Subgroups — #168×#237 #14418912

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic
2	D₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#67⋊#168	C₂	1	2	yes	maximal, complemented
5	#67×#168	C₂	1	2	yes	maximal, complemented
6	#11748329	C₂	1	2	yes	maximal, complemented
7	C₂×Dic₃×#168	C₂	1	2	yes	maximal, complemented
8	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746857	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746853	C₂	1	1	yes	maximal, characteristic, complemented
11	Dic₆×#168	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×#168	—	3	1	no	maximal, Hall
13	C₂×C₅×#237	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊#168	C₂²	1	2	yes	—
16	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
17	C₄×C₅×#67	C₂²	1	2	yes	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
19	C₅×#892	C₄	1	1	yes	characteristic
20	C₅×#887	C₄	1	1	yes	characteristic
21	C₅×#67⋊C₄	C₄	1	2	yes	—
22	C₅×#877	C₄	1	2	yes	—
23	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₂×D₃×#168	C₂²	1	1	yes	characteristic
27	C₂×D₃×#168	C₂²	1	1	yes	characteristic
28	#91114	C₂²	1	2	yes	—
29	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₃×C₂²⋊#168	C₂²	1	2	yes	—
32	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
33	C₃×C₄×#168	C₂²	1	1	yes	characteristic
34	Dic₃⋊#168	C₂²	1	2	yes	—
35	Dic₃⋊#168	C₂²	1	2	yes	—
36	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
37	Dic₃×#168	C₂²	1	2	yes	—
38	Dic₃×#168	C₂²	1	2	yes	—
39	Dic₃×#168	C₂²	1	2	yes	—
40	Dic₃×#168	C₂²	1	1	yes	characteristic
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	C₈×#237	—	5	1	no	maximal, Hall
43	C₄×C₅×#41	—	3	1	no	—
44	Q₈×#168	—	3	1	no	—
45	Q₈×#168	—	3	1	no	—
46	D₄×#168	—	3	2	no	—
47	D₄×#168	—	3	2	no	—
48	D₄×#168	—	3	1	no	—
49	D₄×#168	D₃	1	1	yes	characteristic, complemented
50	#65214	—	3	2	no	—
51	#65214	—	3	1	no	—
52	C₂×C₄×#168	—	3	2	no	—
53	C₂×C₄×#168	—	3	1	no	—
54	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂×C₅×#67	C₂×C₄	1	2	yes	—
57	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
58	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
59	C₅×#237	C₈	1	8	yes	complemented
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₃⋊#168	—	2	4	no	—
68	C₂×C₃⋊#168	C₂³	1	2	yes	—
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₅×#217	C₂×C₄	1	2	yes	—
72	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
80	C₄×C₅×Dic₃	C₂³	1	2	yes	—
81	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	—	2	4	no	—
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	D₃×#168	—	2	2	no	—
87	D₃×#168	—	2	2	no	—
88	C₄×#237	D₅	1	1	yes	characteristic
89	C₃×C₈×D₄	—	5	1	no	—
90	C₈×#67	—	5	2	no	—
91	C₂×C₈×Dic₃	—	5	2	no	—
92	D₄×C₃⋊C₈	—	5	1	no	—
93	#4833	—	5	1	no	—
94	#4830	—	5	1	no	—
95	#67⋊C₈	—	5	2	no	—
96	#4718	—	5	2	no	—
97	C₄×D₃×C₈	—	5	1	no	—
98	C₈×Dic₆	—	5	1	no	—
99	C₂×C₅×#41	—	3	1	no	—
100	C₄×C₅×Q₈	—	3	1	no	—
101	C₄×C₅×Q₈	—	3	1	no	—
102	C₄×C₅×D₄	—	3	1	no	—
103	C₄×C₅×D₄	—	3	2	no	—
104	C₄×C₅×D₄	—	3	2	no	—
105	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
106	C₅×#117	—	3	1	no	—
107	C₅×#117	—	3	2	no	—
108	C₂×C₄²×C₅	—	3	2	no	—
109	C₂×C₄²×C₅	—	3	1	no	—
110	C₂²×#168	—	3	2	no	—
111	C₂²×#168	—	3	1	no	—
112	C₂²×#168	—	3	1	no	—
113	C₂²×#168	C₂×D₃	1	2	yes	—
114	C₂²⋊#168	—	3	2	no	—
115	C₂²⋊#168	—	3	2	no	—
116	C₂²⋊#168	C₂×D₃	1	2	yes	—
117	C₄⋊#168	—	3	1	no	—
118	C₄⋊#168	—	3	2	no	—
119	C₄⋊#168	—	3	2	no	—
120	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
121	C₄×#168	—	3	1	no	—
122	C₄×#168	—	3	2	no	—
123	C₄×#168	—	3	2	no	—
124	C₄×#168	—	3	1	no	—
125	C₄×#168	—	3	2	no	—
126	C₄×#168	—	3	1	no	—
127	C₄×#168	C₂×D₃	1	1	yes	characteristic
128	C₈×#41	—	15	1	no	Sylow
129	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
130	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×D₄	C₂×C₈	1	4	yes	complemented
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×#67	C₂×C₈	1	8	yes	complemented
139	C₂×C₅×Dic₃	—	2	4	no	—
140	C₂×C₅×Dic₃	C₂×C₈	1	8	yes	complemented
141	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
143	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
145	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×C₅×D₃	—	2	1	no	—
147	C₄×C₅×D₃	—	2	1	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	C₂×C₈	1	4	yes	complemented
150	C₅×Dic₆	C₂×C₈	1	4	yes	complemented
151	C₃⋊#168	—	2	2	no	—
152	C₃⋊#168	—	2	1	no	—
153	C₃⋊#168	#41	1	2	yes	complemented
154	C₃×#168	—	2	2	no	—
155	C₃×#168	—	2	1	no	—
156	C₃×#168	#41	1	2	yes	complemented
157	C₂×#237	Dic₅	1	1	yes	characteristic
158	C₂²×C₃×C₈	—	5	2	no	—
159	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
160	D₄×Dic₃	Dic₅	1	1	yes	characteristic
161	C₄×#67	C₂×D₅	1	2	yes	—
162	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	—
163	C₂²×C₃⋊C₈	—	5	2	no	—
164	C₂×D₃×C₈	—	5	1	no	—
165	C₂×D₃×C₈	—	5	1	no	—
166	#892	Dic₅	1	1	yes	characteristic
167	#887	Dic₅	1	1	yes	characteristic
168	#67⋊C₄	Dic₅	1	2	yes	—
169	#877	Dic₅	1	2	yes	—
170	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
171	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄⋊C₈	—	5	1	no	—
173	C₃×C₂²⋊C₈	—	5	2	no	—
174	C₃×C₄×C₈	—	5	1	no	—
175	#830	—	5	2	no	—
176	(C₂×D₃)⋊C₈	—	5	2	no	—
177	Dic₃⋊C₈	—	5	2	no	—
178	Dic₃⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	2	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	—	5	1	no	—
182	C₈×Dic₃	—	5	2	no	—
183	C₈×Dic₃	—	5	2	no	—
184	C₄⋊(C₃⋊C₈)	—	5	1	no	—
185	C₄×C₃⋊C₈	—	5	1	no	—
186	C₅×#41	—	3	8	no	—
187	C₂×C₅×Q₈	—	3	1	no	—
188	C₂×C₅×D₄	—	3	2	no	—
189	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	—	3	2	no	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	3	2	no	—
193	C₂²×C₄×C₅	—	3	1	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
196	C₅×C₄⋊C₄	—	3	2	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	—	3	1	no	—
199	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
200	C₅×C₂²⋊C₄	—	3	2	no	—
201	C₅×C₂²⋊C₄	—	3	2	no	—
202	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
203	C₄²×C₅	—	3	2	no	—
204	C₄²×C₅	—	3	1	no	—
205	C₄²×C₅	—	3	2	no	—
206	C₄²×C₅	—	3	1	no	—
207	C₄²×C₅	—	3	1	no	—
208	C₄²×C₅	—	3	2	no	—
209	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₂×#168	—	2	4	no	—
211	C₂×#168	—	3	1	no	—
212	C₂×#168	—	3	1	no	—
213	C₂×#168	—	3	2	no	—
214	C₂×#168	—	6	2	no	—
215	C₂×#168	—	6	4	no	—
216	C₂×#168	—	6	2	no	—
217	C₂×#168	C₂²×D₃	1	2	yes	—
218	C₂×#168	C₂²×D₃	1	1	yes	characteristic
219	C₂×#168	C₂²×D₃	1	1	yes	characteristic
220	C₄×#41	—	3	1	no	—
221	C₈×Q₈	—	15	1	no	—
222	C₈×Q₈	—	15	1	no	—
223	C₈×D₄	—	5	1	no	—
224	C₈×D₄	—	15	2	no	—
225	C₈×D₄	—	15	2	no	—
226	C₈×D₄	—	15	1	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₂×C₄×C₈	—	15	1	no	—
230	C₂×C₄×C₈	—	15	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	C₂²×C₈	1	4	yes	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₅×D₃	—	2	1	no	—
236	C₂×C₅×D₃	—	2	1	no	—
237	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₅×Dic₃	—	2	1	no	—
244	C₅×Dic₃	—	2	2	no	—
245	C₅×Dic₃	C₂²×C₈	1	4	yes	—
246	C₅×Dic₃	C₂²×C₈	1	2	yes	—
247	C₅×Dic₃	#131	1	2	yes	—
248	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
250	C₂×#67	C₂×Dic₅	1	2	yes	—
251	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
252	C₂²×Dic₃	C₂×Dic₅	1	2	yes	—
253	#237	#168	1	8	yes	direct product factor
254	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
257	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	2	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	10	4	no	—
262	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
263	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
264	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
265	#217	C₂×Dic₅	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
267	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
268	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
269	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
270	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
271	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
272	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
273	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
274	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
275	C₄×Dic₃	C₂²×D₅	1	2	yes	—
276	C₂×C₃⋊C₈	—	5	1	no	—
277	C₂×C₃⋊C₈	—	5	1	no	—
278	C₂×C₃⋊C₈	—	5	2	no	—
279	C₂×C₃⋊C₈	—	10	4	no	—
280	D₃×C₈	—	10	2	no	—
281	D₃×C₈	—	10	2	no	—
282	C₂³×C₅	—	3	1	no	—
283	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
284	C₅×Q₈	—	3	4	no	—
285	C₅×D₄	—	3	8	no	—
286	C₅×D₄	D₃×C₈	1	4	yes	complemented
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	3	8	no	—
290	C₂×C₄×C₅	—	3	1	no	—
291	C₂×C₄×C₅	—	3	1	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	3	4	no	—
294	C₂×C₄×C₅	—	3	2	no	—
295	C₂×C₄×C₅	—	3	1	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	4	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	1	no	—
300	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	#168	—	2	2	no	—
305	#168	—	2	1	no	—
306	#168	—	3	2	no	—
307	#168	—	6	1	no	—
308	#168	—	6	2	no	—
309	#168	#237	1	2	yes	direct product factor
310	C₂×#41	—	3	1	no	—
311	C₂²×C₈	—	5	2	no	—
312	C₂²×C₈	—	15	1	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	—	15	2	no	—
315	C₄×Q₈	—	3	1	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	2	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	D₃×D₅	1	1	yes	characteristic
321	#117	—	3	1	no	—
322	#117	—	3	2	no	—
323	C₂×C₄²	—	3	2	no	—
324	C₂×C₄²	—	3	1	no	—
325	C₄⋊C₈	—	5	1	no	—
326	C₄⋊C₈	—	15	2	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	—	15	1	no	—
329	C₂²⋊C₈	—	5	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	C₄×C₈	—	5	1	no	—
333	C₄×C₈	—	15	1	no	—
334	C₄×C₈	—	15	1	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	—	15	1	no	—
339	C₂×C₃×C₅	—	2	4	no	—
340	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
342	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
343	C₅×D₃	—	2	2	no	—
344	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
345	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
346	C₃×D₄	C₂×#168	1	4	yes	complemented
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
353	#67	C₂×#168	1	8	yes	complemented
354	C₂×Dic₃	—	2	4	no	—
355	C₂×Dic₃	C₂×#168	1	8	yes	complemented
356	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
357	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
358	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
359	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
360	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
361	C₄×D₃	—	2	1	no	—
362	C₄×D₃	—	2	1	no	—
363	C₄×D₃	—	2	2	no	—
364	C₄×D₃	C₂×#168	1	4	yes	complemented
365	Dic₆	C₂×#168	1	4	yes	complemented
366	C₃×C₈	—	5	2	no	—
367	C₃×C₈	—	10	1	no	—
368	C₃×C₈	—	10	2	no	—
369	C₃⋊C₈	—	5	2	no	—
370	C₃⋊C₈	—	10	1	no	—
371	C₃⋊C₈	—	10	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	3	2	no	—
375	C₂²×C₅	—	6	1	no	—
376	C₂²×C₅	—	6	1	no	—
377	C₂²×C₅	C₂×D₃×C₈	1	4	yes	—
378	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	3	2	no	—
382	C₄×C₅	—	3	4	no	—
383	C₄×C₅	—	3	2	no	—
384	C₄×C₅	—	6	2	no	—
385	C₄×C₅	—	6	1	no	—
386	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
387	C₄×C₅	C₂×#237	1	1	yes	characteristic
388	C₄×C₅	D₃×#41	1	1	yes	characteristic
389	#41	—	3	8	no	—
390	C₂×Q₈	—	3	1	no	—
391	C₂×D₄	—	3	2	no	—
392	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
393	C₂²×C₄	—	3	2	no	—
394	C₂²×C₄	—	3	1	no	—
395	C₂²×C₄	—	3	2	no	—
396	C₂²×C₄	—	3	1	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	C₂×D₃×D₅	1	2	yes	—
399	C₂×C₈	—	5	1	no	—
400	C₂×C₈	—	5	1	no	—
401	C₂×C₈	—	5	2	no	—
402	C₂×C₈	—	10	4	no	—
403	C₂×C₈	—	15	1	no	—
404	C₂×C₈	—	15	1	no	—
405	C₂×C₈	—	15	2	no	—
406	C₂×C₈	—	30	2	no	—
407	C₂×C₈	—	30	2	no	—
408	C₂×C₈	—	30	4	no	—
409	C₄⋊C₄	—	3	2	no	—
410	C₄⋊C₄	—	3	2	no	—
411	C₄⋊C₄	—	3	1	no	—
412	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	3	2	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	D₃×Dic₅	1	2	yes	—
416	C₄²	—	3	2	no	—
417	C₄²	—	3	1	no	—
418	C₄²	—	3	2	no	—
419	C₄²	—	3	1	no	—
420	C₄²	—	3	1	no	—
421	C₄²	—	3	2	no	—
422	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
423	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	C₂²×#168	1	4	yes	—
427	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
428	C₂×D₃	—	2	1	no	—
429	C₂×D₃	—	2	1	no	—
430	C₂×D₃	C₂²×#168	1	2	yes	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	C₂²×#168	1	2	yes	—
434	C₃×C₄	D₅×#41	1	1	yes	characteristic
435	C₃×C₄	D₅×#41	1	1	yes	characteristic
436	Dic₃	—	2	2	no	—
437	Dic₃	—	2	1	no	—
438	Dic₃	C₂²×#168	1	4	yes	—
439	Dic₃	C₂²×#168	1	2	yes	—
440	Dic₃	#4094	1	2	yes	—
441	C₂×C₅	—	2	4	no	—
442	C₂×C₅	—	6	2	no	—
443	C₂×C₅	C₄×#237	1	1	yes	characteristic
444	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
445	C₂×C₅	D₃×#131	1	1	yes	characteristic
446	C₂³	—	3	1	no	—
447	C₂³	C₂×D₃×Dic₅	1	2	yes	—
448	Q₈	—	3	4	no	—
449	D₄	—	3	8	no	—
450	D₄	D₃×#168	1	4	yes	complemented
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	3	1	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	3	8	no	—
457	C₂×C₄	—	3	4	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	3	1	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	—	6	4	no	—
462	C₂×C₄	—	6	1	no	—
463	C₂×C₄	—	6	1	no	—
464	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
465	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
466	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	5	2	no	—
469	C₈	—	10	2	no	—
470	C₈	—	10	1	no	—
471	C₈	—	15	2	no	—
472	C₈	—	30	1	no	—
473	C₈	—	30	2	no	—
474	C₂×C₃	—	2	4	no	—
475	C₂×C₃	C₂³×#168	1	1	yes	characteristic
476	C₂×C₃	C₂×#4094	1	1	yes	characteristic
477	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
478	D₃	—	2	2	no	—
479	C₅	C₈×#237	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	3	2	no	—
483	C₂²	—	6	1	no	—
484	C₂²	—	6	1	no	—
485	C₂²	C₂×D₃×#168	1	4	yes	—
486	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	3	2	no	—
490	C₄	—	3	2	no	—
491	C₄	—	3	4	no	—
492	C₄	—	6	2	no	—
493	C₄	—	6	1	no	—
494	C₄	C₂×D₃×#168	1	2	yes	—
495	C₄	D₅×#237	1	1	yes	characteristic
496	C₄	#92024	1	1	yes	characteristic
497	C₃	#41×#168	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	2	4	no	—
499	C₂	—	6	2	no	—
500	C₂	C₂²×D₃×#168	1	1	yes	characteristic
501	C₂	Dic₅×#237	1	1	yes	characteristic
502	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₄×C₅×D₄	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#237	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. D₄×C₃⋊#168	C₂	semidirect
3. C₃×D₄×#168	C₂	semidirect
4. #67⋊#168	C₂	semidirect
5. #67×#168	C₂	semidirect
6. #11748329	C₂	semidirect
7. C₂×Dic₃×#168	C₂	semidirect
8. C₄×D₃×#168	C₂	semidirect
9. #11746857	C₂	semidirect
10. #11746853	C₂	semidirect
11. Dic₆×#168	C₂	semidirect
49. D₄×#168	D₃	semidirect
59. C₅×#237	C₈	semidirect
131. C₃×C₅×D₄	C₂×C₈	semidirect
138. C₅×#67	C₂×C₈	semidirect
140. C₂×C₅×Dic₃	C₂×C₈	semidirect
149. C₄×C₅×D₃	C₂×C₈	semidirect
150. C₅×Dic₆	C₂×C₈	semidirect
153. C₃⋊#168	#41	semidirect
156. C₃×#168	#41	semidirect
253. #237	#168	direct (N × H)
286. C₅×D₄	D₃×C₈	semidirect
309. #168	#237	direct (N × H)
346. C₃×D₄	C₂×#168	semidirect
353. #67	C₂×#168	semidirect
355. C₂×Dic₃	C₂×#168	semidirect
364. C₄×D₃	C₂×#168	semidirect
365. Dic₆	C₂×#168	semidirect
423. C₃×C₅	C₈×#41	semidirect
450. D₄	D₃×#168	semidirect
479. C₅	C₈×#237	semidirect
497. C₃	#41×#168	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#237	2
D₄×C₃⋊#168	2
C₃×D₄×#168	2
#67⋊#168	2
#67×#168	2
#11748329	2
C₂×Dic₃×#168	2
C₄×D₃×#168	2
#11746857	2
#11746853	2
Dic₆×#168	2
#41×#168	3
C₈×#237	5