Subgroups — C₃×#10613604 #14439643

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4064	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4062	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#4061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66009	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65479	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65457	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65456	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65381	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65348	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64997	C₂	1	1	yes	maximal, characteristic, complemented
16	#10613604	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#713	C₂²	1	1	yes	characteristic
18	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#711	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×#4093	C₂²	1	1	yes	characteristic
28	C₃×#4090	C₂²	1	1	yes	characteristic
29	C₃×#4090	C₂²	1	1	yes	characteristic
30	C₂×C₃×#689	C₂²	1	1	yes	characteristic
31	C₂×C₃×#689	C₂²	1	1	yes	characteristic
32	C₂×C₃×#689	C₂²	1	1	yes	characteristic
33	C₂×C₃×#689	C₂²	1	1	yes	characteristic
34	C₂×C₃×#689	C₂²	1	1	yes	characteristic
35	C₂×C₃×#688	C₂²	1	1	yes	characteristic
36	C₃×#4082	C₂²	1	1	yes	characteristic
37	C₂×C₃×#687	C₂²	1	1	yes	characteristic
38	C₂×C₃×#686	C₂²	1	1	yes	characteristic
39	C₃×#4064	—	2	4	no	—
40	C₃×D₅×Q₁₆	—	2	4	no	—
41	C₃×#4062	—	2	4	no	—
42	C₃×#4061	—	2	4	no	—
43	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
44	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
45	C₂×C₃×#677	C₂²	1	1	yes	characteristic
46	C₂×C₃×#677	C₂²	1	1	yes	characteristic
47	C₂×C₃×#676	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
49	C₃×#4042	—	2	2	no	—
50	C₃×#4040	—	2	2	no	—
51	C₃×#4029	—	2	2	no	—
52	C₃×#4024	—	2	2	no	—
53	C₃×#4021	C₂²	1	1	yes	characteristic
54	C₃×#4018	C₂²	1	1	yes	characteristic
55	C₃×#4015	C₂²	1	1	yes	characteristic
56	C₃×C₅×#97	C₂²	1	1	yes	characteristic
57	C₃×#3947	C₂²	1	1	yes	characteristic
58	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
59	C₃×C₄×#168	C₂²	1	1	yes	characteristic
60	C₃×#3156	—	5	1	no	maximal, Hall
61	C₂×#4064	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×#4062	C₂×C₃	1	1	yes	characteristic
64	C₂×#4061	C₂×C₃	1	1	yes	characteristic, complemented
65	#66058	C₂×C₃	1	1	yes	characteristic, complemented
66	#66009	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
68	#65479	C₂×C₃	1	1	yes	characteristic, complemented
69	#65470	C₂×C₃	1	1	yes	characteristic, complemented
70	#65457	C₂×C₃	1	1	yes	characteristic, complemented
71	#65456	C₂×C₃	1	1	yes	characteristic, complemented
72	#65381	C₂×C₃	1	1	yes	characteristic, complemented
73	#65348	C₂×C₃	1	1	yes	characteristic, complemented
74	#65004	C₂×C₃	1	1	yes	characteristic, complemented
75	#64997	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
81	C₂²×C₃×Dic₅	—	2	1	no	—
82	C₃×#713	—	2	2	no	—
83	C₃×#713	—	2	2	no	—
84	C₃×Q₈×D₅	—	2	2	no	—
85	C₃×Q₈×D₅	—	2	2	no	—
86	C₃×Q₈×D₅	—	2	2	no	—
87	C₃×Q₈×D₅	—	2	2	no	—
88	C₃×#711	—	2	2	no	—
89	C₃×#711	—	2	2	no	—
90	C₂×C₃×D₂₀	—	2	1	no	—
91	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×D₅	—	2	1	no	—
93	C₂×C₃×C₄×D₅	—	2	1	no	—
94	C₂×C₃×C₄×D₅	—	2	1	no	—
95	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₁₀	—	2	1	no	—
97	C₂×C₃×Dic₁₀	—	2	1	no	—
98	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
101	C₃×C₅×Q₁₆	—	2	2	no	—
102	C₃×C₅×Q₁₆	—	2	2	no	—
103	C₃×C₅×SD₁₆	—	2	2	no	—
104	C₃×C₅×SD₁₆	—	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	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₃×C₂²⋊Dic₅	—	2	2	no	—
111	C₃×#689	—	2	2	no	—
112	C₃×#689	—	2	2	no	—
113	C₃×#689	—	2	2	no	—
114	C₃×#689	—	2	2	no	—
115	C₃×#689	—	2	2	no	—
116	C₃×#688	—	2	2	no	—
117	C₃×#687	—	2	2	no	—
118	C₃×#686	—	2	2	no	—
119	C₃×#685	—	2	2	no	—
120	C₃×#685	—	2	2	no	—
121	C₃×#685	D₄	1	2	yes	—
122	C₃×C₄⋊Dic₅	—	2	2	no	—
123	C₃×#683	—	2	2	no	—
124	C₃×#683	—	2	2	no	—
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×Dic₂₀	—	2	2	no	—
130	C₃×Dic₂₀	—	2	2	no	—
131	C₃×#677	—	2	2	no	—
132	C₃×#677	—	2	2	no	—
133	C₃×#676	D₄	1	4	yes	—
134	C₃×C₈×D₅	D₄	1	4	yes	—
135	C₂×C₃×#137	—	5	1	no	—
136	C₂×C₃×#137	—	5	1	no	—
137	C₂×C₃×#135	—	5	1	no	—
138	C₂²×C₃×Q₁₆	—	5	1	no	—
139	C₃×#536	—	5	1	no	—
140	C₃×#536	—	5	1	no	—
141	C₃×#497	—	5	1	no	—
142	C₃×#497	—	5	1	no	—
143	C₃×#497	—	5	1	no	—
144	C₃×#497	D₅	1	1	yes	characteristic, complemented
145	C₃×#495	—	5	1	no	—
146	C₃×#495	—	5	1	no	—
147	C₃×#494	—	5	1	no	—
148	C₃×#494	—	5	1	no	—
149	C₃×#405	—	5	1	no	—
150	C₂×#713	C₂²×C₃	1	1	yes	characteristic
151	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
152	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
153	C₂×#711	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#124	C₂²×C₃	1	1	yes	characteristic
160	#4093	C₂²×C₃	1	1	yes	characteristic
161	#4090	C₂²×C₃	1	1	yes	characteristic
162	#4090	C₂²×C₃	1	1	yes	characteristic
163	C₂×#689	C₂²×C₃	1	1	yes	characteristic
164	C₂×#689	C₂²×C₃	1	1	yes	characteristic
165	C₂×#689	C₂²×C₃	1	1	yes	characteristic
166	C₂×#689	C₂²×C₃	1	1	yes	characteristic
167	C₂×#689	C₂²×C₃	1	1	yes	characteristic
168	C₂×#688	C₂²×C₃	1	1	yes	characteristic
169	#4082	C₂²×C₃	1	1	yes	characteristic
170	C₂×#687	C₂²×C₃	1	1	yes	characteristic
171	C₂×#686	C₂²×C₃	1	1	yes	characteristic
172	#4064	—	2	4	no	—
173	D₅×Q₁₆	—	2	4	no	—
174	#4062	—	2	4	no	—
175	#4061	—	2	4	no	—
176	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
177	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
178	C₂×#677	C₂²×C₃	1	1	yes	characteristic
179	C₂×#677	C₂²×C₃	1	1	yes	characteristic
180	C₂×#676	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
182	#4042	—	2	2	no	—
183	#4040	—	2	2	no	—
184	#4029	—	2	2	no	—
185	#4024	—	2	2	no	—
186	#4021	C₂²×C₃	1	1	yes	characteristic
187	#4018	C₂²×C₃	1	1	yes	characteristic
188	#4015	C₂²×C₃	1	1	yes	characteristic
189	C₅×#97	C₂²×C₃	1	1	yes	characteristic
190	#3947	C₂²×C₃	1	1	yes	characteristic
191	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
192	C₄×#168	C₂²×C₃	1	1	yes	characteristic
193	#3156	—	5	1	no	Sylow
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂²×C₃×D₅	—	2	1	no	—
196	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	2	1	no	—
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×Q₈	—	2	1	no	—
202	C₃×C₅×Q₈	—	2	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
209	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
210	C₃×C₂²⋊D₅	—	4	2	no	—
211	C₂×C₃×Dic₅	—	2	1	no	—
212	C₂×C₃×Dic₅	—	2	1	no	—
213	C₂×C₃×Dic₅	—	2	1	no	—
214	C₂×C₃×Dic₅	—	4	2	no	—
215	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
216	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
217	C₃×D₂₀	—	2	1	no	—
218	C₃×D₂₀	—	2	1	no	—
219	C₃×D₂₀	—	4	2	no	—
220	C₃×C₄×D₅	—	4	2	no	—
221	C₃×C₄×D₅	—	4	2	no	—
222	C₃×C₄×D₅	—	4	2	no	—
223	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
224	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
225	C₃×Dic₁₀	—	2	1	no	—
226	C₃×Dic₁₀	—	2	1	no	—
227	C₃×Dic₁₀	—	2	1	no	—
228	C₃×Dic₁₀	—	2	1	no	—
229	C₃×Dic₁₀	—	2	1	no	—
230	C₃×Dic₁₀	—	2	1	no	—
231	C₃×Dic₁₀	—	4	2	no	—
232	C₃×Dic₁₀	—	4	2	no	—
233	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
234	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
235	C₃×#168	C₂×D₄	1	2	yes	—
236	C₃×#168	C₂×D₄	1	2	yes	—
237	C₂×C₃×#41	—	5	1	no	—
238	C₂×C₃×#41	—	5	1	no	—
239	C₂²×C₃×Q₈	—	5	1	no	—
240	C₂²×C₃×Q₈	—	5	1	no	—
241	C₃×#137	—	10	4	no	—
242	C₃×#137	—	10	4	no	—
243	C₃×#135	—	10	4	no	—
244	C₂×C₃×Q₁₆	—	5	1	no	—
245	C₂×C₃×Q₁₆	—	5	1	no	—
246	C₂×C₃×Q₁₆	—	5	1	no	—
247	C₂×C₃×Q₁₆	—	5	1	no	—
248	C₂×C₃×Q₁₆	—	5	1	no	—
249	C₂×C₃×Q₁₆	—	5	1	no	—
250	C₂×C₃×Q₁₆	—	5	1	no	—
251	C₂×C₃×Q₁₆	—	10	4	no	—
252	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
253	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
254	C₂×C₃×SD₁₆	—	5	1	no	—
255	C₂×C₃×SD₁₆	—	5	1	no	—
256	C₂×C₃×SD₁₆	—	5	1	no	—
257	C₂×C₃×SD₁₆	—	5	1	no	—
258	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
259	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
260	C₂×C₃×D₈	—	5	1	no	—
261	C₂×C₃×M₁₆	—	5	1	no	—
262	C₂²×C₃×C₈	—	5	1	no	—
263	C₃×C₄⋊Q₈	—	5	1	no	—
264	C₃×C₄⋊Q₈	—	5	1	no	—
265	C₃×C₄⋊Q₈	—	5	1	no	—
266	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
267	C₃×#124	—	5	1	no	—
268	C₃×#124	—	5	1	no	—
269	C₃×#124	—	5	1	no	—
270	C₃×#124	C₂×D₅	1	1	yes	characteristic
271	C₃×#123	—	10	2	no	—
272	C₃×#123	—	10	2	no	—
273	C₃×C₂²⋊Q₈	—	10	2	no	—
274	C₃×C₂²⋊Q₈	—	10	2	no	—
275	C₃×#117	—	5	1	no	—
276	C₃×#97	—	5	1	no	—
277	C₃×#97	C₂×D₅	1	1	yes	characteristic
278	C₃×C₄×C₈	—	5	1	no	—
279	C₃×C₄×C₈	—	5	1	no	—
280	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₂²⋊D₅	—	2	1	no	—
285	C₂²×Dic₅	—	2	1	no	—
286	#713	—	2	2	no	—
287	#713	—	2	2	no	—
288	Q₈×D₅	—	2	2	no	—
289	Q₈×D₅	—	2	2	no	—
290	Q₈×D₅	—	2	2	no	—
291	Q₈×D₅	—	2	2	no	—
292	#711	—	2	2	no	—
293	#711	—	2	2	no	—
294	C₂×D₂₀	—	2	1	no	—
295	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₄×D₅	—	2	1	no	—
297	C₂×C₄×D₅	—	2	1	no	—
298	C₂×C₄×D₅	—	2	1	no	—
299	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
300	C₂×Dic₁₀	—	2	1	no	—
301	C₂×Dic₁₀	—	2	1	no	—
302	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
303	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
304	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
305	C₅×Q₁₆	—	2	2	no	—
306	C₅×Q₁₆	—	2	2	no	—
307	C₅×SD₁₆	—	2	2	no	—
308	C₅×SD₁₆	—	2	2	no	—
309	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₂²⋊C₄	—	2	2	no	—
313	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
314	C₂²⋊Dic₅	—	2	2	no	—
315	#689	—	2	2	no	—
316	#689	—	2	2	no	—
317	#689	—	2	2	no	—
318	#689	—	2	2	no	—
319	#689	—	2	2	no	—
320	#688	—	2	2	no	—
321	#687	—	2	2	no	—
322	#686	—	2	2	no	—
323	#685	—	2	2	no	—
324	#685	—	2	2	no	—
325	#685	C₃×D₄	1	2	yes	—
326	C₄⋊Dic₅	—	2	2	no	—
327	#683	—	2	2	no	—
328	#683	—	2	2	no	—
329	#683	C₃×D₄	1	2	yes	—
330	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
331	C₂×#168	C₂³×C₃	1	1	yes	characteristic
332	C₂×#168	C₂³×C₃	1	1	yes	characteristic
333	Dic₂₀	—	2	2	no	—
334	Dic₂₀	—	2	2	no	—
335	#677	—	2	2	no	—
336	#677	—	2	2	no	—
337	#676	C₃×D₄	1	4	yes	—
338	C₈×D₅	C₃×D₄	1	4	yes	—
339	C₂×#137	—	5	1	no	—
340	C₂×#137	—	5	1	no	—
341	C₂×#135	—	5	1	no	—
342	C₂²×Q₁₆	—	5	1	no	—
343	#536	—	5	1	no	—
344	#536	—	5	1	no	—
345	#497	—	5	1	no	—
346	#497	—	5	1	no	—
347	#497	—	5	1	no	—
348	#497	C₃×D₅	1	1	yes	characteristic, complemented
349	#495	—	5	1	no	—
350	#495	—	5	1	no	—
351	#494	—	5	1	no	—
352	#494	—	5	1	no	—
353	#405	—	5	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	2	no	—
356	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₃×D₅	—	2	2	no	—
358	C₂×C₃×D₅	—	4	1	no	—
359	C₂×C₃×D₅	—	4	2	no	—
360	C₂×C₃×D₅	#127	1	2	yes	—
361	C₃×C₄×C₅	—	2	2	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
367	C₃×Dic₅	—	2	2	no	—
368	C₃×Dic₅	—	4	1	no	—
369	C₃×Dic₅	—	4	1	no	—
370	C₃×Dic₅	—	4	1	no	—
371	C₃×Dic₅	#127	1	2	yes	—
372	C₃×#41	—	10	2	no	—
373	C₃×#41	—	10	2	no	—
374	C₃×#41	—	10	2	no	—
375	C₃×#41	—	10	2	no	—
376	C₂×C₃×Q₈	—	5	1	no	—
377	C₂×C₃×Q₈	—	5	1	no	—
378	C₂×C₃×Q₈	—	5	1	no	—
379	C₂×C₃×Q₈	—	10	1	no	—
380	C₂×C₃×Q₈	—	10	1	no	—
381	C₂×C₃×Q₈	—	10	2	no	—
382	C₂×C₃×Q₈	—	10	2	no	—
383	C₂×C₃×Q₈	—	10	2	no	—
384	C₂×C₃×Q₈	—	10	2	no	—
385	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
386	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
387	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
388	C₂×C₃×D₄	—	5	1	no	—
389	C₂×C₃×D₄	—	10	1	no	—
390	C₂×C₃×D₄	—	10	1	no	—
391	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	—	5	1	no	—
393	C₂²×C₃×C₄	—	10	1	no	—
394	C₂²×C₃×C₄	—	10	1	no	—
395	C₂²×C₃×C₄	—	10	1	no	—
396	C₂²×C₃×C₄	—	10	1	no	—
397	C₃×Q₁₆	—	2	2	no	—
398	C₃×Q₁₆	—	2	2	no	—
399	C₃×Q₁₆	—	10	2	no	—
400	C₃×Q₁₆	—	10	2	no	—
401	C₃×Q₁₆	—	10	2	no	—
402	C₃×Q₁₆	—	10	2	no	—
403	C₃×Q₁₆	—	10	2	no	—
404	C₃×Q₁₆	—	10	2	no	—
405	C₃×Q₁₆	—	10	2	no	—
406	C₃×SD₁₆	—	2	2	no	—
407	C₃×SD₁₆	—	2	2	no	—
408	C₃×SD₁₆	—	10	2	no	—
409	C₃×SD₁₆	—	10	2	no	—
410	C₃×SD₁₆	—	10	2	no	—
411	C₃×SD₁₆	—	10	2	no	—
412	C₃×D₈	—	10	2	no	—
413	C₃×M₁₆	—	5	4	no	—
414	C₂×C₃×C₈	—	5	1	no	—
415	C₂×C₃×C₈	—	5	1	no	—
416	C₂×C₃×C₈	—	5	4	no	—
417	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
418	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	5	2	no	—
421	C₃×C₄⋊C₄	—	10	2	no	—
422	C₃×C₄⋊C₄	—	10	2	no	—
423	C₃×C₄⋊C₄	—	10	2	no	—
424	C₃×C₂²⋊C₄	—	2	2	no	—
425	C₃×C₂²⋊C₄	—	5	2	no	—
426	C₃×C₂²⋊C₄	—	10	2	no	—
427	C₃×C₂²⋊C₄	—	10	2	no	—
428	C₃×C₂²⋊C₄	—	10	2	no	—
429	C₃×C₄²	—	5	1	no	—
430	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
431	C₂³×C₅	—	2	1	no	—
432	C₂²×D₅	—	2	1	no	—
433	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
434	C₅×Q₈	—	2	1	no	—
435	C₅×Q₈	—	2	1	no	—
436	C₅×Q₈	—	2	1	no	—
437	C₅×Q₈	—	2	1	no	—
438	C₅×Q₈	—	2	1	no	—
439	C₅×Q₈	—	2	1	no	—
440	C₅×D₄	—	2	1	no	—
441	C₅×D₄	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
446	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
447	C₂²⋊D₅	—	4	2	no	—
448	C₂×Dic₅	—	2	1	no	—
449	C₂×Dic₅	—	2	1	no	—
450	C₂×Dic₅	—	2	1	no	—
451	C₂×Dic₅	—	4	2	no	—
452	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
453	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
454	D₂₀	—	2	1	no	—
455	D₂₀	—	2	1	no	—
456	D₂₀	—	4	2	no	—
457	C₄×D₅	—	4	2	no	—
458	C₄×D₅	—	4	2	no	—
459	C₄×D₅	—	4	2	no	—
460	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
461	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
462	Dic₁₀	—	2	1	no	—
463	Dic₁₀	—	2	1	no	—
464	Dic₁₀	—	2	1	no	—
465	Dic₁₀	—	2	1	no	—
466	Dic₁₀	—	2	1	no	—
467	Dic₁₀	—	2	1	no	—
468	Dic₁₀	—	4	2	no	—
469	Dic₁₀	—	4	2	no	—
470	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
471	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
472	#168	C₂×C₃×D₄	1	2	yes	—
473	#168	C₂×C₃×D₄	1	2	yes	—
474	C₂×#41	—	5	1	no	—
475	C₂×#41	—	5	1	no	—
476	C₂²×Q₈	—	5	1	no	—
477	C₂²×Q₈	—	5	1	no	—
478	#137	—	10	4	no	—
479	#137	—	10	4	no	—
480	#135	—	10	4	no	—
481	C₂×Q₁₆	—	5	1	no	—
482	C₂×Q₁₆	—	5	1	no	—
483	C₂×Q₁₆	—	5	1	no	—
484	C₂×Q₁₆	—	5	1	no	—
485	C₂×Q₁₆	—	5	1	no	—
486	C₂×Q₁₆	—	5	1	no	—
487	C₂×Q₁₆	—	5	1	no	—
488	C₂×Q₁₆	—	10	4	no	—
489	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
490	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
491	C₂×SD₁₆	—	5	1	no	—
492	C₂×SD₁₆	—	5	1	no	—
493	C₂×SD₁₆	—	5	1	no	—
494	C₂×SD₁₆	—	5	1	no	—
495	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
496	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
497	C₂×D₈	—	5	1	no	—
498	C₂×M₁₆	—	5	1	no	—
499	C₂²×C₈	—	5	1	no	—
500	C₄⋊Q₈	—	5	1	no	—
501	C₄⋊Q₈	—	5	1	no	—
502	C₄⋊Q₈	—	5	1	no	—
503	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
504	#124	—	5	1	no	—
505	#124	—	5	1	no	—
506	#124	—	5	1	no	—
507	#124	C₂×C₃×D₅	1	1	yes	characteristic
508	#123	—	10	2	no	—
509	#123	—	10	2	no	—
510	C₂²⋊Q₈	—	10	2	no	—
511	C₂²⋊Q₈	—	10	2	no	—
512	#117	—	5	1	no	—
513	#97	—	5	1	no	—
514	#97	C₂×C₃×D₅	1	1	yes	characteristic
515	C₄×C₈	—	5	1	no	—
516	C₄×C₈	—	5	1	no	—
517	C₂×C₃×C₅	—	8	1	no	—
518	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
519	C₂×C₃×C₅	#578	1	2	yes	—
520	C₃×D₅	—	2	2	no	—
521	C₃×D₅	—	8	1	no	—
522	C₂³×C₃	—	2	1	no	—
523	C₂³×C₃	—	5	1	no	—
524	C₂³×C₃	—	10	1	no	—
525	C₃×Q₈	—	2	1	no	—
526	C₃×Q₈	—	2	1	no	—
527	C₃×Q₈	—	2	1	no	—
528	C₃×Q₈	—	2	1	no	—
529	C₃×Q₈	—	2	1	no	—
530	C₃×Q₈	—	2	1	no	—
531	C₃×Q₈	—	10	1	no	—
532	C₃×Q₈	—	10	1	no	—
533	C₃×Q₈	—	10	1	no	—
534	C₃×Q₈	—	10	1	no	—
535	C₃×Q₈	—	10	1	no	—
536	C₃×Q₈	—	10	1	no	—
537	C₃×Q₈	—	20	2	no	—
538	C₃×Q₈	—	20	2	no	—
539	C₃×D₄	—	2	1	no	—
540	C₃×D₄	—	2	1	no	—
541	C₃×D₄	—	10	1	no	—
542	C₃×D₄	—	10	1	no	—
543	C₃×D₄	—	20	2	no	—
544	C₃×D₄	—	20	2	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	5	1	no	—
549	C₂×C₃×C₄	—	5	2	no	—
550	C₂×C₃×C₄	—	5	2	no	—
551	C₂×C₃×C₄	—	5	2	no	—
552	C₂×C₃×C₄	—	10	1	no	—
553	C₂×C₃×C₄	—	10	1	no	—
554	C₂×C₃×C₄	—	10	1	no	—
555	C₂×C₃×C₄	—	20	2	no	—
556	C₂×C₃×C₄	—	20	2	no	—
557	C₂×C₃×C₄	—	20	2	no	—
558	C₂×C₃×C₄	—	20	2	no	—
559	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
560	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
561	C₃×C₈	—	5	2	no	—
562	C₃×C₈	—	5	2	no	—
563	C₃×C₈	D₄×D₅	1	2	yes	—
564	C₃×C₈	D₄×D₅	1	2	yes	—
565	C₂²×C₅	—	4	2	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
568	C₂×D₅	—	2	2	no	—
569	C₂×D₅	—	4	2	no	—
570	C₂×D₅	—	4	1	no	—
571	C₂×D₅	C₃×#127	1	2	yes	—
572	C₄×C₅	—	2	2	no	—
573	C₄×C₅	—	4	1	no	—
574	C₄×C₅	—	4	1	no	—
575	C₄×C₅	—	4	1	no	—
576	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
577	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
578	Dic₅	—	2	2	no	—
579	Dic₅	—	4	1	no	—
580	Dic₅	—	4	1	no	—
581	Dic₅	—	4	1	no	—
582	Dic₅	C₃×#127	1	2	yes	—
583	#41	—	10	2	no	—
584	#41	—	10	2	no	—
585	#41	—	10	2	no	—
586	#41	—	10	2	no	—
587	C₂×Q₈	—	5	1	no	—
588	C₂×Q₈	—	5	1	no	—
589	C₂×Q₈	—	5	1	no	—
590	C₂×Q₈	—	10	1	no	—
591	C₂×Q₈	—	10	1	no	—
592	C₂×Q₈	—	10	2	no	—
593	C₂×Q₈	—	10	2	no	—
594	C₂×Q₈	—	10	2	no	—
595	C₂×Q₈	—	10	2	no	—
596	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
597	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
598	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
599	C₂×D₄	—	5	1	no	—
600	C₂×D₄	—	10	1	no	—
601	C₂×D₄	—	10	1	no	—
602	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
603	C₂²×C₄	—	5	1	no	—
604	C₂²×C₄	—	10	1	no	—
605	C₂²×C₄	—	10	1	no	—
606	C₂²×C₄	—	10	1	no	—
607	C₂²×C₄	—	10	1	no	—
608	Q₁₆	—	2	2	no	—
609	Q₁₆	—	2	2	no	—
610	Q₁₆	—	10	2	no	—
611	Q₁₆	—	10	2	no	—
612	Q₁₆	—	10	2	no	—
613	Q₁₆	—	10	2	no	—
614	Q₁₆	—	10	2	no	—
615	Q₁₆	—	10	2	no	—
616	Q₁₆	—	10	2	no	—
617	SD₁₆	—	2	2	no	—
618	SD₁₆	—	2	2	no	—
619	SD₁₆	—	10	2	no	—
620	SD₁₆	—	10	2	no	—
621	SD₁₆	—	10	2	no	—
622	SD₁₆	—	10	2	no	—
623	D₈	—	10	2	no	—
624	M₁₆	—	5	4	no	—
625	C₂×C₈	—	5	1	no	—
626	C₂×C₈	—	5	1	no	—
627	C₂×C₈	—	5	4	no	—
628	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
629	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	5	2	no	—
632	C₄⋊C₄	—	10	2	no	—
633	C₄⋊C₄	—	10	2	no	—
634	C₄⋊C₄	—	10	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	5	2	no	—
637	C₂²⋊C₄	—	10	2	no	—
638	C₂²⋊C₄	—	10	2	no	—
639	C₂²⋊C₄	—	10	2	no	—
640	C₄²	—	5	1	no	—
641	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
642	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
643	C₂²×C₃	—	4	1	no	—
644	C₂²×C₃	—	4	2	no	—
645	C₂²×C₃	—	5	2	no	—
646	C₂²×C₃	—	10	2	no	—
647	C₂²×C₃	—	20	1	no	—
648	C₂²×C₃	—	20	2	no	—
649	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	4	1	no	—
654	C₃×C₄	—	5	2	no	—
655	C₃×C₄	—	10	2	no	—
656	C₃×C₄	—	20	1	no	—
657	C₃×C₄	—	20	1	no	—
658	C₃×C₄	—	20	1	no	—
659	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
660	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
661	C₂×C₅	—	8	1	no	—
662	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
663	C₂×C₅	C₃×#578	1	2	yes	—
664	D₅	—	2	2	no	—
665	D₅	—	8	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	5	1	no	—
668	C₂³	—	10	1	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	2	1	no	—
671	Q₈	—	2	1	no	—
672	Q₈	—	2	1	no	—
673	Q₈	—	2	1	no	—
674	Q₈	—	2	1	no	—
675	Q₈	—	10	1	no	—
676	Q₈	—	10	1	no	—
677	Q₈	—	10	1	no	—
678	Q₈	—	10	1	no	—
679	Q₈	—	10	1	no	—
680	Q₈	—	10	1	no	—
681	Q₈	—	20	2	no	—
682	Q₈	—	20	2	no	—
683	D₄	—	2	1	no	—
684	D₄	—	2	1	no	—
685	D₄	—	10	1	no	—
686	D₄	—	10	1	no	—
687	D₄	—	20	2	no	—
688	D₄	—	20	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	5	1	no	—
693	C₂×C₄	—	5	2	no	—
694	C₂×C₄	—	5	2	no	—
695	C₂×C₄	—	5	2	no	—
696	C₂×C₄	—	10	1	no	—
697	C₂×C₄	—	10	1	no	—
698	C₂×C₄	—	10	1	no	—
699	C₂×C₄	—	20	2	no	—
700	C₂×C₄	—	20	2	no	—
701	C₂×C₄	—	20	2	no	—
702	C₂×C₄	—	20	2	no	—
703	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
704	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
705	C₈	—	5	2	no	—
706	C₈	—	5	2	no	—
707	C₈	C₃×D₄×D₅	1	2	yes	—
708	C₈	C₃×D₄×D₅	1	2	yes	—
709	C₂×C₃	—	8	1	no	—
710	C₂×C₃	—	10	2	no	—
711	C₂×C₃	—	40	1	no	—
712	C₂×C₃	D₅×#127	1	1	yes	characteristic
713	C₂×C₃	#66113	1	2	yes	—
714	C₅	C₃×#3156	1	1	yes	characteristic, complemented, Sylow
715	C₂²	—	4	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	5	2	no	—
718	C₂²	—	10	2	no	—
719	C₂²	—	20	2	no	—
720	C₂²	—	20	1	no	—
721	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	5	2	no	—
727	C₄	—	10	2	no	—
728	C₄	—	20	1	no	—
729	C₄	—	20	1	no	—
730	C₄	—	20	1	no	—
731	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
732	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
733	C₃	#10613604	1	1	yes	characteristic, direct product factor, Sylow
734	C₂	—	8	1	no	—
735	C₂	—	10	2	no	—
736	C₂	—	40	1	no	—
737	C₂	C₃×D₅×#127	1	1	yes	characteristic
738	C₂	C₃×#66113	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×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4062	C₂
hypercenter	C₃×#497	D₅
hypocenter	C₅	C₃×#3156
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4064	C₂	semidirect
2. C₂×C₃×D₅×Q₁₆	C₂	semidirect
4. C₂×C₃×#4061	C₂	semidirect
5. C₃×#66058	C₂	semidirect
6. C₃×#66009	C₂	semidirect
7. C₃×C₅×#497	C₂	semidirect
8. C₃×#65479	C₂	semidirect
9. C₃×#65470	C₂	semidirect
10. C₃×#65457	C₂	semidirect
11. C₃×#65456	C₂	semidirect
12. C₃×#65381	C₂	semidirect
13. C₃×#65348	C₂	semidirect
14. C₃×#65004	C₂	semidirect
15. C₃×#64997	C₂	semidirect
16. #10613604	C₃	direct (N × H)
61. C₂×#4064	C₂×C₃	semidirect
62. C₂×D₅×Q₁₆	C₂×C₃	semidirect
64. C₂×#4061	C₂×C₃	semidirect
65. #66058	C₂×C₃	semidirect
66. #66009	C₂×C₃	semidirect
67. C₅×#497	C₂×C₃	semidirect
68. #65479	C₂×C₃	semidirect
69. #65470	C₂×C₃	semidirect
70. #65457	C₂×C₃	semidirect
71. #65456	C₂×C₃	semidirect
72. #65381	C₂×C₃	semidirect
73. #65348	C₂×C₃	semidirect
74. #65004	C₂×C₃	semidirect
75. #64997	C₂×C₃	semidirect
144. C₃×#497	D₅	semidirect
348. #497	C₃×D₅	semidirect
642. C₃×C₅	#3156	semidirect
714. C₅	C₃×#3156	semidirect
733. C₃	#10613604	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×#4064	2
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×#4062	2
C₂×C₃×#4061	2
C₃×#66058	2
C₃×#66009	2
C₃×C₅×#497	2
C₃×#65479	2
C₃×#65470	2
C₃×#65457	2
C₃×#65456	2
C₃×#65381	2
C₃×#65348	2
C₃×#65004	2
C₃×#64997	2
#10613604	3
C₃×#3156	5

Subgroups — C3×#10613604 #14439643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613604 #14439643