Subgroups — D₃×#65124 #14413793

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₃×D₅	C₂	1	1	yes	maximal, characteristic
2	#11750936	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65124	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#3952	C₂	1	2	yes	maximal
6	#11747600	C₂	1	2	yes	maximal, complemented
7	D₃×#3947	C₂	1	2	yes	maximal, complemented
8	#11747588	C₂	1	2	yes	maximal, complemented
9	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746871	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746867	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#65124	—	3	1	no	maximal, Hall
13	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃×D₅	C₄	1	1	yes	characteristic
15	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
16	C₄²×D₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
20	C₄×#1200	C₄	1	1	yes	characteristic
21	C₄×#1200	C₄	1	1	yes	characteristic
22	C₄×#1200	C₂²	1	1	yes	characteristic
23	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
24	C₄×D₃×Dic₅	C₄	1	1	yes	characteristic
25	C₄×D₃×Dic₅	C₂²	1	1	yes	characteristic
26	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
27	C₄×D₅×Dic₃	C₄	1	1	yes	characteristic
28	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×D₃×#168	C₂²	1	2	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	#91104	C₂²	1	2	yes	—
32	#91099	C₂²	1	2	yes	complemented
33	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
34	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
35	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3952	C₂²	1	2	yes	—
37	C₃×#3947	C₂²	1	2	yes	complemented
38	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
39	Dic₃⋊#168	C₂²	1	2	yes	complemented
40	#90957	C₂²	1	2	yes	—
41	#90955	C₂²	1	2	yes	—
42	#90954	C₂²	1	2	yes	complemented
43	#90952	C₂²	1	2	yes	complemented
44	D₃×#432	—	5	1	no	maximal, Hall
45	C₂×C₄²×D₅	—	3	1	no	—
46	C₂×C₅×C₄⋊C₈	—	3	1	no	—
47	C₂×#3952	—	3	2	no	—
48	C₂×#3947	—	3	2	no	—
49	C₂×C₄⋊#168	—	3	1	no	—
50	#65124	—	3	1	no	—
51	#65124	—	3	1	no	—
52	#65124	—	3	2	no	—
53	#65124	—	3	2	no	—
54	#65124	—	3	1	no	—
55	#65124	D₃	1	1	yes	characteristic, direct product factor
56	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
66	C₂×#1200	C₂×C₄	1	1	yes	characteristic
67	C₂×#1200	C₂×C₄	1	1	yes	characteristic
68	C₂×#1200	C₂×C₄	1	1	yes	characteristic
69	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
75	C₄×D₃×D₅	—	2	4	no	—
76	C₄×D₃×D₅	—	2	4	no	—
77	C₄×D₃×D₅	—	2	2	no	—
78	C₄×D₃×D₅	—	2	2	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
84	C₂×C₃⋊#168	C₂³	1	2	yes	—
85	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
89	C₅×D₃×C₈	—	2	4	no	—
90	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×#168	C₂³	1	2	yes	—
94	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
95	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
96	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
97	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
98	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
99	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
100	D₃×#168	—	2	4	no	—
101	C₂×C₄²×D₃	—	5	1	no	—
102	C₃×#432	—	5	1	no	—
103	#4926	—	5	1	no	—
104	#4835	—	5	1	no	—
105	#4835	—	5	1	no	—
106	D₃×C₄⋊C₈	—	5	1	no	—
107	D₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
108	D₃×C₂²⋊C₈	—	5	2	no	—
109	#4719	—	5	2	no	—
110	#4705	—	5	2	no	—
111	D₃×#97	—	5	2	no	—
112	C₂²×C₄×D₅	—	3	1	no	—
113	C₂²×C₄×D₅	—	3	1	no	—
114	C₂²×C₄×D₅	—	3	1	no	—
115	C₂²×C₅×C₈	—	3	2	no	—
116	C₂×C₄²×C₅	—	3	1	no	—
117	C₂×C₄×Dic₅	—	3	1	no	—
118	C₂×C₄×Dic₅	—	3	1	no	—
119	C₂×C₄×Dic₅	—	3	1	no	—
120	C₂²×#168	—	3	2	no	—
121	C₄²×D₅	—	3	1	no	—
122	C₄²×D₅	—	3	1	no	—
123	C₄²×D₅	—	3	1	no	—
124	C₄²×D₅	—	3	1	no	—
125	C₄²×D₅	—	3	1	no	—
126	C₄²×D₅	—	3	1	no	—
127	C₄²×D₅	—	3	1	no	—
128	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
129	C₅×C₄⋊C₈	—	3	2	no	—
130	C₅×C₄⋊C₈	—	3	1	no	—
131	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
132	#3952	—	3	2	no	—
133	#3952	—	3	2	no	—
134	#3952	—	3	2	no	—
135	#3952	C₂×D₃	1	2	yes	—
136	#3947	—	3	2	no	—
137	#3947	—	3	2	no	—
138	#3947	—	3	2	no	—
139	#3947	C₂×D₃	1	2	yes	complemented
140	C₄⋊#168	—	3	1	no	—
141	C₄⋊#168	—	3	2	no	—
142	C₄⋊#168	C₂×D₃	1	1	yes	characteristic, complemented
143	C₂×#432	—	15	1	no	Sylow
144	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₃×D₅	—	2	2	no	—
148	C₂×D₃×D₅	—	2	2	no	—
149	C₂×D₃×D₅	M₁₆	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
156	C₄×D₁₅	—	2	2	no	—
157	C₄×D₁₅	—	2	2	no	—
158	C₄×D₁₅	—	2	1	no	—
159	C₄×D₁₅	—	2	1	no	—
160	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
163	C₄×C₅×D₃	—	2	2	no	—
164	C₄×C₅×D₃	M₁₆	1	4	yes	—
165	C₄×C₅×D₃	#41	1	2	yes	—
166	C₄×C₅×D₃	#41	1	2	yes	—
167	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₄×D₅	—	2	2	no	—
171	C₃×C₄×D₅	—	2	2	no	—
172	C₃×C₄×D₅	—	2	1	no	—
173	C₃×C₄×D₅	—	2	1	no	—
174	#1200	—	2	2	no	—
175	#1200	—	2	2	no	—
176	#1200	—	2	2	no	—
177	D₃×Dic₅	—	2	2	no	—
178	D₃×Dic₅	—	2	2	no	—
179	D₃×Dic₅	—	2	2	no	—
180	D₅×Dic₃	—	2	2	no	—
181	D₅×Dic₃	—	2	2	no	—
182	D₅×Dic₃	—	2	2	no	—
183	C₃×C₅×C₈	—	2	2	no	—
184	C₃⋊#168	—	2	2	no	—
185	C₃×#168	—	2	2	no	—
186	C₅×C₃⋊C₈	—	2	2	no	—
187	C₂²×C₄×D₃	—	5	1	no	—
188	C₂²×C₄×D₃	—	5	1	no	—
189	C₂²×C₄×D₃	—	5	1	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₂×C₄×Dic₃	—	5	1	no	—
192	C₂×C₄×Dic₃	—	5	1	no	—
193	C₂×C₄×Dic₃	—	5	1	no	—
194	C₂×D₃×C₈	—	5	2	no	—
195	C₂×D₃×C₈	C₂×D₅	1	2	yes	—
196	C₄²×D₃	—	5	1	no	—
197	C₄²×D₃	—	5	1	no	—
198	C₄²×D₃	—	5	1	no	—
199	C₄²×D₃	—	5	1	no	—
200	C₄²×D₃	—	5	1	no	—
201	C₄²×D₃	—	5	1	no	—
202	C₄²×D₃	—	5	1	no	—
203	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
204	C₃×C₄⋊C₈	—	5	1	no	—
205	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
206	C₃×C₂²⋊C₈	—	5	2	no	—
207	C₃×#97	—	5	2	no	—
208	#830	—	5	2	no	—
209	(C₂×D₃)⋊C₈	—	5	2	no	—
210	(C₂×D₃)⋊C₈	—	5	2	no	—
211	#815	—	5	2	no	—
212	#815	—	5	2	no	—
213	Dic₃⋊C₈	—	5	2	no	—
214	Dic₃⋊C₈	C₂×D₅	1	2	yes	complemented
215	C₄⋊(C₃⋊C₈)	—	5	1	no	—
216	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
217	#803	—	5	2	no	—
218	C₂³×D₅	—	3	1	no	—
219	C₂²×C₄×C₅	—	3	1	no	—
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂²×C₄×C₅	—	3	1	no	—
222	C₂²×Dic₅	—	3	1	no	—
223	C₂²×Dic₅	—	3	1	no	—
224	C₂²×Dic₅	—	3	1	no	—
225	C₂×C₄×D₅	—	3	1	no	—
226	C₂×C₄×D₅	—	3	1	no	—
227	C₂×C₄×D₅	—	3	1	no	—
228	C₂×C₄×D₅	—	3	1	no	—
229	C₂×C₄×D₅	—	3	1	no	—
230	C₂×C₄×D₅	—	3	1	no	—
231	C₂×C₄×D₅	—	3	1	no	—
232	C₂×C₄×D₅	—	3	1	no	—
233	C₂×C₄×D₅	—	3	1	no	—
234	C₂×C₄×D₅	—	6	4	no	—
235	C₂×C₄×D₅	—	6	2	no	—
236	C₂×C₄×D₅	—	6	2	no	—
237	C₂×C₄×D₅	—	6	4	no	—
238	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
239	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₅×C₈	—	3	2	no	—
242	C₂×C₅×C₈	—	6	4	no	—
243	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
244	C₄²×C₅	—	3	1	no	—
245	C₄²×C₅	—	3	1	no	—
246	C₄²×C₅	—	3	1	no	—
247	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
248	C₄×Dic₅	—	3	1	no	—
249	C₄×Dic₅	—	3	1	no	—
250	C₄×Dic₅	—	3	1	no	—
251	C₄×Dic₅	—	3	1	no	—
252	C₄×Dic₅	—	3	1	no	—
253	C₄×Dic₅	—	3	1	no	—
254	C₄×Dic₅	—	3	1	no	—
255	C₄×Dic₅	—	3	1	no	—
256	C₄×Dic₅	—	3	1	no	—
257	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
258	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
259	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
260	C₂×#168	—	3	2	no	—
261	C₂×#168	—	6	4	no	—
262	C₂×#168	C₂²×D₃	1	2	yes	—
263	C₂²×C₄²	—	15	1	no	—
264	#432	—	5	1	no	—
265	#432	—	15	2	no	—
266	#432	—	15	2	no	—
267	#432	—	15	1	no	—
268	#432	—	15	1	no	—
269	#432	—	15	1	no	—
270	C₂×C₄⋊C₈	—	3	1	no	—
271	C₂×C₄⋊C₈	—	15	1	no	—
272	C₂×C₂²⋊C₈	—	15	2	no	—
273	C₂×#97	—	15	2	no	—
274	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
275	C₂×D₁₅	—	2	1	no	—
276	C₂×D₁₅	—	2	1	no	—
277	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
278	C₂×C₅×D₃	#117	1	2	yes	—
279	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
280	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
281	C₂×C₃×D₅	—	2	1	no	—
282	C₂×C₃×D₅	—	2	1	no	—
283	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
284	D₃×D₅	—	2	8	no	—
285	C₃×C₄×C₅	—	2	1	no	—
286	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
287	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
289	Dic₁₅	—	2	1	no	—
290	Dic₁₅	—	2	1	no	—
291	Dic₁₅	—	2	1	no	—
292	C₃×Dic₅	—	2	1	no	—
293	C₃×Dic₅	—	2	1	no	—
294	C₃×Dic₅	—	2	1	no	—
295	C₅×Dic₃	—	2	1	no	—
296	C₅×Dic₃	#117	1	2	yes	—
297	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
298	C₂³×D₃	—	5	1	no	—
299	C₂²×C₃×C₄	—	5	1	no	—
300	C₂²×C₃×C₄	—	5	1	no	—
301	C₂²×C₃×C₄	—	5	1	no	—
302	C₂²×Dic₃	—	5	1	no	—
303	C₂²×Dic₃	—	5	1	no	—
304	C₂²×Dic₃	—	5	1	no	—
305	C₂×C₄×D₃	—	5	1	no	—
306	C₂×C₄×D₃	—	5	1	no	—
307	C₂×C₄×D₃	—	5	1	no	—
308	C₂×C₄×D₃	—	5	1	no	—
309	C₂×C₄×D₃	—	5	1	no	—
310	C₂×C₄×D₃	—	5	1	no	—
311	C₂×C₄×D₃	—	5	1	no	—
312	C₂×C₄×D₃	—	5	1	no	—
313	C₂×C₄×D₃	—	5	1	no	—
314	C₂×C₄×D₃	—	10	4	no	—
315	C₂×C₄×D₃	—	10	4	no	—
316	C₂×C₄×D₃	—	10	2	no	—
317	C₂×C₄×D₃	—	10	2	no	—
318	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
319	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
320	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
321	C₂×C₃×C₈	—	5	2	no	—
322	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
323	C₃×C₄²	—	5	1	no	—
324	C₃×C₄²	—	5	1	no	—
325	C₃×C₄²	—	5	1	no	—
326	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
327	C₄×Dic₃	—	5	1	no	—
328	C₄×Dic₃	—	5	1	no	—
329	C₄×Dic₃	—	5	1	no	—
330	C₄×Dic₃	—	5	1	no	—
331	C₄×Dic₃	—	5	1	no	—
332	C₄×Dic₃	—	5	1	no	—
333	C₄×Dic₃	—	5	1	no	—
334	C₄×Dic₃	—	5	1	no	—
335	C₄×Dic₃	—	5	1	no	—
336	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
337	C₄×Dic₃	C₄×D₅	1	1	yes	characteristic
338	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
339	C₂×C₃⋊C₈	—	5	2	no	—
340	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
341	D₃×C₈	—	2	4	no	—
342	D₃×C₈	—	10	4	no	—
343	C₂³×C₅	—	3	1	no	—
344	C₂²×D₅	—	3	1	no	—
345	C₂²×D₅	—	3	4	no	—
346	C₂²×D₅	—	6	2	no	—
347	C₂²×D₅	—	6	2	no	—
348	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄×C₅	—	3	1	no	—
350	C₂×C₄×C₅	—	3	1	no	—
351	C₂×C₄×C₅	—	3	4	no	—
352	C₂×C₄×C₅	—	3	2	no	—
353	C₂×C₄×C₅	—	3	2	no	—
354	C₂×C₄×C₅	—	3	1	no	—
355	C₂×C₄×C₅	—	6	2	no	—
356	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
359	C₂×Dic₅	—	3	1	no	—
360	C₂×Dic₅	—	3	1	no	—
361	C₂×Dic₅	—	3	1	no	—
362	C₂×Dic₅	—	6	2	no	—
363	C₂×Dic₅	—	6	2	no	—
364	C₂×Dic₅	—	6	2	no	—
365	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
366	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
367	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
368	C₄×D₅	—	2	2	no	—
369	C₄×D₅	—	2	2	no	—
370	C₄×D₅	—	2	1	no	—
371	C₄×D₅	—	2	1	no	—
372	C₄×D₅	—	6	2	no	—
373	C₄×D₅	—	6	2	no	—
374	C₄×D₅	—	6	2	no	—
375	C₄×D₅	—	6	2	no	—
376	C₄×D₅	—	6	2	no	—
377	C₄×D₅	—	6	2	no	—
378	C₄×D₅	—	6	2	no	—
379	C₄×D₅	—	6	2	no	—
380	C₄×D₅	—	6	1	no	—
381	C₄×D₅	—	6	1	no	—
382	C₅×C₈	—	2	2	no	—
383	C₅×C₈	—	6	2	no	—
384	#168	—	2	2	no	—
385	#168	—	6	2	no	—
386	C₂³×C₄	—	15	1	no	—
387	C₂³×C₄	—	15	1	no	—
388	C₂³×C₄	—	15	1	no	—
389	C₂²×C₈	—	3	2	no	—
390	C₂²×C₈	—	15	2	no	—
391	C₂×C₄²	—	3	1	no	—
392	C₂×C₄²	—	5	1	no	—
393	C₂×C₄²	—	15	1	no	—
394	C₂×C₄²	—	15	1	no	—
395	C₂×C₄²	—	15	1	no	—
396	C₂×C₄²	—	15	1	no	—
397	C₂×C₄²	—	15	1	no	—
398	C₂×C₄²	—	15	1	no	—
399	C₂×C₄²	—	15	1	no	—
400	C₂×C₄²	—	15	1	no	—
401	C₂×C₄²	—	15	1	no	—
402	C₂×C₄²	—	15	1	no	—
403	C₄⋊C₈	—	3	2	no	—
404	C₄⋊C₈	—	3	1	no	—
405	C₄⋊C₈	—	5	1	no	—
406	C₄⋊C₈	—	15	2	no	—
407	C₄⋊C₈	—	15	1	no	—
408	C₄⋊C₈	D₃×D₅	1	1	yes	characteristic, complemented
409	C₂²⋊C₈	—	5	2	no	—
410	C₂²⋊C₈	—	15	2	no	—
411	C₂²⋊C₈	—	15	2	no	—
412	C₂²⋊C₈	—	15	2	no	—
413	#97	—	5	2	no	—
414	#97	—	15	2	no	—
415	#97	—	15	2	no	—
416	#97	—	15	2	no	—
417	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
418	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
419	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
420	D₁₅	—	2	2	no	—
421	C₃×D₅	—	2	2	no	—
422	C₅×D₃	#432	1	4	yes	complemented
423	C₂³×C₃	—	5	1	no	—
424	C₂²×D₃	—	5	1	no	—
425	C₂²×D₃	—	5	4	no	—
426	C₂²×D₃	—	10	2	no	—
427	C₂²×D₃	—	10	2	no	—
428	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
429	C₂×C₃×C₄	—	5	1	no	—
430	C₂×C₃×C₄	—	5	1	no	—
431	C₂×C₃×C₄	—	5	1	no	—
432	C₂×C₃×C₄	—	10	2	no	—
433	C₂×C₃×C₄	—	10	1	no	—
434	C₂×C₃×C₄	—	10	1	no	—
435	C₂×C₃×C₄	—	10	2	no	—
436	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
439	C₂×Dic₃	—	5	1	no	—
440	C₂×Dic₃	—	5	1	no	—
441	C₂×Dic₃	—	5	1	no	—
442	C₂×Dic₃	—	10	2	no	—
443	C₂×Dic₃	—	10	2	no	—
444	C₂×Dic₃	—	10	2	no	—
445	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
446	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
447	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
448	C₄×D₃	—	2	2	no	—
449	C₄×D₃	—	10	2	no	—
450	C₄×D₃	—	10	2	no	—
451	C₄×D₃	—	10	2	no	—
452	C₄×D₃	—	10	2	no	—
453	C₄×D₃	—	10	2	no	—
454	C₄×D₃	—	10	1	no	—
455	C₄×D₃	—	10	1	no	—
456	C₄×D₃	—	10	2	no	—
457	C₄×D₃	—	10	2	no	—
458	C₄×D₃	—	10	2	no	—
459	C₄×D₃	#676	1	4	yes	—
460	C₄×D₃	#711	1	2	yes	—
461	C₄×D₃	#713	1	2	yes	—
462	C₃×C₈	—	2	2	no	—
463	C₃×C₈	—	10	2	no	—
464	C₃⋊C₈	—	2	2	no	—
465	C₃⋊C₈	—	10	2	no	—
466	C₂²×C₅	—	3	2	no	—
467	C₂²×C₅	—	3	2	no	—
468	C₂²×C₅	—	3	2	no	—
469	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
470	C₂×D₅	—	2	1	no	—
471	C₂×D₅	—	2	1	no	—
472	C₂×D₅	—	3	2	no	—
473	C₂×D₅	—	6	8	no	—
474	C₂×D₅	—	6	1	no	—
475	C₂×D₅	—	6	1	no	—
476	C₂×D₅	D₃×M₁₆	1	2	yes	—
477	C₄×C₅	—	2	1	no	—
478	C₄×C₅	—	3	2	no	—
479	C₄×C₅	—	3	2	no	—
480	C₄×C₅	—	6	1	no	—
481	C₄×C₅	D₃×M₁₆	1	2	yes	—
482	C₄×C₅	D₃×#41	1	1	yes	characteristic
483	C₄×C₅	D₃×#41	1	1	yes	characteristic
484	Dic₅	—	2	1	no	—
485	Dic₅	—	2	1	no	—
486	Dic₅	—	2	1	no	—
487	Dic₅	—	6	1	no	—
488	Dic₅	—	6	1	no	—
489	Dic₅	—	6	1	no	—
490	C₂⁴	—	15	1	no	—
491	C₂²×C₄	—	3	1	no	—
492	C₂²×C₄	—	3	1	no	—
493	C₂²×C₄	—	3	1	no	—
494	C₂²×C₄	—	5	1	no	—
495	C₂²×C₄	—	5	1	no	—
496	C₂²×C₄	—	5	1	no	—
497	C₂²×C₄	—	15	1	no	—
498	C₂²×C₄	—	15	1	no	—
499	C₂²×C₄	—	15	1	no	—
500	C₂²×C₄	—	15	1	no	—
501	C₂²×C₄	—	15	1	no	—
502	C₂²×C₄	—	15	1	no	—
503	C₂²×C₄	—	15	1	no	—
504	C₂²×C₄	—	15	1	no	—
505	C₂²×C₄	—	15	1	no	—
506	C₂²×C₄	—	15	1	no	—
507	C₂²×C₄	—	15	1	no	—
508	C₂²×C₄	—	15	1	no	—
509	C₂²×C₄	—	30	4	no	—
510	C₂²×C₄	—	30	2	no	—
511	C₂²×C₄	—	30	2	no	—
512	C₂²×C₄	—	30	4	no	—
513	C₂×C₈	—	3	2	no	—
514	C₂×C₈	—	5	2	no	—
515	C₂×C₈	—	6	4	no	—
516	C₂×C₈	—	15	2	no	—
517	C₂×C₈	—	30	4	no	—
518	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
519	C₄²	—	3	1	no	—
520	C₄²	—	3	1	no	—
521	C₄²	—	3	1	no	—
522	C₄²	—	5	1	no	—
523	C₄²	—	5	1	no	—
524	C₄²	—	5	1	no	—
525	C₄²	—	15	1	no	—
526	C₄²	—	15	1	no	—
527	C₄²	—	15	1	no	—
528	C₄²	—	15	1	no	—
529	C₄²	—	15	1	no	—
530	C₄²	—	15	1	no	—
531	C₄²	—	15	1	no	—
532	C₄²	—	15	1	no	—
533	C₄²	—	15	1	no	—
534	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
535	C₃×C₅	C₂×#432	1	1	yes	characteristic, complemented, Hall
536	C₂²×C₃	—	5	2	no	—
537	C₂²×C₃	—	10	1	no	—
538	C₂²×C₃	—	10	1	no	—
539	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
540	C₂×D₃	—	5	2	no	—
541	C₂×D₃	—	10	1	no	—
542	C₂×D₃	—	10	1	no	—
543	C₂×D₃	—	10	8	no	—
544	C₂×D₃	#4038	1	2	yes	—
545	C₂×D₃	C₂×#676	1	2	yes	—
546	C₂×D₃	D₅×M₁₆	1	2	yes	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	10	1	no	—
549	C₃×C₄	—	10	1	no	—
550	C₃×C₄	—	10	1	no	—
551	C₃×C₄	C₂×#676	1	2	yes	—
552	C₃×C₄	C₂×#711	1	1	yes	characteristic
553	C₃×C₄	C₂×#713	1	1	yes	characteristic
554	Dic₃	—	2	1	no	—
555	Dic₃	—	10	1	no	—
556	Dic₃	—	10	1	no	—
557	Dic₃	—	10	1	no	—
558	Dic₃	#4038	1	2	yes	—
559	Dic₃	C₂×#676	1	2	yes	—
560	C₂×C₅	—	3	4	no	—
561	C₂×C₅	D₃×#117	1	1	yes	characteristic
562	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
563	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
564	D₅	—	2	2	no	—
565	D₅	—	6	2	no	—
566	C₂³	—	3	1	no	—
567	C₂³	—	5	1	no	—
568	C₂³	—	15	4	no	—
569	C₂³	—	15	1	no	—
570	C₂³	—	30	2	no	—
571	C₂³	—	30	2	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	3	1	no	—
574	C₂×C₄	—	3	4	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	3	2	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	5	1	no	—
579	C₂×C₄	—	5	1	no	—
580	C₂×C₄	—	5	1	no	—
581	C₂×C₄	—	6	2	no	—
582	C₂×C₄	—	10	2	no	—
583	C₂×C₄	—	10	2	no	—
584	C₂×C₄	—	10	1	no	—
585	C₂×C₄	—	10	1	no	—
586	C₂×C₄	—	15	1	no	—
587	C₂×C₄	—	15	1	no	—
588	C₂×C₄	—	15	1	no	—
589	C₂×C₄	—	30	2	no	—
590	C₂×C₄	—	30	2	no	—
591	C₂×C₄	—	30	2	no	—
592	C₂×C₄	—	30	2	no	—
593	C₂×C₄	—	30	2	no	—
594	C₂×C₄	—	30	2	no	—
595	C₂×C₄	—	30	2	no	—
596	C₂×C₄	—	30	2	no	—
597	C₂×C₄	—	30	2	no	—
598	C₂×C₄	—	30	2	no	—
599	C₂×C₄	—	30	2	no	—
600	C₂×C₄	—	30	1	no	—
601	C₂×C₄	—	30	1	no	—
602	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
603	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	6	2	no	—
607	C₈	—	10	2	no	—
608	C₈	—	30	2	no	—
609	C₂×C₃	—	10	2	no	—
610	C₂×C₃	C₂×#4038	1	1	yes	characteristic
611	C₂×C₃	C₂²×#676	1	1	yes	characteristic
612	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
613	D₃	—	10	2	no	—
614	D₃	#65124	1	4	yes	direct product factor
615	C₅	D₃×#432	1	1	yes	characteristic, complemented, Sylow
616	C₂²	—	3	2	no	—
617	C₂²	—	3	2	no	—
618	C₂²	—	3	2	no	—
619	C₂²	—	5	2	no	—
620	C₂²	—	10	1	no	—
621	C₂²	—	10	1	no	—
622	C₂²	—	15	2	no	—
623	C₂²	—	30	8	no	—
624	C₂²	—	30	1	no	—
625	C₂²	—	30	1	no	—
626	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
627	C₄	—	2	1	no	—
628	C₄	—	3	2	no	—
629	C₄	—	3	2	no	—
630	C₄	—	6	1	no	—
631	C₄	—	10	1	no	—
632	C₄	—	10	1	no	—
633	C₄	—	10	1	no	—
634	C₄	—	30	1	no	—
635	C₄	—	30	1	no	—
636	C₄	—	30	1	no	—
637	C₄	D₃×#676	1	2	yes	—
638	C₄	D₃×#711	1	1	yes	characteristic
639	C₄	D₃×#713	1	1	yes	characteristic
640	C₃	C₂×#65124	1	1	yes	characteristic, complemented, Sylow
641	C₂	—	3	4	no	—
642	C₂	—	10	2	no	—
643	C₂	—	30	2	no	—
644	C₂	D₃×#4038	1	1	yes	characteristic
645	C₂	C₂×D₃×#676	1	1	yes	characteristic
646	C₂	D₃×D₅×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×C₄⋊C₈	C₂²
prime radical	C₂²×D₃×D₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄⋊C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#432
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11750936	C₂	semidirect
3. C₅×D₃×C₄⋊C₈	C₂	semidirect
4. C₃×#65124	C₂	semidirect
6. #11747600	C₂	semidirect
7. D₃×#3947	C₂	semidirect
8. #11747588	C₂	semidirect
9. D₃×C₄⋊#168	C₂	semidirect
10. #11746871	C₂	semidirect
11. #11746867	C₂	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
32. #91099	C₂²	semidirect
33. C₄⋊(C₃⋊#168)	C₂²	semidirect
34. C₅×Dic₃⋊C₈	C₂²	semidirect
35. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
37. C₃×#3947	C₂²	semidirect
38. C₃×C₄⋊#168	C₂²	semidirect
39. Dic₃⋊#168	C₂²	semidirect
42. #90954	C₂²	semidirect
43. #90952	C₂²	semidirect
55. #65124	D₃	direct (N × H)
107. D₃×C₄⋊C₈	D₅	semidirect
131. C₅×C₄⋊C₈	C₂×D₃	semidirect
139. #3947	C₂×D₃	semidirect
142. C₄⋊#168	C₂×D₃	semidirect
205. C₃×C₄⋊C₈	C₂×D₅	semidirect
214. Dic₃⋊C₈	C₂×D₅	semidirect
216. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
408. C₄⋊C₈	D₃×D₅	semidirect
422. C₅×D₃	#432	semidirect
535. C₃×C₅	C₂×#432	semidirect
614. D₃	#65124	direct (N × H)
615. C₅	D₃×#432	semidirect
640. C₃	C₂×#65124	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₃×D₅	2
#11750936	2
C₅×D₃×C₄⋊C₈	2
C₃×#65124	2
D₃×#3952	2
#11747600	2
D₃×#3947	2
#11747588	2
D₃×C₄⋊#168	2
#11746871	2
#11746867	2
C₂×#65124	3
D₃×#432	5

Subgroups — D3×#65124 #14413793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65124 #14413793