Subgroups — #14418929

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	#67⋊#168	C₂	1	4	yes	maximal, complemented
5	#11746998	C₂	1	2	yes	maximal, complemented
6	C₄×D₃×#168	C₂	1	2	yes	maximal, complemented
7	#11746876	C₂	1	2	yes	maximal, complemented
8	#11746857	C₂	1	2	yes	maximal, complemented
9	#41×#168	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₄	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	2	yes	—
13	C₄×C₅×#67	C₄	1	2	yes	—
14	C₄×C₅×#67	C₂²	1	2	yes	—
15	C₅×#926	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₅×#872	C₄	1	2	yes	—
19	C₄²×C₅×D₃	C₂²	1	2	yes	—
20	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
21	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₂×D₃×#168	C₂²	1	4	yes	—
23	C₄×C₃⋊#168	C₂²	1	2	yes	—
24	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
26	C₃×C₂²⋊#168	C₂²	1	2	yes	—
27	C₃×C₄⋊#168	C₂²	1	2	yes	—
28	C₃×C₄×#168	C₂²	1	2	yes	—
29	Dic₃⋊#168	C₂²	1	4	yes	—
30	(C₂×D₃)⋊#168	C₂²	1	4	yes	—
31	Dic₃×#168	C₂²	1	4	yes	—
32	#79276	—	5	1	no	maximal, Hall
33	C₄×C₅×#41	—	3	1	no	—
34	Q₈×#168	—	3	2	no	—
35	D₄×#168	—	3	4	no	—
36	D₄×#168	—	3	2	no	—
37	#65214	—	3	2	no	—
38	#65214	D₃	1	1	yes	characteristic, complemented
39	C₂×C₄×#168	—	3	2	no	—
40	C₂×C₄×#168	—	3	1	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	C₂×C₄	1	2	yes	—
45	C₅×#235	C₈	1	8	yes	complemented
46	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
48	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
49	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
50	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₃⋊#168	—	2	4	no	—
56	C₂×C₃⋊#168	C₂³	1	2	yes	—
57	C₂×C₃⋊#168	C₂³	1	2	yes	—
58	C₅×#217	C₂×C₄	1	2	yes	—
59	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
60	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
61	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
62	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
64	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
65	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
66	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂×C₃×#168	C₂³	1	4	yes	—
69	D₃×#168	—	2	8	no	—
70	C₄×#235	D₅	1	1	yes	characteristic
71	C₃×#431	—	5	1	no	—
72	C₂×C₄×C₃⋊C₈	—	5	1	no	—
73	#4834	—	5	2	no	—
74	#4830	—	5	2	no	—
75	#67⋊C₈	—	5	4	no	—
76	#4685	—	5	2	no	—
77	C₄×D₃×C₈	—	5	2	no	—
78	C₂×C₅×#41	—	3	1	no	—
79	C₄×C₅×Q₈	—	3	1	no	—
80	C₄×C₅×Q₈	—	3	1	no	—
81	C₄×C₅×D₄	—	3	2	no	—
82	C₄×C₅×D₄	—	3	2	no	—
83	C₄×C₅×D₄	—	3	1	no	—
84	C₄×C₅×D₄	—	3	1	no	—
85	C₅×#117	—	3	1	no	—
86	C₅×#117	—	3	2	no	—
87	C₂×C₄²×C₅	—	3	2	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂²×#168	—	3	2	no	—
90	C₂²×#168	—	3	4	no	—
91	C₂²⋊#168	—	3	4	no	—
92	C₂²⋊#168	C₂×D₃	1	2	yes	—
93	C₄⋊#168	—	3	4	no	—
94	C₄⋊#168	C₂×D₃	1	2	yes	—
95	C₄×#168	—	3	2	no	—
96	C₄×#168	—	3	1	no	—
97	C₄×#168	—	3	1	no	—
98	C₄×#168	—	3	4	no	—
99	C₄×#168	C₂×D₃	1	2	yes	—
100	C₈×#41	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₅×#67	C₂×C₈	1	8	yes	complemented
113	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
114	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
116	C₅×D₁₂	C₂×C₈	1	4	yes	complemented
117	C₄×C₅×D₃	—	2	4	no	—
118	C₄×C₅×D₃	—	2	4	no	—
119	C₄×C₅×D₃	C₂×C₈	1	8	yes	complemented
120	C₅×Dic₆	C₂×C₈	1	4	yes	complemented
121	C₃⋊#168	—	2	2	no	—
122	C₃⋊#168	#41	1	4	yes	complemented
123	C₃×#168	—	2	4	no	—
124	C₂×#235	Dic₅	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
126	C₄×#67	Dic₅	1	2	yes	—
127	C₄×#67	C₂×D₅	1	2	yes	—
128	#926	Dic₅	1	1	yes	characteristic
129	C₂²×C₃⋊C₈	—	5	2	no	—
130	C₂×D₃×C₈	—	5	4	no	—
131	C₄×D₁₂	Dic₅	1	1	yes	characteristic
132	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
133	#872	Dic₅	1	2	yes	—
134	C₄²×D₃	C₂×D₅	1	2	yes	—
135	C₄×Dic₆	Dic₅	1	1	yes	characteristic
136	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
137	C₃×C₄⋊C₈	—	5	2	no	—
138	C₃×C₂²⋊C₈	—	5	2	no	—
139	C₃×C₄×C₈	—	5	2	no	—
140	(C₂×D₃)⋊C₈	—	5	4	no	—
141	Dic₃⋊C₈	—	5	4	no	—
142	C₈×Dic₃	—	5	4	no	—
143	C₄×C₃⋊C₈	—	5	1	no	—
144	C₄×C₃⋊C₈	—	5	1	no	—
145	C₄×C₃⋊C₈	—	5	2	no	—
146	C₅×#41	—	3	8	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×D₄	—	3	2	no	—
149	C₂×C₅×D₄	—	3	1	no	—
150	C₂²×C₄×C₅	—	3	2	no	—
151	C₂²×C₄×C₅	—	3	2	no	—
152	C₂²×C₄×C₅	—	3	2	no	—
153	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
156	C₅×C₄⋊C₄	—	3	2	no	—
157	C₅×C₄⋊C₄	—	3	2	no	—
158	C₅×C₄⋊C₄	—	3	1	no	—
159	C₅×C₄⋊C₄	—	3	1	no	—
160	C₅×C₂²⋊C₄	—	3	2	no	—
161	C₅×C₂²⋊C₄	—	3	2	no	—
162	C₅×C₂²⋊C₄	—	3	2	no	—
163	C₄²×C₅	—	3	2	no	—
164	C₄²×C₅	—	3	2	no	—
165	C₄²×C₅	—	3	2	no	—
166	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
167	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
168	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
169	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
170	C₂×#168	—	3	2	no	—
171	C₂×#168	—	3	2	no	—
172	C₂×#168	—	6	8	no	—
173	C₂×#168	—	6	4	no	—
174	C₂×#168	C₂²×D₃	1	4	yes	—
175	C₄×#41	—	3	1	no	—
176	C₈×Q₈	—	15	2	no	—
177	C₈×D₄	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	#431	—	5	1	no	—
180	#431	—	15	2	no	—
181	C₂×C₄×C₈	—	15	2	no	—
182	C₂×C₄×C₈	—	15	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	2	no	—
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	2	yes	—
196	C₅×Dic₃	—	2	2	no	—
197	C₅×Dic₃	—	2	2	no	—
198	C₅×Dic₃	C₂²×C₈	1	4	yes	—
199	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₂×#67	C₂×Dic₅	1	2	yes	—
203	#235	#168	1	8	yes	complemented
204	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
206	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
207	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
208	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
209	C₂×C₃×C₈	—	5	4	no	—
210	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
211	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
212	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
213	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
214	#217	C₂×Dic₅	1	2	yes	—
215	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
216	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
217	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
218	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
219	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
220	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
221	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
222	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
223	C₄×Dic₃	C₂²×D₅	1	2	yes	—
224	C₂×C₃⋊C₈	—	5	2	no	—
225	C₂×C₃⋊C₈	—	5	2	no	—
226	C₂×C₃⋊C₈	—	10	4	no	—
227	D₃×C₈	—	10	8	no	—
228	C₂³×C₅	—	3	2	no	—
229	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₅×Q₈	—	3	4	no	—
231	C₅×D₄	—	3	8	no	—
232	C₅×D₄	—	3	4	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	3	8	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	2	no	—
239	C₂×C₄×C₅	—	6	4	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
242	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
248	#168	—	2	4	no	—
249	#168	—	3	4	no	—
250	#168	—	6	2	no	—
251	C₂×#41	—	3	1	no	—
252	C₂²×C₈	—	15	4	no	—
253	C₂²×C₈	—	15	2	no	—
254	C₄×Q₈	—	3	1	no	—
255	C₄×Q₈	—	3	1	no	—
256	C₄×D₄	—	3	2	no	—
257	C₄×D₄	—	3	2	no	—
258	C₄×D₄	—	3	1	no	—
259	C₄×D₄	—	3	1	no	—
260	#117	—	3	1	no	—
261	#117	—	3	2	no	—
262	C₂×C₄²	—	3	2	no	—
263	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	5	2	no	—
265	C₄⋊C₈	—	15	4	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₄×C₈	—	5	2	no	—
269	C₄×C₈	—	15	4	no	—
270	C₄×C₈	—	15	2	no	—
271	C₄×C₈	—	15	1	no	—
272	C₄×C₈	—	15	1	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₅×D₃	—	2	4	no	—
278	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
279	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₂×#168	1	4	yes	complemented
283	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
289	#67	C₂×#168	1	8	yes	complemented
290	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
291	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
292	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
293	D₁₂	C₂×#168	1	4	yes	complemented
294	C₄×D₃	—	2	4	no	—
295	C₄×D₃	—	2	4	no	—
296	C₄×D₃	C₂×#168	1	8	yes	complemented
297	Dic₆	C₂×#168	1	4	yes	complemented
298	C₃×C₈	—	10	4	no	—
299	C₃⋊C₈	—	5	4	no	—
300	C₃⋊C₈	—	10	2	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	3	4	no	—
304	C₂²×C₅	—	6	2	no	—
305	C₂²×C₅	—	6	2	no	—
306	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
307	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	3	4	no	—
311	C₄×C₅	—	6	2	no	—
312	C₄×C₅	—	6	2	no	—
313	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
314	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
315	C₄×C₅	#907	1	2	yes	—
316	C₄×C₅	D₃×#41	1	2	yes	—
317	#41	—	3	8	no	—
318	C₂×Q₈	—	3	1	no	—
319	C₂×D₄	—	3	2	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂²×C₄	—	3	2	no	—
322	C₂²×C₄	—	3	2	no	—
323	C₂²×C₄	—	3	2	no	—
324	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
325	C₂²×C₄	D₃×Dic₅	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
327	C₂×C₈	—	5	4	no	—
328	C₂×C₈	—	15	2	no	—
329	C₂×C₈	—	15	2	no	—
330	C₂×C₈	—	30	8	no	—
331	C₂×C₈	—	30	4	no	—
332	C₄⋊C₄	—	3	2	no	—
333	C₄⋊C₄	—	3	2	no	—
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₂²⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	3	2	no	—
338	C₂²⋊C₄	—	3	2	no	—
339	C₄²	—	3	2	no	—
340	C₄²	—	3	2	no	—
341	C₄²	—	3	2	no	—
342	C₄²	D₃×Dic₅	1	1	yes	characteristic
343	C₄²	D₃×Dic₅	1	1	yes	characteristic
344	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
345	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	C₂²×#168	1	2	yes	—
350	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
351	C₂×D₃	—	2	2	no	—
352	C₂×D₃	—	2	2	no	—
353	C₂×D₃	C₂²×#168	1	4	yes	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	C₂²×#168	1	2	yes	—
357	C₃×C₄	C₂²×#168	1	2	yes	—
358	C₃×C₄	#4094	1	2	yes	—
359	C₃×C₄	D₅×#41	1	2	yes	—
360	Dic₃	—	2	2	no	—
361	Dic₃	—	2	2	no	—
362	Dic₃	C₂²×#168	1	4	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	6	4	no	—
365	C₂×C₅	#5522	1	1	yes	characteristic
366	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
367	C₂×C₅	C₂×#907	1	1	yes	characteristic
368	C₂³	—	3	2	no	—
369	C₂³	C₂×D₃×Dic₅	1	1	yes	characteristic
370	Q₈	—	3	4	no	—
371	D₄	—	3	8	no	—
372	D₄	—	3	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	3	2	no	—
376	C₂×C₄	—	3	8	no	—
377	C₂×C₄	—	3	2	no	—
378	C₂×C₄	—	3	2	no	—
379	C₂×C₄	—	6	4	no	—
380	C₂×C₄	—	6	4	no	—
381	C₂×C₄	D₃×#168	1	4	yes	complemented
382	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
383	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
384	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
385	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
386	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
388	C₈	—	10	4	no	—
389	C₈	—	15	4	no	—
390	C₈	—	30	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	C₂³×#168	1	1	yes	characteristic
393	C₂×C₃	C₂×#4094	1	1	yes	characteristic
394	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
395	D₃	—	2	4	no	—
396	C₅	#79276	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	3	4	no	—
400	C₂²	—	6	2	no	—
401	C₂²	—	6	2	no	—
402	C₂²	C₂×D₃×#168	1	2	yes	—
403	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	3	4	no	—
407	C₄	—	6	2	no	—
408	C₄	—	6	2	no	—
409	C₄	C₂×D₃×#168	1	2	yes	—
410	C₄	C₂×D₃×#168	1	2	yes	—
411	C₄	#91288	1	2	yes	—
412	C₄	#92016	1	2	yes	—
413	C₃	#41×#168	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	6	4	no	—
416	C₂	C₂²×D₃×#168	1	1	yes	characteristic
417	C₂	C₂×#91288	1	1	yes	characteristic
418	C₂	#11754455	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₈×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₃⋊#168	C₂	semidirect
3. C₃×#65214	C₂	semidirect
4. #67⋊#168	C₂	semidirect
5. #11746998	C₂	semidirect
6. C₄×D₃×#168	C₂	semidirect
7. #11746876	C₂	semidirect
8. #11746857	C₂	semidirect
38. #65214	D₃	semidirect
45. C₅×#235	C₈	semidirect
105. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
112. C₅×#67	C₂×C₈	semidirect
116. C₅×D₁₂	C₂×C₈	semidirect
119. C₄×C₅×D₃	C₂×C₈	semidirect
120. C₅×Dic₆	C₂×C₈	semidirect
122. C₃⋊#168	#41	semidirect
203. #235	#168	semidirect
241. C₂×C₄×C₅	D₃×C₈	semidirect
282. C₂×C₃×C₄	C₂×#168	semidirect
289. #67	C₂×#168	semidirect
293. D₁₂	C₂×#168	semidirect
296. C₄×D₃	C₂×#168	semidirect
297. Dic₆	C₂×#168	semidirect
346. C₃×C₅	C₈×#41	semidirect
381. C₂×C₄	D₃×#168	semidirect
396. C₅	#79276	semidirect
413. 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×#235	2
C₂×C₄×C₃⋊#168	2
C₃×#65214	2
#67⋊#168	2
#11746998	2
C₄×D₃×#168	2
#11746876	2
#11746857	2
#41×#168	3
#79276	5