Subgroups — C₂×#11751212 #14414689

Order 1920.

1128 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	C₂³×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#1220	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91114	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751212	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91104	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#91098	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65400	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×#1220	C₄	1	1	yes	characteristic
12	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	—	2	4	no	—
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	4	yes	complemented
17	C₂×#6719	C₄	1	1	yes	characteristic
18	C₄×#1220	C₄	1	4	yes	—
19	C₄×#1220	C₂²	1	4	yes	—
20	C₂×#6714	C₄	1	1	yes	characteristic
21	C₂×#6712	C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₂×#6705	—	2	4	no	—
26	C₂×#6705	C₂²	1	4	yes	complemented
27	#91114	C₂²	1	4	yes	complemented
28	#91104	C₂²	1	4	yes	complemented
29	#91099	C₂²	1	4	yes	complemented
30	#91098	C₂²	1	4	yes	complemented
31	C₂×#5111	—	5	1	no	maximal, Hall
32	C₂³×C₅×C₈	D₃	1	1	yes	characteristic, complemented
33	C₂×C₄×C₂²⋊D₅	—	3	1	no	—
34	C₂²×#676	—	3	1	no	—
35	C₂×C₂²⋊#168	—	3	1	no	—
36	#65400	—	3	8	no	—
37	C₂×#3952	—	3	1	no	—
38	C₂×#3947	—	3	1	no	—
39	C₂×#3946	—	3	1	no	—
40	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×#1220	—	2	4	no	—
49	C₂×#1220	C₂×C₄	1	4	yes	—
50	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
51	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
52	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×D₁₅	—	2	2	no	—
54	C₂×C₄×D₁₅	—	2	2	no	—
55	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
56	C₂×C₄×D₁₅	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	—	2	2	no	—
58	C₂×C₃×C₅×C₈	—	2	8	no	—
59	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	#6719	C₂×C₄	1	4	yes	—
63	#6714	C₂×C₄	1	4	yes	—
64	#6712	C₂×C₄	1	4	yes	—
65	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	—	2	2	no	—
68	C₂×C₃⋊#168	—	2	2	no	—
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	2	yes	—
71	#6705	—	2	8	no	—
72	C₂³×C₃×C₈	D₅	1	1	yes	characteristic, complemented
73	C₂×C₄×#67	—	5	1	no	—
74	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
75	C₂×#830	—	5	1	no	—
76	#5111	—	5	8	no	—
77	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
78	C₂×#815	—	5	1	no	—
79	C₂×Dic₃⋊C₈	—	5	1	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₂²⋊D₅	—	3	1	no	—
82	C₂²×C₄×D₅	—	3	1	no	—
83	C₂²×C₅×C₈	—	2	4	no	—
84	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂×D₃	1	4	yes	complemented
87	C₂×C₂²⋊Dic₅	—	3	1	no	—
88	C₄×C₂²⋊D₅	—	3	4	no	—
89	C₄×C₂²⋊D₅	—	3	4	no	—
90	C₂×#685	—	3	1	no	—
91	C₂×#683	—	3	1	no	—
92	C₂×C₄×Dic₅	—	3	1	no	—
93	C₂²×#168	—	3	1	no	—
94	C₂²×#168	—	3	1	no	—
95	C₂×#676	—	3	4	no	—
96	C₂×#676	—	6	4	no	—
97	C₂²⋊#168	—	3	4	no	—
98	#3952	—	3	4	no	—
99	#3947	—	3	4	no	—
100	#3946	—	3	4	no	—
101	C₂×#435	—	15	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	M₁₆	1	4	yes	complemented
105	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
106	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×D₁₅	—	2	2	no	—
108	C₂²×D₁₅	—	2	2	no	—
109	C₂²×D₁₅	—	2	2	no	—
110	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	#1220	—	2	8	no	—
121	C₂×Dic₁₅	—	2	2	no	—
122	C₂×Dic₁₅	—	2	2	no	—
123	C₂×Dic₁₅	—	2	2	no	—
124	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
125	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
126	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
127	C₄×D₁₅	—	2	4	no	—
128	C₄×D₁₅	—	2	2	no	—
129	C₄×D₁₅	—	2	2	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
132	C₃⋊#168	—	2	2	no	—
133	C₃⋊#168	—	2	2	no	—
134	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
135	C₂²×#67	—	5	1	no	—
136	C₂²×C₄×D₃	—	5	1	no	—
137	C₂²×C₃×C₈	—	2	4	no	—
138	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
140	C₂²×C₃×C₈	C₂×D₅	1	4	yes	complemented
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	—	5	1	no	—
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	C₂²×C₃⋊C₈	—	5	1	no	—
149	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
150	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
151	#830	—	5	4	no	—
152	(C₂×D₃)⋊C₈	—	5	4	no	—
153	#815	—	5	4	no	—
154	Dic₃⋊C₈	—	5	4	no	—
155	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
156	C₂³×D₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	—	3	4	no	—
164	C₂×C₂²⋊D₅	—	6	4	no	—
165	C₂²×Dic₅	—	3	1	no	—
166	C₂²×Dic₅	—	3	1	no	—
167	C₂²×Dic₅	—	3	1	no	—
168	C₂×C₄×D₅	—	3	2	no	—
169	C₂×C₄×D₅	—	3	2	no	—
170	C₂×C₄×D₅	—	6	2	no	—
171	C₂×C₄×D₅	—	6	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	8	no	—
174	C₂×C₅×C₈	#67	1	4	yes	complemented
175	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
176	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
177	C₂²⋊Dic₅	—	3	4	no	—
178	#685	—	3	4	no	—
179	#683	—	3	4	no	—
180	C₄×Dic₅	—	3	2	no	—
181	C₄×Dic₅	—	3	2	no	—
182	C₂×#168	—	3	2	no	—
183	C₂×#168	—	3	2	no	—
184	C₂×#168	—	6	2	no	—
185	C₂×#168	—	6	2	no	—
186	#676	—	6	8	no	—
187	C₂²×M₁₆	—	15	1	no	—
188	C₂³×C₈	D₁₅	1	1	yes	characteristic, complemented
189	C₂×C₄×D₄	—	15	1	no	—
190	#435	—	15	8	no	—
191	C₂×C₄⋊C₈	—	15	1	no	—
192	C₂×C₂²⋊C₈	—	15	1	no	—
193	C₂×C₂²⋊C₈	—	15	1	no	—
194	C₂×#97	—	15	1	no	—
195	C₂²×C₃×C₅	—	2	2	no	—
196	C₂²×C₃×C₅	—	2	2	no	—
197	C₂²×C₃×C₅	—	2	8	no	—
198	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
199	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
200	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
201	C₂²×C₃×C₅	#131	1	2	yes	—
202	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₂×D₁₅	—	2	2	no	—
204	C₂×D₁₅	—	2	2	no	—
205	C₂×D₁₅	—	2	2	no	—
206	C₂×D₁₅	—	4	4	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
209	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	Dic₁₅	—	2	2	no	—
212	Dic₁₅	—	2	2	no	—
213	Dic₁₅	—	2	2	no	—
214	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
215	C₂³×D₃	—	5	1	no	—
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	—	2	2	no	—
218	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₂×#67	—	5	4	no	—
223	C₂×#67	—	10	4	no	—
224	C₂²×Dic₃	—	5	1	no	—
225	C₂²×Dic₃	—	5	1	no	—
226	C₂²×Dic₃	—	5	1	no	—
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	—	2	8	no	—
233	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
234	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
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	—	5	2	no	—
240	C₄×Dic₃	—	5	2	no	—
241	C₂×C₃⋊C₈	—	5	2	no	—
242	C₂×C₃⋊C₈	—	5	2	no	—
243	C₂×C₃⋊C₈	—	10	2	no	—
244	C₂×C₃⋊C₈	—	10	2	no	—
245	ΓL(1,𝔽₂₅)	—	10	8	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
249	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
250	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
251	C₂²×D₅	—	3	2	no	—
252	C₂²×D₅	—	6	2	no	—
253	C₂²×D₅	—	6	2	no	—
254	C₂²×D₅	—	6	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₄×C₅	#235	1	2	yes	—
262	C₂×C₄×C₅	C₂×#67	1	2	yes	—
263	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
264	C₂²⋊D₅	—	6	8	no	—
265	C₂×Dic₅	—	3	2	no	—
266	C₂×Dic₅	—	3	2	no	—
267	C₂×Dic₅	—	3	2	no	—
268	C₂×Dic₅	—	6	2	no	—
269	C₂×Dic₅	—	6	2	no	—
270	C₂×Dic₅	—	6	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	C₂×#67	1	4	yes	complemented
276	#168	—	6	2	no	—
277	#168	—	6	2	no	—
278	C₂²×D₄	—	15	1	no	—
279	C₂³×C₄	—	15	1	no	—
280	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
281	C₂×M₁₆	—	15	4	no	—
282	C₂×M₁₆	—	30	4	no	—
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	15	1	no	—
285	C₂²×C₈	—	15	1	no	—
286	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
287	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
288	C₂²×C₈	C₂×D₁₅	1	4	yes	complemented
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	—	15	1	no	—
295	C₄⋊C₈	—	15	4	no	—
296	C₂²⋊C₈	—	15	4	no	—
297	C₂²⋊C₈	—	15	4	no	—
298	#97	—	15	4	no	—
299	C₂×C₃×C₅	—	2	4	no	—
300	C₂×C₃×C₅	#435	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
304	D₁₅	—	4	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	#676	1	4	yes	complemented
308	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
309	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
310	C₂²×D₃	—	5	2	no	—
311	C₂²×D₃	—	10	2	no	—
312	C₂²×D₃	—	10	2	no	—
313	C₂²×D₃	—	10	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
319	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
320	C₂×C₃×C₄	#709	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
322	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
323	#67	—	10	8	no	—
324	C₂×Dic₃	—	5	2	no	—
325	C₂×Dic₃	—	5	2	no	—
326	C₂×Dic₃	—	5	2	no	—
327	C₂×Dic₃	—	10	2	no	—
328	C₂×Dic₃	—	10	2	no	—
329	C₂×Dic₃	—	10	2	no	—
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	C₂×C₂²⋊D₅	1	4	yes	complemented
335	C₃⋊C₈	—	10	2	no	—
336	C₃⋊C₈	—	10	2	no	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	8	no	—
340	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
341	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
342	C₂²×C₅	#901	1	2	yes	—
343	C₂²×C₅	C₄×#67	1	2	yes	—
344	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
345	C₂×D₅	—	6	2	no	—
346	C₂×D₅	—	6	2	no	—
347	C₂×D₅	—	6	2	no	—
348	C₂×D₅	—	12	4	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	C₄×#67	1	2	yes	—
351	C₄×C₅	C₂×#235	1	1	yes	characteristic
352	C₄×C₅	C₂²×#67	1	1	yes	characteristic
353	Dic₅	—	6	2	no	—
354	Dic₅	—	6	2	no	—
355	Dic₅	—	6	2	no	—
356	C₂⁴	—	15	1	no	—
357	C₂⁴	C₄×D₁₅	1	1	yes	characteristic
358	C₂×D₄	—	15	4	no	—
359	C₂×D₄	—	30	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	15	1	no	—
363	C₂²×C₄	—	15	1	no	—
364	C₂²×C₄	—	15	1	no	—
365	C₂²×C₄	—	15	2	no	—
366	C₂²×C₄	—	15	2	no	—
367	C₂²×C₄	—	30	2	no	—
368	C₂²×C₄	—	30	2	no	—
369	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
370	C₂²×C₄	C₄×D₁₅	1	2	yes	—
371	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
372	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
373	M₁₆	—	30	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	8	no	—
376	C₂×C₈	—	15	2	no	—
377	C₂×C₈	—	15	2	no	—
378	C₂×C₈	—	30	2	no	—
379	C₂×C₈	—	30	2	no	—
380	C₂×C₈	#1220	1	4	yes	complemented
381	C₂×C₈	C₂²×D₁₅	1	2	yes	—
382	C₂×C₈	C₂²×D₁₅	1	2	yes	—
383	C₄⋊C₄	—	15	4	no	—
384	C₂²⋊C₄	—	15	4	no	—
385	C₂²⋊C₄	—	15	4	no	—
386	C₄²	—	15	2	no	—
387	C₄²	—	15	2	no	—
388	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	8	no	—
392	C₂²×C₃	C₂×#676	1	2	yes	—
393	C₂²×C₃	C₂×#676	1	4	yes	complemented
394	C₂²×C₃	#4047	1	2	yes	—
395	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
396	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
397	C₂×D₃	—	10	2	no	—
398	C₂×D₃	—	10	2	no	—
399	C₂×D₃	—	10	2	no	—
400	C₂×D₃	—	20	4	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
403	C₃×C₄	C₂×#709	1	1	yes	characteristic
404	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
405	Dic₃	—	10	2	no	—
406	Dic₃	—	10	2	no	—
407	Dic₃	—	10	2	no	—
408	C₂×C₅	—	2	4	no	—
409	C₂×C₅	#5111	1	4	yes	complemented
410	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
411	C₂×C₅	C₂×#901	1	1	yes	characteristic
412	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
413	D₅	—	12	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	15	2	no	—
417	C₂³	—	30	2	no	—
418	C₂³	—	30	2	no	—
419	C₂³	—	30	2	no	—
420	C₂³	#6705	1	4	yes	complemented
421	C₂³	C₂×C₄×D₁₅	1	2	yes	—
422	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
423	D₄	—	30	8	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	15	2	no	—
429	C₂×C₄	—	15	2	no	—
430	C₂×C₄	—	15	2	no	—
431	C₂×C₄	—	30	2	no	—
432	C₂×C₄	—	30	2	no	—
433	C₂×C₄	—	30	2	no	—
434	C₂×C₄	—	30	4	no	—
435	C₂×C₄	—	30	2	no	—
436	C₂×C₄	—	30	2	no	—
437	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
438	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
439	C₂×C₄	#6817	1	2	yes	—
440	C₂×C₄	C₂×#1220	1	2	yes	—
441	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	30	2	no	—
444	C₈	—	30	2	no	—
445	C₈	C₂×#1220	1	4	yes	complemented
446	C₂×C₃	—	2	4	no	—
447	C₂×C₃	#65400	1	4	yes	complemented
448	C₂×C₃	C₂²×#676	1	1	yes	characteristic
449	C₂×C₃	C₂×#4047	1	1	yes	characteristic
450	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
451	D₃	—	20	2	no	—
452	C₅	C₂×#5111	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	2	2	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	30	2	no	—
457	C₂²	—	30	2	no	—
458	C₂²	—	30	2	no	—
459	C₂²	—	60	4	no	—
460	C₂²	C₂×#6705	1	2	yes	—
461	C₂²	C₂×#6705	1	4	yes	complemented
462	C₂²	#91790	1	2	yes	—
463	C₂²	C₄×#1220	1	2	yes	—
464	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	30	2	no	—
467	C₄	—	30	2	no	—
468	C₄	—	30	2	no	—
469	C₄	C₄×#1220	1	2	yes	—
470	C₄	C₂×#6817	1	1	yes	characteristic
471	C₄	C₂²×#1220	1	1	yes	characteristic
472	C₃	C₂×#65400	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	4	no	—
474	C₂	—	60	2	no	—
475	C₂	#11751212	1	4	yes	direct product factor
476	C₂	C₂²×#6705	1	1	yes	characteristic
477	C₂	C₂×#91790	1	1	yes	characteristic
478	C₂	C₂×C₄×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×#1220	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₈	D₁₅
hypocenter	C₃×C₅	C₂×#435
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×C₈	C₂	semidirect
3. C₂²×#6705	C₂	semidirect
4. C₂×#91114	C₂	semidirect
5. #11751212	C₂	direct (N × H)
6. C₂×#91104	C₂	semidirect
7. C₂×#91099	C₂	semidirect
8. C₂×#91098	C₂	semidirect
16. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₂×#6705	C₂²	semidirect
27. #91114	C₂²	semidirect
28. #91104	C₂²	semidirect
29. #91099	C₂²	semidirect
30. #91098	C₂²	semidirect
32. C₂³×C₅×C₈	D₃	semidirect
59. C₂×C₃×C₅×C₈	D₄	semidirect
72. C₂³×C₃×C₈	D₅	semidirect
86. C₂²×C₅×C₈	C₂×D₃	semidirect
104. C₂³×C₃×C₅	M₁₆	semidirect
131. C₃×C₅×C₈	C₂×D₄	semidirect
140. C₂²×C₃×C₈	C₂×D₅	semidirect
174. C₂×C₅×C₈	#67	semidirect
188. C₂³×C₈	D₁₅	semidirect
200. C₂²×C₃×C₅	C₂×M₁₆	semidirect
233. C₂×C₃×C₈	C₂²⋊D₅	semidirect
248. C₂³×C₅	ΓL(1,𝔽₂₅)	semidirect
275. C₅×C₈	C₂×#67	semidirect
288. C₂²×C₈	C₂×D₁₅	semidirect
300. C₂×C₃×C₅	#435	semidirect
307. C₂³×C₃	#676	semidirect
334. C₃×C₈	C₂×C₂²⋊D₅	semidirect
341. C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
380. C₂×C₈	#1220	semidirect
388. C₃×C₅	C₂×#435	semidirect
393. C₂²×C₃	C₂×#676	semidirect
409. C₂×C₅	#5111	semidirect
420. C₂³	#6705	semidirect
445. C₈	C₂×#1220	semidirect
447. C₂×C₃	#65400	semidirect
452. C₅	C₂×#5111	semidirect
461. C₂²	C₂×#6705	semidirect
472. C₃	C₂×#65400	semidirect
475. C₂	#11751212	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×C₈	2
C₂×C₄×#1220	2
C₂²×#6705	2
C₂×#91114	2
#11751212	2
C₂×#91104	2
C₂×#91099	2
C₂×#91098	2
C₂×#65400	3
C₂×#5111	5

Subgroups — C2×#11751212 #14414689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751212 #14414689