Subgroups — C₃×#10612387 #14427787

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4062	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65961	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65460	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65403	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65327	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65149	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65102	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65064	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65061	C₂	1	1	yes	maximal, characteristic, complemented
16	#10612387	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#713	C₂²	1	1	yes	characteristic
18	C₂×C₃×#711	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₃×#4092	C₂²	1	1	yes	characteristic
25	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4084	C₂²	1	1	yes	characteristic
27	C₃×#4083	—	2	1	no	—
28	C₃×D₄×Dic₅	—	2	1	no	—
29	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4076	C₂²	1	1	yes	characteristic
31	C₃×#4070	C₂²	1	1	yes	characteristic
32	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
33	C₃×#4062	—	2	4	no	—
34	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₈×D₅	—	2	4	no	—
36	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
40	C₃×#4043	C₂²	1	1	yes	characteristic
41	C₃×#4041	C₂²	1	1	yes	characteristic
42	C₃×#4040	—	2	1	no	—
43	C₃×#4039	—	2	1	no	—
44	C₃×#4038	C₂²	1	1	yes	characteristic
45	C₃×#4038	C₂²	1	1	yes	characteristic
46	C₃×#4029	—	2	1	no	—
47	C₃×#4028	—	2	1	no	—
48	C₃×#4027	—	2	1	no	—
49	C₃×#4027	—	2	1	no	—
50	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3953	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3939	C₂²	1	1	yes	characteristic, complemented
61	C₃×#3939	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3050	—	5	1	no	maximal, Hall
63	C₂×#4062	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
65	#65961	C₂×C₃	1	1	yes	characteristic, complemented
66	#65940	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
68	#65460	C₂×C₃	1	1	yes	characteristic, complemented
69	#65403	C₂×C₃	1	1	yes	characteristic, complemented
70	#65340	C₂×C₃	1	1	yes	characteristic, complemented
71	#65327	C₂×C₃	1	1	yes	characteristic, complemented
72	#65153	C₂×C₃	1	1	yes	characteristic, complemented
73	#65149	C₂×C₃	1	1	yes	characteristic, complemented
74	#65102	C₂×C₃	1	1	yes	characteristic, complemented
75	#65093	C₂×C₃	1	1	yes	characteristic, complemented
76	#65064	C₂×C₃	1	1	yes	characteristic, complemented
77	#65061	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
84	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
85	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
86	C₂²×C₃×Dic₅	—	2	1	no	—
87	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
88	C₃×#713	—	2	2	no	—
89	C₃×#713	—	2	2	no	—
90	C₃×#711	—	2	2	no	—
91	C₃×#711	—	2	2	no	—
92	C₂×C₃×D₂₀	—	2	1	no	—
93	C₂×C₃×D₂₀	—	2	1	no	—
94	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	—	2	2	no	—
96	C₂×C₃×C₄×D₅	—	2	2	no	—
97	C₂×C₃×C₄×D₅	—	2	1	no	—
98	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
102	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
103	C₃×C₅×SD₁₆	—	2	2	no	—
104	C₂×C₃×C₅×C₈	—	2	2	no	—
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₂²⋊Dic₅	—	2	1	no	—
113	C₃×C₂²⋊Dic₅	—	2	1	no	—
114	C₃×#689	—	2	2	no	—
115	C₃×#686	—	2	2	no	—
116	C₃×#685	—	2	1	no	—
117	C₃×#685	—	2	1	no	—
118	C₃×#685	—	2	1	no	—
119	C₃×#685	—	2	1	no	—
120	C₃×#685	—	2	1	no	—
121	C₃×#685	—	2	1	no	—
122	C₃×C₄⋊Dic₅	—	2	1	no	—
123	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
124	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
125	C₃×#683	—	2	1	no	—
126	C₃×#683	—	2	1	no	—
127	C₃×C₄×Dic₅	—	2	1	no	—
128	C₃×C₄×Dic₅	—	2	1	no	—
129	C₂×C₃×#168	—	2	2	no	—
130	C₂×C₃×#168	C₂³	1	1	yes	characteristic
131	C₂×C₃×#168	C₂³	1	1	yes	characteristic
132	C₃×#677	—	2	2	no	—
133	C₃×C₈×D₅	—	2	2	no	—
134	C₃×C₈×D₅	—	2	2	no	—
135	C₃×C₈×D₅	—	2	2	no	—
136	C₃×C₈×D₅	D₄	1	4	yes	complemented
137	C₂×C₃×#135	—	5	1	no	—
138	C₂³×C₃×C₈	—	5	1	no	—
139	C₃×#525	—	5	1	no	—
140	C₃×#525	—	5	1	no	—
141	C₃×#467	—	5	1	no	—
142	C₃×#467	—	5	1	no	—
143	C₃×#466	—	5	1	no	—
144	C₃×#466	—	5	1	no	—
145	C₃×#465	—	5	1	no	—
146	C₃×#465	—	5	1	no	—
147	C₃×#465	—	5	1	no	—
148	C₃×#465	D₅	1	1	yes	characteristic, complemented
149	C₃×#427	—	5	1	no	—
150	C₃×#416	—	5	1	no	—
151	C₃×#416	—	5	1	no	—
152	C₂×#713	C₂²×C₃	1	1	yes	characteristic
153	C₂×#711	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
156	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×#121	C₂²×C₃	1	1	yes	characteristic
159	#4092	C₂²×C₃	1	1	yes	characteristic
160	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
161	#4084	C₂²×C₃	1	1	yes	characteristic
162	#4083	—	2	1	no	—
163	D₄×Dic₅	—	2	1	no	—
164	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
165	#4076	C₂²×C₃	1	1	yes	characteristic
166	#4070	C₂²×C₃	1	1	yes	characteristic
167	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
168	#4062	—	2	4	no	—
169	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂×C₈×D₅	—	2	4	no	—
171	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
175	#4043	C₂²×C₃	1	1	yes	characteristic
176	#4041	C₂²×C₃	1	1	yes	characteristic
177	#4040	—	2	1	no	—
178	#4039	—	2	1	no	—
179	#4038	C₂²×C₃	1	1	yes	characteristic
180	#4038	C₂²×C₃	1	1	yes	characteristic
181	#4029	—	2	1	no	—
182	#4028	—	2	1	no	—
183	#4027	—	2	1	no	—
184	#4027	—	2	1	no	—
185	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
188	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
190	#3953	C₂²×C₃	1	1	yes	characteristic, complemented
191	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
192	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
194	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
195	#3939	C₂²×C₃	1	1	yes	characteristic, complemented
196	#3939	C₂²×C₃	1	1	yes	characteristic, complemented
197	#3050	—	5	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₃×D₅	—	2	2	no	—
201	C₂²×C₃×D₅	—	2	2	no	—
202	C₂²×C₃×D₅	—	2	2	no	—
203	C₂²×C₃×D₅	—	2	1	no	—
204	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
218	C₃×C₂²⋊D₅	—	4	2	no	—
219	C₃×C₂²⋊D₅	—	4	2	no	—
220	C₃×C₂²⋊D₅	—	4	2	no	—
221	C₂×C₃×Dic₅	—	2	2	no	—
222	C₂×C₃×Dic₅	—	2	1	no	—
223	C₂×C₃×Dic₅	—	2	1	no	—
224	C₂×C₃×Dic₅	—	2	1	no	—
225	C₂×C₃×Dic₅	—	4	2	no	—
226	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
228	C₃×D₂₀	—	2	1	no	—
229	C₃×D₂₀	—	2	1	no	—
230	C₃×D₂₀	—	4	2	no	—
231	C₃×D₂₀	—	4	2	no	—
232	C₃×C₄×D₅	—	2	2	no	—
233	C₃×C₄×D₅	—	2	1	no	—
234	C₃×C₄×D₅	—	2	1	no	—
235	C₃×C₄×D₅	—	2	2	no	—
236	C₃×C₄×D₅	—	4	2	no	—
237	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
238	C₃×C₄×D₅	#41	1	2	yes	—
239	C₃×Dic₁₀	—	2	1	no	—
240	C₃×Dic₁₀	—	2	1	no	—
241	C₃×C₅×C₈	—	2	1	no	—
242	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
243	C₃×#168	—	2	1	no	—
244	C₃×#168	C₂×D₄	1	2	yes	—
245	C₂×C₃×#41	—	5	1	no	—
246	C₂×C₃×#41	—	5	1	no	—
247	C₂³×C₃×C₄	—	5	1	no	—
248	C₃×#135	—	10	4	no	—
249	C₂×C₃×Q₁₆	—	5	1	no	—
250	C₂×C₃×SD₁₆	—	5	1	no	—
251	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
252	C₂×C₃×D₈	—	5	1	no	—
253	C₂²×C₃×C₈	—	5	1	no	—
254	C₂²×C₃×C₈	—	5	1	no	—
255	C₂²×C₃×C₈	—	5	1	no	—
256	C₂²×C₃×C₈	—	5	1	no	—
257	C₂²×C₃×C₈	—	5	1	no	—
258	C₂²×C₃×C₈	—	10	4	no	—
259	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
260	C₃×#123	—	10	1	no	—
261	C₃×#123	—	10	1	no	—
262	C₃×C₂²⋊Q₈	—	5	1	no	—
263	C₃×C₂²⋊Q₈	—	5	1	no	—
264	C₃×C₂²⋊Q₈	—	5	1	no	—
265	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
266	C₃×#121	—	5	1	no	—
267	C₃×#121	—	5	1	no	—
268	C₃×#121	—	5	1	no	—
269	C₃×#121	C₂×D₅	1	1	yes	characteristic
270	C₃×#120	—	10	1	no	—
271	C₃×#120	—	10	1	no	—
272	C₃×C₄×D₄	—	10	1	no	—
273	C₃×C₄×D₄	—	10	1	no	—
274	C₃×C₄×D₄	—	10	1	no	—
275	C₃×C₄×D₄	—	10	1	no	—
276	C₃×#117	—	5	1	no	—
277	C₃×#117	—	5	1	no	—
278	C₃×#107	—	5	1	no	—
279	C₃×#107	—	5	1	no	—
280	C₃×#106	—	5	1	no	—
281	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
282	C₃×#103	—	5	1	no	—
283	C₃×#103	—	5	1	no	—
284	C₃×#103	—	5	1	no	—
285	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
286	C₃×#102	—	5	1	no	—
287	C₃×#102	—	5	1	no	—
288	C₃×#102	—	5	1	no	—
289	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
290	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
291	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×D₄	—	2	1	no	—
293	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₂²⋊D₅	—	2	1	no	—
296	C₂×C₂²⋊D₅	—	2	1	no	—
297	C₂×C₂²⋊D₅	—	2	1	no	—
298	C₂²×Dic₅	—	2	1	no	—
299	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
300	#713	—	2	2	no	—
301	#713	—	2	2	no	—
302	#711	—	2	2	no	—
303	#711	—	2	2	no	—
304	C₂×D₂₀	—	2	1	no	—
305	C₂×D₂₀	—	2	1	no	—
306	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₄×D₅	—	2	2	no	—
308	C₂×C₄×D₅	—	2	2	no	—
309	C₂×C₄×D₅	—	2	1	no	—
310	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
311	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
314	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
315	C₅×SD₁₆	—	2	2	no	—
316	C₂×C₅×C₈	—	2	2	no	—
317	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	—	2	1	no	—
320	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
321	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊Dic₅	—	2	1	no	—
325	C₂²⋊Dic₅	—	2	1	no	—
326	#689	—	2	2	no	—
327	#686	—	2	2	no	—
328	#685	—	2	1	no	—
329	#685	—	2	1	no	—
330	#685	—	2	1	no	—
331	#685	—	2	1	no	—
332	#685	—	2	1	no	—
333	#685	—	2	1	no	—
334	C₄⋊Dic₅	—	2	1	no	—
335	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
336	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
337	#683	—	2	1	no	—
338	#683	—	2	1	no	—
339	C₄×Dic₅	—	2	1	no	—
340	C₄×Dic₅	—	2	1	no	—
341	C₂×#168	—	2	2	no	—
342	C₂×#168	C₂³×C₃	1	1	yes	characteristic
343	C₂×#168	C₂³×C₃	1	1	yes	characteristic
344	#677	—	2	2	no	—
345	C₈×D₅	—	2	2	no	—
346	C₈×D₅	—	2	2	no	—
347	C₈×D₅	—	2	2	no	—
348	C₈×D₅	C₃×D₄	1	4	yes	complemented
349	C₂×#135	—	5	1	no	—
350	C₂³×C₈	—	5	1	no	—
351	#525	—	5	1	no	—
352	#525	—	5	1	no	—
353	#467	—	5	1	no	—
354	#467	—	5	1	no	—
355	#466	—	5	1	no	—
356	#466	—	5	1	no	—
357	#465	—	5	1	no	—
358	#465	—	5	1	no	—
359	#465	—	5	1	no	—
360	#465	C₃×D₅	1	1	yes	characteristic, complemented
361	#427	—	5	1	no	—
362	#416	—	5	1	no	—
363	#416	—	5	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	#135	1	2	yes	complemented
370	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₃×D₅	—	2	8	no	—
372	C₂×C₃×D₅	—	2	1	no	—
373	C₂×C₃×D₅	—	2	1	no	—
374	C₂×C₃×D₅	—	2	1	no	—
375	C₂×C₃×D₅	—	2	1	no	—
376	C₂×C₃×D₅	—	4	1	no	—
377	C₂×C₃×D₅	—	4	1	no	—
378	C₂×C₃×D₅	—	4	1	no	—
379	C₂×C₃×D₅	#121	1	2	yes	—
380	C₂×C₃×D₅	#135	1	2	yes	complemented
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	4	1	no	—
383	C₃×C₄×C₅	—	4	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
387	C₃×Dic₅	—	2	1	no	—
388	C₃×Dic₅	—	4	1	no	—
389	C₃×Dic₅	—	4	1	no	—
390	C₃×Dic₅	—	4	1	no	—
391	C₃×Dic₅	#121	1	2	yes	—
392	C₂⁴×C₃	—	5	1	no	—
393	C₃×#41	—	10	2	no	—
394	C₃×#41	—	10	2	no	—
395	C₃×#41	—	10	2	no	—
396	C₃×#41	—	10	2	no	—
397	C₂×C₃×Q₈	—	5	1	no	—
398	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
399	C₂×C₃×D₄	—	2	1	no	—
400	C₂×C₃×D₄	—	5	1	no	—
401	C₂×C₃×D₄	—	10	1	no	—
402	C₂×C₃×D₄	—	10	1	no	—
403	C₂×C₃×D₄	—	10	1	no	—
404	C₂×C₃×D₄	—	10	1	no	—
405	C₂×C₃×D₄	—	10	1	no	—
406	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	—	10	2	no	—
413	C₂²×C₃×C₄	—	10	2	no	—
414	C₂²×C₃×C₄	—	10	1	no	—
415	C₂²×C₃×C₄	—	10	1	no	—
416	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
417	C₃×Q₁₆	—	10	2	no	—
418	C₃×SD₁₆	—	2	2	no	—
419	C₃×SD₁₆	—	10	2	no	—
420	C₃×D₈	—	10	2	no	—
421	C₂×C₃×C₈	—	2	2	no	—
422	C₂×C₃×C₈	—	5	1	no	—
423	C₂×C₃×C₈	—	5	4	no	—
424	C₂×C₃×C₈	—	5	1	no	—
425	C₂×C₃×C₈	—	10	2	no	—
426	C₂×C₃×C₈	—	10	2	no	—
427	C₂×C₃×C₈	—	10	2	no	—
428	C₂×C₃×C₈	—	10	2	no	—
429	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
430	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
431	C₃×C₄⋊C₄	—	2	1	no	—
432	C₃×C₄⋊C₄	—	5	1	no	—
433	C₃×C₄⋊C₄	—	5	1	no	—
434	C₃×C₄⋊C₄	—	10	1	no	—
435	C₃×C₄⋊C₄	—	10	1	no	—
436	C₃×C₄⋊C₄	—	10	1	no	—
437	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
438	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
439	C₃×C₂²⋊C₄	—	2	1	no	—
440	C₃×C₂²⋊C₄	—	2	1	no	—
441	C₃×C₂²⋊C₄	—	10	1	no	—
442	C₃×C₂²⋊C₄	—	10	1	no	—
443	C₃×C₂²⋊C₄	—	10	1	no	—
444	C₃×C₂²⋊C₄	—	10	1	no	—
445	C₃×C₂²⋊C₄	—	10	1	no	—
446	C₃×C₂²⋊C₄	—	10	1	no	—
447	C₃×C₂²⋊C₄	—	10	1	no	—
448	C₃×C₂²⋊C₄	—	10	1	no	—
449	C₃×C₄²	—	10	1	no	—
450	C₃×C₄²	—	10	1	no	—
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
453	C₂²×D₅	—	2	2	no	—
454	C₂²×D₅	—	2	2	no	—
455	C₂²×D₅	—	2	2	no	—
456	C₂²×D₅	—	2	1	no	—
457	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
459	C₅×Q₈	—	2	1	no	—
460	C₅×Q₈	—	2	1	no	—
461	C₅×D₄	—	2	1	no	—
462	C₅×D₄	—	2	1	no	—
463	C₅×D₄	—	4	2	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
470	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
471	C₂²⋊D₅	—	4	2	no	—
472	C₂²⋊D₅	—	4	2	no	—
473	C₂²⋊D₅	—	4	2	no	—
474	C₂×Dic₅	—	2	2	no	—
475	C₂×Dic₅	—	2	1	no	—
476	C₂×Dic₅	—	2	1	no	—
477	C₂×Dic₅	—	2	1	no	—
478	C₂×Dic₅	—	4	2	no	—
479	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
480	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
481	D₂₀	—	2	1	no	—
482	D₂₀	—	2	1	no	—
483	D₂₀	—	4	2	no	—
484	D₂₀	—	4	2	no	—
485	C₄×D₅	—	2	2	no	—
486	C₄×D₅	—	2	1	no	—
487	C₄×D₅	—	2	1	no	—
488	C₄×D₅	—	2	2	no	—
489	C₄×D₅	—	4	2	no	—
490	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
491	C₄×D₅	C₃×#41	1	2	yes	—
492	Dic₁₀	—	2	1	no	—
493	Dic₁₀	—	2	1	no	—
494	C₅×C₈	—	2	1	no	—
495	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
496	#168	—	2	1	no	—
497	#168	C₂×C₃×D₄	1	2	yes	—
498	C₂×#41	—	5	1	no	—
499	C₂×#41	—	5	1	no	—
500	C₂³×C₄	—	5	1	no	—
501	#135	—	10	4	no	—
502	C₂×Q₁₆	—	5	1	no	—
503	C₂×SD₁₆	—	5	1	no	—
504	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
505	C₂×D₈	—	5	1	no	—
506	C₂²×C₈	—	5	1	no	—
507	C₂²×C₈	—	5	1	no	—
508	C₂²×C₈	—	5	1	no	—
509	C₂²×C₈	—	5	1	no	—
510	C₂²×C₈	—	5	1	no	—
511	C₂²×C₈	—	10	4	no	—
512	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
513	#123	—	10	1	no	—
514	#123	—	10	1	no	—
515	C₂²⋊Q₈	—	5	1	no	—
516	C₂²⋊Q₈	—	5	1	no	—
517	C₂²⋊Q₈	—	5	1	no	—
518	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
519	#121	—	5	1	no	—
520	#121	—	5	1	no	—
521	#121	—	5	1	no	—
522	#121	C₂×C₃×D₅	1	1	yes	characteristic
523	#120	—	10	1	no	—
524	#120	—	10	1	no	—
525	C₄×D₄	—	10	1	no	—
526	C₄×D₄	—	10	1	no	—
527	C₄×D₄	—	10	1	no	—
528	C₄×D₄	—	10	1	no	—
529	#117	—	5	1	no	—
530	#117	—	5	1	no	—
531	#107	—	5	1	no	—
532	#107	—	5	1	no	—
533	#106	—	5	1	no	—
534	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
535	#103	—	5	1	no	—
536	#103	—	5	1	no	—
537	#103	—	5	1	no	—
538	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
539	#102	—	5	1	no	—
540	#102	—	5	1	no	—
541	#102	—	5	1	no	—
542	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	—	8	1	no	—
545	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
548	C₃×D₅	—	2	2	no	—
549	C₃×D₅	—	2	2	no	—
550	C₃×D₅	—	8	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	5	1	no	—
553	C₂³×C₃	—	5	1	no	—
554	C₂³×C₃	—	10	2	no	—
555	C₂³×C₃	—	10	2	no	—
556	C₂³×C₃	—	10	2	no	—
557	C₂³×C₃	—	10	1	no	—
558	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
559	C₃×Q₈	—	2	1	no	—
560	C₃×Q₈	—	2	1	no	—
561	C₃×Q₈	—	10	1	no	—
562	C₃×Q₈	—	10	1	no	—
563	C₃×D₄	—	2	1	no	—
564	C₃×D₄	—	2	1	no	—
565	C₃×D₄	—	4	2	no	—
566	C₃×D₄	—	10	1	no	—
567	C₃×D₄	—	10	1	no	—
568	C₃×D₄	—	20	2	no	—
569	C₃×D₄	—	20	2	no	—
570	C₃×D₄	—	20	2	no	—
571	C₃×D₄	—	20	2	no	—
572	C₃×D₄	—	20	2	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	5	1	no	—
579	C₂×C₃×C₄	—	5	2	no	—
580	C₂×C₃×C₄	—	5	2	no	—
581	C₂×C₃×C₄	—	5	1	no	—
582	C₂×C₃×C₄	—	10	2	no	—
583	C₂×C₃×C₄	—	10	2	no	—
584	C₂×C₃×C₄	—	10	2	no	—
585	C₂×C₃×C₄	—	10	1	no	—
586	C₂×C₃×C₄	—	10	1	no	—
587	C₂×C₃×C₄	—	10	1	no	—
588	C₂×C₃×C₄	—	10	1	no	—
589	C₂×C₃×C₄	—	10	1	no	—
590	C₂×C₃×C₄	—	20	2	no	—
591	C₂×C₃×C₄	—	20	2	no	—
592	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
593	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
594	C₃×C₈	—	2	1	no	—
595	C₃×C₈	—	5	2	no	—
596	C₃×C₈	—	10	1	no	—
597	C₃×C₈	D₄×D₅	1	2	yes	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	4	1	no	—
601	C₂²×C₅	—	4	1	no	—
602	C₂²×C₅	—	4	1	no	—
603	C₂²×C₅	C₃×#135	1	2	yes	complemented
604	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
605	C₂×D₅	—	2	8	no	—
606	C₂×D₅	—	2	1	no	—
607	C₂×D₅	—	2	1	no	—
608	C₂×D₅	—	2	1	no	—
609	C₂×D₅	—	2	1	no	—
610	C₂×D₅	—	4	1	no	—
611	C₂×D₅	—	4	1	no	—
612	C₂×D₅	—	4	1	no	—
613	C₂×D₅	C₃×#121	1	2	yes	—
614	C₂×D₅	C₃×#135	1	2	yes	complemented
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	—	4	1	no	—
618	C₄×C₅	—	4	1	no	—
619	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
620	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
621	Dic₅	—	2	1	no	—
622	Dic₅	—	4	1	no	—
623	Dic₅	—	4	1	no	—
624	Dic₅	—	4	1	no	—
625	Dic₅	C₃×#121	1	2	yes	—
626	C₂⁴	—	5	1	no	—
627	#41	—	10	2	no	—
628	#41	—	10	2	no	—
629	#41	—	10	2	no	—
630	#41	—	10	2	no	—
631	C₂×Q₈	—	5	1	no	—
632	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	5	1	no	—
635	C₂×D₄	—	10	1	no	—
636	C₂×D₄	—	10	1	no	—
637	C₂×D₄	—	10	1	no	—
638	C₂×D₄	—	10	1	no	—
639	C₂×D₄	—	10	1	no	—
640	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	1	no	—
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	5	1	no	—
645	C₂²×C₄	—	5	1	no	—
646	C₂²×C₄	—	10	2	no	—
647	C₂²×C₄	—	10	2	no	—
648	C₂²×C₄	—	10	1	no	—
649	C₂²×C₄	—	10	1	no	—
650	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
651	Q₁₆	—	10	2	no	—
652	SD₁₆	—	2	2	no	—
653	SD₁₆	—	10	2	no	—
654	D₈	—	10	2	no	—
655	C₂×C₈	—	2	2	no	—
656	C₂×C₈	—	5	1	no	—
657	C₂×C₈	—	5	4	no	—
658	C₂×C₈	—	5	1	no	—
659	C₂×C₈	—	10	2	no	—
660	C₂×C₈	—	10	2	no	—
661	C₂×C₈	—	10	2	no	—
662	C₂×C₈	—	10	2	no	—
663	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
664	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	5	1	no	—
667	C₄⋊C₄	—	5	1	no	—
668	C₄⋊C₄	—	10	1	no	—
669	C₄⋊C₄	—	10	1	no	—
670	C₄⋊C₄	—	10	1	no	—
671	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
672	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	10	1	no	—
676	C₂²⋊C₄	—	10	1	no	—
677	C₂²⋊C₄	—	10	1	no	—
678	C₂²⋊C₄	—	10	1	no	—
679	C₂²⋊C₄	—	10	1	no	—
680	C₂²⋊C₄	—	10	1	no	—
681	C₂²⋊C₄	—	10	1	no	—
682	C₂²⋊C₄	—	10	1	no	—
683	C₄²	—	10	1	no	—
684	C₄²	—	10	1	no	—
685	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	—	5	2	no	—
692	C₂²×C₃	—	5	2	no	—
693	C₂²×C₃	—	10	8	no	—
694	C₂²×C₃	—	10	1	no	—
695	C₂²×C₃	—	10	1	no	—
696	C₂²×C₃	—	10	1	no	—
697	C₂²×C₃	—	10	1	no	—
698	C₂²×C₃	—	20	1	no	—
699	C₂²×C₃	—	20	1	no	—
700	C₂²×C₃	—	20	1	no	—
701	C₂²×C₃	#4062	1	2	yes	complemented
702	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	1	no	—
706	C₃×C₄	—	4	1	no	—
707	C₃×C₄	—	5	2	no	—
708	C₃×C₄	—	10	1	no	—
709	C₃×C₄	—	20	1	no	—
710	C₃×C₄	—	20	1	no	—
711	C₃×C₄	—	20	1	no	—
712	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
713	C₃×C₄	D₅×#41	1	1	yes	characteristic
714	C₂×C₅	—	2	2	no	—
715	C₂×C₅	—	8	1	no	—
716	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
717	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
718	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
719	D₅	—	2	2	no	—
720	D₅	—	2	2	no	—
721	D₅	—	8	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	5	1	no	—
724	C₂³	—	5	1	no	—
725	C₂³	—	10	2	no	—
726	C₂³	—	10	2	no	—
727	C₂³	—	10	2	no	—
728	C₂³	—	10	1	no	—
729	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	10	1	no	—
733	Q₈	—	10	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	2	1	no	—
736	D₄	—	4	2	no	—
737	D₄	—	10	1	no	—
738	D₄	—	10	1	no	—
739	D₄	—	20	2	no	—
740	D₄	—	20	2	no	—
741	D₄	—	20	2	no	—
742	D₄	—	20	2	no	—
743	D₄	—	20	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	5	1	no	—
750	C₂×C₄	—	5	2	no	—
751	C₂×C₄	—	5	2	no	—
752	C₂×C₄	—	5	1	no	—
753	C₂×C₄	—	10	2	no	—
754	C₂×C₄	—	10	2	no	—
755	C₂×C₄	—	10	2	no	—
756	C₂×C₄	—	10	1	no	—
757	C₂×C₄	—	10	1	no	—
758	C₂×C₄	—	10	1	no	—
759	C₂×C₄	—	10	1	no	—
760	C₂×C₄	—	10	1	no	—
761	C₂×C₄	—	20	2	no	—
762	C₂×C₄	—	20	2	no	—
763	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
764	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
765	C₈	—	2	1	no	—
766	C₈	—	5	2	no	—
767	C₈	—	10	1	no	—
768	C₈	C₃×D₄×D₅	1	2	yes	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	8	1	no	—
771	C₂×C₃	—	10	2	no	—
772	C₂×C₃	—	10	2	no	—
773	C₂×C₃	—	40	1	no	—
774	C₂×C₃	D₅×#121	1	1	yes	characteristic
775	C₂×C₃	C₂×#4062	1	1	yes	characteristic
776	C₂×C₃	D₅×#135	1	1	yes	characteristic
777	C₅	C₃×#3050	1	1	yes	characteristic, complemented, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	5	2	no	—
784	C₂²	—	5	2	no	—
785	C₂²	—	10	8	no	—
786	C₂²	—	10	1	no	—
787	C₂²	—	10	1	no	—
788	C₂²	—	10	1	no	—
789	C₂²	—	10	1	no	—
790	C₂²	—	20	1	no	—
791	C₂²	—	20	1	no	—
792	C₂²	—	20	1	no	—
793	C₂²	C₃×#4062	1	2	yes	complemented
794	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	4	1	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	5	2	no	—
800	C₄	—	10	1	no	—
801	C₄	—	20	1	no	—
802	C₄	—	20	1	no	—
803	C₄	—	20	1	no	—
804	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
805	C₄	C₃×D₅×#41	1	1	yes	characteristic
806	C₃	#10612387	1	1	yes	characteristic, direct product factor, Sylow
807	C₂	—	2	2	no	—
808	C₂	—	8	1	no	—
809	C₂	—	10	2	no	—
810	C₂	—	10	2	no	—
811	C₂	—	40	1	no	—
812	C₂	C₃×D₅×#121	1	1	yes	characteristic
813	C₂	C₂×C₃×#4062	1	1	yes	characteristic
814	C₂	C₃×D₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#465	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#465	D₅
hypocenter	C₅	C₃×#3050
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#465

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4062	C₂	semidirect
2. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₃×#65961	C₂	semidirect
4. C₃×#65940	C₂	semidirect
5. C₃×C₅×#465	C₂	semidirect
6. C₃×#65460	C₂	semidirect
7. C₃×#65403	C₂	semidirect
8. C₃×#65340	C₂	semidirect
9. C₃×#65327	C₂	semidirect
10. C₃×#65153	C₂	semidirect
11. C₃×#65149	C₂	semidirect
12. C₃×#65102	C₂	semidirect
13. C₃×#65093	C₂	semidirect
14. C₃×#65064	C₂	semidirect
15. C₃×#65061	C₂	semidirect
16. #10612387	C₃	direct (N × H)
20. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₂×C₃×#689	C₂²	semidirect
29. C₂×C₃×#686	C₂²	semidirect
34. C₂×C₃×#677	C₂²	semidirect
50. C₃×C₅×#106	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×#3967	C₂²	semidirect
54. C₃×#3964	C₂²	semidirect
55. C₃×#3953	C₂²	semidirect
56. C₃×#3949	C₂²	semidirect
57. C₃×#3948	C₂²	semidirect
58. C₃×#3942	C₂²	semidirect
59. C₃×#3941	C₂²	semidirect
60. C₃×#3939	C₂²	semidirect
61. C₃×#3939	C₂²	semidirect
63. C₂×#4062	C₂×C₃	semidirect
64. C₂²×C₈×D₅	C₂×C₃	semidirect
65. #65961	C₂×C₃	semidirect
66. #65940	C₂×C₃	semidirect
67. C₅×#465	C₂×C₃	semidirect
68. #65460	C₂×C₃	semidirect
69. #65403	C₂×C₃	semidirect
70. #65340	C₂×C₃	semidirect
71. #65327	C₂×C₃	semidirect
72. #65153	C₂×C₃	semidirect
73. #65149	C₂×C₃	semidirect
74. #65102	C₂×C₃	semidirect
75. #65093	C₂×C₃	semidirect
76. #65064	C₂×C₃	semidirect
77. #65061	C₂×C₃	semidirect
136. C₃×C₈×D₅	D₄	semidirect
148. C₃×#465	D₅	semidirect
155. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
160. C₂×#689	C₂²×C₃	semidirect
164. C₂×#686	C₂²×C₃	semidirect
169. C₂×#677	C₂²×C₃	semidirect
185. C₅×#106	C₂²×C₃	semidirect
186. C₅×#103	C₂²×C₃	semidirect
187. C₅×#102	C₂²×C₃	semidirect
188. #3967	C₂²×C₃	semidirect
189. #3964	C₂²×C₃	semidirect
190. #3953	C₂²×C₃	semidirect
191. #3949	C₂²×C₃	semidirect
192. #3948	C₂²×C₃	semidirect
193. #3942	C₂²×C₃	semidirect
194. #3941	C₂²×C₃	semidirect
195. #3939	C₂²×C₃	semidirect
196. #3939	C₂²×C₃	semidirect
251. C₂×C₃×SD₁₆	C₂×D₅	semidirect
281. C₃×#106	C₂×D₅	semidirect
285. C₃×#103	C₂×D₅	semidirect
289. C₃×#102	C₂×D₅	semidirect
348. C₈×D₅	C₃×D₄	semidirect
360. #465	C₃×D₅	semidirect
369. C₂²×C₃×C₅	#135	semidirect
380. C₂×C₃×D₅	#135	semidirect
504. C₂×SD₁₆	C₂×C₃×D₅	semidirect
534. #106	C₂×C₃×D₅	semidirect
538. #103	C₂×C₃×D₅	semidirect
542. #102	C₂×C₃×D₅	semidirect
603. C₂²×C₅	C₃×#135	semidirect
614. C₂×D₅	C₃×#135	semidirect
685. C₃×C₅	#3050	semidirect
701. C₂²×C₃	#4062	semidirect
777. C₅	C₃×#3050	semidirect
793. C₂²	C₃×#4062	semidirect
806. C₃	#10612387	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×#4062	2
C₂²×C₃×C₈×D₅	2
C₃×#65961	2
C₃×#65940	2
C₃×C₅×#465	2
C₃×#65460	2
C₃×#65403	2
C₃×#65340	2
C₃×#65327	2
C₃×#65153	2
C₃×#65149	2
C₃×#65102	2
C₃×#65093	2
C₃×#65064	2
C₃×#65061	2
#10612387	3
C₃×#3050	5

Subgroups — C3×#10612387 #14427787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612387 #14427787