Subgroups — C₂×#11748508 #14414734

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⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6650	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	#11748508	C₂	1	8	yes	maximal, direct product factor
6	C₂×Dic₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×(C₂×D₃)⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90953	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65300	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#168	—	2	4	no	—
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊#168	C₂²	1	4	yes	complemented
17	C₂×C₅×#217	C₄	1	1	yes	characteristic
18	C₄×C₅×#67	C₄	1	4	yes	—
19	C₄×C₅×#67	C₂²	1	4	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
21	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
22	C₂×C₄×C₅×Dic₃	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×#6650	—	2	4	no	—
26	C₂×#6650	C₂²	1	4	yes	complemented
27	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
28	Dic₃⋊#168	C₂²	1	4	yes	complemented
29	(C₂×D₃)⋊#168	C₂²	1	4	yes	complemented
30	#90953	C₂²	1	4	yes	complemented
31	C₂×#4730	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×D₄	—	3	1	no	—
33	C₂²×#681	—	3	1	no	—
34	C₂³×#168	—	3	1	no	—
35	C₂×C₂²⋊#168	—	3	1	no	—
36	C₂×C₂²⋊#168	D₃	1	1	yes	characteristic, complemented
37	#65300	—	3	8	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	C₂×#3935	—	3	1	no	—
40	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₅×D₃	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×C₅×#67	—	2	4	no	—
49	C₂×C₅×#67	C₂×C₄	1	4	yes	—
50	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×C₅×D₃	—	2	2	no	—
54	C₂×C₄×C₅×D₃	—	2	2	no	—
55	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
57	C₂×C₃⋊#168	—	2	2	no	—
58	C₂×C₃⋊#168	—	2	8	no	—
59	C₂×C₃⋊#168	D₄	1	4	yes	complemented
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₂×C₃⋊#168	C₂³	1	2	yes	—
62	C₅×#217	C₂×C₄	1	4	yes	—
63	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
64	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
65	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
66	C₄×C₅×Dic₃	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	#6650	—	2	8	no	—
72	C₂×C₄×#67	D₅	1	1	yes	characteristic
73	C₂³×C₃⋊C₈	—	5	1	no	—
74	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
75	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
76	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
77	C₂×#815	—	5	1	no	—
78	C₂×Dic₃⋊C₈	—	5	1	no	—
79	#4730	—	5	8	no	—
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	3	1	no	—
82	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
83	C₄×C₅×D₄	—	3	4	no	—
84	C₄×C₅×D₄	—	3	4	no	—
85	C₂×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
87	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
88	C₂×C₄²×C₅	—	3	1	no	—
89	C₂×#681	—	3	4	no	—
90	C₂×#681	—	6	4	no	—
91	C₂²×#168	—	3	1	no	—
92	C₂²×#168	—	3	4	no	—
93	C₂²×#168	—	3	1	no	—
94	C₂²×#168	—	6	4	no	—
95	C₂²×#168	C₂×D₃	1	1	yes	characteristic
96	C₂²×#168	C₂×D₃	1	1	yes	characteristic
97	C₂²⋊#168	—	3	4	no	—
98	C₂²⋊#168	C₂×D₃	1	4	yes	complemented
99	C₄⋊#168	—	3	4	no	—
100	#3935	—	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×C₅×D₃	—	2	2	no	—
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	2	2	no	—
110	C₂²×C₅×D₃	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	C₅×#67	—	2	8	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
125	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
126	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
127	C₄×C₅×D₃	—	2	4	no	—
128	C₄×C₅×D₃	—	2	2	no	—
129	C₄×C₅×D₃	—	2	2	no	—
130	C₃⋊#168	—	2	2	no	—
131	C₃⋊#168	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	Dic₅	1	1	yes	characteristic
136	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
137	C₂²×C₃×C₈	—	5	1	no	—
138	C₂²×C₃×C₈	—	5	1	no	—
139	C₂×#217	Dic₅	1	1	yes	characteristic
140	C₄×#67	Dic₅	1	4	yes	—
141	C₄×#67	C₂×D₅	1	4	yes	—
142	C₂×(C₂×D₃)⋊C₄	Dic₅	1	1	yes	characteristic
143	C₂×Dic₃⋊C₄	Dic₅	1	1	yes	characteristic
144	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
145	C₂²×C₃⋊C₈	—	5	1	no	—
146	C₂²×C₃⋊C₈	—	5	4	no	—
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	C₂²×C₃⋊C₈	—	10	4	no	—
149	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
150	C₂×ΓL(1,𝔽₂₅)	—	10	4	no	—
151	C₃×C₂²⋊C₈	—	5	4	no	—
152	(C₂×D₃)⋊C₈	—	5	4	no	—
153	#815	—	5	4	no	—
154	Dic₃⋊C₈	—	5	4	no	—
155	C₂⁴×C₅	—	3	1	no	—
156	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
157	C₂×C₅×D₄	—	3	4	no	—
158	C₂×C₅×D₄	—	6	4	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	3	1	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	3	1	no	—
164	C₂²×C₄×C₅	—	3	2	no	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	—	6	2	no	—
167	C₂²×C₄×C₅	—	6	2	no	—
168	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×C₄⋊C₄	—	3	4	no	—
173	C₅×C₂²⋊C₄	—	3	4	no	—
174	C₅×C₂²⋊C₄	—	3	4	no	—
175	C₄²×C₅	—	3	2	no	—
176	C₄²×C₅	—	3	2	no	—
177	#681	—	6	8	no	—
178	C₂×#168	—	2	2	no	—
179	C₂×#168	—	2	2	no	—
180	C₂×#168	—	3	4	no	—
181	C₂×#168	—	3	2	no	—
182	C₂×#168	—	3	2	no	—
183	C₂×#168	—	6	8	no	—
184	C₂×#168	—	6	2	no	—
185	C₂×#168	C₂²×D₃	1	2	yes	—
186	C₂×#168	C₂²×D₃	1	2	yes	—
187	C₂²×M₁₆	—	15	1	no	—
188	C₂³×C₈	—	15	1	no	—
189	C₂×C₄×D₄	—	3	1	no	—
190	#435	—	15	8	no	—
191	C₂×C₄⋊C₈	—	15	1	no	—
192	C₂×C₂²⋊C₈	—	5	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×C₅×D₃	—	2	2	no	—
204	C₂×C₅×D₃	—	2	2	no	—
205	C₂×C₅×D₃	—	2	2	no	—
206	C₂×C₅×D₃	—	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	C₅×Dic₃	—	2	2	no	—
212	C₅×Dic₃	—	2	2	no	—
213	C₅×Dic₃	—	2	2	no	—
214	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
215	C₂³×D₃	C₂×Dic₅	1	1	yes	characteristic
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	—	2	2	no	—
218	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂×Dic₅	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	—	2	4	no	—
223	C₂×#67	C₂×Dic₅	1	4	yes	—
224	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
225	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
226	C₂²×Dic₃	C₂×Dic₅	1	1	yes	characteristic
227	C₂×C₄×D₃	—	2	2	no	—
228	C₂×C₄×D₃	—	2	2	no	—
229	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
230	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
231	C₂×C₃×C₈	—	5	2	no	—
232	C₂×C₃×C₈	—	5	2	no	—
233	C₂×C₃×C₈	—	10	2	no	—
234	C₂×C₃×C₈	—	10	2	no	—
235	#217	C₂×Dic₅	1	4	yes	—
236	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
237	Dic₃⋊C₄	C₂×Dic₅	1	4	yes	—
238	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
239	C₄×Dic₃	C₂²×D₅	1	2	yes	—
240	C₂×C₃⋊C₈	—	5	4	no	—
241	C₂×C₃⋊C₈	—	5	2	no	—
242	C₂×C₃⋊C₈	—	5	2	no	—
243	C₂×C₃⋊C₈	—	10	8	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	—	3	2	no	—
249	C₂³×C₅	—	6	2	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	—	6	2	no	—
252	C₂³×C₅	ΓL(1,𝔽₂₅)	1	4	yes	complemented
253	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
254	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
255	C₅×D₄	—	6	8	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	3	2	no	—
261	C₂×C₄×C₅	—	3	2	no	—
262	C₂×C₄×C₅	—	3	2	no	—
263	C₂×C₄×C₅	—	6	2	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	4	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	6	2	no	—
269	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
270	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
271	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
272	C₂×C₄×C₅	#237	1	2	yes	—
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	#168	—	2	2	no	—
275	#168	—	2	2	no	—
276	#168	—	3	4	no	—
277	#168	—	6	2	no	—
278	C₂²×D₄	—	3	1	no	—
279	C₂³×C₄	—	3	1	no	—
280	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
281	C₂×M₁₆	—	15	4	no	—
282	C₂×M₁₆	—	30	4	no	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	15	1	no	—
286	C₂²×C₈	—	15	4	no	—
287	C₂²×C₈	—	15	1	no	—
288	C₂²×C₈	—	30	4	no	—
289	C₄×D₄	—	3	4	no	—
290	C₄×D₄	—	3	4	no	—
291	C₂×C₄⋊C₄	—	3	1	no	—
292	C₂×C₂²⋊C₄	—	3	1	no	—
293	C₂×C₂²⋊C₄	—	3	1	no	—
294	C₂×C₄²	—	3	1	no	—
295	C₄⋊C₈	—	15	4	no	—
296	C₂²⋊C₈	—	5	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	C₅×D₃	—	4	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	#681	1	4	yes	complemented
308	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
309	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
310	C₂²×D₃	—	2	2	no	—
311	C₂²×D₃	—	2	2	no	—
312	C₂²×D₃	—	2	2	no	—
313	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
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	D₄×D₅	1	2	yes	—
319	C₂×C₃×C₄	#711	1	2	yes	—
320	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
321	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
323	#67	—	2	8	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	—	2	2	no	—
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
328	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
329	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
330	C₄×D₃	—	2	2	no	—
331	C₄×D₃	—	2	2	no	—
332	C₄×D₃	—	2	4	no	—
333	C₃×C₈	—	10	2	no	—
334	C₃×C₈	—	10	2	no	—
335	C₃⋊C₈	—	5	4	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	—	6	2	no	—
341	C₂²×C₅	—	6	2	no	—
342	C₂²×C₅	—	6	2	no	—
343	C₂²×C₅	—	12	4	no	—
344	C₂²×C₅	#67⋊C₄	1	2	yes	—
345	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
346	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	4	yes	complemented
347	C₂²×C₅	#907	1	2	yes	—
348	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	—	6	2	no	—
352	C₄×C₅	—	6	2	no	—
353	C₄×C₅	#67⋊C₄	1	2	yes	—
354	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
355	C₄×C₅	C₂×#237	1	1	yes	characteristic
356	C₂⁴	—	3	1	no	—
357	C₂⁴	D₃×Dic₅	1	1	yes	characteristic
358	C₂×D₄	—	3	4	no	—
359	C₂×D₄	—	6	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	6	2	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
370	C₂²×C₄	D₃×Dic₅	1	2	yes	—
371	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
372	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
373	M₁₆	—	30	8	no	—
374	C₂×C₈	—	5	2	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	10	2	no	—
377	C₂×C₈	—	10	2	no	—
378	C₂×C₈	—	15	4	no	—
379	C₂×C₈	—	15	2	no	—
380	C₂×C₈	—	15	2	no	—
381	C₂×C₈	—	30	8	no	—
382	C₂×C₈	—	30	2	no	—
383	C₄⋊C₄	—	3	4	no	—
384	C₂²⋊C₄	—	3	4	no	—
385	C₂²⋊C₄	—	3	4	no	—
386	C₄²	—	3	2	no	—
387	C₄²	—	3	2	no	—
388	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	8	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	C₂×#681	1	2	yes	—
393	C₂²×C₃	C₂×#681	1	4	yes	complemented
394	C₂²×C₃	D₄×Dic₅	1	2	yes	—
395	C₂²×C₃	#4094	1	2	yes	—
396	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	2	2	no	—
400	C₂×D₃	—	4	4	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	D₄×Dic₅	1	2	yes	—
403	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
404	C₃×C₄	C₂×#711	1	1	yes	characteristic
405	Dic₃	—	2	2	no	—
406	Dic₃	—	2	2	no	—
407	Dic₃	—	2	2	no	—
408	C₂×C₅	—	2	4	no	—
409	C₂×C₅	—	12	2	no	—
410	C₂×C₅	#4730	1	4	yes	complemented
411	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
412	C₂×C₅	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
413	C₂×C₅	C₂×#907	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	3	2	no	—
417	C₂³	—	6	2	no	—
418	C₂³	—	6	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	#6650	1	4	yes	complemented
421	C₂³	C₂×D₃×Dic₅	1	2	yes	—
422	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
423	D₄	—	6	8	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	4	no	—
437	C₂×C₄	#6780	1	2	yes	—
438	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
439	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
440	C₂×C₄	#6790	1	2	yes	—
441	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
442	C₈	—	10	2	no	—
443	C₈	—	10	2	no	—
444	C₈	—	15	4	no	—
445	C₈	—	30	2	no	—
446	C₂×C₃	—	2	4	no	—
447	C₂×C₃	#65300	1	4	yes	complemented
448	C₂×C₃	C₂²×#681	1	1	yes	characteristic
449	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
450	C₂×C₃	C₂×#4094	1	1	yes	characteristic
451	D₃	—	4	2	no	—
452	C₅	C₂×#4730	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	6	2	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	12	4	no	—
460	C₂²	#91288	1	2	yes	—
461	C₂²	C₂×#6650	1	2	yes	—
462	C₂²	C₂×#6650	1	4	yes	complemented
463	C₂²	#67⋊Dic₅	1	2	yes	—
464	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	6	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₄	#67⋊Dic₅	1	2	yes	—
470	C₄	C₂×#6780	1	1	yes	characteristic
471	C₄	C₂×#6790	1	1	yes	characteristic
472	C₃	C₂×#65300	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	4	no	—
474	C₂	—	12	2	no	—
475	C₂	#11748508	1	4	yes	direct product factor
476	C₂	C₂×#91288	1	1	yes	characteristic
477	C₂	C₂²×#6650	1	1	yes	characteristic
478	C₂	C₂×#67⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₅×#67	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#435
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃⋊#168	C₂	semidirect
3. C₂²×#6650	C₂	semidirect
4. C₂×C₃×C₂²⋊#168	C₂	semidirect
5. #11748508	C₂	direct (N × H)
6. C₂×Dic₃⋊#168	C₂	semidirect
7. C₂×(C₂×D₃)⋊#168	C₂	semidirect
8. C₂×#90953	C₂	semidirect
16. C₂²×C₃⋊#168	C₂²	semidirect
26. C₂×#6650	C₂²	semidirect
27. C₃×C₂²⋊#168	C₂²	semidirect
28. Dic₃⋊#168	C₂²	semidirect
29. (C₂×D₃)⋊#168	C₂²	semidirect
30. #90953	C₂²	semidirect
36. C₂×C₂²⋊#168	D₃	semidirect
59. C₂×C₃⋊#168	D₄	semidirect
98. C₂²⋊#168	C₂×D₃	semidirect
104. C₂³×C₃×C₅	M₁₆	semidirect
131. C₃⋊#168	C₂×D₄	semidirect
200. C₂²×C₃×C₅	C₂×M₁₆	semidirect
252. C₂³×C₅	ΓL(1,𝔽₂₅)	semidirect
300. C₂×C₃×C₅	#435	semidirect
307. C₂³×C₃	#681	semidirect
346. C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
388. C₃×C₅	C₂×#435	semidirect
393. C₂²×C₃	C₂×#681	semidirect
410. C₂×C₅	#4730	semidirect
420. C₂³	#6650	semidirect
447. C₂×C₃	#65300	semidirect
452. C₅	C₂×#4730	semidirect
462. C₂²	C₂×#6650	semidirect
472. C₃	C₂×#65300	semidirect
475. C₂	#11748508	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⋊#168	2
C₂×C₄×C₅×#67	2
C₂²×#6650	2
C₂×C₃×C₂²⋊#168	2
#11748508	2
C₂×Dic₃⋊#168	2
C₂×(C₂×D₃)⋊#168	2
C₂×#90953	2
C₂×#65300	3
C₂×#4730	5

Subgroups — C2×#11748508 #14414734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748508 #14414734