Subgroups — C₂×#11747698 #14414629

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#1202	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6648	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747698	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65123	—	3	1	no	maximal, Hall
10	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂²×#1202	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	—	2	4	no	—
19	C₂×C₃×C₈×D₅	C₂²	1	4	yes	complemented
20	C₂×Dic₃⋊Dic₅	C₄	1	1	yes	characteristic
21	C₂×#6667	C₄	1	1	yes	characteristic
22	C₂×#6665	C₄	1	1	yes	characteristic
23	C₄×#1202	C₄	1	4	yes	—
24	C₄×#1202	C₂²	1	4	yes	—
25	C₂×#6648	—	2	4	no	—
26	C₂×#6648	C₂²	1	4	yes	complemented
27	#91104	C₂²	1	4	yes	complemented
28	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
29	#90955	C₂²	1	4	yes	complemented
30	Dic₃×#168	C₂²	1	4	yes	complemented
31	C₂×C₈×#67	—	5	1	no	maximal, Hall
32	C₂²×C₈×D₅	—	3	1	no	—
33	C₂²×C₈×D₅	D₃	1	1	yes	characteristic, complemented
34	C₂×C₄×D₂₀	—	3	1	no	—
35	C₂×C₅×C₄⋊C₈	—	3	1	no	—
36	C₂×#3952	—	3	1	no	—
37	C₂×#3952	—	3	1	no	—
38	C₂×C₄×#168	—	3	1	no	—
39	#65123	—	3	8	no	—
40	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₁₅	—	2	2	no	—
45	C₂×C₄×D₁₅	—	2	2	no	—
46	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
47	C₂×C₄×D₁₅	C₂³	1	2	yes	—
48	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	—	2	2	no	—
52	C₂×C₃×C₄×D₅	—	2	2	no	—
53	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
55	C₂×#1202	C₈	1	8	yes	complemented
56	C₂×#1202	C₂×C₄	1	4	yes	—
57	C₂×C₃×C₅×C₈	—	2	2	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₂×C₃⋊#168	—	2	2	no	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
62	C₄×C₅×Dic₃	C₂³	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂×C₃×#168	D₄	1	4	yes	complemented
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×C₈×D₅	—	2	8	no	—
68	Dic₃⋊Dic₅	C₂×C₄	1	4	yes	—
69	#6667	C₂×C₄	1	4	yes	—
70	#6665	C₂×C₄	1	4	yes	—
71	#6648	—	2	8	no	—
72	C₂³×C₃×C₈	—	5	1	no	—
73	C₂×C₄×#67	—	5	1	no	—
74	C₂²×D₃×C₈	—	5	1	no	—
75	C₂×#830	—	5	1	no	—
76	C₈×#67	—	5	8	no	—
77	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
78	C₂×Dic₃⋊C₈	D₅	1	1	yes	characteristic, complemented
79	C₂×C₈×Dic₃	—	5	1	no	—
80	C₂²×D₂₀	—	3	1	no	—
81	C₂²×C₄×D₅	—	3	1	no	—
82	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₅×C₈	—	3	1	no	—
84	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×#685	—	3	1	no	—
87	C₂×#685	—	3	1	no	—
88	C₂×C₄⋊Dic₅	—	3	1	no	—
89	C₂²×#168	—	3	1	no	—
90	C₂²×#168	C₂×D₃	1	1	yes	characteristic
91	C₂×C₈×D₅	—	2	4	no	—
92	C₂×C₈×D₅	—	3	4	no	—
93	C₂×C₈×D₅	—	6	4	no	—
94	C₂×C₈×D₅	C₂×D₃	1	4	yes	complemented
95	C₄×D₂₀	—	3	4	no	—
96	C₄×D₂₀	—	3	4	no	—
97	C₅×C₄⋊C₈	—	3	4	no	—
98	#3952	—	3	4	no	—
99	#3952	—	3	4	no	—
100	C₄×#168	—	3	4	no	—
101	C₂×C₈×D₄	—	15	1	no	Sylow
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×D₁₅	—	2	2	no	—
104	C₂²×D₁₅	—	2	2	no	—
105	C₂²×D₁₅	C₂×C₈	1	4	yes	complemented
106	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₃×D₅	—	2	2	no	—
108	C₂²×C₃×D₅	—	2	2	no	—
109	C₂²×C₃×D₅	C₂×C₈	1	4	yes	complemented
110	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×Dic₁₅	—	2	2	no	—
116	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
117	C₄×D₁₅	—	2	4	no	—
118	C₄×D₁₅	—	2	2	no	—
119	C₄×D₁₅	—	2	2	no	—
120	C₂×C₅×Dic₃	—	2	2	no	—
121	C₂×C₅×Dic₃	C₂×C₈	1	4	yes	complemented
122	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
123	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₃×C₄×D₅	—	2	4	no	—
127	C₃×C₄×D₅	—	2	2	no	—
128	C₃×C₄×D₅	—	2	2	no	—
129	#1202	C₂×C₈	1	16	yes	complemented
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃⋊#168	—	2	2	no	—
132	C₃×#168	C₂×D₄	1	4	yes	complemented
133	C₅×C₃⋊C₈	—	2	2	no	—
134	C₂³×C₃×C₄	—	5	1	no	—
135	C₂²×#67	—	5	1	no	—
136	C₂²×C₄×D₃	—	5	1	no	—
137	C₂²×C₃×C₈	—	5	1	no	—
138	C₂²×C₃×C₈	—	5	4	no	—
139	C₂²×C₃×C₈	—	10	4	no	—
140	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
141	C₂×#217	—	5	1	no	—
142	C₄×#67	—	5	4	no	—
143	C₄×#67	—	5	4	no	—
144	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
145	C₂×Dic₃⋊C₄	—	5	1	no	—
146	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
149	C₂×D₃×C₈	—	5	4	no	—
150	C₂×D₃×C₈	—	10	4	no	—
151	#830	—	5	4	no	—
152	(C₂×D₃)⋊C₈	—	5	4	no	—
153	Dic₃⋊C₈	C₂×D₅	1	4	yes	complemented
154	C₈×Dic₃	—	5	4	no	—
155	C₂³×D₅	—	3	1	no	—
156	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	3	1	no	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂²×Dic₅	—	3	1	no	—
161	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
162	C₂×D₂₀	—	3	8	no	—
163	C₂×D₂₀	—	3	4	no	—
164	C₂×C₄×D₅	—	2	2	no	—
165	C₂×C₄×D₅	—	2	2	no	—
166	C₂×C₄×D₅	—	3	2	no	—
167	C₂×C₄×D₅	—	3	2	no	—
168	C₂×C₄×D₅	—	6	2	no	—
169	C₂×C₄×D₅	—	6	2	no	—
170	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
171	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	6	2	no	—
175	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
176	C₄²×C₅	—	3	2	no	—
177	C₄²×C₅	—	3	2	no	—
178	#685	—	3	4	no	—
179	#685	—	3	4	no	—
180	C₄⋊Dic₅	—	3	4	no	—
181	C₂×#168	—	3	2	no	—
182	C₂×#168	—	6	2	no	—
183	C₂×#168	#67	1	4	yes	complemented
184	C₂×#168	C₂²×D₃	1	2	yes	—
185	C₈×D₅	—	2	8	no	—
186	C₈×D₅	—	6	8	no	—
187	C₂³×C₈	—	5	1	no	—
188	C₂³×C₈	—	15	1	no	—
189	C₂×C₄×D₄	—	15	1	no	—
190	C₈×D₄	—	15	8	no	—
191	C₂×C₄⋊C₈	—	3	1	no	—
192	C₂×C₂²⋊C₈	—	15	1	no	—
193	C₂×C₂²⋊C₈	—	15	1	no	—
194	C₂×C₄×C₈	—	15	1	no	—
195	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
197	C₂²×C₃×C₅	#131	1	2	yes	—
198	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×D₁₅	—	2	2	no	—
200	C₂×D₁₅	—	2	2	no	—
201	C₂×D₁₅	—	2	8	no	—
202	C₂×D₁₅	C₂²×C₈	1	4	yes	complemented
203	C₂×C₃×D₅	—	2	2	no	—
204	C₂×C₃×D₅	—	2	2	no	—
205	C₂×C₃×D₅	—	2	8	no	—
206	C₂×C₃×D₅	C₂²×C₈	1	4	yes	complemented
207	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
208	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
210	Dic₁₅	—	2	2	no	—
211	C₃×Dic₅	—	2	2	no	—
212	C₅×Dic₃	—	2	2	no	—
213	C₅×Dic₃	C₂²×C₈	1	4	yes	complemented
214	C₂⁴×C₃	—	5	1	no	—
215	C₂³×D₃	—	5	1	no	—
216	C₂²×C₃×C₄	—	5	1	no	—
217	C₂²×C₃×C₄	—	5	2	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	—	10	2	no	—
220	C₂²×C₃×C₄	—	10	2	no	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₂×#67	—	5	8	no	—
223	C₂×#67	—	5	4	no	—
224	C₂²×Dic₃	—	5	1	no	—
225	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
226	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
227	C₂×C₄×D₃	—	5	2	no	—
228	C₂×C₄×D₃	—	5	2	no	—
229	C₂×C₄×D₃	—	10	2	no	—
230	C₂×C₄×D₃	—	10	2	no	—
231	C₂×C₃×C₈	—	2	2	no	—
232	C₂×C₃×C₈	—	5	4	no	—
233	C₂×C₃×C₈	—	5	2	no	—
234	C₂×C₃×C₈	—	10	8	no	—
235	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
236	#217	—	5	4	no	—
237	(C₂×D₃)⋊C₄	—	5	4	no	—
238	Dic₃⋊C₄	—	5	4	no	—
239	C₄×Dic₃	C₄×D₅	1	2	yes	—
240	C₄×Dic₃	C₂²×D₅	1	2	yes	—
241	C₂×C₃⋊C₈	—	2	2	no	—
242	C₂×C₃⋊C₈	—	5	2	no	—
243	C₂×C₃⋊C₈	—	10	2	no	—
244	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
245	D₃×C₈	—	10	8	no	—
246	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂²×D₅	—	2	2	no	—
248	C₂²×D₅	—	2	2	no	—
249	C₂²×D₅	—	3	4	no	—
250	C₂²×D₅	—	3	2	no	—
251	C₂²×D₅	—	6	2	no	—
252	C₂²×D₅	—	6	2	no	—
253	C₂²×D₅	D₃×C₈	1	4	yes	complemented
254	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₄×C₅	—	3	4	no	—
256	C₂×C₄×C₅	—	3	2	no	—
257	C₂×C₄×C₅	—	3	2	no	—
258	C₂×C₄×C₅	—	6	2	no	—
259	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂×C₄×C₅	#235	1	2	yes	—
261	C₂×C₄×C₅	C₂×#67	1	2	yes	—
262	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
263	C₂×Dic₅	—	2	2	no	—
264	C₂×Dic₅	—	3	2	no	—
265	C₂×Dic₅	—	6	2	no	—
266	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
267	D₂₀	—	3	16	no	—
268	C₄×D₅	—	2	4	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	2	2	no	—
271	C₄×D₅	—	6	4	no	—
272	C₄×D₅	—	6	2	no	—
273	C₄×D₅	—	6	2	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	—	6	2	no	—
276	#168	—	6	2	no	—
277	#168	C₂×#67	1	4	yes	complemented
278	C₂²×D₄	—	15	1	no	—
279	C₂³×C₄	—	5	1	no	—
280	C₂³×C₄	—	15	1	no	—
281	C₂²×C₈	—	3	1	no	—
282	C₂²×C₈	—	5	1	no	—
283	C₂²×C₈	—	5	4	no	—
284	C₂²×C₈	—	10	4	no	—
285	C₂²×C₈	—	15	4	no	—
286	C₂²×C₈	—	15	1	no	—
287	C₂²×C₈	—	30	4	no	—
288	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
289	C₄×D₄	—	15	4	no	—
290	C₄×D₄	—	15	4	no	—
291	C₂×C₄⋊C₄	—	15	1	no	—
292	C₂×C₂²⋊C₄	—	15	1	no	—
293	C₂×C₂²⋊C₄	—	15	1	no	—
294	C₂×C₄²	—	3	1	no	—
295	C₄⋊C₈	—	3	4	no	—
296	C₂²⋊C₈	—	15	4	no	—
297	C₂²⋊C₈	—	15	4	no	—
298	C₄×C₈	—	15	4	no	—
299	C₂×C₃×C₅	C₈×D₄	1	4	yes	complemented
300	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	D₁₅	—	2	4	no	—
304	C₃×D₅	—	2	4	no	—
305	C₂³×C₃	—	5	2	no	—
306	C₂³×C₃	—	5	4	no	—
307	C₂³×C₃	—	10	2	no	—
308	C₂³×C₃	—	10	2	no	—
309	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
310	C₂²×D₃	—	5	2	no	—
311	C₂²×D₃	—	5	4	no	—
312	C₂²×D₃	—	10	2	no	—
313	C₂²×D₃	—	10	2	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	10	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	4	no	—
319	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
320	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
321	C₂×C₃×C₄	#713	1	2	yes	—
322	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
323	#67	—	5	16	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	—	5	2	no	—
326	C₂×Dic₃	—	10	2	no	—
327	C₂×Dic₃	C₈×D₅	1	4	yes	complemented
328	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
329	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
330	C₄×D₃	—	10	2	no	—
331	C₄×D₃	—	10	2	no	—
332	C₄×D₃	—	10	4	no	—
333	C₃×C₈	—	2	2	no	—
334	C₃×C₈	—	5	4	no	—
335	C₃⋊C₈	—	2	2	no	—
336	C₃⋊C₈	—	10	2	no	—
337	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
338	C₂²×C₅	#901	1	2	yes	—
339	C₂²×C₅	C₄×#67	1	2	yes	—
340	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
341	C₂×D₅	—	2	2	no	—
342	C₂×D₅	—	2	2	no	—
343	C₂×D₅	—	2	8	no	—
344	C₂×D₅	—	3	4	no	—
345	C₂×D₅	—	6	2	no	—
346	C₂×D₅	—	6	2	no	—
347	C₂×D₅	—	6	8	no	—
348	C₂×D₅	C₂×D₃×C₈	1	4	yes	complemented
349	C₄×C₅	—	3	4	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	C₄×#67	1	2	yes	—
352	C₄×C₅	C₂×#235	1	1	yes	characteristic
353	C₄×C₅	C₂²×#67	1	1	yes	characteristic
354	Dic₅	—	2	2	no	—
355	Dic₅	—	6	2	no	—
356	C₂⁴	—	5	1	no	—
357	C₂⁴	—	15	1	no	—
358	C₂×D₄	—	15	4	no	—
359	C₂×D₄	—	15	8	no	—
360	C₂²×C₄	—	3	1	no	—
361	C₂²×C₄	—	3	1	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	5	2	no	—
364	C₂²×C₄	—	5	2	no	—
365	C₂²×C₄	—	10	2	no	—
366	C₂²×C₄	—	10	2	no	—
367	C₂²×C₄	—	15	1	no	—
368	C₂²×C₄	—	15	2	no	—
369	C₂²×C₄	—	15	2	no	—
370	C₂²×C₄	—	30	2	no	—
371	C₂²×C₄	—	30	2	no	—
372	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	5	4	no	—
376	C₂×C₈	—	5	2	no	—
377	C₂×C₈	—	6	2	no	—
378	C₂×C₈	—	10	8	no	—
379	C₂×C₈	—	15	2	no	—
380	C₂×C₈	—	30	8	no	—
381	C₂×C₈	—	30	2	no	—
382	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
383	C₄⋊C₄	—	15	4	no	—
384	C₂²⋊C₄	—	15	4	no	—
385	C₂²⋊C₄	—	15	4	no	—
386	C₄²	—	3	2	no	—
387	C₄²	—	3	2	no	—
388	C₃×C₅	C₂×C₈×D₄	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	5	4	no	—
390	C₂²×C₃	—	10	2	no	—
391	C₂²×C₃	—	10	2	no	—
392	C₂²×C₃	—	10	8	no	—
393	C₂²×C₃	#4039	1	2	yes	—
394	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
395	C₂²×C₃	#4053	1	2	yes	—
396	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₂×D₃	—	5	4	no	—
398	C₂×D₃	—	10	2	no	—
399	C₂×D₃	—	10	2	no	—
400	C₂×D₃	—	10	8	no	—
401	C₃×C₄	—	10	2	no	—
402	C₃×C₄	#4039	1	2	yes	—
403	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
404	C₃×C₄	C₂×#713	1	1	yes	characteristic
405	Dic₃	—	2	2	no	—
406	Dic₃	—	10	2	no	—
407	Dic₃	C₂×C₈×D₅	1	4	yes	complemented
408	C₂×C₅	C₈×#67	1	4	yes	complemented
409	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
410	C₂×C₅	C₂×#901	1	1	yes	characteristic
411	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
412	D₅	—	2	4	no	—
413	D₅	—	6	4	no	—
414	C₂³	—	5	2	no	—
415	C₂³	—	5	4	no	—
416	C₂³	—	10	2	no	—
417	C₂³	—	10	2	no	—
418	C₂³	—	15	2	no	—
419	C₂³	—	15	4	no	—
420	C₂³	—	30	2	no	—
421	C₂³	—	30	2	no	—
422	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
423	D₄	—	15	16	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	4	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	5	2	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	10	2	no	—
430	C₂×C₄	—	10	4	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	15	2	no	—
434	C₂×C₄	—	30	2	no	—
435	C₂×C₄	—	30	4	no	—
436	C₂×C₄	—	30	2	no	—
437	C₂×C₄	—	30	2	no	—
438	C₂×C₄	#6773	1	2	yes	—
439	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
440	C₂×C₄	D₅×#67	1	2	yes	—
441	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	5	4	no	—
444	C₈	—	6	2	no	—
445	C₈	—	30	2	no	—
446	C₂×C₃	—	10	4	no	—
447	C₂×C₃	#65123	1	4	yes	complemented
448	C₂×C₃	C₂×#4039	1	1	yes	characteristic
449	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
450	C₂×C₃	C₂×#4053	1	1	yes	characteristic
451	D₃	—	10	4	no	—
452	C₅	C₂×C₈×#67	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	5	4	no	—
454	C₂²	—	10	2	no	—
455	C₂²	—	10	2	no	—
456	C₂²	—	10	8	no	—
457	C₂²	—	15	4	no	—
458	C₂²	—	30	2	no	—
459	C₂²	—	30	2	no	—
460	C₂²	—	30	8	no	—
461	C₂²	D₃×C₈×D₅	1	2	yes	—
462	C₂²	#91266	1	2	yes	—
463	C₂²	#91444	1	2	yes	—
464	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
465	C₄	—	3	4	no	—
466	C₄	—	6	2	no	—
467	C₄	—	10	2	no	—
468	C₄	—	30	2	no	—
469	C₄	#91444	1	2	yes	—
470	C₄	C₂×#6773	1	1	yes	characteristic
471	C₄	C₂×D₅×#67	1	1	yes	characteristic
472	C₃	C₂×#65123	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	10	4	no	—
474	C₂	—	30	4	no	—
475	C₂	#11747698	1	4	yes	direct product factor
476	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic
477	C₂	C₂×#91266	1	1	yes	characteristic
478	C₂	C₂×#91444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×#1202	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₈×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₈×D₅	C₂	semidirect
3. C₂²×#6648	C₂	semidirect
4. C₂×#91104	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
6. C₂×#90955	C₂	semidirect
7. C₂×Dic₃×#168	C₂	semidirect
8. #11747698	C₂	direct (N × H)
19. C₂×C₃×C₈×D₅	C₂²	semidirect
26. C₂×#6648	C₂²	semidirect
27. #91104	C₂²	semidirect
28. C₅×Dic₃⋊C₈	C₂²	semidirect
29. #90955	C₂²	semidirect
30. Dic₃×#168	C₂²	semidirect
33. C₂²×C₈×D₅	D₃	semidirect
55. C₂×#1202	C₈	semidirect
65. C₂×C₃×#168	D₄	semidirect
78. C₂×Dic₃⋊C₈	D₅	semidirect
94. C₂×C₈×D₅	C₂×D₃	semidirect
105. C₂²×D₁₅	C₂×C₈	semidirect
109. C₂²×C₃×D₅	C₂×C₈	semidirect
121. C₂×C₅×Dic₃	C₂×C₈	semidirect
129. #1202	C₂×C₈	semidirect
132. C₃×#168	C₂×D₄	semidirect
153. Dic₃⋊C₈	C₂×D₅	semidirect
183. C₂×#168	#67	semidirect
202. C₂×D₁₅	C₂²×C₈	semidirect
206. C₂×C₃×D₅	C₂²×C₈	semidirect
213. C₅×Dic₃	C₂²×C₈	semidirect
253. C₂²×D₅	D₃×C₈	semidirect
277. #168	C₂×#67	semidirect
299. C₂×C₃×C₅	C₈×D₄	semidirect
327. C₂×Dic₃	C₈×D₅	semidirect
348. C₂×D₅	C₂×D₃×C₈	semidirect
388. C₃×C₅	C₂×C₈×D₄	semidirect
407. Dic₃	C₂×C₈×D₅	semidirect
408. C₂×C₅	C₈×#67	semidirect
447. C₂×C₃	#65123	semidirect
452. C₅	C₂×C₈×#67	semidirect
472. C₃	C₂×#65123	semidirect
475. C₂	#11747698	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×C₈×D₅	2
C₂×C₄×#1202	2
C₂²×#6648	2
C₂×#91104	2
C₂×C₅×Dic₃⋊C₈	2
C₂×#90955	2
C₂×Dic₃×#168	2
#11747698	2
C₂×#65123	3
C₂×C₈×#67	5

Subgroups — C2×#11747698 #14414629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11747698 #14414629