Subgroups — C₃×#10600701 #14297421

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3946	C₂	1	2	yes	maximal, complemented
5	C₃×#64770	C₂	1	2	yes	maximal, complemented
6	#10600701	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×Dic₅	C₄	1	1	yes	characteristic
9	C₂³×C₃×Dic₅	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₃×C₄×Dic₅	—	2	4	no	—
12	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
13	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	2	yes	—
17	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
18	C₃×C₂²⋊#168	—	2	2	no	—
19	C₃×#3946	—	2	4	no	—
20	C₃×#1797	—	5	1	no	maximal, Hall
21	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
22	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic
24	C₂×#3946	C₂×C₃	1	2	yes	complemented
25	#64770	C₂×C₃	1	2	yes	complemented
26	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	—	2	2	no	—
34	C₂²×C₃×Dic₅	—	2	2	no	—
35	C₂²×C₃×Dic₅	—	2	2	no	—
36	C₂²×C₃×Dic₅	—	2	2	no	—
37	C₂²×C₃×Dic₅	—	2	2	no	—
38	C₂²×C₃×Dic₅	C₈	1	4	yes	complemented
39	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₃×C₄×Dic₅	—	2	2	no	—
47	C₃×C₄×Dic₅	—	2	2	no	—
48	C₃×C₄×Dic₅	—	2	2	no	—
49	C₃×C₄×Dic₅	D₄	1	4	yes	—
50	C₂×C₃×#168	—	2	2	no	—
51	C₂×C₃×#168	—	2	2	no	—
52	C₂×C₃×#168	—	2	2	no	—
53	C₂²×C₃×C₄²	—	5	1	no	—
54	C₂×C₃×C₄⋊C₈	—	5	2	no	—
55	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
56	C₂×C₃×C₂²⋊C₈	D₅	1	1	yes	characteristic
57	C₃×#336	—	5	2	no	—
58	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₂³×Dic₅	C₃×C₄	1	1	yes	characteristic
60	C₂³×Dic₅	C₃×C₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
62	C₂×C₄×Dic₅	—	2	4	no	—
63	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
67	C₂²×#168	C₂²×C₃	1	2	yes	—
68	C₅×C₂²⋊C₈	—	2	2	no	—
69	C₂²⋊#168	—	2	2	no	—
70	#3946	—	2	4	no	—
71	#1797	—	5	1	no	Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂×C₈	1	2	yes	—
78	C₂³×C₃×C₅	M₁₆	1	2	yes	—
79	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	#41	1	2	yes	—
89	C₂×C₃×Dic₅	—	2	8	no	—
90	C₂×C₃×Dic₅	—	2	1	no	—
91	C₂×C₃×Dic₅	—	2	1	no	—
92	C₂×C₃×Dic₅	—	2	1	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	2	1	no	—
95	C₂×C₃×Dic₅	—	2	1	no	—
96	C₂×C₃×Dic₅	—	2	8	no	—
97	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
98	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
100	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
101	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
102	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
103	C₃×C₅×C₈	—	4	2	no	—
104	C₃×#168	—	4	2	no	—
105	C₂³×C₃×C₄	—	5	1	no	—
106	C₂³×C₃×C₄	—	5	1	no	—
107	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
108	C₂²×C₃×C₈	—	5	2	no	—
109	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
110	C₂×C₃×C₄²	—	5	1	no	—
111	C₂×C₃×C₄²	—	5	1	no	—
112	C₂×C₃×C₄²	—	5	1	no	—
113	C₂×C₃×C₄²	—	5	1	no	—
114	C₂×C₃×C₄²	—	10	4	no	—
115	C₃×C₄⋊C₈	—	10	4	no	—
116	C₃×C₂²⋊C₈	—	2	2	no	—
117	C₃×C₂²⋊C₈	—	10	2	no	—
118	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
123	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂²×Dic₅	—	2	2	no	—
126	C₂²×Dic₅	—	2	2	no	—
127	C₂²×Dic₅	—	2	2	no	—
128	C₂²×Dic₅	—	2	2	no	—
129	C₂²×Dic₅	—	2	2	no	—
130	C₂²×Dic₅	C₃×C₈	1	4	yes	complemented
131	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₄×Dic₅	—	2	2	no	—
139	C₄×Dic₅	—	2	2	no	—
140	C₄×Dic₅	—	2	2	no	—
141	C₄×Dic₅	C₃×D₄	1	4	yes	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	—	2	2	no	—
144	C₂×#168	—	2	2	no	—
145	C₂²×C₄²	—	5	1	no	—
146	C₂×C₄⋊C₈	—	5	2	no	—
147	C₂×C₂²⋊C₈	—	5	1	no	—
148	C₂×C₂²⋊C₈	C₃×D₅	1	1	yes	characteristic
149	#336	—	5	2	no	—
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	C₄⋊C₈	1	4	yes	complemented
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	#117	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
162	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	#121	1	2	yes	—
166	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
167	C₃×Dic₅	—	2	2	no	—
168	C₃×Dic₅	—	2	2	no	—
169	C₃×Dic₅	—	2	2	no	—
170	C₃×Dic₅	C₂²⋊C₈	1	4	yes	complemented
171	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	2	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	—	5	1	no	—
175	C₂²×C₃×C₄	—	5	4	no	—
176	C₂²×C₃×C₄	—	5	1	no	—
177	C₂²×C₃×C₄	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₂²×C₃×C₄	—	10	2	no	—
181	C₂²×C₃×C₄	—	10	2	no	—
182	C₂²×C₃×C₄	—	10	2	no	—
183	C₂²×C₃×C₄	—	10	2	no	—
184	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
185	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
187	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
188	C₂×C₃×C₈	—	2	2	no	—
189	C₂×C₃×C₈	—	2	2	no	—
190	C₂×C₃×C₈	—	2	2	no	—
191	C₂×C₃×C₈	—	10	2	no	—
192	C₂×C₃×C₈	—	10	2	no	—
193	C₂×C₃×C₈	—	10	2	no	—
194	C₃×C₄²	—	5	4	no	—
195	C₃×C₄²	—	10	2	no	—
196	C₃×C₄²	—	10	2	no	—
197	C₃×C₄²	—	10	2	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	C₃×C₄⋊C₄	1	2	yes	—
203	C₂³×C₅	C₂×C₃×C₈	1	2	yes	—
204	C₂³×C₅	C₃×M₁₆	1	2	yes	—
205	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₅	C₃×#41	1	2	yes	—
215	C₂×Dic₅	—	2	8	no	—
216	C₂×Dic₅	—	2	1	no	—
217	C₂×Dic₅	—	2	1	no	—
218	C₂×Dic₅	—	2	1	no	—
219	C₂×Dic₅	—	2	1	no	—
220	C₂×Dic₅	—	2	1	no	—
221	C₂×Dic₅	—	2	1	no	—
222	C₂×Dic₅	—	2	8	no	—
223	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
224	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
225	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
226	C₂×Dic₅	C₂×C₃×C₈	1	2	yes	—
227	C₂×Dic₅	C₃×M₁₆	1	2	yes	—
228	C₂×Dic₅	C₃×M₁₆	1	2	yes	—
229	C₅×C₈	—	4	2	no	—
230	#168	—	4	2	no	—
231	C₂³×C₄	—	5	1	no	—
232	C₂³×C₄	—	5	1	no	—
233	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
234	C₂²×C₈	—	5	2	no	—
235	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	—	5	1	no	—
240	C₂×C₄²	—	10	4	no	—
241	C₄⋊C₈	—	10	4	no	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	10	2	no	—
244	C₂×C₃×C₅	—	2	4	no	—
245	C₂×C₃×C₅	#380	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
247	C₂×C₃×C₅	#407	1	1	yes	characteristic
248	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
249	C₂×C₃×C₅	#423	1	1	yes	characteristic
250	C₂×C₃×C₅	#431	1	1	yes	characteristic
251	C₂×C₃×C₅	#432	1	1	yes	characteristic
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	2	1	no	—
255	C₂³×C₃	—	2	1	no	—
256	C₂³×C₃	C₈×D₅	1	2	yes	—
257	C₂³×C₃	#676	1	2	yes	—
258	C₂³×C₃	#683	1	2	yes	—
259	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	5	2	no	—
265	C₂×C₃×C₄	—	5	2	no	—
266	C₂×C₃×C₄	—	5	2	no	—
267	C₂×C₃×C₄	—	5	2	no	—
268	C₂×C₃×C₄	—	5	2	no	—
269	C₂×C₃×C₄	—	5	2	no	—
270	C₂×C₃×C₄	—	10	8	no	—
271	C₂×C₃×C₄	—	10	8	no	—
272	C₂×C₃×C₄	—	10	1	no	—
273	C₂×C₃×C₄	—	10	1	no	—
274	C₂×C₃×C₄	—	10	1	no	—
275	C₂×C₃×C₄	—	10	1	no	—
276	C₂×C₃×C₄	—	10	1	no	—
277	C₂×C₃×C₄	—	10	1	no	—
278	C₂×C₃×C₄	#683	1	2	yes	—
279	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
280	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
281	C₂×C₃×C₄	#711	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
283	C₃×C₈	—	4	2	no	—
284	C₃×C₈	—	20	2	no	—
285	C₂²×C₅	—	2	2	no	—
286	C₂²×C₅	—	2	2	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	C₃×C₄⋊C₈	1	4	yes	complemented
292	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
294	C₂²×C₅	C₃×#117	1	1	yes	characteristic
295	C₂²×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
296	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
297	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
298	C₂²×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	C₃×#121	1	2	yes	—
301	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
302	Dic₅	—	2	2	no	—
303	Dic₅	—	2	2	no	—
304	Dic₅	—	2	2	no	—
305	Dic₅	C₃×C₂²⋊C₈	1	4	yes	complemented
306	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	4	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	10	2	no	—
315	C₂²×C₄	—	10	2	no	—
316	C₂²×C₄	—	10	2	no	—
317	C₂²×C₄	—	10	2	no	—
318	C₂²×C₄	—	10	2	no	—
319	C₂²×C₄	C₃×Dic₁₀	1	2	yes	—
320	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
321	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
322	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	10	2	no	—
327	C₂×C₈	—	10	2	no	—
328	C₂×C₈	—	10	2	no	—
329	C₄²	—	5	4	no	—
330	C₄²	—	10	2	no	—
331	C₄²	—	10	2	no	—
332	C₄²	—	10	2	no	—
333	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	#3946	1	4	yes	complemented
341	C₂²×C₃	#4023	1	1	yes	characteristic
342	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
344	C₂²×C₃	C₂×#676	1	1	yes	characteristic
345	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
346	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
347	C₂²×C₃	C₂×#683	1	1	yes	characteristic
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	5	4	no	—
350	C₃×C₄	—	10	2	no	—
351	C₃×C₄	—	10	2	no	—
352	C₃×C₄	—	10	2	no	—
353	C₃×C₄	#4024	1	2	yes	—
354	C₃×C₄	#4085	1	2	yes	—
355	C₂×C₅	—	2	4	no	—
356	C₂×C₅	C₃×#380	1	1	yes	characteristic
357	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
358	C₂×C₅	C₃×#407	1	1	yes	characteristic
359	C₂×C₅	C₂×C₃×C₄⋊C₈	1	1	yes	characteristic
360	C₂×C₅	C₃×#423	1	1	yes	characteristic
361	C₂×C₅	C₃×#431	1	1	yes	characteristic
362	C₂×C₅	C₃×#432	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	C₃×C₈×D₅	1	2	yes	—
368	C₂³	C₃×#676	1	2	yes	—
369	C₂³	C₃×#683	1	2	yes	—
370	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	5	2	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	10	8	no	—
382	C₂×C₄	—	10	8	no	—
383	C₂×C₄	—	10	1	no	—
384	C₂×C₄	—	10	1	no	—
385	C₂×C₄	—	10	1	no	—
386	C₂×C₄	—	10	1	no	—
387	C₂×C₄	—	10	1	no	—
388	C₂×C₄	—	10	1	no	—
389	C₂×C₄	C₃×#683	1	2	yes	—
390	C₂×C₄	C₂×C₃×Dic₁₀	1	1	yes	characteristic
391	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
392	C₂×C₄	C₃×#711	1	2	yes	—
393	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	20	2	no	—
396	C₂×C₃	—	2	4	no	—
397	C₂×C₃	#65007	1	1	yes	characteristic
398	C₂×C₃	#65008	1	1	yes	characteristic
399	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
400	C₂×C₃	#65015	1	1	yes	characteristic
401	C₂×C₃	#65231	1	1	yes	characteristic
402	C₂×C₃	C₂×#3946	1	1	yes	characteristic
403	C₂×C₃	#65407	1	1	yes	characteristic
404	C₅	C₃×#1797	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	C₃×#3946	1	4	yes	complemented
412	C₂²	C₃×#4023	1	1	yes	characteristic
413	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²	C₂×C₃×C₈×D₅	1	1	yes	characteristic
415	C₂²	C₂×C₃×#676	1	1	yes	characteristic
416	C₂²	C₃×D₅×M₁₆	1	1	yes	characteristic
417	C₂²	C₃×D₅×M₁₆	1	1	yes	characteristic
418	C₂²	C₂×C₃×#683	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	5	4	no	—
421	C₄	—	10	2	no	—
422	C₄	—	10	2	no	—
423	C₄	—	10	2	no	—
424	C₄	C₃×#4024	1	2	yes	—
425	C₄	C₃×#4085	1	2	yes	—
426	C₃	#10600701	1	1	yes	characteristic, direct product factor, Sylow
427	C₂	—	2	4	no	—
428	C₂	C₃×#65007	1	1	yes	characteristic
429	C₂	C₃×#65008	1	1	yes	characteristic
430	C₂	C₃×D₅×C₂²⋊C₈	1	1	yes	characteristic
431	C₂	C₃×#65015	1	1	yes	characteristic
432	C₂	C₃×#65231	1	1	yes	characteristic
433	C₂	C₂×C₃×#3946	1	1	yes	characteristic
434	C₂	C₃×#65407	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂²×C₃×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₂²⋊C₈	D₅
hypocenter	C₅	C₃×#1797
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×#3946	C₂	semidirect
5. C₃×#64770	C₂	semidirect
6. #10600701	C₃	direct (N × H)
24. C₂×#3946	C₂×C₃	semidirect
25. #64770	C₂×C₃	semidirect
38. C₂²×C₃×Dic₅	C₈	semidirect
130. C₂²×Dic₅	C₃×C₈	semidirect
156. C₂²×C₃×C₅	C₄⋊C₈	semidirect
170. C₃×Dic₅	C₂²⋊C₈	semidirect
291. C₂²×C₅	C₃×C₄⋊C₈	semidirect
305. Dic₅	C₃×C₂²⋊C₈	semidirect
333. C₃×C₅	#1797	semidirect
340. C₂²×C₃	#3946	semidirect
404. C₅	C₃×#1797	semidirect
411. C₂²	C₃×#3946	semidirect
426. C₃	#10600701	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×Dic₅	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₃×C₂²⋊#168	2
C₂×C₃×#3946	2
C₃×#64770	2
#10600701	3
C₃×#1797	5

Subgroups — C3×#10600701 #14297421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600701 #14297421