Subgroups — C₃×#10613579 #14439544

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 804 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	C₂×C₃×#4060	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66049	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66008	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65457	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65443	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65440	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65362	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65348	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65001	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64997	C₂	1	1	yes	maximal, characteristic, complemented
16	#10613579	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	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
27	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
31	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
32	C₃×#4085	—	2	2	no	—
33	C₃×#4083	—	2	2	no	—
34	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#686	C₂²	1	1	yes	characteristic
37	C₂×C₃×#686	C₂²	1	1	yes	characteristic
38	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
41	C₃×#4062	—	2	4	no	—
42	C₃×#4060	—	2	4	no	—
43	C₃×#4057	—	2	4	no	—
44	C₃×D₅×D₈	—	2	4	no	—
45	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
46	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#676	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₃×#4030	—	2	2	no	—
52	C₃×#4028	—	2	2	no	—
53	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
54	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
55	C₃×#4018	C₂²	1	1	yes	characteristic
56	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3155	—	5	1	no	maximal, Hall
61	C₂×#4062	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×#4060	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×#4057	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
65	#66049	C₂×C₃	1	1	yes	characteristic, complemented
66	#66008	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
68	#65465	C₂×C₃	1	1	yes	characteristic, complemented
69	#65457	C₂×C₃	1	1	yes	characteristic, complemented
70	#65443	C₂×C₃	1	1	yes	characteristic, complemented
71	#65440	C₂×C₃	1	1	yes	characteristic, complemented
72	#65362	C₂×C₃	1	1	yes	characteristic, complemented
73	#65348	C₂×C₃	1	1	yes	characteristic, complemented
74	#65001	C₂×C₃	1	1	yes	characteristic, complemented
75	#64997	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂³×C₃×D₅	—	2	1	no	—
77	C₂³×C₃×D₅	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	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	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
87	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
88	C₂²×C₃×Dic₅	—	2	1	no	—
89	C₃×#713	—	2	2	no	—
90	C₃×#713	—	2	2	no	—
91	C₃×#711	—	2	2	no	—
92	C₃×#711	—	2	2	no	—
93	C₃×D₄×D₅	—	2	2	no	—
94	C₃×D₄×D₅	—	2	2	no	—
95	C₃×D₄×D₅	—	2	2	no	—
96	C₃×D₄×D₅	—	2	2	no	—
97	C₂×C₃×D₂₀	—	2	1	no	—
98	C₂×C₃×D₂₀	—	2	2	no	—
99	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
100	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
101	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄×D₅	—	2	1	no	—
103	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
104	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
105	C₃×C₅×SD₁₆	—	2	2	no	—
106	C₃×C₅×SD₁₆	—	2	2	no	—
107	C₃×C₅×D₈	—	2	2	no	—
108	C₃×C₅×D₈	—	2	2	no	—
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₃×C₂²⋊Dic₅	—	2	2	no	—
114	C₃×#689	—	2	2	no	—
115	C₃×#688	—	2	2	no	—
116	C₃×#687	—	2	2	no	—
117	C₃×#686	—	2	2	no	—
118	C₃×#686	—	2	2	no	—
119	C₃×#686	—	2	2	no	—
120	C₃×#686	—	2	2	no	—
121	C₃×#686	—	2	2	no	—
122	C₃×#685	—	2	2	no	—
123	C₃×#685	—	2	2	no	—
124	C₃×#685	D₄	1	2	yes	—
125	C₃×#683	D₄	1	2	yes	—
126	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₂×C₃×#168	C₂³	1	1	yes	characteristic
129	C₃×D₄₀	—	2	2	no	—
130	C₃×D₄₀	—	2	2	no	—
131	C₃×#677	—	2	2	no	—
132	C₃×#677	—	2	2	no	—
133	C₃×#676	D₄	1	4	yes	complemented
134	C₃×C₈×D₅	D₄	1	4	yes	complemented
135	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
136	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
137	C₂×C₃×#135	—	5	1	no	—
138	C₂²×C₃×D₈	—	5	1	no	—
139	C₃×#535	—	5	1	no	—
140	C₃×#535	—	5	1	no	—
141	C₃×#496	—	5	1	no	—
142	C₃×#496	—	5	1	no	—
143	C₃×#496	—	5	1	no	—
144	C₃×#496	D₅	1	1	yes	characteristic, complemented
145	C₃×#495	—	5	1	no	—
146	C₃×#495	—	5	1	no	—
147	C₃×#493	—	5	1	no	—
148	C₃×#493	—	5	1	no	—
149	C₃×#405	—	5	1	no	—
150	C₂×#713	C₂²×C₃	1	1	yes	characteristic
151	C₂×#711	C₂²×C₃	1	1	yes	characteristic
152	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
153	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
156	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
160	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
163	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
164	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
165	#4085	—	2	2	no	—
166	#4083	—	2	2	no	—
167	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×#686	C₂²×C₃	1	1	yes	characteristic
170	C₂×#686	C₂²×C₃	1	1	yes	characteristic
171	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
174	#4062	—	2	4	no	—
175	#4060	—	2	4	no	—
176	#4057	—	2	4	no	—
177	D₅×D₈	—	2	4	no	—
178	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
179	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂×#676	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
184	#4030	—	2	2	no	—
185	#4028	—	2	2	no	—
186	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
187	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
188	#4018	C₂²×C₃	1	1	yes	characteristic
189	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
190	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3155	—	5	1	no	Sylow
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂²×C₃×D₅	—	2	1	no	—
198	C₂²×C₃×D₅	—	2	1	no	—
199	C₂²×C₃×D₅	—	2	1	no	—
200	C₂²×C₃×D₅	—	4	2	no	—
201	C₂²×C₃×D₅	—	4	2	no	—
202	C₂²×C₃×D₅	—	8	2	no	—
203	C₂²×C₃×D₅	—	8	2	no	—
204	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	2	1	no	—
211	C₃×C₅×D₄	—	2	1	no	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	8	2	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
216	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₃×C₂²⋊D₅	—	4	2	no	—
218	C₃×C₂²⋊D₅	—	4	2	no	—
219	C₃×C₂²⋊D₅	—	4	2	no	—
220	C₃×C₂²⋊D₅	—	8	2	no	—
221	C₃×C₂²⋊D₅	—	8	2	no	—
222	C₂×C₃×Dic₅	—	2	1	no	—
223	C₂×C₃×Dic₅	—	4	2	no	—
224	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
225	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
226	C₃×D₂₀	—	2	1	no	—
227	C₃×D₂₀	—	2	1	no	—
228	C₃×D₂₀	—	2	1	no	—
229	C₃×D₂₀	—	2	1	no	—
230	C₃×D₂₀	—	2	1	no	—
231	C₃×D₂₀	—	2	1	no	—
232	C₃×D₂₀	—	4	2	no	—
233	C₃×D₂₀	—	8	2	no	—
234	C₃×C₄×D₅	—	4	2	no	—
235	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
236	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
237	C₃×Dic₁₀	—	2	1	no	—
238	C₃×Dic₁₀	—	2	1	no	—
239	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
240	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
241	C₃×#168	C₂×D₄	1	2	yes	—
242	C₃×#168	C₂×D₄	1	2	yes	—
243	C₂×C₃×#41	—	5	1	no	—
244	C₂×C₃×#41	—	5	1	no	—
245	C₂²×C₃×D₄	—	5	1	no	—
246	C₂²×C₃×D₄	—	5	1	no	—
247	C₃×AGL(1,ℤ/8)	—	10	4	no	—
248	C₃×AGL(1,ℤ/8)	—	10	4	no	—
249	C₃×#135	—	10	4	no	—
250	C₂×C₃×Q₁₆	—	5	1	no	—
251	C₂×C₃×SD₁₆	—	5	1	no	—
252	C₂×C₃×SD₁₆	—	5	1	no	—
253	C₂×C₃×SD₁₆	—	5	1	no	—
254	C₂×C₃×SD₁₆	—	5	1	no	—
255	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
256	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
257	C₂×C₃×D₈	—	5	1	no	—
258	C₂×C₃×D₈	—	5	1	no	—
259	C₂×C₃×D₈	—	5	1	no	—
260	C₂×C₃×D₈	—	5	1	no	—
261	C₂×C₃×D₈	—	5	1	no	—
262	C₂×C₃×D₈	—	5	1	no	—
263	C₂×C₃×D₈	—	5	1	no	—
264	C₂×C₃×D₈	—	10	4	no	—
265	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
266	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
267	C₂×C₃×M₁₆	—	5	1	no	—
268	C₂²×C₃×C₈	—	5	1	no	—
269	C₃×#127	—	5	1	no	—
270	C₃×#127	—	5	1	no	—
271	C₃×#127	—	5	1	no	—
272	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
273	C₃×#124	—	5	1	no	—
274	C₃×#124	—	5	1	no	—
275	C₃×#124	—	5	1	no	—
276	C₃×#124	C₂×D₅	1	1	yes	characteristic, complemented
277	C₃×#121	—	10	2	no	—
278	C₃×#121	—	10	2	no	—
279	C₃×#120	—	10	2	no	—
280	C₃×#120	—	10	2	no	—
281	C₃×#117	—	5	1	no	—
282	C₃×#97	—	5	1	no	—
283	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
284	C₃×C₄×C₈	—	5	1	no	—
285	C₃×C₄×C₈	—	5	1	no	—
286	C₂³×D₅	—	2	1	no	—
287	C₂³×D₅	—	2	1	no	—
288	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×D₄	—	2	2	no	—
290	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₂²⋊D₅	—	2	1	no	—
294	C₂×C₂²⋊D₅	—	2	1	no	—
295	C₂×C₂²⋊D₅	—	2	1	no	—
296	C₂×C₂²⋊D₅	—	2	2	no	—
297	C₂×C₂²⋊D₅	—	2	2	no	—
298	C₂²×Dic₅	—	2	1	no	—
299	#713	—	2	2	no	—
300	#713	—	2	2	no	—
301	#711	—	2	2	no	—
302	#711	—	2	2	no	—
303	D₄×D₅	—	2	2	no	—
304	D₄×D₅	—	2	2	no	—
305	D₄×D₅	—	2	2	no	—
306	D₄×D₅	—	2	2	no	—
307	C₂×D₂₀	—	2	1	no	—
308	C₂×D₂₀	—	2	2	no	—
309	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
310	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
311	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₄×D₅	—	2	1	no	—
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	C₅×SD₁₆	—	2	2	no	—
317	C₅×D₈	—	2	2	no	—
318	C₅×D₈	—	2	2	no	—
319	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
321	C₅×C₂²⋊C₄	—	2	2	no	—
322	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
323	C₂²⋊Dic₅	—	2	2	no	—
324	#689	—	2	2	no	—
325	#688	—	2	2	no	—
326	#687	—	2	2	no	—
327	#686	—	2	2	no	—
328	#686	—	2	2	no	—
329	#686	—	2	2	no	—
330	#686	—	2	2	no	—
331	#686	—	2	2	no	—
332	#685	—	2	2	no	—
333	#685	—	2	2	no	—
334	#685	C₃×D₄	1	2	yes	—
335	#683	C₃×D₄	1	2	yes	—
336	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
337	C₂×#168	C₂³×C₃	1	1	yes	characteristic
338	C₂×#168	C₂³×C₃	1	1	yes	characteristic
339	D₄₀	—	2	2	no	—
340	D₄₀	—	2	2	no	—
341	#677	—	2	2	no	—
342	#677	—	2	2	no	—
343	#676	C₃×D₄	1	4	yes	complemented
344	C₈×D₅	C₃×D₄	1	4	yes	complemented
345	C₂×AGL(1,ℤ/8)	—	5	1	no	—
346	C₂×AGL(1,ℤ/8)	—	5	1	no	—
347	C₂×#135	—	5	1	no	—
348	C₂²×D₈	—	5	1	no	—
349	#535	—	5	1	no	—
350	#535	—	5	1	no	—
351	#496	—	5	1	no	—
352	#496	—	5	1	no	—
353	#496	—	5	1	no	—
354	#496	C₃×D₅	1	1	yes	characteristic, complemented
355	#495	—	5	1	no	—
356	#495	—	5	1	no	—
357	#493	—	5	1	no	—
358	#493	—	5	1	no	—
359	#405	—	5	1	no	—
360	C₂²×C₃×C₅	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	2	no	—
364	C₂²×C₃×C₅	—	4	2	no	—
365	C₂²×C₃×C₅	—	4	2	no	—
366	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₃×D₅	—	2	2	no	—
368	C₂×C₃×D₅	—	4	1	no	—
369	C₂×C₃×D₅	—	4	1	no	—
370	C₂×C₃×D₅	—	4	1	no	—
371	C₂×C₃×D₅	—	4	2	no	—
372	C₂×C₃×D₅	—	4	2	no	—
373	C₂×C₃×D₅	—	4	2	no	—
374	C₂×C₃×D₅	—	8	4	no	—
375	C₂×C₃×D₅	—	8	4	no	—
376	C₂×C₃×D₅	#127	1	2	yes	—
377	C₃×C₄×C₅	—	2	2	no	—
378	C₃×C₄×C₅	—	4	1	no	—
379	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
381	C₃×Dic₅	—	2	2	no	—
382	C₃×Dic₅	—	4	1	no	—
383	C₃×Dic₅	#127	1	2	yes	—
384	C₂⁴×C₃	—	10	1	no	—
385	C₂⁴×C₃	—	10	1	no	—
386	C₃×#41	—	10	2	no	—
387	C₃×#41	—	10	2	no	—
388	C₃×#41	—	10	2	no	—
389	C₃×#41	—	10	2	no	—
390	C₂×C₃×Q₈	—	5	1	no	—
391	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
392	C₂×C₃×D₄	—	2	2	no	—
393	C₂×C₃×D₄	—	5	1	no	—
394	C₂×C₃×D₄	—	5	1	no	—
395	C₂×C₃×D₄	—	5	1	no	—
396	C₂×C₃×D₄	—	10	1	no	—
397	C₂×C₃×D₄	—	10	2	no	—
398	C₂×C₃×D₄	—	10	2	no	—
399	C₂×C₃×D₄	—	10	2	no	—
400	C₂×C₃×D₄	—	10	2	no	—
401	C₂×C₃×D₄	—	10	1	no	—
402	C₂×C₃×D₄	—	10	1	no	—
403	C₂×C₃×D₄	—	10	2	no	—
404	C₂×C₃×D₄	—	10	2	no	—
405	C₂×C₃×D₄	—	10	1	no	—
406	C₂×C₃×D₄	—	10	2	no	—
407	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
408	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
409	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	10	1	no	—
412	C₂²×C₃×C₄	—	10	1	no	—
413	C₃×Q₁₆	—	10	2	no	—
414	C₃×SD₁₆	—	2	2	no	—
415	C₃×SD₁₆	—	2	2	no	—
416	C₃×SD₁₆	—	10	2	no	—
417	C₃×SD₁₆	—	10	2	no	—
418	C₃×SD₁₆	—	10	2	no	—
419	C₃×SD₁₆	—	10	2	no	—
420	C₃×D₈	—	2	2	no	—
421	C₃×D₈	—	2	2	no	—
422	C₃×D₈	—	10	2	no	—
423	C₃×D₈	—	10	2	no	—
424	C₃×D₈	—	10	2	no	—
425	C₃×D₈	—	10	2	no	—
426	C₃×D₈	—	10	2	no	—
427	C₃×D₈	—	10	2	no	—
428	C₃×D₈	—	10	2	no	—
429	C₃×M₁₆	—	5	4	no	—
430	C₂×C₃×C₈	—	5	1	no	—
431	C₂×C₃×C₈	—	5	1	no	—
432	C₂×C₃×C₈	—	5	4	no	—
433	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
434	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
435	C₃×C₄⋊C₄	—	5	2	no	—
436	C₃×C₂²⋊C₄	—	2	2	no	—
437	C₃×C₂²⋊C₄	—	5	2	no	—
438	C₃×C₂²⋊C₄	—	10	2	no	—
439	C₃×C₂²⋊C₄	—	10	2	no	—
440	C₃×C₂²⋊C₄	—	10	2	no	—
441	C₃×C₄²	—	5	1	no	—
442	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
443	C₂³×C₅	—	2	1	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	2	1	no	—
446	C₂²×D₅	—	2	1	no	—
447	C₂²×D₅	—	2	1	no	—
448	C₂²×D₅	—	2	1	no	—
449	C₂²×D₅	—	4	2	no	—
450	C₂²×D₅	—	4	2	no	—
451	C₂²×D₅	—	8	2	no	—
452	C₂²×D₅	—	8	2	no	—
453	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
454	C₅×Q₈	—	2	1	no	—
455	C₅×Q₈	—	2	1	no	—
456	C₅×D₄	—	2	1	no	—
457	C₅×D₄	—	2	1	no	—
458	C₅×D₄	—	2	1	no	—
459	C₅×D₄	—	2	1	no	—
460	C₅×D₄	—	2	1	no	—
461	C₅×D₄	—	2	1	no	—
462	C₅×D₄	—	8	2	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
465	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
466	C₂²⋊D₅	—	4	2	no	—
467	C₂²⋊D₅	—	4	2	no	—
468	C₂²⋊D₅	—	4	2	no	—
469	C₂²⋊D₅	—	8	2	no	—
470	C₂²⋊D₅	—	8	2	no	—
471	C₂×Dic₅	—	2	1	no	—
472	C₂×Dic₅	—	4	2	no	—
473	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
474	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
475	D₂₀	—	2	1	no	—
476	D₂₀	—	2	1	no	—
477	D₂₀	—	2	1	no	—
478	D₂₀	—	2	1	no	—
479	D₂₀	—	2	1	no	—
480	D₂₀	—	2	1	no	—
481	D₂₀	—	4	2	no	—
482	D₂₀	—	8	2	no	—
483	C₄×D₅	—	4	2	no	—
484	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
485	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
486	Dic₁₀	—	2	1	no	—
487	Dic₁₀	—	2	1	no	—
488	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
489	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
490	#168	C₂×C₃×D₄	1	2	yes	—
491	#168	C₂×C₃×D₄	1	2	yes	—
492	C₂×#41	—	5	1	no	—
493	C₂×#41	—	5	1	no	—
494	C₂²×D₄	—	5	1	no	—
495	C₂²×D₄	—	5	1	no	—
496	AGL(1,ℤ/8)	—	10	4	no	—
497	AGL(1,ℤ/8)	—	10	4	no	—
498	#135	—	10	4	no	—
499	C₂×Q₁₆	—	5	1	no	—
500	C₂×SD₁₆	—	5	1	no	—
501	C₂×SD₁₆	—	5	1	no	—
502	C₂×SD₁₆	—	5	1	no	—
503	C₂×SD₁₆	—	5	1	no	—
504	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
505	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
506	C₂×D₈	—	5	1	no	—
507	C₂×D₈	—	5	1	no	—
508	C₂×D₈	—	5	1	no	—
509	C₂×D₈	—	5	1	no	—
510	C₂×D₈	—	5	1	no	—
511	C₂×D₈	—	5	1	no	—
512	C₂×D₈	—	5	1	no	—
513	C₂×D₈	—	10	4	no	—
514	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
515	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
516	C₂×M₁₆	—	5	1	no	—
517	C₂²×C₈	—	5	1	no	—
518	#127	—	5	1	no	—
519	#127	—	5	1	no	—
520	#127	—	5	1	no	—
521	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
522	#124	—	5	1	no	—
523	#124	—	5	1	no	—
524	#124	—	5	1	no	—
525	#124	C₂×C₃×D₅	1	1	yes	characteristic, complemented
526	#121	—	10	2	no	—
527	#121	—	10	2	no	—
528	#120	—	10	2	no	—
529	#120	—	10	2	no	—
530	#117	—	5	1	no	—
531	#97	—	5	1	no	—
532	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
533	C₄×C₈	—	5	1	no	—
534	C₄×C₈	—	5	1	no	—
535	C₂×C₃×C₅	—	8	1	no	—
536	C₂×C₃×C₅	—	8	1	no	—
537	C₂×C₃×C₅	—	8	1	no	—
538	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
539	C₂×C₃×C₅	#576	1	2	yes	—
540	C₃×D₅	—	2	2	no	—
541	C₃×D₅	—	8	1	no	—
542	C₃×D₅	—	8	1	no	—
543	C₃×D₅	—	8	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	1	no	—
547	C₂³×C₃	—	5	1	no	—
548	C₂³×C₃	—	10	1	no	—
549	C₂³×C₃	—	10	1	no	—
550	C₂³×C₃	—	10	1	no	—
551	C₂³×C₃	—	20	2	no	—
552	C₂³×C₃	—	20	2	no	—
553	C₂³×C₃	—	40	2	no	—
554	C₂³×C₃	—	40	2	no	—
555	C₃×Q₈	—	2	1	no	—
556	C₃×Q₈	—	2	1	no	—
557	C₃×Q₈	—	10	1	no	—
558	C₃×Q₈	—	10	1	no	—
559	C₃×D₄	—	2	1	no	—
560	C₃×D₄	—	2	1	no	—
561	C₃×D₄	—	2	1	no	—
562	C₃×D₄	—	2	1	no	—
563	C₃×D₄	—	2	1	no	—
564	C₃×D₄	—	2	1	no	—
565	C₃×D₄	—	8	2	no	—
566	C₃×D₄	—	10	1	no	—
567	C₃×D₄	—	10	1	no	—
568	C₃×D₄	—	10	1	no	—
569	C₃×D₄	—	10	1	no	—
570	C₃×D₄	—	10	1	no	—
571	C₃×D₄	—	10	1	no	—
572	C₃×D₄	—	20	2	no	—
573	C₃×D₄	—	20	2	no	—
574	C₃×D₄	—	20	2	no	—
575	C₃×D₄	—	20	2	no	—
576	C₃×D₄	—	40	2	no	—
577	C₃×D₄	—	40	2	no	—
578	C₃×D₄	—	40	2	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	5	1	no	—
581	C₂×C₃×C₄	—	5	2	no	—
582	C₂×C₃×C₄	—	5	2	no	—
583	C₂×C₃×C₄	—	5	2	no	—
584	C₂×C₃×C₄	—	10	1	no	—
585	C₂×C₃×C₄	—	20	2	no	—
586	C₂×C₃×C₄	—	20	2	no	—
587	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
588	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
589	C₃×C₈	—	5	2	no	—
590	C₃×C₈	—	5	2	no	—
591	C₃×C₈	D₄×D₅	1	2	yes	—
592	C₃×C₈	D₄×D₅	1	2	yes	—
593	C₂²×C₅	—	4	2	no	—
594	C₂²×C₅	—	4	2	no	—
595	C₂²×C₅	—	4	2	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	4	1	no	—
598	C₂²×C₅	—	4	1	no	—
599	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
600	C₂×D₅	—	2	2	no	—
601	C₂×D₅	—	4	2	no	—
602	C₂×D₅	—	4	2	no	—
603	C₂×D₅	—	4	2	no	—
604	C₂×D₅	—	4	1	no	—
605	C₂×D₅	—	4	1	no	—
606	C₂×D₅	—	4	1	no	—
607	C₂×D₅	—	8	4	no	—
608	C₂×D₅	—	8	4	no	—
609	C₂×D₅	C₃×#127	1	2	yes	—
610	C₄×C₅	—	2	2	no	—
611	C₄×C₅	—	4	1	no	—
612	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
613	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
614	Dic₅	—	2	2	no	—
615	Dic₅	—	4	1	no	—
616	Dic₅	C₃×#127	1	2	yes	—
617	C₂⁴	—	10	1	no	—
618	C₂⁴	—	10	1	no	—
619	#41	—	10	2	no	—
620	#41	—	10	2	no	—
621	#41	—	10	2	no	—
622	#41	—	10	2	no	—
623	C₂×Q₈	—	5	1	no	—
624	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	5	1	no	—
627	C₂×D₄	—	5	1	no	—
628	C₂×D₄	—	5	1	no	—
629	C₂×D₄	—	10	1	no	—
630	C₂×D₄	—	10	2	no	—
631	C₂×D₄	—	10	2	no	—
632	C₂×D₄	—	10	2	no	—
633	C₂×D₄	—	10	2	no	—
634	C₂×D₄	—	10	1	no	—
635	C₂×D₄	—	10	1	no	—
636	C₂×D₄	—	10	2	no	—
637	C₂×D₄	—	10	2	no	—
638	C₂×D₄	—	10	1	no	—
639	C₂×D₄	—	10	2	no	—
640	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
641	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
642	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	10	1	no	—
645	C₂²×C₄	—	10	1	no	—
646	Q₁₆	—	10	2	no	—
647	SD₁₆	—	2	2	no	—
648	SD₁₆	—	2	2	no	—
649	SD₁₆	—	10	2	no	—
650	SD₁₆	—	10	2	no	—
651	SD₁₆	—	10	2	no	—
652	SD₁₆	—	10	2	no	—
653	D₈	—	2	2	no	—
654	D₈	—	2	2	no	—
655	D₈	—	10	2	no	—
656	D₈	—	10	2	no	—
657	D₈	—	10	2	no	—
658	D₈	—	10	2	no	—
659	D₈	—	10	2	no	—
660	D₈	—	10	2	no	—
661	D₈	—	10	2	no	—
662	M₁₆	—	5	4	no	—
663	C₂×C₈	—	5	1	no	—
664	C₂×C₈	—	5	1	no	—
665	C₂×C₈	—	5	4	no	—
666	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
667	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
668	C₄⋊C₄	—	5	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	5	2	no	—
671	C₂²⋊C₄	—	10	2	no	—
672	C₂²⋊C₄	—	10	2	no	—
673	C₂²⋊C₄	—	10	2	no	—
674	C₄²	—	5	1	no	—
675	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
676	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	2	no	—
681	C₂²×C₃	—	4	2	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	—	5	2	no	—
684	C₂²×C₃	—	10	2	no	—
685	C₂²×C₃	—	20	1	no	—
686	C₂²×C₃	—	20	1	no	—
687	C₂²×C₃	—	20	1	no	—
688	C₂²×C₃	—	20	2	no	—
689	C₂²×C₃	—	20	2	no	—
690	C₂²×C₃	—	20	2	no	—
691	C₂²×C₃	—	40	4	no	—
692	C₂²×C₃	—	40	4	no	—
693	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
694	C₃×C₄	—	2	2	no	—
695	C₃×C₄	—	4	1	no	—
696	C₃×C₄	—	5	2	no	—
697	C₃×C₄	—	10	2	no	—
698	C₃×C₄	—	20	1	no	—
699	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
700	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
701	C₂×C₅	—	8	1	no	—
702	C₂×C₅	—	8	1	no	—
703	C₂×C₅	—	8	1	no	—
704	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
705	C₂×C₅	C₃×#576	1	2	yes	—
706	D₅	—	2	2	no	—
707	D₅	—	8	1	no	—
708	D₅	—	8	1	no	—
709	D₅	—	8	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	5	1	no	—
714	C₂³	—	10	1	no	—
715	C₂³	—	10	1	no	—
716	C₂³	—	10	1	no	—
717	C₂³	—	20	2	no	—
718	C₂³	—	20	2	no	—
719	C₂³	—	40	2	no	—
720	C₂³	—	40	2	no	—
721	Q₈	—	2	1	no	—
722	Q₈	—	2	1	no	—
723	Q₈	—	10	1	no	—
724	Q₈	—	10	1	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	1	no	—
727	D₄	—	2	1	no	—
728	D₄	—	2	1	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	1	no	—
731	D₄	—	8	2	no	—
732	D₄	—	10	1	no	—
733	D₄	—	10	1	no	—
734	D₄	—	10	1	no	—
735	D₄	—	10	1	no	—
736	D₄	—	10	1	no	—
737	D₄	—	10	1	no	—
738	D₄	—	20	2	no	—
739	D₄	—	20	2	no	—
740	D₄	—	20	2	no	—
741	D₄	—	20	2	no	—
742	D₄	—	40	2	no	—
743	D₄	—	40	2	no	—
744	D₄	—	40	2	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	5	1	no	—
747	C₂×C₄	—	5	2	no	—
748	C₂×C₄	—	5	2	no	—
749	C₂×C₄	—	5	2	no	—
750	C₂×C₄	—	10	1	no	—
751	C₂×C₄	—	20	2	no	—
752	C₂×C₄	—	20	2	no	—
753	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
754	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
755	C₈	—	5	2	no	—
756	C₈	—	5	2	no	—
757	C₈	C₃×D₄×D₅	1	2	yes	—
758	C₈	C₃×D₄×D₅	1	2	yes	—
759	C₂×C₃	—	8	1	no	—
760	C₂×C₃	—	8	1	no	—
761	C₂×C₃	—	8	1	no	—
762	C₂×C₃	—	10	2	no	—
763	C₂×C₃	—	40	1	no	—
764	C₂×C₃	—	40	1	no	—
765	C₂×C₃	—	40	1	no	—
766	C₂×C₃	D₅×#127	1	1	yes	characteristic
767	C₂×C₃	#66108	1	2	yes	—
768	C₅	C₃×#3155	1	1	yes	characteristic, complemented, Sylow
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	5	2	no	—
776	C₂²	—	10	2	no	—
777	C₂²	—	20	2	no	—
778	C₂²	—	20	2	no	—
779	C₂²	—	20	2	no	—
780	C₂²	—	20	1	no	—
781	C₂²	—	20	1	no	—
782	C₂²	—	20	1	no	—
783	C₂²	—	40	4	no	—
784	C₂²	—	40	4	no	—
785	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	5	2	no	—
789	C₄	—	10	2	no	—
790	C₄	—	20	1	no	—
791	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
792	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
793	C₃	#10613579	1	1	yes	characteristic, direct product factor, Sylow
794	C₂	—	8	1	no	—
795	C₂	—	8	1	no	—
796	C₂	—	8	1	no	—
797	C₂	—	10	2	no	—
798	C₂	—	40	1	no	—
799	C₂	—	40	1	no	—
800	C₂	—	40	1	no	—
801	C₂	C₃×D₅×#127	1	1	yes	characteristic
802	C₂	C₃×#66108	1	2	yes	—

	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×#496	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#496	D₅
hypocenter	C₅	C₃×#3155
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#496

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4062	C₂	semidirect
2. C₂×C₃×#4060	C₂	semidirect
3. C₂×C₃×#4057	C₂	semidirect
4. C₂×C₃×D₅×D₈	C₂	semidirect
5. C₃×#66049	C₂	semidirect
6. C₃×#66008	C₂	semidirect
7. C₃×C₅×#496	C₂	semidirect
8. C₃×#65465	C₂	semidirect
9. C₃×#65457	C₂	semidirect
10. C₃×#65443	C₂	semidirect
11. C₃×#65440	C₂	semidirect
12. C₃×#65362	C₂	semidirect
13. C₃×#65348	C₂	semidirect
14. C₃×#65001	C₂	semidirect
15. C₃×#64997	C₂	semidirect
16. #10613579	C₃	direct (N × H)
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂×C₃×C₅×D₈	C₂²	semidirect
25. C₃×C₅×#127	C₂²	semidirect
26. C₃×C₅×#124	C₂²	semidirect
27. C₃×#4093	C₂²	semidirect
28. C₂×C₃×#689	C₂²	semidirect
29. C₂×C₃×#688	C₂²	semidirect
30. C₃×#4086	C₂²	semidirect
31. C₃×#4086	C₂²	semidirect
34. C₃×#4082	C₂²	semidirect
35. C₂×C₃×#687	C₂²	semidirect
38. C₂×C₃×#686	C₂²	semidirect
39. C₂×C₃×#686	C₂²	semidirect
40. C₂×C₃×#686	C₂²	semidirect
46. C₂×C₃×D₄₀	C₂²	semidirect
47. C₂×C₃×#677	C₂²	semidirect
48. C₂×C₃×#677	C₂²	semidirect
53. C₃×#4021	C₂²	semidirect
54. C₃×#4020	C₂²	semidirect
56. C₃×C₅×#97	C₂²	semidirect
57. C₃×#3947	C₂²	semidirect
58. C₃×C₈×Dic₅	C₂²	semidirect
59. C₃×C₄×#168	C₂²	semidirect
61. C₂×#4062	C₂×C₃	semidirect
62. C₂×#4060	C₂×C₃	semidirect
63. C₂×#4057	C₂×C₃	semidirect
64. C₂×D₅×D₈	C₂×C₃	semidirect
65. #66049	C₂×C₃	semidirect
66. #66008	C₂×C₃	semidirect
67. C₅×#496	C₂×C₃	semidirect
68. #65465	C₂×C₃	semidirect
69. #65457	C₂×C₃	semidirect
70. #65443	C₂×C₃	semidirect
71. #65440	C₂×C₃	semidirect
72. #65362	C₂×C₃	semidirect
73. #65348	C₂×C₃	semidirect
74. #65001	C₂×C₃	semidirect
75. #64997	C₂×C₃	semidirect
133. C₃×#676	D₄	semidirect
134. C₃×C₈×D₅	D₄	semidirect
144. C₃×#496	D₅	semidirect
154. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
155. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
157. C₂×C₅×D₈	C₂²×C₃	semidirect
158. C₅×#127	C₂²×C₃	semidirect
159. C₅×#124	C₂²×C₃	semidirect
160. #4093	C₂²×C₃	semidirect
161. C₂×#689	C₂²×C₃	semidirect
162. C₂×#688	C₂²×C₃	semidirect
163. #4086	C₂²×C₃	semidirect
164. #4086	C₂²×C₃	semidirect
167. #4082	C₂²×C₃	semidirect
168. C₂×#687	C₂²×C₃	semidirect
171. C₂×#686	C₂²×C₃	semidirect
172. C₂×#686	C₂²×C₃	semidirect
173. C₂×#686	C₂²×C₃	semidirect
179. C₂×D₄₀	C₂²×C₃	semidirect
180. C₂×#677	C₂²×C₃	semidirect
181. C₂×#677	C₂²×C₃	semidirect
186. #4021	C₂²×C₃	semidirect
187. #4020	C₂²×C₃	semidirect
189. C₅×#97	C₂²×C₃	semidirect
190. #3947	C₂²×C₃	semidirect
191. C₈×Dic₅	C₂²×C₃	semidirect
192. C₄×#168	C₂²×C₃	semidirect
255. C₂×C₃×SD₁₆	C₂×D₅	semidirect
256. C₂×C₃×SD₁₆	C₂×D₅	semidirect
266. C₂×C₃×D₈	C₂×D₅	semidirect
272. C₃×#127	C₂×D₅	semidirect
276. C₃×#124	C₂×D₅	semidirect
283. C₃×#97	C₂×D₅	semidirect
343. #676	C₃×D₄	semidirect
344. C₈×D₅	C₃×D₄	semidirect
354. #496	C₃×D₅	semidirect
504. C₂×SD₁₆	C₂×C₃×D₅	semidirect
505. C₂×SD₁₆	C₂×C₃×D₅	semidirect
515. C₂×D₈	C₂×C₃×D₅	semidirect
521. #127	C₂×C₃×D₅	semidirect
525. #124	C₂×C₃×D₅	semidirect
532. #97	C₂×C₃×D₅	semidirect
676. C₃×C₅	#3155	semidirect
768. C₅	C₃×#3155	semidirect
793. C₃	#10613579	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
C₂×C₃×#4060	2
C₂×C₃×#4057	2
C₂×C₃×D₅×D₈	2
C₃×#66049	2
C₃×#66008	2
C₃×C₅×#496	2
C₃×#65465	2
C₃×#65457	2
C₃×#65443	2
C₃×#65440	2
C₃×#65362	2
C₃×#65348	2
C₃×#65001	2
C₃×#64997	2
#10613579	3
C₃×#3155	5

Subgroups — C3×#10613579 #14439544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613579 #14439544