Subgroups — D₁₂×#676 #14415720

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#676	C₂	1	2	yes	maximal, complemented
2	C₄×D₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	#11750789	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748101	C₂	1	2	yes	maximal, complemented
7	#11748048	C₂	1	2	yes	maximal, complemented
8	#11747719	C₂	1	2	yes	maximal, complemented
9	#11747009	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747007	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#676	—	3	1	no	maximal, Hall
13	C₂×D₅×D₁₂	C₄	1	1	yes	characteristic
14	C₂×C₄×D₃×D₅	C₂²	1	2	yes	—
15	C₂×#6705	C₂²	1	2	yes	complemented
16	C₄×D₆₀	C₂²	1	1	yes	characteristic
17	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₃×#676	C₂²	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	D₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
23	C₄×#1203	C₂²	1	2	yes	—
24	#91418	C₄	1	1	yes	characteristic
25	Dic₅×D₁₂	C₄	1	1	yes	characteristic
26	D₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic
27	#91405	C₄	1	2	yes	—
28	C₂×#6651	C₂²	1	2	yes	complemented
29	C₂×#6649	C₂²	1	2	yes	—
30	C₂×D₃×#168	C₂²	1	2	yes	complemented
31	D₃×#676	—	2	8	no	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
33	#91104	C₂²	1	2	yes	complemented
34	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic, complemented
35	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	complemented
36	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
40	#90982	C₂²	1	2	yes	complemented
41	#90957	C₂²	1	2	yes	complemented
42	(C₂×D₃)⋊#168	C₂²	1	2	yes	complemented
43	M₁₆×D₁₂	—	5	1	no	maximal, Hall
44	C₂²×#676	—	3	2	no	—
45	C₄×D₄×D₅	—	3	1	no	—
46	C₅×C₈×D₄	—	3	1	no	—
47	#65400	—	3	2	no	—
48	D₄×#168	—	3	1	no	—
49	#65127	—	3	1	no	—
50	#65126	—	3	1	no	—
51	#65019	—	3	2	no	—
52	#65015	—	3	2	no	—
53	#64977	—	3	1	no	—
54	C₄×#676	D₃	1	1	yes	characteristic, complemented
55	C₂²×D₃×D₅	C₂×C₄	1	2	yes	—
56	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×D₁₅	C₂³	1	2	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
60	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₂×#1203	C₂×C₄	1	2	yes	—
64	C₂×#1200	C₂×C₄	1	2	yes	—
65	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
66	C₂×D₅×Dic₃	C₂×C₄	1	2	yes	—
67	D₅×D₁₂	—	2	4	no	—
68	C₄×D₃×D₅	—	2	4	no	—
69	C₄×D₃×D₅	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	#6714	C₂×C₄	1	2	yes	—
74	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃⋊#168	C₂³	1	2	yes	—
76	#6705	—	2	4	no	—
77	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
78	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
80	C₅×D₃×C₈	—	2	4	no	—
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₃×#676	—	2	2	no	—
87	C₃×#676	D₄	1	4	yes	complemented
88	#6668	C₂×C₄	1	2	yes	—
89	#6667	C₂×C₄	1	2	yes	—
90	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
91	#6651	—	2	4	no	—
92	#6649	—	2	4	no	—
93	D₃×#168	—	2	4	no	—
94	C₂×D₃×M₁₆	—	5	2	no	—
95	C₂×C₄×D₁₂	—	5	1	no	—
96	C₃×C₄×M₁₆	—	5	1	no	—
97	#5126	—	5	2	no	—
98	#4924	—	5	1	no	—
99	#4706	—	5	2	no	—
100	#4706	—	5	2	no	—
101	#4688	—	5	1	no	—
102	#4688	—	5	1	no	—
103	C₈×D₁₂	—	5	1	no	—
104	C₈×D₁₂	D₅	1	1	yes	characteristic, complemented
105	C₂×D₄×D₅	—	3	1	no	—
106	C₂²×C₄×D₅	—	3	2	no	—
107	C₂²×C₅×C₈	—	3	2	no	—
108	C₄×C₅×D₄	—	3	1	no	—
109	D₄×Dic₅	—	3	1	no	—
110	C₄×C₂²⋊D₅	—	3	2	no	—
111	C₂²×#168	—	3	2	no	—
112	C₂×#676	—	3	2	no	—
113	C₂×#676	—	3	2	no	—
114	C₂×#676	—	3	2	no	—
115	C₂×#676	—	6	8	no	—
116	C₂×#676	C₂×D₃	1	1	yes	characteristic
117	C₂×#676	C₂×D₃	1	1	yes	characteristic
118	#4039	—	3	1	no	—
119	D₅×C₄⋊C₄	—	3	1	no	—
120	#4027	—	3	2	no	—
121	D₅×C₂²⋊C₄	—	3	2	no	—
122	C₄×D₂₀	—	3	1	no	—
123	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
124	C₅×C₄⋊C₈	—	3	1	no	—
125	C₅×C₂²⋊C₈	—	3	2	no	—
126	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂²⋊#168	—	3	2	no	—
128	#3952	—	3	2	no	—
129	#3952	—	3	2	no	—
130	#3947	C₂×D₃	1	1	yes	characteristic, complemented
131	#3947	C₂×D₃	1	1	yes	characteristic, complemented
132	#3946	—	3	2	no	—
133	C₄⋊#168	—	3	1	no	—
134	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
135	D₄×M₁₆	—	15	1	no	Sylow
136	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₃×D₅	—	2	4	no	—
140	C₂×D₃×D₅	—	2	4	no	—
141	C₂×D₃×D₅	—	4	2	no	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
146	D₆₀	—	2	2	no	—
147	C₄×D₁₅	—	2	2	no	—
148	C₄×D₁₅	—	2	2	no	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
150	C₅×D₁₂	M₁₆	1	4	yes	complemented
151	C₄×C₅×D₃	—	2	2	no	—
152	C₄×C₅×D₃	—	2	2	no	—
153	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
156	C₃×C₄×D₅	—	2	2	no	—
157	C₃×C₄×D₅	—	4	1	no	—
158	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
159	C₃×C₄×D₅	#41	1	2	yes	—
160	#1203	—	2	4	no	—
161	#1200	—	2	4	no	—
162	D₃×Dic₅	—	2	4	no	—
163	D₅×Dic₃	—	2	4	no	—
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
166	C₃⋊#168	—	2	2	no	—
167	C₃×#168	—	2	1	no	—
168	C₃×#168	C₂×D₄	1	2	yes	complemented
169	C₅×C₃⋊C₈	—	2	2	no	—
170	C₂²×D₁₂	—	5	1	no	—
171	C₂²×C₄×D₃	—	5	2	no	—
172	C₂×C₃×M₁₆	—	5	1	no	—
173	C₂×C₃×M₁₆	—	5	1	no	—
174	C₂×C₃×C₄²	—	5	1	no	—
175	C₂×(C₂×D₃)⋊C₄	—	5	2	no	—
176	C₂×C₄⋊Dic₃	—	5	1	no	—
177	C₂×#208	—	5	2	no	—
178	D₃×M₁₆	—	10	8	no	—
179	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
180	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
181	C₂×D₃×C₈	—	5	2	no	—
182	C₂×D₃×C₈	C₂×D₅	1	2	yes	complemented
183	C₄×D₁₂	—	5	1	no	—
184	C₄×D₁₂	—	5	2	no	—
185	C₄×D₁₂	—	5	1	no	—
186	C₄×D₁₂	—	5	2	no	—
187	C₄×D₁₂	—	5	1	no	—
188	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
189	C₃×#97	—	5	1	no	—
190	C₃×#97	—	5	1	no	—
191	C₃×C₄×C₈	—	5	1	no	—
192	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
193	(C₂×D₃)⋊C₈	—	5	2	no	—
194	(C₂×D₃)⋊C₈	—	5	2	no	—
195	(C₂×D₃)⋊C₈	—	5	2	no	—
196	(C₂×D₃)⋊C₈	C₂×D₅	1	2	yes	complemented
197	C₄⋊(C₃⋊C₈)	—	5	1	no	—
198	C₄⋊(C₃⋊C₈)	—	5	2	no	—
199	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic, complemented
200	C₂³×D₅	—	3	2	no	—
201	C₂×C₅×D₄	—	3	1	no	—
202	C₂²×C₄×C₅	—	3	2	no	—
203	C₂×C₂²⋊D₅	—	3	2	no	—
204	C₂²×Dic₅	—	3	2	no	—
205	D₄×D₅	—	6	4	no	—
206	C₂×D₂₀	—	3	1	no	—
207	C₂×C₄×D₅	—	3	2	no	—
208	C₂×C₄×D₅	—	3	2	no	—
209	C₂×C₄×D₅	—	3	2	no	—
210	C₂×C₄×D₅	—	6	4	no	—
211	C₂×C₄×D₅	—	6	4	no	—
212	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
213	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
214	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₅×C₈	—	3	2	no	—
216	C₂×C₅×C₈	—	6	4	no	—
217	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	—	3	1	no	—
220	C₅×C₂²⋊C₄	—	3	2	no	—
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂²⋊Dic₅	—	3	2	no	—
223	#685	—	3	2	no	—
224	#685	—	3	2	no	—
225	C₄⋊Dic₅	—	3	1	no	—
226	#683	—	3	2	no	—
227	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
228	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
229	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
230	C₂×#168	—	3	2	no	—
231	C₂×#168	—	6	4	no	—
232	C₂×#168	C₂²×D₃	1	1	yes	characteristic
233	C₂×#168	C₂²×D₃	1	1	yes	characteristic
234	#676	—	2	2	no	—
235	#676	—	6	4	no	—
236	#676	—	6	4	no	—
237	#676	—	6	4	no	—
238	#676	D₁₂	1	4	yes	direct product factor
239	C₂²×M₁₆	—	15	2	no	—
240	C₂×C₄×D₄	—	15	1	no	—
241	#436	—	15	1	no	—
242	#436	—	15	1	no	—
243	#435	—	15	2	no	—
244	#435	—	15	2	no	—
245	C₈×D₄	—	3	1	no	—
246	C₈×D₄	—	15	1	no	—
247	#423	—	15	1	no	—
248	#407	—	15	2	no	—
249	C₄×M₁₆	—	5	1	no	—
250	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂×D₁₅	—	2	2	no	—
252	C₂×D₁₅	—	2	2	no	—
253	C₂×D₁₅	—	2	2	no	—
254	C₂×C₅×D₃	—	2	2	no	—
255	C₂×C₅×D₃	—	2	2	no	—
256	C₂×C₅×D₃	C₂×M₁₆	1	4	yes	complemented
257	C₂×C₃×D₅	—	2	1	no	—
258	C₂×C₃×D₅	—	2	1	no	—
259	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
260	D₃×D₅	—	4	8	no	—
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
263	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	Dic₁₅	—	2	2	no	—
266	C₃×Dic₅	—	2	1	no	—
267	C₃×Dic₅	—	2	1	no	—
268	C₃×Dic₅	C₄×D₄	1	2	yes	—
269	C₅×Dic₃	—	2	2	no	—
270	C₂³×D₃	—	5	2	no	—
271	C₂²×C₃×C₄	—	5	1	no	—
272	C₂²×C₃×C₄	—	5	1	no	—
273	C₂²×C₃×C₄	—	5	1	no	—
274	C₂²×Dic₃	—	5	2	no	—
275	C₂×D₁₂	—	5	2	no	—
276	C₂×D₁₂	—	5	1	no	—
277	C₂×D₁₂	—	10	4	no	—
278	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
279	C₂×C₄×D₃	—	5	2	no	—
280	C₂×C₄×D₃	—	5	2	no	—
281	C₂×C₄×D₃	—	5	2	no	—
282	C₂×C₄×D₃	—	10	4	no	—
283	C₂×C₄×D₃	—	10	4	no	—
284	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
285	C₃×M₁₆	—	5	4	no	—
286	C₃×M₁₆	—	10	2	no	—
287	C₂×C₃×C₈	—	5	1	no	—
288	C₂×C₃×C₈	—	5	1	no	—
289	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
291	C₃×C₄²	—	5	1	no	—
292	C₃×C₄²	—	5	1	no	—
293	C₃×C₄²	—	5	1	no	—
294	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
295	(C₂×D₃)⋊C₄	—	5	2	no	—
296	(C₂×D₃)⋊C₄	—	5	2	no	—
297	(C₂×D₃)⋊C₄	—	5	2	no	—
298	(C₂×D₃)⋊C₄	C₄×D₅	1	2	yes	—
299	C₄⋊Dic₃	—	5	1	no	—
300	C₄⋊Dic₃	—	5	2	no	—
301	C₄⋊Dic₃	C₄×D₅	1	1	yes	characteristic
302	#208	—	10	4	no	—
303	C₂×C₃⋊C₈	—	5	2	no	—
304	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
305	ΓL(1,𝔽₂₅)	—	10	4	no	—
306	ΓL(1,𝔽₂₅)	—	10	4	no	—
307	D₃×C₈	—	2	4	no	—
308	D₃×C₈	—	10	4	no	—
309	C₂³×C₅	—	3	2	no	—
310	C₂²×D₅	—	3	2	no	—
311	C₂²×D₅	—	6	4	no	—
312	C₂²×D₅	—	6	4	no	—
313	C₂²×D₅	—	12	2	no	—
314	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
315	C₅×D₄	—	3	4	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
322	C₂²⋊D₅	—	6	4	no	—
323	C₂×Dic₅	—	3	2	no	—
324	C₂×Dic₅	—	6	4	no	—
325	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
326	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
327	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
328	D₂₀	—	6	2	no	—
329	C₄×D₅	—	2	2	no	—
330	C₄×D₅	—	4	1	no	—
331	C₄×D₅	—	6	4	no	—
332	C₄×D₅	—	6	2	no	—
333	C₄×D₅	—	6	2	no	—
334	C₄×D₅	—	6	4	no	—
335	C₄×D₅	C₂×D₁₂	1	2	yes	—
336	C₄×D₅	#235	1	2	yes	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	6	2	no	—
339	C₅×C₈	C₂×D₁₂	1	2	yes	complemented
340	#168	—	2	1	no	—
341	#168	—	6	2	no	—
342	#168	C₂×D₁₂	1	2	yes	complemented
343	C₂²×D₄	—	15	1	no	—
344	C₂³×C₄	—	15	2	no	—
345	C₂×M₁₆	—	5	1	no	—
346	C₂×M₁₆	—	5	1	no	—
347	C₂×M₁₆	—	15	2	no	—
348	C₂×M₁₆	—	15	2	no	—
349	C₂×M₁₆	—	15	2	no	—
350	C₂×M₁₆	—	30	8	no	—
351	C₂²×C₈	—	3	2	no	—
352	C₂²×C₈	—	15	2	no	—
353	C₄×D₄	—	3	1	no	—
354	C₄×D₄	—	15	2	no	—
355	C₄×D₄	—	15	1	no	—
356	C₄×D₄	—	15	2	no	—
357	C₄×D₄	—	15	1	no	—
358	C₄×D₄	—	15	1	no	—
359	C₂×C₄⋊C₄	—	15	1	no	—
360	C₂×C₂²⋊C₄	—	15	2	no	—
361	C₂×C₄²	—	5	1	no	—
362	C₄⋊C₈	—	3	1	no	—
363	C₄⋊C₈	—	15	2	no	—
364	C₄⋊C₈	—	15	1	no	—
365	C₂²⋊C₈	—	3	2	no	—
366	C₂²⋊C₈	—	15	2	no	—
367	C₂²⋊C₈	—	15	2	no	—
368	C₂²⋊C₈	—	15	2	no	—
369	#97	—	5	1	no	—
370	#97	—	5	1	no	—
371	C₄×C₈	—	5	1	no	—
372	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
373	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
375	C₂×C₃×C₅	#568	1	1	yes	characteristic
376	D₁₅	—	4	2	no	—
377	C₃×D₅	—	2	2	no	—
378	C₅×D₃	—	2	4	no	—
379	C₂³×C₃	—	5	1	no	—
380	C₂²×D₃	—	5	2	no	—
381	C₂²×D₃	—	10	4	no	—
382	C₂²×D₃	—	10	4	no	—
383	C₂²×D₃	—	20	2	no	—
384	C₂²×D₃	C₂×C₄×D₅	1	2	yes	—
385	C₂×C₃×C₄	—	5	1	no	—
386	C₂×C₃×C₄	—	5	2	no	—
387	C₂×C₃×C₄	—	5	2	no	—
388	C₂×C₃×C₄	—	5	1	no	—
389	C₂×C₃×C₄	—	5	1	no	—
390	C₂×C₃×C₄	—	10	2	no	—
391	C₂×C₃×C₄	—	20	1	no	—
392	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
395	C₂×Dic₃	—	5	2	no	—
396	C₂×Dic₃	—	10	4	no	—
397	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
398	D₁₂	—	10	4	no	—
399	D₁₂	—	10	2	no	—
400	D₁₂	#676	1	4	yes	direct product factor
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	10	4	no	—
404	C₄×D₃	—	10	4	no	—
405	C₄×D₃	—	10	2	no	—
406	C₄×D₃	—	10	2	no	—
407	C₃×C₈	—	2	1	no	—
408	C₃×C₈	—	5	2	no	—
409	C₃×C₈	—	10	1	no	—
410	C₃×C₈	D₄×D₅	1	2	yes	complemented
411	C₃⋊C₈	—	2	2	no	—
412	C₃⋊C₈	—	10	2	no	—
413	C₂²×C₅	—	3	4	no	—
414	C₂²×C₅	—	6	2	no	—
415	C₂²×C₅	—	6	2	no	—
416	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	6	2	no	—
420	C₂×D₅	—	6	2	no	—
421	C₂×D₅	—	6	2	no	—
422	C₂×D₅	—	12	8	no	—
423	C₂×D₅	C₄×D₁₂	1	2	yes	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	6	2	no	—
426	C₄×C₅	D₃×M₁₆	1	2	yes	complemented
427	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
428	C₄×C₅	C₂×#235	1	1	yes	characteristic
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	6	2	no	—
432	Dic₅	C₄×D₁₂	1	2	yes	—
433	C₂⁴	—	15	2	no	—
434	C₂×D₄	—	3	1	no	—
435	C₂×D₄	—	15	2	no	—
436	C₂×D₄	—	15	1	no	—
437	C₂×D₄	—	30	4	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	1	no	—
442	C₂²×C₄	—	15	2	no	—
443	C₂²×C₄	—	15	2	no	—
444	C₂²×C₄	—	15	2	no	—
445	C₂²×C₄	—	15	2	no	—
446	C₂²×C₄	—	30	4	no	—
447	C₂²×C₄	—	30	4	no	—
448	M₁₆	—	5	4	no	—
449	M₁₆	—	10	2	no	—
450	M₁₆	—	30	4	no	—
451	M₁₆	—	30	4	no	—
452	M₁₆	—	30	4	no	—
453	C₂×C₈	—	3	2	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	5	1	no	—
456	C₂×C₈	—	6	4	no	—
457	C₂×C₈	—	15	2	no	—
458	C₂×C₈	—	30	4	no	—
459	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
460	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
461	C₄⋊C₄	—	3	1	no	—
462	C₄⋊C₄	—	15	2	no	—
463	C₄⋊C₄	—	15	1	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	15	2	no	—
466	C₂²⋊C₄	—	15	2	no	—
467	C₂²⋊C₄	—	15	2	no	—
468	C₄²	—	5	1	no	—
469	C₄²	—	5	1	no	—
470	C₄²	—	5	1	no	—
471	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	5	2	no	—
474	C₂²×C₃	—	10	1	no	—
475	C₂²×C₃	—	10	1	no	—
476	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
477	C₂×D₃	—	2	2	no	—
478	C₂×D₃	—	2	2	no	—
479	C₂×D₃	—	10	2	no	—
480	C₂×D₃	—	10	2	no	—
481	C₂×D₃	—	10	2	no	—
482	C₂×D₃	—	20	8	no	—
483	C₂×D₃	C₂×#676	1	4	yes	complemented
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	5	2	no	—
486	C₃×C₄	—	10	1	no	—
487	C₃×C₄	—	10	1	no	—
488	C₃×C₄	C₂×#676	1	2	yes	complemented
489	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
490	C₃×C₄	D₅×#41	1	1	yes	characteristic
491	Dic₃	—	2	2	no	—
492	Dic₃	—	10	2	no	—
493	C₂×C₅	—	6	4	no	—
494	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
495	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
496	C₂×C₅	#5745	1	1	yes	characteristic
497	D₅	—	2	2	no	—
498	D₅	—	12	2	no	—
499	C₂³	—	3	2	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	15	2	no	—
502	C₂³	—	30	4	no	—
503	C₂³	—	30	4	no	—
504	C₂³	—	60	2	no	—
505	D₄	—	3	4	no	—
506	D₄	—	30	4	no	—
507	D₄	—	30	2	no	—
508	C₂×C₄	—	3	2	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	6	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	10	2	no	—
517	C₂×C₄	—	15	2	no	—
518	C₂×C₄	—	20	1	no	—
519	C₂×C₄	—	30	4	no	—
520	C₂×C₄	—	30	4	no	—
521	C₂×C₄	—	30	4	no	—
522	C₂×C₄	—	30	2	no	—
523	C₂×C₄	—	30	2	no	—
524	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
525	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
527	C₈	—	2	1	no	—
528	C₈	—	5	2	no	—
529	C₈	—	6	2	no	—
530	C₈	—	10	1	no	—
531	C₈	—	30	2	no	—
532	C₈	D₅×D₁₂	1	2	yes	complemented
533	C₂×C₃	—	10	2	no	—
534	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
535	C₂×C₃	C₂²×#676	1	1	yes	characteristic
536	C₂×C₃	#66084	1	1	yes	characteristic
537	D₃	—	2	4	no	—
538	D₃	—	20	2	no	—
539	C₅	M₁₆×D₁₂	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	3	4	no	—
541	C₂²	—	5	2	no	—
542	C₂²	—	6	2	no	—
543	C₂²	—	6	2	no	—
544	C₂²	—	10	1	no	—
545	C₂²	—	10	1	no	—
546	C₂²	—	30	2	no	—
547	C₂²	—	30	2	no	—
548	C₂²	—	30	2	no	—
549	C₂²	—	60	8	no	—
550	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	5	2	no	—
553	C₄	—	6	2	no	—
554	C₄	—	10	1	no	—
555	C₄	—	10	1	no	—
556	C₄	—	30	2	no	—
557	C₄	D₃×#676	1	2	yes	complemented
558	C₄	C₂×D₅×D₁₂	1	1	yes	characteristic
559	C₄	D₅×#235	1	1	yes	characteristic
560	C₃	D₄×#676	1	1	yes	characteristic, complemented, Sylow
561	C₂	—	6	4	no	—
562	C₂	—	10	2	no	—
563	C₂	—	60	2	no	—
564	C₂	C₄×D₅×D₁₂	1	1	yes	characteristic
565	C₂	C₂×D₃×#676	1	1	yes	characteristic
566	C₂	#11753949	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×C₈	C₂²
prime radical	C₂×D₅×D₁₂	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
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
1. C₂×D₃×#676	C₂	semidirect
3. #11750789	C₂	semidirect
4. C₅×C₈×D₁₂	C₂	semidirect
5. C₃×C₄×#676	C₂	semidirect
6. #11748101	C₂	semidirect
7. #11748048	C₂	semidirect
8. #11747719	C₂	semidirect
9. #11747009	C₂	semidirect
10. #11747007	C₂	semidirect
11. D₁₂×#168	C₂	semidirect
15. C₂×#6705	C₂²	semidirect
17. C₂×C₅×D₃×C₈	C₂²	semidirect
28. C₂×#6651	C₂²	semidirect
30. C₂×D₃×#168	C₂²	semidirect
32. C₃×C₄×C₅×C₈	C₂²	semidirect
33. #91104	C₂²	semidirect
34. C₄⋊(C₃⋊#168)	C₂²	semidirect
35. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
36. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
37. C₃×#3947	C₂²	semidirect
38. C₃×#3947	C₂²	semidirect
39. C₃×C₄×#168	C₂²	semidirect
40. #90982	C₂²	semidirect
41. #90957	C₂²	semidirect
42. (C₂×D₃)⋊#168	C₂²	semidirect
54. C₄×#676	D₃	semidirect
87. C₃×#676	D₄	semidirect
104. C₈×D₁₂	D₅	semidirect
126. C₄×C₅×C₈	C₂×D₃	semidirect
130. #3947	C₂×D₃	semidirect
131. #3947	C₂×D₃	semidirect
134. C₄×#168	C₂×D₃	semidirect
150. C₅×D₁₂	M₁₆	semidirect
165. C₃×C₅×C₈	C₂×D₄	semidirect
168. C₃×#168	C₂×D₄	semidirect
182. C₂×D₃×C₈	C₂×D₅	semidirect
192. C₃×C₄×C₈	C₂×D₅	semidirect
196. (C₂×D₃)⋊C₈	C₂×D₅	semidirect
199. C₄⋊(C₃⋊C₈)	C₂×D₅	semidirect
238. #676	D₁₂	direct (N × H)
256. C₂×C₅×D₃	C₂×M₁₆	semidirect
262. C₃×C₄×C₅	C₂×M₁₆	semidirect
339. C₅×C₈	C₂×D₁₂	semidirect
342. #168	C₂×D₁₂	semidirect
372. C₄×C₈	D₃×D₅	semidirect
400. D₁₂	#676	direct (N × H)
410. C₃×C₈	D₄×D₅	semidirect
426. C₄×C₅	D₃×M₁₆	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
483. C₂×D₃	C₂×#676	semidirect
488. C₃×C₄	C₂×#676	semidirect
532. C₈	D₅×D₁₂	semidirect
539. C₅	M₁₆×D₁₂	semidirect
557. C₄	D₃×#676	semidirect
560. C₃	D₄×#676	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#676	2
C₄×D₅×D₁₂	2
#11750789	2
C₅×C₈×D₁₂	2
C₃×C₄×#676	2
#11748101	2
#11748048	2
#11747719	2
#11747009	2
#11747007	2
D₁₂×#168	2
D₄×#676	3
M₁₆×D₁₂	5

Subgroups — D12×#676 #14415720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₂×#676 #14415720