Subgroups — D₁₂×#681 #14415753

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₃×#681	C₂	1	2	yes	maximal, complemented
3	#11751025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748346	C₂	1	2	yes	maximal, complemented
6	#11747008	C₂	1	2	yes	maximal, complemented
7	#11746987	C₂	1	4	yes	maximal, complemented
8	D₁₂×#168	C₂	1	2	yes	maximal, complemented
9	D₄×#681	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	2	yes	—
14	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
15	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	C₄	1	2	yes	—
17	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
19	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₄×C₅×D₁₂	C₂²	1	2	yes	—
21	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₃×#681	C₂²	1	1	yes	characteristic
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₂×#6650	C₂²	1	4	yes	complemented
25	D₃×#681	—	2	8	no	—
26	C₂×D₃×#168	C₂²	1	4	yes	complemented
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
28	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
29	C₃×#3935	C₂²	1	2	yes	complemented
30	C₃×C₄×#168	C₂²	1	2	yes	complemented
31	(C₂×D₃)⋊#168	C₂²	1	4	yes	complemented
32	(C₂×D₃)⋊#168	C₂²	1	4	yes	complemented
33	M₁₆×D₁₂	—	5	1	no	maximal, Hall
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₂²×#681	—	3	2	no	—
36	#65496	—	3	2	no	—
37	#65301	—	3	2	no	—
38	#65300	—	3	4	no	—
39	D₄×#168	—	3	2	no	—
40	#65213	—	3	1	no	—
41	C₄×#681	D₃	1	1	yes	characteristic, complemented
42	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
47	C₂×C₅×D₁₂	—	2	4	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	—	2	4	no	—
52	C₂×C₄×C₅×D₃	—	2	4	no	—
53	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	#6710	—	2	4	no	—
62	C₂×C₃⋊#168	C₂³	1	4	yes	—
63	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
66	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
67	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
68	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₃×#681	—	2	2	no	—
71	C₃×#681	D₄	1	4	yes	complemented
72	C₂×C₃×#168	C₂³	1	2	yes	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	#6650	—	2	8	no	—
75	D₃×#168	—	2	8	no	—
76	C₂×D₃×M₁₆	—	5	2	no	—
77	C₂×C₄×D₁₂	D₅	1	1	yes	characteristic
78	C₃×C₄×M₁₆	—	5	1	no	—
79	#5126	—	5	2	no	—
80	#4924	—	5	1	no	—
81	#4706	—	5	4	no	—
82	#4688	—	5	2	no	—
83	C₈×D₁₂	—	5	2	no	—
84	C₂²×C₅×D₄	—	3	1	no	—
85	C₂³×C₄×C₅	—	3	2	no	—
86	C₄×C₅×D₄	—	3	1	no	—
87	C₄×C₅×D₄	—	3	2	no	—
88	C₄×C₅×D₄	—	3	1	no	—
89	C₄×C₅×D₄	—	3	1	no	—
90	C₄×C₅×D₄	—	3	2	no	—
91	C₄×C₅×D₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	—	3	1	no	—
93	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
94	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
95	C₂×#681	—	3	2	no	—
96	C₂×#681	—	3	4	no	—
97	C₂×#681	—	6	8	no	—
98	C₂×#681	C₂×D₃	1	1	yes	characteristic
99	C₂×#681	C₂×D₃	1	1	yes	characteristic
100	C₂²×#168	—	3	4	no	—
101	C₂²⋊#168	—	3	4	no	—
102	C₂²⋊#168	—	3	4	no	—
103	C₄⋊#168	—	3	2	no	—
104	C₄⋊#168	—	3	2	no	—
105	#3935	C₂×D₃	1	2	yes	complemented
106	C₄×#168	C₂×D₃	1	2	yes	complemented
107	D₄×M₁₆	—	15	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₅×D₃	—	2	4	no	—
110	C₂²×C₅×D₃	—	2	4	no	—
111	C₂²×C₅×D₃	—	4	2	no	—
112	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	4	1	no	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂×C₅×Dic₃	—	2	4	no	—
125	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
126	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
127	C₅×D₁₂	—	2	4	no	—
128	C₅×D₁₂	—	2	2	no	—
129	C₅×D₁₂	M₁₆	1	4	yes	complemented
130	C₄×C₅×D₃	—	2	4	no	—
131	C₄×C₅×D₃	—	2	4	no	—
132	C₄×C₅×D₃	—	2	2	no	—
133	C₄×C₅×D₃	—	2	2	no	—
134	C₄×C₅×D₃	—	2	2	no	—
135	C₄×C₅×D₃	—	2	2	no	—
136	C₃⋊#168	—	2	4	no	—
137	C₃×#168	—	2	2	no	—
138	C₃×#168	C₂×D₄	1	4	yes	complemented
139	C₂²×D₁₂	Dic₅	1	1	yes	characteristic
140	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
141	C₂×C₃×M₁₆	—	5	1	no	—
142	C₂×C₃×M₁₆	—	5	1	no	—
143	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
144	C₂×(C₂×D₃)⋊C₄	Dic₅	1	2	yes	—
145	C₂×C₄⋊Dic₃	Dic₅	1	1	yes	characteristic
146	C₂×#208	—	5	2	no	—
147	D₃×M₁₆	—	10	8	no	—
148	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
149	C₂×D₃×C₈	—	5	4	no	—
150	C₄×D₁₂	Dic₅	1	2	yes	—
151	C₄×D₁₂	Dic₅	1	1	yes	characteristic
152	C₄×D₁₂	Dic₅	1	1	yes	characteristic
153	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
154	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
155	C₄×D₁₂	C₂×D₅	1	2	yes	—
156	C₃×#97	—	5	2	no	—
157	C₃×C₄×C₈	—	5	2	no	—
158	(C₂×D₃)⋊C₈	—	5	4	no	—
159	(C₂×D₃)⋊C₈	—	5	4	no	—
160	C₄⋊(C₃⋊C₈)	—	5	2	no	—
161	C₄⋊(C₃⋊C₈)	—	5	2	no	—
162	C₂⁴×C₅	—	3	2	no	—
163	C₂×C₅×D₄	—	3	1	no	—
164	C₂×C₅×D₄	—	3	2	no	—
165	C₂×C₅×D₄	—	3	1	no	—
166	C₂×C₅×D₄	—	6	4	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	—	3	2	no	—
170	C₂²×C₄×C₅	—	3	2	no	—
171	C₂²×C₄×C₅	—	3	2	no	—
172	C₂²×C₄×C₅	—	6	4	no	—
173	C₂²×C₄×C₅	—	6	4	no	—
174	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₅×C₄⋊C₄	—	3	2	no	—
178	C₅×C₄⋊C₄	—	3	1	no	—
179	C₅×C₄⋊C₄	—	3	1	no	—
180	C₅×C₂²⋊C₄	—	3	2	no	—
181	C₅×C₂²⋊C₄	—	3	2	no	—
182	C₅×C₂²⋊C₄	—	3	2	no	—
183	C₅×C₂²⋊C₄	—	3	2	no	—
184	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
185	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
186	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
187	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
188	#681	—	2	2	no	—
189	#681	—	6	4	no	—
190	#681	—	6	8	no	—
191	#681	D₁₂	1	4	yes	direct product factor
192	C₂×#168	—	3	4	no	—
193	C₂×#168	—	6	8	no	—
194	C₂×#168	C₂²×D₃	1	2	yes	—
195	C₂×#168	C₂²×D₃	1	2	yes	—
196	C₂²×M₁₆	—	15	2	no	—
197	C₂×C₄×D₄	—	3	1	no	—
198	#436	—	15	2	no	—
199	#435	—	15	4	no	—
200	C₈×D₄	—	15	2	no	—
201	#423	—	15	1	no	—
202	#407	—	15	2	no	—
203	C₄×M₁₆	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₅×D₃	—	2	2	no	—
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	—	2	2	no	—
211	C₂×C₅×D₃	—	2	2	no	—
212	C₂×C₅×D₃	—	2	2	no	—
213	C₂×C₅×D₃	—	4	8	no	—
214	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
219	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
220	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₅×Dic₃	—	2	2	no	—
223	C₅×Dic₃	—	2	2	no	—
224	C₂³×D₃	C₂×Dic₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
228	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
229	C₂×D₁₂	—	2	4	no	—
230	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
231	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
232	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
233	C₂×C₄×D₃	—	2	4	no	—
234	C₂×C₄×D₃	—	2	4	no	—
235	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
236	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
237	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
238	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
239	C₃×M₁₆	—	5	4	no	—
240	C₃×M₁₆	—	10	2	no	—
241	C₂×C₃×C₈	—	5	2	no	—
242	C₂×C₃×C₈	—	5	2	no	—
243	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
244	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
245	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
246	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
247	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
249	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
251	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
252	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
253	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
254	#208	—	10	4	no	—
255	C₂×C₃⋊C₈	—	5	4	no	—
256	ΓL(1,𝔽₂₅)	—	10	8	no	—
257	D₃×C₈	—	10	8	no	—
258	C₂³×C₅	—	3	2	no	—
259	C₂³×C₅	—	3	2	no	—
260	C₂³×C₅	—	6	4	no	—
261	C₂³×C₅	—	6	4	no	—
262	C₂³×C₅	—	12	2	no	—
263	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₅×D₄	—	3	4	no	—
265	C₅×D₄	—	6	4	no	—
266	C₅×D₄	—	6	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	3	2	no	—
270	C₂×C₄×C₅	—	4	1	no	—
271	C₂×C₄×C₅	—	6	4	no	—
272	C₂×C₄×C₅	—	6	4	no	—
273	C₂×C₄×C₅	—	6	4	no	—
274	C₂×C₄×C₅	—	6	2	no	—
275	C₂×C₄×C₅	—	6	2	no	—
276	C₂×C₄×C₅	—	6	2	no	—
277	C₂×C₄×C₅	—	6	2	no	—
278	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
284	C₂×C₄×C₅	#235	1	2	yes	—
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	#168	—	2	2	no	—
287	#168	—	6	4	no	—
288	#168	C₂×D₁₂	1	4	yes	complemented
289	C₂²×D₄	—	3	1	no	—
290	C₂³×C₄	—	3	2	no	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	1	no	—
293	C₂×M₁₆	—	15	4	no	—
294	C₂×M₁₆	—	15	2	no	—
295	C₂×M₁₆	—	30	8	no	—
296	C₂²×C₈	—	15	4	no	—
297	C₄×D₄	—	3	1	no	—
298	C₄×D₄	—	3	2	no	—
299	C₄×D₄	—	3	1	no	—
300	C₄×D₄	—	3	1	no	—
301	C₄×D₄	—	3	2	no	—
302	C₄×D₄	—	3	1	no	—
303	C₂×C₄⋊C₄	—	3	1	no	—
304	C₂×C₂²⋊C₄	—	3	2	no	—
305	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
306	C₄⋊C₈	—	15	2	no	—
307	C₄⋊C₈	—	15	2	no	—
308	C₂²⋊C₈	—	15	4	no	—
309	C₂²⋊C₈	—	15	4	no	—
310	#97	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
315	C₂×C₃×C₅	#568	1	1	yes	characteristic
316	C₅×D₃	—	2	4	no	—
317	C₅×D₃	—	4	2	no	—
318	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
319	C₂²×D₃	—	2	4	no	—
320	C₂²×D₃	—	2	4	no	—
321	C₂²×D₃	—	4	2	no	—
322	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
323	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	4	1	no	—
326	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
327	C₂×C₃×C₄	#711	1	2	yes	—
328	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
334	C₂×Dic₃	—	2	4	no	—
335	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
336	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
337	D₁₂	—	2	4	no	—
338	D₁₂	—	2	2	no	—
339	D₁₂	#681	1	4	yes	direct product factor
340	C₄×D₃	—	2	2	no	—
341	C₄×D₃	—	2	2	no	—
342	C₄×D₃	—	2	2	no	—
343	C₄×D₃	—	2	2	no	—
344	C₄×D₃	—	2	4	no	—
345	C₄×D₃	—	2	4	no	—
346	C₃×C₈	—	5	4	no	—
347	C₃×C₈	—	10	2	no	—
348	C₃⋊C₈	—	10	4	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	3	4	no	—
352	C₂²×C₅	—	6	2	no	—
353	C₂²×C₅	—	6	2	no	—
354	C₂²×C₅	—	6	2	no	—
355	C₂²×C₅	—	6	2	no	—
356	C₂²×C₅	—	6	2	no	—
357	C₂²×C₅	—	12	8	no	—
358	C₂²×C₅	C₄×D₁₂	1	2	yes	—
359	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	1	no	—
362	C₄×C₅	—	2	1	no	—
363	C₄×C₅	—	6	2	no	—
364	C₄×C₅	—	6	2	no	—
365	C₄×C₅	C₄×D₁₂	1	2	yes	—
366	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
367	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
368	C₄×C₅	C₂×#235	1	1	yes	characteristic
369	C₂⁴	—	3	2	no	—
370	C₂×D₄	—	3	1	no	—
371	C₂×D₄	—	3	2	no	—
372	C₂×D₄	—	3	1	no	—
373	C₂×D₄	—	6	4	no	—
374	C₂²×C₄	—	3	2	no	—
375	C₂²×C₄	—	3	2	no	—
376	C₂²×C₄	—	3	2	no	—
377	C₂²×C₄	—	3	2	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	—	6	4	no	—
380	C₂²×C₄	—	6	4	no	—
381	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
382	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
384	M₁₆	—	5	4	no	—
385	M₁₆	—	10	2	no	—
386	M₁₆	—	30	8	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	15	4	no	—
391	C₂×C₈	—	30	8	no	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	1	no	—
394	C₄⋊C₄	—	3	1	no	—
395	C₂²⋊C₄	—	3	2	no	—
396	C₂²⋊C₄	—	3	2	no	—
397	C₂²⋊C₄	—	3	2	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₄²	D₃×Dic₅	1	1	yes	characteristic
400	C₄²	D₃×Dic₅	1	1	yes	characteristic
401	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
402	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	1	no	—
406	C₂²×C₃	D₄×Dic₅	1	2	yes	—
407	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	2	no	—
410	C₂×D₃	—	2	2	no	—
411	C₂×D₃	—	2	2	no	—
412	C₂×D₃	—	2	2	no	—
413	C₂×D₃	—	4	8	no	—
414	C₂×D₃	C₂×#681	1	4	yes	complemented
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	C₂×#681	1	2	yes	complemented
419	C₃×C₄	D₄×Dic₅	1	2	yes	—
420	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
421	C₃×C₄	C₂×#711	1	1	yes	characteristic
422	Dic₃	—	2	2	no	—
423	Dic₃	—	2	2	no	—
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	6	4	no	—
426	C₂×C₅	—	12	2	no	—
427	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
428	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
429	C₂×C₅	#5745	1	1	yes	characteristic
430	C₂³	—	3	2	no	—
431	C₂³	—	3	2	no	—
432	C₂³	—	6	4	no	—
433	C₂³	—	6	4	no	—
434	C₂³	—	12	2	no	—
435	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
436	D₄	—	3	4	no	—
437	D₄	—	6	4	no	—
438	D₄	—	6	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	3	2	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	6	4	no	—
444	C₂×C₄	—	6	4	no	—
445	C₂×C₄	—	6	4	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	#6772	1	2	yes	—
451	C₂×C₄	D₅×D₁₂	1	2	yes	—
452	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
453	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
454	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
455	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
456	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
458	C₈	—	5	4	no	—
459	C₈	—	10	2	no	—
460	C₈	—	30	4	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	C₂²×#681	1	1	yes	characteristic
463	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
464	C₂×C₃	#66153	1	1	yes	characteristic
465	D₃	—	2	4	no	—
466	D₃	—	4	2	no	—
467	C₅	M₁₆×D₁₂	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	3	4	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	6	2	no	—
474	C₂²	—	6	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	—	12	8	no	—
477	C₂²	Dic₅×D₁₂	1	2	yes	—
478	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	6	2	no	—
483	C₄	—	6	2	no	—
484	C₄	D₃×#681	1	2	yes	complemented
485	C₄	Dic₅×D₁₂	1	2	yes	—
486	C₄	C₂×#6772	1	1	yes	characteristic
487	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
488	C₃	D₄×#681	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	6	4	no	—
491	C₂	—	12	2	no	—
492	C₂	C₂×D₃×#681	1	1	yes	characteristic
493	C₂	#11754125	1	1	yes	characteristic
494	C₂	C₂×Dic₅×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₂²×C₅×D₁₂	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×D₃×#681	C₂	semidirect
3. #11751025	C₂	semidirect
4. C₃×C₄×#681	C₂	semidirect
5. #11748346	C₂	semidirect
6. #11747008	C₂	semidirect
7. #11746987	C₂	semidirect
8. D₁₂×#168	C₂	semidirect
24. C₂×#6650	C₂²	semidirect
26. C₂×D₃×#168	C₂²	semidirect
27. C₄⋊(C₃⋊#168)	C₂²	semidirect
28. C₄⋊(C₃⋊#168)	C₂²	semidirect
29. C₃×#3935	C₂²	semidirect
30. C₃×C₄×#168	C₂²	semidirect
31. (C₂×D₃)⋊#168	C₂²	semidirect
32. (C₂×D₃)⋊#168	C₂²	semidirect
41. C₄×#681	D₃	semidirect
71. C₃×#681	D₄	semidirect
105. #3935	C₂×D₃	semidirect
106. C₄×#168	C₂×D₃	semidirect
129. C₅×D₁₂	M₁₆	semidirect
138. C₃×#168	C₂×D₄	semidirect
191. #681	D₁₂	direct (N × H)
214. C₂×C₅×D₃	C₂×M₁₆	semidirect
219. C₃×C₄×C₅	C₂×M₁₆	semidirect
288. #168	C₂×D₁₂	semidirect
339. D₁₂	#681	direct (N × H)
366. C₄×C₅	D₃×M₁₆	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
414. C₂×D₃	C₂×#681	semidirect
418. C₃×C₄	C₂×#681	semidirect
467. C₅	M₁₆×D₁₂	semidirect
484. C₄	D₃×#681	semidirect
488. C₃	D₄×#681	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₁₂	2
C₂×D₃×#681	2
#11751025	2
C₃×C₄×#681	2
#11748346	2
#11747008	2
#11746987	2
D₁₂×#168	2
D₄×#681	3
M₁₆×D₁₂	5

Subgroups — D12×#681 #14415753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₂×#681 #14415753