Subgroups — C₂×C₃×#66113 #14510131

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4150	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66113	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4064	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×D₅×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4062	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4061	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#4055	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#66113	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×#4150	—	2	4	no	—
17	C₃×#4150	C₂²	1	8	yes	complemented
18	C₃×#4147	—	2	4	no	—
19	C₃×#4147	C₂²	1	8	yes	complemented
20	C₂×C₃×#713	—	2	1	no	—
21	C₂×C₃×#713	C₂²	1	2	yes	—
22	C₂×C₃×Q₈×D₅	—	2	1	no	—
23	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
24	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
25	C₂×C₃×#711	—	2	2	no	—
26	C₂×C₃×#711	C₂²	1	2	yes	—
27	C₂×C₃×#709	—	2	2	no	—
28	C₂×C₃×#709	—	2	1	no	—
29	C₂×C₃×#709	C₂²	1	1	yes	characteristic
30	C₂×C₃×#709	C₂²	1	1	yes	characteristic
31	C₂²×C₃×Dic₁₀	—	2	1	no	—
32	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
33	C₃×C₅×#137	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
35	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
36	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
37	C₃×#4096	C₂²	1	8	yes	complemented
38	C₂×C₃×#689	C₂²	1	2	yes	—
39	C₂×C₃×#689	C₂²	1	2	yes	—
40	C₂×C₃×#689	C₂²	1	1	yes	characteristic
41	C₂×C₃×#689	C₂²	1	8	yes	complemented
42	C₂×C₃×#688	C₂²	1	1	yes	characteristic
43	C₂×C₃×#687	C₂²	1	1	yes	characteristic
44	C₂×C₃×#686	C₂²	1	1	yes	characteristic
45	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
46	C₃×#4064	C₂²	1	16	yes	complemented
47	C₃×D₅×Q₁₆	C₂²	1	16	yes	complemented
48	C₃×#4062	C₂²	1	16	yes	complemented
49	C₃×#4061	C₂²	1	16	yes	complemented
50	C₃×#4055	C₂²	1	8	yes	complemented
51	C₃×#4053	C₂²	1	8	yes	complemented
52	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
53	C₂×C₃×#677	C₂²	1	2	yes	—
54	C₂×C₃×#676	C₂²	1	2	yes	—
55	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
56	C₂×C₃×#578	—	5	1	no	maximal, Hall
57	C₂×#4150	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#4147	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4096	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂²×#689	C₂×C₃	1	1	yes	characteristic, complemented
62	#66113	C₂×C₃	1	16	yes	direct product factor
63	C₂×#4064	C₂×C₃	1	2	yes	complemented
64	C₂×D₅×Q₁₆	C₂×C₃	1	2	yes	complemented
65	C₂×#4062	C₂×C₃	1	2	yes	complemented
66	C₂×#4061	C₂×C₃	1	2	yes	complemented
67	C₂×#4055	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
69	C₃×C₅×#41	—	2	2	no	—
70	C₃×C₅×#41	C₂³	1	4	yes	—
71	C₂×C₃×C₅×Q₈	—	2	1	no	—
72	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
75	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
76	C₂×C₃×C₅×D₄	—	2	1	no	—
77	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	—	2	1	no	—
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
82	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
83	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
84	C₂²×C₃×Dic₅	—	2	1	no	—
85	C₂²×C₃×Dic₅	—	2	2	no	—
86	C₃×#713	—	2	8	no	—
87	C₃×#713	—	2	4	no	—
88	C₃×#713	C₂³	1	8	yes	—
89	C₃×Q₈×D₅	—	2	4	no	—
90	C₃×Q₈×D₅	—	2	4	no	—
91	C₃×Q₈×D₅	—	2	8	no	—
92	C₃×Q₈×D₅	C₂³	1	8	yes	—
93	C₃×Q₈×D₅	C₂³	1	8	yes	—
94	C₃×#711	—	2	16	no	—
95	C₃×#711	—	2	4	no	—
96	C₃×#711	C₂³	1	8	yes	—
97	C₃×#709	—	2	2	no	—
98	C₃×#709	—	2	16	no	—
99	C₃×#709	—	2	8	no	—
100	C₃×#709	D₄	1	4	yes	—
101	C₃×#709	C₂³	1	4	yes	—
102	C₃×#709	C₂³	1	4	yes	—
103	C₂×C₃×D₂₀	—	2	2	no	—
104	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
105	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₄×D₅	—	2	2	no	—
107	C₂×C₃×C₄×D₅	—	2	2	no	—
108	C₂×C₃×C₄×D₅	—	2	1	no	—
109	C₂×C₃×C₄×D₅	—	2	2	no	—
110	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
111	C₂×C₃×Dic₁₀	—	2	1	no	—
112	C₂×C₃×Dic₁₀	—	2	2	no	—
113	C₂×C₃×Dic₁₀	—	2	2	no	—
114	C₂×C₃×Dic₁₀	—	2	2	no	—
115	C₂×C₃×Dic₁₀	—	2	8	no	—
116	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
117	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
118	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
119	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
120	C₃×C₅×Q₁₆	C₂³	1	8	yes	—
121	C₃×C₅×SD₁₆	C₂³	1	8	yes	—
122	C₃×C₅×M₁₆	C₂³	1	4	yes	—
123	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
124	C₃×#689	C₂³	1	8	yes	—
125	C₃×#689	C₂³	1	8	yes	—
126	C₃×#689	C₂³	1	4	yes	—
127	C₃×#688	C₂³	1	4	yes	—
128	C₃×#687	C₂³	1	4	yes	—
129	C₃×#686	C₂³	1	4	yes	—
130	C₂×C₃×#168	C₂³	1	1	yes	characteristic
131	C₂×C₃×#168	C₂³	1	1	yes	characteristic
132	C₂×C₃×#168	C₂³	1	4	yes	—
133	C₃×Dic₂₀	C₂³	1	8	yes	—
134	C₃×#677	C₂³	1	8	yes	—
135	C₃×#676	C₂³	1	8	yes	—
136	C₃×C₈×D₅	C₂³	1	8	yes	—
137	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
138	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
139	C₃×#578	—	5	16	no	—
140	C₂×C₃×#137	—	5	2	no	—
141	C₂×C₃×#137	—	5	2	no	—
142	C₂×C₃×#137	—	5	1	no	—
143	C₂×C₃×#137	D₅	1	1	yes	characteristic, complemented
144	C₂×C₃×#135	—	5	1	no	—
145	C₂×C₃×#135	—	5	2	no	—
146	C₂²×C₃×Q₁₆	—	5	1	no	—
147	C₂²×C₃×Q₁₆	—	5	2	no	—
148	C₂×C₃×#131	—	5	1	no	—
149	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
151	#4150	—	2	4	no	—
152	#4150	C₂²×C₃	1	8	yes	complemented
153	#4147	—	2	4	no	—
154	#4147	C₂²×C₃	1	8	yes	complemented
155	C₂×#713	—	2	1	no	—
156	C₂×#713	C₂²×C₃	1	2	yes	—
157	C₂×Q₈×D₅	—	2	1	no	—
158	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
159	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
160	C₂×#711	—	2	2	no	—
161	C₂×#711	C₂²×C₃	1	2	yes	—
162	C₂×#709	—	2	2	no	—
163	C₂×#709	—	2	1	no	—
164	C₂×#709	C₂²×C₃	1	1	yes	characteristic
165	C₂×#709	C₂²×C₃	1	1	yes	characteristic
166	C₂²×Dic₁₀	—	2	1	no	—
167	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
168	C₅×#137	C₂²×C₃	1	8	yes	complemented
169	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
170	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
171	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
172	#4096	C₂²×C₃	1	8	yes	complemented
173	C₂×#689	C₂²×C₃	1	2	yes	—
174	C₂×#689	C₂²×C₃	1	2	yes	—
175	C₂×#689	C₂²×C₃	1	1	yes	characteristic
176	C₂×#689	C₂²×C₃	1	8	yes	complemented
177	C₂×#688	C₂²×C₃	1	1	yes	characteristic
178	C₂×#687	C₂²×C₃	1	1	yes	characteristic
179	C₂×#686	C₂²×C₃	1	1	yes	characteristic
180	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
181	#4064	C₂²×C₃	1	16	yes	complemented
182	D₅×Q₁₆	C₂²×C₃	1	16	yes	complemented
183	#4062	C₂²×C₃	1	16	yes	complemented
184	#4061	C₂²×C₃	1	16	yes	complemented
185	#4055	C₂²×C₃	1	8	yes	complemented
186	#4053	C₂²×C₃	1	8	yes	complemented
187	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
188	C₂×#677	C₂²×C₃	1	2	yes	—
189	C₂×#676	C₂²×C₃	1	2	yes	—
190	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
191	C₂×#578	—	5	1	no	Sylow
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₃×D₅	—	2	1	no	—
195	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	2	no	—
198	C₃×C₅×Q₈	—	2	4	no	—
199	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
200	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
201	C₃×C₅×D₄	—	2	4	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	C₂⁴	1	2	yes	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	2	no	—
206	C₂×C₃×C₄×C₅	—	2	4	no	—
207	C₂×C₃×C₄×C₅	—	2	4	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
210	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
212	C₃×C₂²⋊D₅	—	2	4	no	—
213	C₃×C₂²⋊D₅	—	2	8	no	—
214	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	—
215	C₂×C₃×Dic₅	—	2	1	no	—
216	C₂×C₃×Dic₅	—	2	2	no	—
217	C₂×C₃×Dic₅	—	2	4	no	—
218	C₂×C₃×Dic₅	—	2	8	no	—
219	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
220	C₃×D₂₀	—	2	8	no	—
221	C₃×D₂₀	—	2	1	no	—
222	C₃×D₂₀	C₂×D₄	1	4	yes	—
223	C₃×D₂₀	C₂⁴	1	2	yes	—
224	C₃×C₄×D₅	—	2	8	no	—
225	C₃×C₄×D₅	—	2	8	no	—
226	C₃×C₄×D₅	—	2	4	no	—
227	C₃×C₄×D₅	—	2	8	no	—
228	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
229	C₃×C₄×D₅	C₂⁴	1	4	yes	—
230	C₃×Dic₁₀	—	2	4	no	—
231	C₃×Dic₁₀	—	2	2	no	—
232	C₃×Dic₁₀	—	2	1	no	—
233	C₃×Dic₁₀	—	2	8	no	—
234	C₃×Dic₁₀	—	2	8	no	—
235	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
236	C₃×Dic₁₀	C₂⁴	1	4	yes	—
237	C₃×Dic₁₀	C₂⁴	1	2	yes	—
238	C₃×C₅×C₈	C₂⁴	1	4	yes	—
239	C₃×#168	C₂⁴	1	2	yes	—
240	C₃×#168	C₂⁴	1	2	yes	—
241	C₃×2₋¹⁺⁴	—	5	8	no	—
242	C₃×2₋¹⁺⁴	—	5	8	no	—
243	C₃×2₋¹⁺⁴	—	10	4	no	—
244	C₃×2₋¹⁺⁴	—	10	4	no	—
245	C₂×C₃×#41	—	5	1	no	—
246	C₂×C₃×#41	—	5	2	no	—
247	C₂×C₃×#41	—	5	2	no	—
248	C₂×C₃×#41	—	5	1	no	—
249	C₂×C₃×#41	—	10	2	no	—
250	C₂×C₃×#41	—	10	1	no	—
251	C₂×C₃×#41	—	10	2	no	—
252	C₂×C₃×#41	—	10	1	no	—
253	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
254	C₂²×C₃×Q₈	—	5	2	no	—
255	C₂²×C₃×Q₈	—	5	2	no	—
256	C₂²×C₃×Q₈	—	5	1	no	—
257	C₂²×C₃×Q₈	—	10	1	no	—
258	C₂²×C₃×Q₈	—	10	1	no	—
259	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
260	C₃×#137	—	5	16	no	—
261	C₃×#137	—	5	16	no	—
262	C₃×#137	—	5	8	no	—
263	C₃×#137	C₂×D₅	1	8	yes	complemented
264	C₃×#135	—	5	8	no	—
265	C₃×#135	—	5	16	no	—
266	C₂×C₃×Q₁₆	—	5	1	no	—
267	C₂×C₃×Q₁₆	—	5	2	no	—
268	C₂×C₃×Q₁₆	—	5	2	no	—
269	C₂×C₃×Q₁₆	—	5	8	no	—
270	C₂×C₃×Q₁₆	—	5	16	no	—
271	C₂×C₃×Q₁₆	—	5	2	no	—
272	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
273	C₂×C₃×SD₁₆	—	5	1	no	—
274	C₂×C₃×SD₁₆	—	5	1	no	—
275	C₂×C₃×SD₁₆	—	5	2	no	—
276	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
277	C₂×C₃×D₈	—	5	1	no	—
278	C₃×#131	—	5	8	no	—
279	C₂×C₃×M₁₆	—	5	2	no	—
280	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
281	C₂²×C₃×C₈	—	5	1	no	—
282	C₂²×C₃×C₈	—	5	2	no	—
283	C₅×#41	—	2	2	no	—
284	C₅×#41	C₂³×C₃	1	4	yes	—
285	C₂×C₅×Q₈	—	2	1	no	—
286	C₂×C₅×Q₈	—	2	2	no	—
287	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
288	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
290	C₂×C₅×D₄	—	2	1	no	—
291	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	—	2	1	no	—
293	C₂²×C₄×C₅	—	2	1	no	—
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₂²⋊D₅	—	2	1	no	—
296	C₂×C₂²⋊D₅	—	2	2	no	—
297	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
298	C₂²×Dic₅	—	2	1	no	—
299	C₂²×Dic₅	—	2	2	no	—
300	#713	—	2	8	no	—
301	#713	—	2	4	no	—
302	#713	C₂³×C₃	1	8	yes	—
303	Q₈×D₅	—	2	4	no	—
304	Q₈×D₅	—	2	4	no	—
305	Q₈×D₅	—	2	8	no	—
306	Q₈×D₅	C₂³×C₃	1	8	yes	—
307	Q₈×D₅	C₂³×C₃	1	8	yes	—
308	#711	—	2	16	no	—
309	#711	—	2	4	no	—
310	#711	C₂³×C₃	1	8	yes	—
311	#709	—	2	2	no	—
312	#709	—	2	16	no	—
313	#709	—	2	8	no	—
314	#709	C₃×D₄	1	4	yes	—
315	#709	C₂³×C₃	1	4	yes	—
316	#709	C₂³×C₃	1	4	yes	—
317	C₂×D₂₀	—	2	2	no	—
318	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
319	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₄×D₅	—	2	2	no	—
321	C₂×C₄×D₅	—	2	2	no	—
322	C₂×C₄×D₅	—	2	1	no	—
323	C₂×C₄×D₅	—	2	2	no	—
324	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
325	C₂×Dic₁₀	—	2	1	no	—
326	C₂×Dic₁₀	—	2	2	no	—
327	C₂×Dic₁₀	—	2	2	no	—
328	C₂×Dic₁₀	—	2	2	no	—
329	C₂×Dic₁₀	—	2	8	no	—
330	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
331	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
332	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
333	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
334	C₅×Q₁₆	C₂³×C₃	1	8	yes	—
335	C₅×SD₁₆	C₂³×C₃	1	8	yes	—
336	C₅×M₁₆	C₂³×C₃	1	4	yes	—
337	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
338	#689	C₂³×C₃	1	4	yes	—
339	#689	C₂³×C₃	1	8	yes	—
340	#689	C₂³×C₃	1	8	yes	—
341	#688	C₂³×C₃	1	4	yes	—
342	#687	C₂³×C₃	1	4	yes	—
343	#686	C₂³×C₃	1	4	yes	—
344	C₂×#168	C₂³×C₃	1	4	yes	—
345	C₂×#168	C₂³×C₃	1	1	yes	characteristic
346	C₂×#168	C₂³×C₃	1	1	yes	characteristic
347	Dic₂₀	C₂³×C₃	1	8	yes	—
348	#677	C₂³×C₃	1	8	yes	—
349	#676	C₂³×C₃	1	8	yes	—
350	C₈×D₅	C₂³×C₃	1	8	yes	—
351	C₂×2₋¹⁺⁴	—	5	1	no	—
352	C₂×2₋¹⁺⁴	—	5	1	no	—
353	#578	—	5	16	no	—
354	C₂×#137	—	5	2	no	—
355	C₂×#137	—	5	2	no	—
356	C₂×#137	—	5	1	no	—
357	C₂×#137	C₃×D₅	1	1	yes	characteristic, complemented
358	C₂×#135	—	5	1	no	—
359	C₂×#135	—	5	2	no	—
360	C₂²×Q₁₆	—	5	1	no	—
361	C₂²×Q₁₆	—	5	2	no	—
362	C₂×#131	—	5	1	no	—
363	C₂²×C₃×C₅	—	2	2	no	—
364	C₂²×C₃×C₅	—	2	2	no	—
365	C₂²×C₃×C₅	—	4	2	no	—
366	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
367	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₃×D₅	—	2	4	no	—
369	C₂×C₃×D₅	—	2	2	no	—
370	C₂×C₃×D₅	—	4	2	no	—
371	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	4	no	—
374	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
376	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
377	C₃×Dic₅	—	2	2	no	—
378	C₃×Dic₅	—	2	4	no	—
379	C₃×Dic₅	C₂²×D₄	1	4	yes	—
380	C₃×#41	—	2	2	no	—
381	C₃×#41	—	5	4	no	—
382	C₃×#41	—	5	4	no	—
383	C₃×#41	—	5	8	no	—
384	C₃×#41	—	5	8	no	—
385	C₃×#41	—	5	4	no	—
386	C₃×#41	—	10	16	no	—
387	C₃×#41	—	10	8	no	—
388	C₃×#41	—	10	4	no	—
389	C₃×#41	—	10	4	no	—
390	C₃×#41	—	10	16	no	—
391	C₃×#41	—	10	8	no	—
392	C₃×#41	—	10	2	no	—
393	C₃×#41	C₂²×D₅	1	4	yes	—
394	C₂×C₃×Q₈	—	2	1	no	—
395	C₂×C₃×Q₈	—	2	2	no	—
396	C₂×C₃×Q₈	—	5	1	no	—
397	C₂×C₃×Q₈	—	5	8	no	—
398	C₂×C₃×Q₈	—	5	8	no	—
399	C₂×C₃×Q₈	—	5	1	no	—
400	C₂×C₃×Q₈	—	5	2	no	—
401	C₂×C₃×Q₈	—	5	4	no	—
402	C₂×C₃×Q₈	—	10	2	no	—
403	C₂×C₃×Q₈	—	10	2	no	—
404	C₂×C₃×Q₈	—	10	8	no	—
405	C₂×C₃×Q₈	—	10	4	no	—
406	C₂×C₃×Q₈	—	10	4	no	—
407	C₂×C₃×Q₈	—	10	8	no	—
408	C₂×C₃×Q₈	—	10	1	no	—
409	C₂×C₃×Q₈	—	10	2	no	—
410	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
411	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
412	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	5	2	no	—
415	C₂×C₃×D₄	—	5	1	no	—
416	C₂×C₃×D₄	—	5	1	no	—
417	C₂×C₃×D₄	—	10	2	no	—
418	C₂×C₃×D₄	—	10	2	no	—
419	C₂×C₃×D₄	—	10	1	no	—
420	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	—	2	1	no	—
422	C₂²×C₃×C₄	—	2	1	no	—
423	C₂²×C₃×C₄	—	5	2	no	—
424	C₂²×C₃×C₄	—	10	2	no	—
425	C₂²×C₃×C₄	—	10	2	no	—
426	C₂²×C₃×C₄	—	10	2	no	—
427	C₂²×C₃×C₄	—	10	2	no	—
428	C₂²×C₃×C₄	—	10	1	no	—
429	C₂²×C₃×C₄	—	10	1	no	—
430	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
431	C₃×Q₁₆	—	5	4	no	—
432	C₃×Q₁₆	—	5	8	no	—
433	C₃×Q₁₆	—	5	8	no	—
434	C₃×Q₁₆	—	5	8	no	—
435	C₃×Q₁₆	C₂²×D₅	1	8	yes	—
436	C₃×SD₁₆	—	5	4	no	—
437	C₃×SD₁₆	—	5	4	no	—
438	C₃×SD₁₆	—	5	8	no	—
439	C₃×SD₁₆	C₂²×D₅	1	8	yes	—
440	C₃×D₈	—	5	4	no	—
441	C₃×M₁₆	—	5	8	no	—
442	C₃×M₁₆	C₂²×D₅	1	4	yes	—
443	C₂×C₃×C₈	—	5	1	no	—
444	C₂×C₃×C₈	—	5	1	no	—
445	C₂×C₃×C₈	—	5	4	no	—
446	C₂×C₃×C₈	—	5	8	no	—
447	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
448	C₂³×C₅	—	2	1	no	—
449	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
450	C₂²×D₅	—	2	1	no	—
451	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	—	2	2	no	—
454	C₅×Q₈	—	2	4	no	—
455	C₅×Q₈	C₂⁴×C₃	1	2	yes	—
456	C₅×Q₈	C₂⁴×C₃	1	4	yes	—
457	C₅×D₄	—	2	4	no	—
458	C₅×D₄	—	2	1	no	—
459	C₅×D₄	C₂⁴×C₃	1	2	yes	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	2	no	—
462	C₂×C₄×C₅	—	2	4	no	—
463	C₂×C₄×C₅	—	2	4	no	—
464	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
466	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
467	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
468	C₂²⋊D₅	—	2	4	no	—
469	C₂²⋊D₅	—	2	8	no	—
470	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	—
471	C₂×Dic₅	—	2	1	no	—
472	C₂×Dic₅	—	2	2	no	—
473	C₂×Dic₅	—	2	4	no	—
474	C₂×Dic₅	—	2	8	no	—
475	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
476	D₂₀	—	2	8	no	—
477	D₂₀	—	2	1	no	—
478	D₂₀	C₂×C₃×D₄	1	4	yes	—
479	D₂₀	C₂⁴×C₃	1	2	yes	—
480	C₄×D₅	—	2	8	no	—
481	C₄×D₅	—	2	8	no	—
482	C₄×D₅	—	2	4	no	—
483	C₄×D₅	—	2	8	no	—
484	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
485	C₄×D₅	C₂⁴×C₃	1	4	yes	—
486	Dic₁₀	—	2	4	no	—
487	Dic₁₀	—	2	2	no	—
488	Dic₁₀	—	2	1	no	—
489	Dic₁₀	—	2	8	no	—
490	Dic₁₀	—	2	8	no	—
491	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
492	Dic₁₀	C₂⁴×C₃	1	4	yes	—
493	Dic₁₀	C₂⁴×C₃	1	2	yes	—
494	C₅×C₈	C₂⁴×C₃	1	4	yes	—
495	#168	C₂⁴×C₃	1	2	yes	—
496	#168	C₂⁴×C₃	1	2	yes	—
497	2₋¹⁺⁴	—	5	8	no	—
498	2₋¹⁺⁴	—	5	8	no	—
499	2₋¹⁺⁴	—	10	4	no	—
500	2₋¹⁺⁴	—	10	4	no	—
501	C₂×#41	—	5	1	no	—
502	C₂×#41	—	5	2	no	—
503	C₂×#41	—	5	2	no	—
504	C₂×#41	—	5	1	no	—
505	C₂×#41	—	10	2	no	—
506	C₂×#41	—	10	1	no	—
507	C₂×#41	—	10	2	no	—
508	C₂×#41	—	10	1	no	—
509	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
510	C₂²×Q₈	—	5	2	no	—
511	C₂²×Q₈	—	5	2	no	—
512	C₂²×Q₈	—	5	1	no	—
513	C₂²×Q₈	—	10	1	no	—
514	C₂²×Q₈	—	10	1	no	—
515	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
516	#137	—	5	16	no	—
517	#137	—	5	16	no	—
518	#137	—	5	8	no	—
519	#137	C₂×C₃×D₅	1	8	yes	complemented
520	#135	—	5	8	no	—
521	#135	—	5	16	no	—
522	C₂×Q₁₆	—	5	1	no	—
523	C₂×Q₁₆	—	5	2	no	—
524	C₂×Q₁₆	—	5	2	no	—
525	C₂×Q₁₆	—	5	8	no	—
526	C₂×Q₁₆	—	5	16	no	—
527	C₂×Q₁₆	—	5	2	no	—
528	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
529	C₂×SD₁₆	—	5	1	no	—
530	C₂×SD₁₆	—	5	1	no	—
531	C₂×SD₁₆	—	5	2	no	—
532	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
533	C₂×D₈	—	5	1	no	—
534	#131	—	5	8	no	—
535	C₂×M₁₆	—	5	2	no	—
536	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
537	C₂²×C₈	—	5	1	no	—
538	C₂²×C₈	—	5	2	no	—
539	C₂×C₃×C₅	—	2	2	no	—
540	C₂×C₃×C₅	—	4	2	no	—
541	C₂×C₃×C₅	#578	1	2	yes	complemented
542	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
543	C₃×D₅	—	2	4	no	—
544	C₃×D₅	—	4	2	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	5	2	no	—
547	C₂³×C₃	—	10	1	no	—
548	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
549	C₃×Q₈	—	2	4	no	—
550	C₃×Q₈	—	2	2	no	—
551	C₃×Q₈	—	2	1	no	—
552	C₃×Q₈	—	5	4	no	—
553	C₃×Q₈	—	5	4	no	—
554	C₃×Q₈	—	5	2	no	—
555	C₃×Q₈	—	10	8	no	—
556	C₃×Q₈	—	10	8	no	—
557	C₃×Q₈	—	10	4	no	—
558	C₃×Q₈	—	10	2	no	—
559	C₃×Q₈	—	10	1	no	—
560	C₃×Q₈	C₂³×D₅	1	2	yes	—
561	C₃×Q₈	C₂³×D₅	1	4	yes	—
562	C₃×D₄	—	2	4	no	—
563	C₃×D₄	—	2	1	no	—
564	C₃×D₄	—	5	8	no	—
565	C₃×D₄	—	5	4	no	—
566	C₃×D₄	—	5	2	no	—
567	C₃×D₄	—	10	8	no	—
568	C₃×D₄	—	10	8	no	—
569	C₃×D₄	—	10	4	no	—
570	C₃×D₄	—	10	1	no	—
571	C₃×D₄	C₂³×D₅	1	2	yes	—
572	C₂×C₃×C₄	—	2	4	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	4	no	—
576	C₂×C₃×C₄	—	5	2	no	—
577	C₂×C₃×C₄	—	5	4	no	—
578	C₂×C₃×C₄	—	5	4	no	—
579	C₂×C₃×C₄	—	10	8	no	—
580	C₂×C₃×C₄	—	10	8	no	—
581	C₂×C₃×C₄	—	10	8	no	—
582	C₂×C₃×C₄	—	10	8	no	—
583	C₂×C₃×C₄	—	10	4	no	—
584	C₂×C₃×C₄	—	10	1	no	—
585	C₂×C₃×C₄	—	10	2	no	—
586	C₂×C₃×C₄	—	10	4	no	—
587	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
588	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
589	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
590	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
591	C₃×C₈	—	5	2	no	—
592	C₃×C₈	—	5	2	no	—
593	C₃×C₈	C₂³×D₅	1	4	yes	—
594	C₂²×C₅	—	2	2	no	—
595	C₂²×C₅	—	2	2	no	—
596	C₂²×C₅	—	4	2	no	—
597	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
598	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
599	C₂×D₅	—	2	4	no	—
600	C₂×D₅	—	2	2	no	—
601	C₂×D₅	—	4	2	no	—
602	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	4	no	—
605	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
606	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
607	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
608	Dic₅	—	2	2	no	—
609	Dic₅	—	2	4	no	—
610	Dic₅	C₂²×C₃×D₄	1	4	yes	—
611	#41	—	2	2	no	—
612	#41	—	5	4	no	—
613	#41	—	5	4	no	—
614	#41	—	5	8	no	—
615	#41	—	5	8	no	—
616	#41	—	5	4	no	—
617	#41	—	10	16	no	—
618	#41	—	10	8	no	—
619	#41	—	10	4	no	—
620	#41	—	10	4	no	—
621	#41	—	10	16	no	—
622	#41	—	10	8	no	—
623	#41	—	10	2	no	—
624	#41	C₂²×C₃×D₅	1	4	yes	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	5	1	no	—
628	C₂×Q₈	—	5	8	no	—
629	C₂×Q₈	—	5	8	no	—
630	C₂×Q₈	—	5	1	no	—
631	C₂×Q₈	—	5	2	no	—
632	C₂×Q₈	—	5	4	no	—
633	C₂×Q₈	—	10	2	no	—
634	C₂×Q₈	—	10	2	no	—
635	C₂×Q₈	—	10	8	no	—
636	C₂×Q₈	—	10	4	no	—
637	C₂×Q₈	—	10	4	no	—
638	C₂×Q₈	—	10	8	no	—
639	C₂×Q₈	—	10	1	no	—
640	C₂×Q₈	—	10	2	no	—
641	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
642	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
643	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	5	2	no	—
646	C₂×D₄	—	5	1	no	—
647	C₂×D₄	—	5	1	no	—
648	C₂×D₄	—	10	2	no	—
649	C₂×D₄	—	10	2	no	—
650	C₂×D₄	—	10	1	no	—
651	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	5	2	no	—
655	C₂²×C₄	—	10	2	no	—
656	C₂²×C₄	—	10	2	no	—
657	C₂²×C₄	—	10	2	no	—
658	C₂²×C₄	—	10	2	no	—
659	C₂²×C₄	—	10	1	no	—
660	C₂²×C₄	—	10	1	no	—
661	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
662	Q₁₆	—	5	4	no	—
663	Q₁₆	—	5	8	no	—
664	Q₁₆	—	5	8	no	—
665	Q₁₆	—	5	8	no	—
666	Q₁₆	C₂²×C₃×D₅	1	8	yes	—
667	SD₁₆	—	5	4	no	—
668	SD₁₆	—	5	4	no	—
669	SD₁₆	—	5	8	no	—
670	SD₁₆	C₂²×C₃×D₅	1	8	yes	—
671	D₈	—	5	4	no	—
672	M₁₆	—	5	8	no	—
673	M₁₆	C₂²×C₃×D₅	1	4	yes	—
674	C₂×C₈	—	5	1	no	—
675	C₂×C₈	—	5	1	no	—
676	C₂×C₈	—	5	4	no	—
677	C₂×C₈	—	5	8	no	—
678	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
679	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
680	C₂²×C₃	—	2	2	no	—
681	C₂²×C₃	—	2	2	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	—	5	4	no	—
684	C₂²×C₃	—	10	4	no	—
685	C₂²×C₃	—	10	2	no	—
686	C₂²×C₃	—	20	2	no	—
687	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
688	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	2	4	no	—
691	C₃×C₄	—	5	4	no	—
692	C₃×C₄	—	10	2	no	—
693	C₃×C₄	—	10	4	no	—
694	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
695	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
696	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
697	C₂×C₅	—	2	2	no	—
698	C₂×C₅	—	4	2	no	—
699	C₂×C₅	C₃×#578	1	2	yes	complemented
700	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
701	D₅	—	2	4	no	—
702	D₅	—	4	2	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	5	2	no	—
705	C₂³	—	10	1	no	—
706	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	5	4	no	—
711	Q₈	—	5	2	no	—
712	Q₈	—	5	4	no	—
713	Q₈	—	10	8	no	—
714	Q₈	—	10	8	no	—
715	Q₈	—	10	4	no	—
716	Q₈	—	10	1	no	—
717	Q₈	—	10	2	no	—
718	Q₈	C₂³×C₃×D₅	1	2	yes	—
719	Q₈	C₂³×C₃×D₅	1	4	yes	—
720	D₄	—	2	4	no	—
721	D₄	—	2	1	no	—
722	D₄	—	5	8	no	—
723	D₄	—	5	4	no	—
724	D₄	—	5	2	no	—
725	D₄	—	10	8	no	—
726	D₄	—	10	8	no	—
727	D₄	—	10	4	no	—
728	D₄	—	10	1	no	—
729	D₄	C₂³×C₃×D₅	1	2	yes	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	5	2	no	—
735	C₂×C₄	—	5	4	no	—
736	C₂×C₄	—	5	4	no	—
737	C₂×C₄	—	10	8	no	—
738	C₂×C₄	—	10	8	no	—
739	C₂×C₄	—	10	8	no	—
740	C₂×C₄	—	10	8	no	—
741	C₂×C₄	—	10	1	no	—
742	C₂×C₄	—	10	2	no	—
743	C₂×C₄	—	10	4	no	—
744	C₂×C₄	—	10	4	no	—
745	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
746	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
747	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
748	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
749	C₈	—	5	2	no	—
750	C₈	—	5	2	no	—
751	C₈	C₂³×C₃×D₅	1	4	yes	—
752	C₂×C₃	—	2	2	no	—
753	C₂×C₃	—	4	2	no	—
754	C₂×C₃	—	10	4	no	—
755	C₂×C₃	—	20	2	no	—
756	C₂×C₃	#66113	1	2	yes	direct product factor
757	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
758	C₅	C₂×C₃×#578	1	1	yes	characteristic, complemented, Sylow
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	5	4	no	—
763	C₂²	—	10	4	no	—
764	C₂²	—	10	2	no	—
765	C₂²	—	20	2	no	—
766	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
767	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
768	C₄	—	2	2	no	—
769	C₄	—	2	4	no	—
770	C₄	—	5	4	no	—
771	C₄	—	10	2	no	—
772	C₄	—	10	4	no	—
773	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
774	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
775	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
776	C₃	C₂×#66113	1	1	yes	characteristic, direct product factor, Sylow
777	C₂	—	2	2	no	—
778	C₂	—	4	2	no	—
779	C₂	—	10	4	no	—
780	C₂	—	20	2	no	—
781	C₂	C₃×#66113	1	2	yes	direct product factor
782	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#137	D₅
hypocenter	C₅	C₂×C₃×#578
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4150	C₂	semidirect
2. C₂×C₃×#4147	C₂	semidirect
3. C₂×C₃×C₅×#137	C₂	semidirect
4. C₂×C₃×#4096	C₂	semidirect
5. C₂²×C₃×#689	C₂	semidirect
6. C₃×#66113	C₂	direct (N × H)
7. C₂×C₃×#4064	C₂	semidirect
8. C₂×C₃×D₅×Q₁₆	C₂	semidirect
9. C₂×C₃×#4062	C₂	semidirect
10. C₂×C₃×#4061	C₂	semidirect
11. C₂×C₃×#4055	C₂	semidirect
12. C₂×C₃×#4053	C₂	semidirect
13. C₂×#66113	C₃	direct (N × H)
17. C₃×#4150	C₂²	semidirect
19. C₃×#4147	C₂²	semidirect
33. C₃×C₅×#137	C₂²	semidirect
37. C₃×#4096	C₂²	semidirect
41. C₂×C₃×#689	C₂²	semidirect
46. C₃×#4064	C₂²	semidirect
47. C₃×D₅×Q₁₆	C₂²	semidirect
48. C₃×#4062	C₂²	semidirect
49. C₃×#4061	C₂²	semidirect
50. C₃×#4055	C₂²	semidirect
51. C₃×#4053	C₂²	semidirect
57. C₂×#4150	C₂×C₃	semidirect
58. C₂×#4147	C₂×C₃	semidirect
59. C₂×C₅×#137	C₂×C₃	semidirect
60. C₂×#4096	C₂×C₃	semidirect
61. C₂²×#689	C₂×C₃	semidirect
62. #66113	C₂×C₃	direct (N × H)
63. C₂×#4064	C₂×C₃	semidirect
64. C₂×D₅×Q₁₆	C₂×C₃	semidirect
65. C₂×#4062	C₂×C₃	semidirect
66. C₂×#4061	C₂×C₃	semidirect
67. C₂×#4055	C₂×C₃	semidirect
68. C₂×#4053	C₂×C₃	semidirect
143. C₂×C₃×#137	D₅	semidirect
152. #4150	C₂²×C₃	semidirect
154. #4147	C₂²×C₃	semidirect
168. C₅×#137	C₂²×C₃	semidirect
172. #4096	C₂²×C₃	semidirect
176. C₂×#689	C₂²×C₃	semidirect
181. #4064	C₂²×C₃	semidirect
182. D₅×Q₁₆	C₂²×C₃	semidirect
183. #4062	C₂²×C₃	semidirect
184. #4061	C₂²×C₃	semidirect
185. #4055	C₂²×C₃	semidirect
186. #4053	C₂²×C₃	semidirect
263. C₃×#137	C₂×D₅	semidirect
357. C₂×#137	C₃×D₅	semidirect
519. #137	C₂×C₃×D₅	semidirect
541. C₂×C₃×C₅	#578	semidirect
679. C₃×C₅	C₂×#578	semidirect
699. C₂×C₅	C₃×#578	semidirect
756. C₂×C₃	#66113	direct (N × H)
758. C₅	C₂×C₃×#578	semidirect
776. C₃	C₂×#66113	direct (N × H)
781. C₂	C₃×#66113	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×#4150	2
C₂×C₃×#4147	2
C₂×C₃×C₅×#137	2
C₂×C₃×#4096	2
C₂²×C₃×#689	2
C₃×#66113	2
C₂×C₃×#4064	2
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×#4062	2
C₂×C₃×#4061	2
C₂×C₃×#4055	2
C₂×C₃×#4053	2
C₂×#66113	3
C₂×C₃×#578	5

Subgroups — C2×C3×#66113 #14510131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66113 #14510131