Subgroups — C₂×#67×#168 #14414635

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	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91114	C₂	1	1	yes	maximal, characteristic, complemented
5	#67×#168	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×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄×#168	—	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	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂×C₅×#217	C₄	1	1	yes	characteristic
16	C₄×C₅×#67	C₄	1	4	yes	—
17	C₄×C₅×#67	C₂²	1	4	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₃×#168	—	2	4	no	—
22	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#168	C₂²	1	4	yes	complemented
25	C₂×D₃×#168	—	2	4	no	—
26	C₂×D₃×#168	C₂²	1	4	yes	complemented
27	#91114	C₂²	1	4	yes	complemented
28	Dic₃⋊#168	C₂²	1	4	yes	complemented
29	(C₂×D₃)⋊#168	C₂²	1	4	yes	complemented
30	Dic₃×#168	C₂²	1	4	yes	complemented
31	C₂×C₈×#67	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×D₄	—	3	1	no	—
33	C₂³×#168	—	3	1	no	—
34	C₂³×#168	D₃	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊#168	—	3	1	no	—
36	C₂×C₂²⋊#168	—	3	1	no	—
37	D₄×#168	—	3	8	no	—
38	C₂×C₄⋊#168	—	3	1	no	—
39	C₂×C₄×#168	—	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	C₈	1	8	yes	complemented
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	2	no	—
59	C₂×C₃⋊#168	C₂³	1	2	yes	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₅×#217	C₂×C₄	1	4	yes	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
63	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
64	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂³	1	2	yes	—
66	C₂×C₃×#168	—	2	2	no	—
67	C₂×C₃×#168	—	2	8	no	—
68	C₂×C₃×#168	D₄	1	4	yes	complemented
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#168	C₂³	1	2	yes	—
71	D₃×#168	—	2	8	no	—
72	C₂³×C₃×C₈	—	5	1	no	—
73	C₂×C₄×#67	D₅	1	1	yes	characteristic
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	—	5	1	no	—
79	C₂×C₈×Dic₃	—	5	1	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	C₂²×#168	—	2	4	no	—
90	C₂²×#168	—	3	1	no	—
91	C₂²×#168	—	3	1	no	—
92	C₂²×#168	—	3	4	no	—
93	C₂²×#168	—	6	4	no	—
94	C₂²×#168	C₂×D₃	1	1	yes	characteristic
95	C₂²×#168	C₂×D₃	1	1	yes	characteristic
96	C₂²×#168	C₂×D₃	1	4	yes	complemented
97	C₂²⋊#168	—	3	4	no	—
98	C₂²⋊#168	—	3	4	no	—
99	C₄⋊#168	—	3	4	no	—
100	C₄×#168	—	3	4	no	—
101	C₂×C₈×D₄	—	15	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂×C₈	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	C₂×C₈	1	4	yes	complemented
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	C₂×C₈	1	16	yes	complemented
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	2	2	no	—
123	C₂×C₅×Dic₃	C₂×C₈	1	4	yes	complemented
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	—	2	2	no	—
132	C₃×#168	—	2	2	no	—
133	C₃×#168	C₂×D₄	1	4	yes	complemented
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	C₂²×C₃×C₈	—	5	4	no	—
140	C₂²×C₃×C₈	—	10	4	no	—
141	C₂×#217	Dic₅	1	1	yes	characteristic
142	C₄×#67	Dic₅	1	4	yes	—
143	C₄×#67	C₂×D₅	1	4	yes	—
144	C₂×(C₂×D₃)⋊C₄	Dic₅	1	1	yes	characteristic
145	C₂×Dic₃⋊C₄	Dic₅	1	1	yes	characteristic
146	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
147	C₂²×C₃⋊C₈	—	5	1	no	—
148	C₂²×C₃⋊C₈	—	5	1	no	—
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	—	5	4	no	—
154	C₈×Dic₃	—	5	4	no	—
155	C₂⁴×C₅	—	3	1	no	—
156	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
157	C₂×C₅×D₄	—	3	8	no	—
158	C₂×C₅×D₄	—	3	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	C₂×#168	—	2	2	no	—
178	C₂×#168	—	2	8	no	—
179	C₂×#168	—	3	2	no	—
180	C₂×#168	—	3	2	no	—
181	C₂×#168	—	6	2	no	—
182	C₂×#168	—	6	2	no	—
183	C₂×#168	—	6	8	no	—
184	C₂×#168	#67	1	4	yes	direct product factor
185	C₂×#168	C₂²×D₃	1	2	yes	—
186	C₂×#168	C₂²×D₃	1	2	yes	—
187	C₂³×C₈	—	5	1	no	—
188	C₂³×C₈	—	15	1	no	—
189	C₂×C₄×D₄	—	3	1	no	—
190	C₈×D₄	—	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×C₄×C₈	—	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	C₂²×C₈	1	2	yes	—
200	C₂²×C₃×C₅	C₂²×C₈	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	8	no	—
206	C₂×C₅×D₃	C₂²×C₈	1	4	yes	complemented
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	C₂²×C₈	1	4	yes	complemented
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	#168	1	8	yes	direct product factor
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	4	no	—
232	C₂×C₃×C₈	—	5	2	no	—
233	C₂×C₃×C₈	—	5	2	no	—
234	C₂×C₃×C₈	—	10	8	no	—
235	C₂×C₃×C₈	—	10	2	no	—
236	#217	C₂×Dic₅	1	4	yes	—
237	(C₂×D₃)⋊C₄	C₂×Dic₅	1	4	yes	—
238	Dic₃⋊C₄	C₂×Dic₅	1	4	yes	—
239	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
240	C₄×Dic₃	C₂²×D₅	1	2	yes	—
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	D₃×C₈	—	10	8	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	3	4	no	—
249	C₂³×C₅	—	3	2	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	—	6	2	no	—
252	C₂³×C₅	D₃×C₈	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	—	3	16	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	4	no	—
261	C₂×C₄×C₅	—	3	2	no	—
262	C₂×C₄×C₅	—	3	2	no	—
263	C₂×C₄×C₅	—	3	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	#235	1	2	yes	—
272	C₂×C₄×C₅	C₂×#67	1	2	yes	—
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	#168	—	2	2	no	—
275	#168	—	6	2	no	—
276	#168	—	6	2	no	—
277	#168	C₂×#67	1	4	yes	direct product factor
278	C₂²×D₄	—	3	1	no	—
279	C₂³×C₄	—	3	1	no	—
280	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
281	C₂²×C₈	—	5	1	no	—
282	C₂²×C₈	—	5	4	no	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	10	4	no	—
285	C₂²×C₈	—	15	4	no	—
286	C₂²×C₈	—	15	1	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	—	15	4	no	—
297	C₂²⋊C₈	—	15	4	no	—
298	C₄×C₈	—	15	4	no	—
299	C₂×C₃×C₅	—	2	4	no	—
300	C₂×C₃×C₅	C₈×D₄	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
304	C₅×D₃	—	2	4	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	C₂×#168	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	C₂×#168	1	4	yes	complemented
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	C₂×#168	1	16	yes	direct product factor
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	—	2	2	no	—
326	C₂×Dic₃	C₂×#168	1	4	yes	complemented
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	—	5	4	no	—
334	C₃×C₈	—	10	2	no	—
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	—	3	4	no	—
341	C₂²×C₅	—	6	2	no	—
342	C₂²×C₅	—	6	2	no	—
343	C₂²×C₅	—	6	8	no	—
344	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
345	C₂²×C₅	C₂×D₃×C₈	1	4	yes	complemented
346	C₂²×C₅	#901	1	2	yes	—
347	C₂²×C₅	C₄×#67	1	2	yes	—
348	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	3	4	no	—
351	C₄×C₅	—	6	2	no	—
352	C₄×C₅	—	6	2	no	—
353	C₄×C₅	C₄×#67	1	2	yes	—
354	C₄×C₅	C₂×#235	1	1	yes	characteristic
355	C₄×C₅	C₂²×#67	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	—	3	8	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	C₂×C₈	—	5	4	no	—
374	C₂×C₈	—	5	2	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	10	8	no	—
377	C₂×C₈	—	10	2	no	—
378	C₂×C₈	—	15	2	no	—
379	C₂×C₈	—	15	2	no	—
380	C₂×C₈	—	30	8	no	—
381	C₂×C₈	—	30	2	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×C₈×D₄	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	C₂²×#168	1	2	yes	—
393	C₂²×C₃	C₂²×#168	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	8	no	—
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	2	2	no	—
400	C₂×D₃	C₂²×#168	1	4	yes	complemented
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	C₂²×#168	1	4	yes	complemented
408	C₂×C₅	—	2	4	no	—
409	C₂×C₅	—	6	4	no	—
410	C₂×C₅	C₈×#67	1	4	yes	complemented
411	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
412	C₂×C₅	C₂×#901	1	1	yes	characteristic
413	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	3	2	no	—
417	C₂³	—	3	4	no	—
418	C₂³	—	6	2	no	—
419	C₂³	—	6	2	no	—
420	C₂³	D₃×#168	1	4	yes	complemented
421	C₂³	C₂×D₃×Dic₅	1	2	yes	—
422	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
423	D₄	—	3	16	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	4	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	3	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	C₂×D₃×Dic₅	1	2	yes	—
438	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
439	C₂×C₄	#6782	1	2	yes	—
440	C₂×C₄	D₅×#67	1	2	yes	—
441	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
442	C₈	—	5	4	no	—
443	C₈	—	10	2	no	—
444	C₈	—	30	2	no	—
445	C₈	—	30	2	no	—
446	C₂×C₃	—	2	4	no	—
447	C₂×C₃	D₄×#168	1	4	yes	complemented
448	C₂×C₃	C₂³×#168	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	—	2	4	no	—
452	C₅	C₂×C₈×#67	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	2	2	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	3	4	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	8	no	—
459	C₂²	—	6	2	no	—
460	C₂²	C₂×D₃×#168	1	2	yes	—
461	C₂²	C₂×D₃×#168	1	4	yes	complemented
462	C₂²	#91286	1	2	yes	—
463	C₂²	Dic₅×#67	1	2	yes	—
464	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	3	4	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₄	Dic₅×#67	1	2	yes	—
470	C₄	C₂×#6782	1	1	yes	characteristic
471	C₄	C₂×D₅×#67	1	1	yes	characteristic
472	C₃	C₂×D₄×#168	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	2	4	no	—
474	C₂	—	6	4	no	—
475	C₂	#67×#168	1	4	yes	direct product factor
476	C₂	C₂²×D₃×#168	1	1	yes	characteristic
477	C₂	C₂×#91286	1	1	yes	characteristic
478	C₂	C₂×Dic₅×#67	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	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×C₈×D₄
LCS	G ▷ C₂×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
2. C₂³×C₃×#168	C₂	semidirect
3. C₂²×D₃×#168	C₂	semidirect
4. C₂×#91114	C₂	semidirect
5. #67×#168	C₂	direct (N × H)
6. C₂×Dic₃⋊#168	C₂	semidirect
7. C₂×(C₂×D₃)⋊#168	C₂	semidirect
8. C₂×Dic₃×#168	C₂	semidirect
24. C₂²×C₃×#168	C₂²	semidirect
26. C₂×D₃×#168	C₂²	semidirect
27. #91114	C₂²	semidirect
28. Dic₃⋊#168	C₂²	semidirect
29. (C₂×D₃)⋊#168	C₂²	semidirect
30. Dic₃×#168	C₂²	semidirect
34. C₂³×#168	D₃	semidirect
48. C₂×C₅×#67	C₈	semidirect
68. C₂×C₃×#168	D₄	semidirect
96. C₂²×#168	C₂×D₃	semidirect
104. C₂³×C₃×C₅	C₂×C₈	semidirect
109. C₂²×C₅×D₃	C₂×C₈	semidirect
120. C₅×#67	C₂×C₈	semidirect
123. C₂×C₅×Dic₃	C₂×C₈	semidirect
133. C₃×#168	C₂×D₄	semidirect
184. C₂×#168	#67	direct (N × H)
200. C₂²×C₃×C₅	C₂²×C₈	semidirect
206. C₂×C₅×D₃	C₂²×C₈	semidirect
213. C₅×Dic₃	C₂²×C₈	semidirect
222. C₂×#67	#168	direct (N × H)
252. C₂³×C₅	D₃×C₈	semidirect
277. #168	C₂×#67	direct (N × H)
300. C₂×C₃×C₅	C₈×D₄	semidirect
307. C₂³×C₃	C₂×#168	semidirect
312. C₂²×D₃	C₂×#168	semidirect
323. #67	C₂×#168	direct (N × H)
326. C₂×Dic₃	C₂×#168	semidirect
345. C₂²×C₅	C₂×D₃×C₈	semidirect
388. C₃×C₅	C₂×C₈×D₄	semidirect
393. C₂²×C₃	C₂²×#168	semidirect
400. C₂×D₃	C₂²×#168	semidirect
407. Dic₃	C₂²×#168	semidirect
410. C₂×C₅	C₈×#67	semidirect
420. C₂³	D₃×#168	semidirect
447. C₂×C₃	D₄×#168	semidirect
452. C₅	C₂×C₈×#67	semidirect
461. C₂²	C₂×D₃×#168	semidirect
472. C₃	C₂×D₄×#168	semidirect
475. C₂	#67×#168	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×#67	2
C₂³×C₃×#168	2
C₂²×D₃×#168	2
C₂×#91114	2
#67×#168	2
C₂×Dic₃⋊#168	2
C₂×(C₂×D₃)⋊#168	2
C₂×Dic₃×#168	2
C₂×D₄×#168	3
C₂×C₈×#67	5

Subgroups — C2×#67×#168 #14414635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#67×#168 #14414635