4094	C₂×C₃	1	2	yes	complemented
35	#65523	C₂×C₃	1	2	yes	complemented
36	#65301	C₂×C₃	1	2	yes	complemented
37	#65300	C₂×C₃	1	4	yes	complemented
38	D₄×#168	C₂×C₃	1	2	yes	complemented
39	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
40	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
46	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×#681	—	2	2	no	—
61	C₃×#681	—	2	8	no	—
62	C₃×#681	D₄	1	4	yes	complemented
63	C₂×C₃×#168	—	2	4	no	—
64	C₂×C₃×#168	—	2	8	no	—
65	C₂×C₃×#168	C₂³	1	2	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₂×C₃×#168	C₂³	1	2	yes	—
68	C₂×C₃×#168	C₂³	1	2	yes	—
69	C₂×C₃×#131	—	5	2	no	—
70	C₃×#532	D₅	1	1	yes	characteristic
71	C₃×#436	—	5	2	no	—
72	C₃×#435	—	5	4	no	—
73	C₃×C₈×D₄	—	5	2	no	—
74	C₂×C₃×C₄⋊C₈	—	5	1	no	—
75	C₃×#408	—	5	2	no	—
76	C₃×C₄×M₁₆	—	5	1	no	—
77	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
78	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
79	C₅×#127	C₃×C₄	1	1	yes	characteristic
80	C₅×#124	C₃×C₄	1	2	yes	—
81	C₅×#121	C₃×C₄	1	2	yes	—
82	C₅×#121	C₃×C₄	1	2	yes	—
83	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
85	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
86	#4094	—	2	8	no	—
87	C₂×#681	C₂²×C₃	1	4	yes	—
88	C₂×#681	C₂²×C₃	1	1	yes	characteristic
89	C₂×#681	C₂²×C₃	1	1	yes	characteristic
90	C₂²×#168	C₂²×C₃	1	4	yes	—
91	C₂²×#168	C₂²×C₃	1	2	yes	—
92	C₂²⋊#168	C₂²×C₃	1	4	yes	—
93	C₂²⋊#168	C₂²×C₃	1	4	yes	—
94	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
95	C₄⋊#168	C₂²×C₃	1	2	yes	—
96	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
97	#3935	C₂²×C₃	1	2	yes	—
98	C₄×#168	C₂²×C₃	1	2	yes	—
99	#2935	—	5	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₃×C₅×D₄	—	2	8	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	2	4	no	—
106	C₃×C₅×D₄	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×#168	—	2	2	no	—
121	C₃×#168	—	2	2	no	—
122	C₃×#168	—	2	2	no	—
123	C₃×#168	C₂×D₄	1	4	yes	—
124	C₂×C₃×#41	C₂×D₅	1	2	yes	—
125	C₃×#131	—	10	8	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	—	5	4	no	—
128	C₂×C₃×M₁₆	—	5	1	no	—
129	C₂²×C₃×C₈	—	5	2	no	—
130	C₂²×C₃×C₈	—	5	4	no	—
131	C₃×C₄⋊Q₈	Dic₅	1	1	yes	characteristic
132	C₃×#127	Dic₅	1	1	yes	characteristic
133	C₃×#124	Dic₅	1	2	yes	—
134	C₃×#121	Dic₅	1	2	yes	—
135	C₃×#121	Dic₅	1	2	yes	—
136	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
137	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
138	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄⋊C₈	—	5	1	no	—
140	C₃×C₄⋊C₈	—	5	2	no	—
141	C₃×C₄⋊C₈	—	5	1	no	—
142	C₃×C₂²⋊C₈	—	5	4	no	—
143	C₃×C₂²⋊C₈	—	5	4	no	—
144	C₃×#97	—	5	2	no	—
145	C₃×C₄×C₈	—	5	2	no	—
146	C₅×#41	—	2	4	no	—
147	C₅×#41	—	2	4	no	—
148	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
149	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
150	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
151	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
153	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
158	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
159	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
160	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
161	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
165	#681	—	2	2	no	—
166	#681	—	2	8	no	—
167	#681	C₃×D₄	1	4	yes	complemented
168	C₂×#168	—	2	4	no	—
169	C₂×#168	—	2	8	no	—
170	C₂×#168	C₂³×C₃	1	2	yes	—
171	C₂×#168	C₂³×C₃	1	2	yes	—
172	C₂×#168	C₂³×C₃	1	2	yes	—
173	C₂×#168	C₂³×C₃	1	2	yes	—
174	C₂×#131	—	5	2	no	—
175	#532	C₃×D₅	1	1	yes	characteristic
176	#436	—	5	2	no	—
177	#435	—	5	4	no	—
178	C₈×D₄	—	5	2	no	—
179	C₂×C₄⋊C₈	—	5	1	no	—
180	#408	—	5	2	no	—
181	C₄×M₁₆	—	5	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	4	no	—
185	C₂²×C₃×C₅	—	2	4	no	—
186	C₂²×C₃×C₅	—	2	4	no	—
187	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
188	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	—	2	1	no	—
193	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	complemented
195	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
197	C₃×#41	—	2	4	no	—
198	C₃×#41	—	2	4	no	—
199	C₂×C₃×Q₈	C₂×Dic₅	1	2	yes	—
200	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
201	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
202	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
203	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₃×M₁₆	—	5	4	no	—
209	C₃×M₁₆	—	10	8	no	—
210	C₃×M₁₆	—	10	2	no	—
211	C₂×C₃×C₈	—	5	2	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	5	2	no	—
215	C₂×C₃×C₈	—	10	8	no	—
216	C₂×C₃×C₈	—	10	4	no	—
217	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
218	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
219	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
220	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
221	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
222	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
223	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
224	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
225	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
226	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
227	C₅×Q₈	—	2	4	no	—
228	C₅×D₄	—	2	8	no	—
229	C₅×D₄	—	2	4	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	4	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
240	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₃×#41	1	2	yes	—
244	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
245	#168	—	2	2	no	—
246	#168	—	2	2	no	—
247	#168	—	2	2	no	—
248	#168	C₂×C₃×D₄	1	4	yes	—
249	C₂×#41	C₂×C₃×D₅	1	2	yes	—
250	#131	—	10	8	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂×M₁₆	—	5	4	no	—
253	C₂×M₁₆	—	5	1	no	—
254	C₂²×C₈	—	5	2	no	—
255	C₂²×C₈	—	5	4	no	—
256	C₄⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
257	#127	C₃×Dic₅	1	1	yes	characteristic
258	#124	C₃×Dic₅	1	2	yes	—
259	#121	C₃×Dic₅	1	2	yes	—
260	#121	C₃×Dic₅	1	2	yes	—
261	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
262	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
263	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	5	1	no	—
265	C₄⋊C₈	—	5	2	no	—
266	C₄⋊C₈	—	5	1	no	—
267	C₂²⋊C₈	—	5	4	no	—
268	C₂²⋊C₈	—	5	4	no	—
269	#97	—	5	2	no	—
270	C₄×C₈	—	5	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	4	4	no	—
273	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
275	C₂×C₃×C₅	#568	1	1	yes	characteristic
276	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
277	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
278	C₃×Q₈	—	2	4	no	—
279	C₃×D₄	—	2	8	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	4	no	—
282	C₃×D₄	—	4	2	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
288	C₂×C₃×C₄	#711	1	2	yes	—
289	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
293	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
296	C₃×C₈	—	5	4	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃×C₈	—	10	2	no	—
299	C₃×C₈	—	10	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	2	4	no	—
304	C₂²×C₅	—	2	4	no	—
305	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
306	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	4	no	—
311	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
312	C₄×C₅	C₃×#131	1	2	yes	complemented
313	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
314	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	C₂×Q₈	C₂×C₃×Dic₅	1	2	yes	—
318	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
319	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
320	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
321	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
322	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	M₁₆	—	5	4	no	—
327	M₁₆	—	10	8	no	—
328	M₁₆	—	10	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	2	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	10	8	no	—
334	C₂×C₈	—	10	4	no	—
335	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
336	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
337	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
338	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
339	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
340	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
341	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
342	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	4	no	—
347	C₂²×C₃	—	2	4	no	—
348	C₂²×C₃	—	2	4	no	—
349	C₂²×C₃	D₄×Dic₅	1	2	yes	—
350	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	D₄×Dic₅	1	2	yes	—
356	C₃×C₄	#4094	1	2	yes	complemented
357	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
358	C₃×C₄	C₂×#711	1	1	yes	characteristic
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	—	4	4	no	—
361	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
362	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
363	C₂×C₅	C₃×#568	1	1	yes	characteristic
364	C₂³	C₂²×C₃×Dic₅	1	4	yes	—
365	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	D₄	—	2	8	no	—
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
376	C₂×C₄	C₃×#711	1	2	yes	—
377	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
381	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
384	C₈	—	5	4	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	2	no	—
387	C₈	—	10	2	no	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	4	4	no	—
390	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
391	C₂×C₃	C₂×#4094	1	1	yes	characteristic
392	C₂×C₃	#66153	1	1	yes	characteristic
393	C₅	C₃×#2935	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	C₃×D₄×Dic₅	1	2	yes	—
400	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	C₃×D₄×Dic₅	1	2	yes	—
406	C₄	C₃×#4094	1	2	yes	complemented
407	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
408	C₄	C₂×C₃×#711	1	1	yes	characteristic
409	C₃	#10615008	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	4	4	no	—
412	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
413	C₂	C₂×C₃×#4094	1	1	yes	characteristic
414	C₂	C₃×#66153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#2935
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₃×#65523	C₂	semidirect
4. C₃×#65301	C₂	semidirect
5. C₃×#65300	C₂	semidirect
6. C₃×D₄×#168	C₂	semidirect
7. C₂×C₃×C₄⋊#168	C₂	semidirect
8. C₃×C₄×#681	C₂	semidirect
9. #10615008	C₃	direct (N × H)
34. C₂×#4094	C₂×C₃	semidirect
35. #65523	C₂×C₃	semidirect
36. #65301	C₂×C₃	semidirect
37. #65300	C₂×C₃	semidirect
38. D₄×#168	C₂×C₃	semidirect
39. C₂×C₄⋊#168	C₂×C₃	semidirect
40. C₄×#681	C₂×C₃	semidirect
62. C₃×#681	D₄	semidirect
167. #681	C₃×D₄	semidirect
194. C₃×C₄×C₅	#131	semidirect
312. C₄×C₅	C₃×#131	semidirect
343. C₃×C₅	#2935	semidirect
356. C₃×C₄	#4094	semidirect
393. C₅	C₃×#2935	semidirect
406. C₄	C₃×#4094	semidirect
409. C₃	#10615008	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×C₅×#532	2
C₂×C₃×#4094	2
C₃×#65523	2
C₃×#65301	2
C₃×#65300	2
C₃×D₄×#168	2
C₂×C₃×C₄⋊#168	2
C₃×C₄×#681	2
#10615008	3
C₃×#2935	5

Subgroups — C3×#10615008 #14415841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615008 #14415841