Subgroups — C₃×#10611690 #14418566

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65912	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65128	C₂	1	1	yes	maximal, characteristic
5	C₃×#65128	C₂	1	1	yes	maximal, characteristic
6	C₃×#65126	C₂	1	1	yes	maximal, characteristic
7	C₃×#65120	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64997	C₂	1	1	yes	maximal, characteristic
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic
12	C₃×#64990	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64990	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64978	C₂	1	1	yes	maximal, characteristic
15	C₃×#64968	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611690	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×#4092	C₄	1	1	yes	characteristic
19	C₃×#4090	C₄	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	1	yes	characteristic
21	C₂×C₃×#676	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4043	C₄	1	1	yes	characteristic
25	C₃×#4042	C₄	1	1	yes	characteristic
26	C₃×#4042	C₄	1	1	yes	characteristic
27	C₃×#4035	C₄	1	1	yes	characteristic
28	C₃×#4035	C₄	1	1	yes	characteristic
29	C₃×#4034	C₄	1	1	yes	characteristic
30	C₃×#4018	C₂²	1	1	yes	characteristic
31	C₃×#4018	C₂²	1	1	yes	characteristic
32	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
33	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₃×C₅×#97	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3947	C₂²	1	1	yes	characteristic
43	C₃×#3947	C₂²	1	1	yes	characteristic
44	C₃×#3947	C₂²	1	1	yes	characteristic
45	C₃×#3947	C₂²	1	1	yes	characteristic
46	C₃×#3946	C₂²	1	1	yes	characteristic
47	C₃×#3946	C₂²	1	1	yes	characteristic
48	C₃×#3946	C₂²	1	1	yes	characteristic
49	C₃×#3946	C₂²	1	1	yes	characteristic
50	C₃×#3946	C₂²	1	1	yes	characteristic
51	C₃×#3946	C₂²	1	1	yes	characteristic
52	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
53	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
54	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
55	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
56	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
57	C₃×#3935	C₂²	1	1	yes	characteristic
58	C₃×#3935	C₂²	1	1	yes	characteristic
59	C₃×C₄×#168	C₂²	1	1	yes	characteristic
60	C₃×#2961	—	5	1	no	maximal, Hall
61	#65912	C₂×C₃	1	1	yes	characteristic
62	C₅×#446	C₂×C₃	1	1	yes	characteristic, complemented
63	#65313	C₂×C₃	1	1	yes	characteristic, complemented
64	#65128	C₂×C₃	1	1	yes	characteristic
65	#65128	C₂×C₃	1	1	yes	characteristic
66	#65126	C₂×C₃	1	1	yes	characteristic
67	#65120	C₂×C₃	1	1	yes	characteristic, complemented
68	#65117	C₂×C₃	1	1	yes	characteristic, complemented
69	#65117	C₂×C₃	1	1	yes	characteristic, complemented
70	#64997	C₂×C₃	1	1	yes	characteristic
71	D₅×#97	C₂×C₃	1	1	yes	characteristic
72	#64990	C₂×C₃	1	1	yes	characteristic, complemented
73	#64990	C₂×C₃	1	1	yes	characteristic, complemented
74	#64978	C₂×C₃	1	1	yes	characteristic
75	#64968	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×#685	C₂×C₄	1	1	yes	characteristic
94	C₃×#685	C₂×C₄	1	1	yes	characteristic
95	C₃×#685	C₂×C₄	1	1	yes	characteristic
96	C₃×#685	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₃×#683	C₂×C₄	1	1	yes	characteristic
101	C₃×#683	C₂×C₄	1	1	yes	characteristic
102	C₃×#683	C₂×C₄	1	1	yes	characteristic
103	C₃×#683	C₂×C₄	1	1	yes	characteristic
104	C₃×#683	C₂×C₄	1	1	yes	characteristic
105	C₃×#683	C₂×C₄	1	1	yes	characteristic
106	C₃×#683	C₂×C₄	1	1	yes	characteristic
107	C₃×#683	C₂×C₄	1	1	yes	characteristic
108	C₃×#683	C₂×C₄	1	1	yes	characteristic
109	C₃×#683	C₂×C₄	1	1	yes	characteristic
110	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
112	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
113	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
114	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
115	C₂×C₃×#168	C₂³	1	1	yes	characteristic
116	C₂×C₃×#168	C₂³	1	1	yes	characteristic
117	C₂×C₃×#168	C₂³	1	1	yes	characteristic
118	C₂×C₃×#168	C₂³	1	1	yes	characteristic
119	C₃×#676	—	2	2	no	—
120	C₃×#676	—	2	2	no	—
121	C₃×C₈×D₅	—	2	2	no	—
122	C₃×C₈×D₅	Q₈	1	4	yes	complemented
123	C₃×#533	—	5	1	no	—
124	C₃×#446	—	5	1	no	—
125	C₃×#446	—	5	1	no	—
126	C₃×#446	—	5	1	no	—
127	C₃×#446	—	5	1	no	—
128	C₃×#446	—	5	1	no	—
129	C₃×#446	—	5	1	no	—
130	C₃×#446	—	5	1	no	—
131	C₃×#446	D₅	1	1	yes	characteristic, complemented
132	C₃×#424	—	5	1	no	—
133	C₃×#424	—	5	1	no	—
134	C₃×#423	—	5	1	no	—
135	C₃×#405	—	5	1	no	—
136	C₃×#405	—	5	1	no	—
137	C₂×C₃×#97	—	5	1	no	—
138	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
139	#4092	C₃×C₄	1	1	yes	characteristic
140	#4090	C₃×C₄	1	1	yes	characteristic
141	C₂×#676	C₂²×C₃	1	1	yes	characteristic
142	C₂×#676	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
145	#4043	C₃×C₄	1	1	yes	characteristic
146	#4042	C₃×C₄	1	1	yes	characteristic
147	#4042	C₃×C₄	1	1	yes	characteristic
148	#4035	C₃×C₄	1	1	yes	characteristic
149	#4035	C₃×C₄	1	1	yes	characteristic
150	#4034	C₃×C₄	1	1	yes	characteristic
151	#4018	C₂²×C₃	1	1	yes	characteristic
152	#4018	C₂²×C₃	1	1	yes	characteristic
153	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
154	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
155	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
156	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
157	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	C₅×#97	C₂²×C₃	1	1	yes	characteristic
161	C₅×#97	C₂²×C₃	1	1	yes	characteristic
162	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
163	#3947	C₂²×C₃	1	1	yes	characteristic
164	#3947	C₂²×C₃	1	1	yes	characteristic
165	#3947	C₂²×C₃	1	1	yes	characteristic
166	#3947	C₂²×C₃	1	1	yes	characteristic
167	#3946	C₂²×C₃	1	1	yes	characteristic
168	#3946	C₂²×C₃	1	1	yes	characteristic
169	#3946	C₂²×C₃	1	1	yes	characteristic
170	#3946	C₂²×C₃	1	1	yes	characteristic
171	#3946	C₂²×C₃	1	1	yes	characteristic
172	#3946	C₂²×C₃	1	1	yes	characteristic
173	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
174	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
175	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
176	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
177	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
178	#3935	C₂²×C₃	1	1	yes	characteristic
179	#3935	C₂²×C₃	1	1	yes	characteristic
180	C₄×#168	C₂²×C₃	1	1	yes	characteristic
181	#2961	—	5	1	no	Sylow
182	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
183	C₃×C₅×Q₈	—	4	1	no	—
184	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
191	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₄×D₅	—	4	1	no	—
199	C₃×C₄×D₅	—	4	1	no	—
200	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
201	C₃×C₄×D₅	#41	1	2	yes	—
202	C₃×Dic₁₀	—	4	1	no	—
203	C₃×Dic₁₀	—	4	1	no	—
204	C₃×Dic₁₀	—	4	1	no	—
205	C₃×C₅×C₈	—	2	1	no	—
206	C₃×C₅×C₈	—	2	1	no	—
207	C₃×C₅×C₈	—	2	1	no	—
208	C₃×C₅×C₈	C₂×Q₈	1	2	yes	—
209	C₃×#168	—	2	1	no	—
210	C₃×#168	—	2	1	no	—
211	C₃×#168	—	2	1	no	—
212	C₃×#168	C₂×Q₈	1	2	yes	—
213	C₂×C₃×M₁₆	—	5	1	no	—
214	C₂×C₃×M₁₆	—	5	1	no	—
215	C₂²×C₃×C₈	—	5	1	no	—
216	C₂²×C₃×C₈	—	5	1	no	—
217	C₃×C₄⋊Q₈	—	5	1	no	—
218	C₃×C₄⋊Q₈	—	5	1	no	—
219	C₃×#125	—	5	1	no	—
220	C₃×#125	—	5	1	no	—
221	C₃×C₂²⋊Q₈	—	5	1	no	—
222	C₃×C₂²⋊Q₈	—	5	1	no	—
223	C₃×C₂²⋊Q₈	—	5	1	no	—
224	C₃×C₂²⋊Q₈	—	5	1	no	—
225	C₃×C₄×Q₈	—	5	1	no	—
226	C₃×C₄×Q₈	—	5	1	no	—
227	C₃×C₄×Q₈	—	5	1	no	—
228	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
229	C₃×#117	—	5	1	no	—
230	C₃×#117	—	5	1	no	—
231	C₂×C₃×C₄²	—	5	1	no	—
232	C₃×C₄⋊C₈	—	5	1	no	—
233	C₃×C₄⋊C₈	—	5	1	no	—
234	C₃×C₄⋊C₈	—	5	1	no	—
235	C₃×C₄⋊C₈	—	5	1	no	—
236	C₃×C₄⋊C₈	—	5	1	no	—
237	C₃×C₄⋊C₈	—	5	1	no	—
238	C₃×C₄⋊C₈	—	5	1	no	—
239	C₃×C₄⋊C₈	—	5	1	no	—
240	C₃×C₄⋊C₈	—	5	1	no	—
241	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
242	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
243	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
244	C₃×#97	—	5	1	no	—
245	C₃×#97	—	5	1	no	—
246	C₃×#97	—	5	1	no	—
247	C₃×#97	—	5	1	no	—
248	C₃×#97	—	5	1	no	—
249	C₃×#97	—	5	1	no	—
250	C₃×#97	C₂×D₅	1	1	yes	characteristic
251	C₃×#97	C₂×D₅	1	1	yes	characteristic
252	C₃×C₄×C₈	—	5	1	no	—
253	C₃×C₄×C₈	—	5	1	no	—
254	C₃×C₄×C₈	—	5	1	no	—
255	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
256	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
257	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
258	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
259	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
260	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
261	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
262	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
263	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
267	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
268	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
269	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
270	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
271	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
273	#685	C₂×C₃×C₄	1	1	yes	characteristic
274	#685	C₂×C₃×C₄	1	1	yes	characteristic
275	#685	C₂×C₃×C₄	1	1	yes	characteristic
276	#685	C₂×C₃×C₄	1	1	yes	characteristic
277	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
278	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
279	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
280	#683	C₂×C₃×C₄	1	1	yes	characteristic
281	#683	C₂×C₃×C₄	1	1	yes	characteristic
282	#683	C₂×C₃×C₄	1	1	yes	characteristic
283	#683	C₂×C₃×C₄	1	1	yes	characteristic
284	#683	C₂×C₃×C₄	1	1	yes	characteristic
285	#683	C₂×C₃×C₄	1	1	yes	characteristic
286	#683	C₂×C₃×C₄	1	1	yes	characteristic
287	#683	C₂×C₃×C₄	1	1	yes	characteristic
288	#683	C₂×C₃×C₄	1	1	yes	characteristic
289	#683	C₂×C₃×C₄	1	1	yes	characteristic
290	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
291	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
292	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
293	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
294	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
295	C₂×#168	C₂³×C₃	1	1	yes	characteristic
296	C₂×#168	C₂³×C₃	1	1	yes	characteristic
297	C₂×#168	C₂³×C₃	1	1	yes	characteristic
298	C₂×#168	C₂³×C₃	1	1	yes	characteristic
299	#676	—	2	2	no	—
300	#676	—	2	2	no	—
301	C₈×D₅	—	2	2	no	—
302	C₈×D₅	C₃×Q₈	1	4	yes	complemented
303	#533	—	5	1	no	—
304	#446	—	5	1	no	—
305	#446	—	5	1	no	—
306	#446	—	5	1	no	—
307	#446	—	5	1	no	—
308	#446	—	5	1	no	—
309	#446	—	5	1	no	—
310	#446	—	5	1	no	—
311	#446	C₃×D₅	1	1	yes	characteristic, complemented
312	#424	—	5	1	no	—
313	#424	—	5	1	no	—
314	#423	—	5	1	no	—
315	#405	—	5	1	no	—
316	#405	—	5	1	no	—
317	C₂×#97	—	5	1	no	—
318	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
319	C₂×C₃×D₅	—	2	1	no	—
320	C₂×C₃×D₅	—	2	1	no	—
321	C₂×C₃×D₅	C₄×Q₈	1	2	yes	—
322	C₃×C₄×C₅	—	2	1	no	—
323	C₃×C₄×C₅	—	2	1	no	—
324	C₃×C₄×C₅	—	2	1	no	—
325	C₃×C₄×C₅	—	2	1	no	—
326	C₃×C₄×C₅	—	2	1	no	—
327	C₃×C₄×C₅	—	2	1	no	—
328	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
329	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₃×Dic₅	—	2	1	no	—
331	C₃×Dic₅	—	2	1	no	—
332	C₃×Dic₅	—	2	1	no	—
333	C₃×Dic₅	—	2	1	no	—
334	C₃×Dic₅	—	2	1	no	—
335	C₃×Dic₅	—	2	1	no	—
336	C₃×Dic₅	C₄×Q₈	1	2	yes	—
337	C₂×C₃×Q₈	—	5	1	no	—
338	C₂×C₃×Q₈	—	5	1	no	—
339	C₂×C₃×Q₈	—	5	1	no	—
340	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
341	C₂²×C₃×C₄	—	5	1	no	—
342	C₂²×C₃×C₄	—	5	1	no	—
343	C₂²×C₃×C₄	—	5	1	no	—
344	C₃×M₁₆	—	10	2	no	—
345	C₃×M₁₆	—	10	2	no	—
346	C₂×C₃×C₈	—	5	1	no	—
347	C₂×C₃×C₈	—	5	4	no	—
348	C₂×C₃×C₈	—	5	1	no	—
349	C₂×C₃×C₈	—	5	1	no	—
350	C₂×C₃×C₈	—	5	1	no	—
351	C₂×C₃×C₈	—	10	2	no	—
352	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
353	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
354	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
355	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
356	C₃×C₄⋊C₄	—	5	1	no	—
357	C₃×C₄⋊C₄	—	5	1	no	—
358	C₃×C₄⋊C₄	—	5	1	no	—
359	C₃×C₄⋊C₄	—	5	1	no	—
360	C₃×C₄⋊C₄	—	5	1	no	—
361	C₃×C₄⋊C₄	—	5	1	no	—
362	C₃×C₄⋊C₄	—	5	1	no	—
363	C₃×C₄⋊C₄	—	5	1	no	—
364	C₃×C₄⋊C₄	—	5	1	no	—
365	C₃×C₄⋊C₄	—	5	1	no	—
366	C₃×C₄⋊C₄	—	5	1	no	—
367	C₃×C₄⋊C₄	—	5	1	no	—
368	C₃×C₄⋊C₄	—	5	1	no	—
369	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
370	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
371	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
372	C₃×C₂²⋊C₄	—	5	1	no	—
373	C₃×C₂²⋊C₄	—	5	1	no	—
374	C₃×C₂²⋊C₄	—	5	1	no	—
375	C₃×C₂²⋊C₄	—	5	1	no	—
376	C₃×C₄²	—	5	1	no	—
377	C₃×C₄²	—	5	1	no	—
378	C₃×C₄²	—	5	1	no	—
379	C₃×C₄²	—	5	1	no	—
380	C₃×C₄²	—	5	1	no	—
381	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
382	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
383	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
384	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
385	C₅×Q₈	—	4	1	no	—
386	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
389	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
390	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
391	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
392	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
393	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
394	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
395	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
396	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
397	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
398	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
399	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
400	C₄×D₅	—	4	1	no	—
401	C₄×D₅	—	4	1	no	—
402	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
403	C₄×D₅	C₃×#41	1	2	yes	—
404	Dic₁₀	—	4	1	no	—
405	Dic₁₀	—	4	1	no	—
406	Dic₁₀	—	4	1	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	2	1	no	—
409	C₅×C₈	—	2	1	no	—
410	C₅×C₈	C₂×C₃×Q₈	1	2	yes	—
411	#168	—	2	1	no	—
412	#168	—	2	1	no	—
413	#168	—	2	1	no	—
414	#168	C₂×C₃×Q₈	1	2	yes	—
415	C₂×M₁₆	—	5	1	no	—
416	C₂×M₁₆	—	5	1	no	—
417	C₂²×C₈	—	5	1	no	—
418	C₂²×C₈	—	5	1	no	—
419	C₄⋊Q₈	—	5	1	no	—
420	C₄⋊Q₈	—	5	1	no	—
421	#125	—	5	1	no	—
422	#125	—	5	1	no	—
423	C₂²⋊Q₈	—	5	1	no	—
424	C₂²⋊Q₈	—	5	1	no	—
425	C₂²⋊Q₈	—	5	1	no	—
426	C₂²⋊Q₈	—	5	1	no	—
427	C₄×Q₈	—	5	1	no	—
428	C₄×Q₈	—	5	1	no	—
429	C₄×Q₈	—	5	1	no	—
430	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
431	#117	—	5	1	no	—
432	#117	—	5	1	no	—
433	C₂×C₄²	—	5	1	no	—
434	C₄⋊C₈	—	5	1	no	—
435	C₄⋊C₈	—	5	1	no	—
436	C₄⋊C₈	—	5	1	no	—
437	C₄⋊C₈	—	5	1	no	—
438	C₄⋊C₈	—	5	1	no	—
439	C₄⋊C₈	—	5	1	no	—
440	C₄⋊C₈	—	5	1	no	—
441	C₄⋊C₈	—	5	1	no	—
442	C₄⋊C₈	—	5	1	no	—
443	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
444	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
445	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
446	#97	—	5	1	no	—
447	#97	—	5	1	no	—
448	#97	—	5	1	no	—
449	#97	—	5	1	no	—
450	#97	—	5	1	no	—
451	#97	—	5	1	no	—
452	#97	C₂×C₃×D₅	1	1	yes	characteristic
453	#97	C₂×C₃×D₅	1	1	yes	characteristic
454	C₄×C₈	—	5	1	no	—
455	C₄×C₈	—	5	1	no	—
456	C₄×C₈	—	5	1	no	—
457	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
458	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
459	C₂×C₃×C₅	#568	1	1	yes	characteristic
460	C₂×C₃×C₅	#568	1	1	yes	characteristic
461	C₃×D₅	—	2	2	no	—
462	C₂³×C₃	—	5	1	no	—
463	C₃×Q₈	—	4	1	no	—
464	C₃×Q₈	—	20	1	no	—
465	C₃×Q₈	—	20	1	no	—
466	C₃×Q₈	—	20	1	no	—
467	C₂×C₃×C₄	—	5	1	no	—
468	C₂×C₃×C₄	—	5	2	no	—
469	C₂×C₃×C₄	—	5	2	no	—
470	C₂×C₃×C₄	—	5	1	no	—
471	C₂×C₃×C₄	—	5	1	no	—
472	C₂×C₃×C₄	—	5	1	no	—
473	C₂×C₃×C₄	—	5	1	no	—
474	C₂×C₃×C₄	—	5	1	no	—
475	C₂×C₃×C₄	—	5	1	no	—
476	C₂×C₃×C₄	—	20	1	no	—
477	C₂×C₃×C₄	—	20	1	no	—
478	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
485	C₃×C₈	—	2	1	no	—
486	C₃×C₈	—	2	1	no	—
487	C₃×C₈	—	2	1	no	—
488	C₃×C₈	—	5	2	no	—
489	C₃×C₈	—	10	1	no	—
490	C₃×C₈	—	10	1	no	—
491	C₃×C₈	—	10	1	no	—
492	C₃×C₈	Q₈×D₅	1	2	yes	—
493	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
494	C₂×D₅	—	2	1	no	—
495	C₂×D₅	—	2	1	no	—
496	C₂×D₅	C₃×C₄×Q₈	1	2	yes	—
497	C₄×C₅	—	2	1	no	—
498	C₄×C₅	—	2	1	no	—
499	C₄×C₅	—	2	1	no	—
500	C₄×C₅	—	2	1	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
504	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
505	Dic₅	—	2	1	no	—
506	Dic₅	—	2	1	no	—
507	Dic₅	—	2	1	no	—
508	Dic₅	—	2	1	no	—
509	Dic₅	—	2	1	no	—
510	Dic₅	—	2	1	no	—
511	Dic₅	C₃×C₄×Q₈	1	2	yes	—
512	C₂×Q₈	—	5	1	no	—
513	C₂×Q₈	—	5	1	no	—
514	C₂×Q₈	—	5	1	no	—
515	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
516	C₂²×C₄	—	5	1	no	—
517	C₂²×C₄	—	5	1	no	—
518	C₂²×C₄	—	5	1	no	—
519	M₁₆	—	10	2	no	—
520	M₁₆	—	10	2	no	—
521	C₂×C₈	—	5	1	no	—
522	C₂×C₈	—	5	4	no	—
523	C₂×C₈	—	5	1	no	—
524	C₂×C₈	—	5	1	no	—
525	C₂×C₈	—	5	1	no	—
526	C₂×C₈	—	10	2	no	—
527	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
528	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
529	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
530	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
531	C₄⋊C₄	—	5	1	no	—
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	5	1	no	—
537	C₄⋊C₄	—	5	1	no	—
538	C₄⋊C₄	—	5	1	no	—
539	C₄⋊C₄	—	5	1	no	—
540	C₄⋊C₄	—	5	1	no	—
541	C₄⋊C₄	—	5	1	no	—
542	C₄⋊C₄	—	5	1	no	—
543	C₄⋊C₄	—	5	1	no	—
544	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
545	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
546	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	5	1	no	—
549	C₂²⋊C₄	—	5	1	no	—
550	C₂²⋊C₄	—	5	1	no	—
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	1	no	—
555	C₄²	—	5	1	no	—
556	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
557	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
558	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
559	C₃×C₅	#2961	1	1	yes	characteristic, complemented, Hall
560	C₂²×C₃	—	5	2	no	—
561	C₂²×C₃	—	10	1	no	—
562	C₂²×C₃	—	10	1	no	—
563	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	2	1	no	—
569	C₃×C₄	—	2	1	no	—
570	C₃×C₄	—	5	2	no	—
571	C₃×C₄	—	10	1	no	—
572	C₃×C₄	—	10	1	no	—
573	C₃×C₄	—	10	1	no	—
574	C₃×C₄	—	10	1	no	—
575	C₃×C₄	—	10	1	no	—
576	C₃×C₄	—	10	1	no	—
577	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
578	C₃×C₄	D₅×#41	1	1	yes	characteristic
579	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
580	C₂×C₅	C₃×#568	1	1	yes	characteristic
581	C₂×C₅	C₃×#568	1	1	yes	characteristic
582	D₅	—	2	2	no	—
583	C₂³	—	5	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	20	1	no	—
586	Q₈	—	20	1	no	—
587	Q₈	—	20	1	no	—
588	C₂×C₄	—	5	1	no	—
589	C₂×C₄	—	5	2	no	—
590	C₂×C₄	—	5	2	no	—
591	C₂×C₄	—	5	1	no	—
592	C₂×C₄	—	5	1	no	—
593	C₂×C₄	—	5	1	no	—
594	C₂×C₄	—	5	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	5	1	no	—
597	C₂×C₄	—	20	1	no	—
598	C₂×C₄	—	20	1	no	—
599	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
600	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
601	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
602	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
603	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
604	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
605	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
606	C₈	—	2	1	no	—
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	5	2	no	—
610	C₈	—	10	1	no	—
611	C₈	—	10	1	no	—
612	C₈	—	10	1	no	—
613	C₈	C₃×Q₈×D₅	1	2	yes	—
614	C₂×C₃	—	10	2	no	—
615	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
616	C₂×C₃	#66079	1	1	yes	characteristic
617	C₂×C₃	#66084	1	1	yes	characteristic
618	C₅	C₃×#2961	1	1	yes	characteristic, complemented, Sylow
619	C₂²	—	5	2	no	—
620	C₂²	—	10	1	no	—
621	C₂²	—	10	1	no	—
622	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	5	2	no	—
630	C₄	—	10	1	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	1	no	—
633	C₄	—	10	1	no	—
634	C₄	—	10	1	no	—
635	C₄	—	10	1	no	—
636	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
637	C₄	C₃×D₅×#41	1	1	yes	characteristic
638	C₃	#10611690	1	1	yes	characteristic, direct product factor, Sylow
639	C₂	—	10	2	no	—
640	C₂	C₃×C₄×Q₈×D₅	1	1	yes	characteristic
641	C₂	C₃×#66079	1	1	yes	characteristic
642	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#446	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#446	D₅
hypocenter	C₅	C₃×#2961
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. C₃×#65313	C₂	semidirect
7. C₃×#65120	C₂	semidirect
8. C₃×#65117	C₂	semidirect
9. C₃×#65117	C₂	semidirect
12. C₃×#64990	C₂	semidirect
13. C₃×#64990	C₂	semidirect
15. C₃×#64968	C₂	semidirect
16. #10611690	C₃	direct (N × H)
62. C₅×#446	C₂×C₃	semidirect
63. #65313	C₂×C₃	semidirect
67. #65120	C₂×C₃	semidirect
68. #65117	C₂×C₃	semidirect
69. #65117	C₂×C₃	semidirect
72. #64990	C₂×C₃	semidirect
73. #64990	C₂×C₃	semidirect
75. #64968	C₂×C₃	semidirect
122. C₃×C₈×D₅	Q₈	semidirect
131. C₃×#446	D₅	semidirect
302. C₈×D₅	C₃×Q₈	semidirect
311. #446	C₃×D₅	semidirect
559. C₃×C₅	#2961	semidirect
618. C₅	C₃×#2961	semidirect
638. C₃	#10611690	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#65912	2
C₃×C₅×#446	2
C₃×#65313	2
C₃×#65128	2
C₃×#65126	2
C₃×#65120	2
C₃×#65117	2
C₃×#64997	2
C₃×D₅×#97	2
C₃×#64990	2
C₃×#64978	2
C₃×#64968	2
#10611690	3
C₃×#2961	5

Subgroups — C3×#10611690 #14418566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611690 #14418566