Subgroups — #14295019

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×(C₂×D₃)⋊#168	C₂	1	1	yes	maximal, characteristic
5	C₂×#90951	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64770	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745966	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×C₂²⋊C₈	—	3	1	no	maximal, Hall
9	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×D₃×Dic₅	C₄	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
17	C₂×Dic₃×Dic₅	C₄	1	2	yes	—
18	C₄×D₃×Dic₅	—	2	2	no	—
19	C₄×D₃×Dic₅	—	2	2	no	—
20	C₈×Dic₁₅	—	2	2	no	—
21	C₅×(C₂×D₃)⋊C₈	C₄	1	4	yes	complemented
22	(C₂×D₃)⋊#168	C₄	1	4	yes	complemented
23	#90951	—	2	2	no	—
24	#68599	—	5	1	no	maximal, Hall
25	C₂²×C₄×Dic₅	—	3	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
27	C₂×C₂²⋊#168	—	3	1	no	—
28	C₂×C₈×Dic₅	—	3	1	no	—
29	C₂×C₈×Dic₅	—	3	1	no	—
30	#64770	—	3	1	no	—
31	#64770	D₃	1	1	yes	characteristic, complemented
32	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×Dic₁₅	C₂×C₄	1	2	yes	—
35	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×C₅×D₃	—	2	1	no	—
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
41	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
43	C₂×D₃×Dic₅	—	2	4	no	—
44	C₂×D₃×Dic₅	—	2	4	no	—
45	C₂×D₃×Dic₅	C₈	1	8	yes	complemented
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
49	C₄×Dic₁₅	D₄	1	2	yes	—
50	C₄×Dic₁₅	D₄	1	2	yes	—
51	C₂×C₃⋊#168	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₂×C₃⋊#168	C₂×C₄	1	2	yes	complemented
54	C₂×C₅×C₃⋊C₈	—	2	1	no	—
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₂×C₃×#168	—	2	1	no	—
60	C₂×C₃×#168	—	2	1	no	—
61	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
62	Dic₃×Dic₅	—	2	4	no	—
63	C₂×C₄²×D₃	—	5	1	no	—
64	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
65	C₂×(C₂×D₃)⋊C₈	D₅	1	1	yes	characteristic
66	C₂×C₈×Dic₃	—	5	1	no	—
67	C₂×C₈×Dic₃	—	5	1	no	—
68	C₃×#336	—	5	1	no	—
69	#4524	—	5	1	no	—
70	C₂³×C₄×C₅	—	3	1	no	—
71	C₂³×Dic₅	—	3	2	no	—
72	C₂²×C₅×C₈	—	3	1	no	—
73	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₄×Dic₅	—	3	1	no	—
75	C₂×C₄×Dic₅	—	3	2	no	—
76	C₂×C₄×Dic₅	—	6	2	no	—
77	C₂×C₄×Dic₅	—	6	2	no	—
78	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
79	C₂²×#168	—	3	1	no	—
80	C₂²×#168	C₂×D₃	1	1	yes	characteristic
81	C₅×C₂²⋊C₈	—	3	4	no	—
82	C₂²⋊#168	—	3	4	no	—
83	C₈×Dic₅	—	6	2	no	—
84	C₈×Dic₅	—	6	2	no	—
85	C₄×C₂²⋊C₈	—	15	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₂²×C₅×D₃	—	2	1	no	—
89	C₂²×C₅×D₃	—	2	2	no	—
90	C₂²×C₅×D₃	C₄²	1	2	yes	—
91	C₂²×C₅×D₃	C₂×C₈	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×Dic₁₅	C₂²⋊C₄	1	4	yes	—
99	C₂×Dic₁₅	C₂×C₈	1	4	yes	—
100	C₂×Dic₁₅	M₁₆	1	4	yes	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	C₄²	1	2	yes	—
104	C₄×C₅×D₃	—	2	2	no	—
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₄×C₅×D₃	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	C₂×C₈	1	4	yes	—
111	D₃×Dic₅	—	2	16	no	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃⋊#168	—	2	2	no	—
114	C₃×#168	—	2	2	no	—
115	C₅×C₃⋊C₈	—	2	2	no	—
116	C₂²×C₄×D₃	—	5	2	no	—
117	C₂²×C₄×D₃	C₂×D₅	1	1	yes	characteristic
118	C₂²×C₃×C₈	—	5	1	no	—
119	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	5	1	no	—
121	C₂×C₄×Dic₃	—	5	1	no	—
122	C₂×C₄×Dic₃	—	5	2	no	—
123	C₂²×C₃⋊C₈	—	5	1	no	—
124	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
125	C₄²×D₃	—	10	2	no	—
126	C₄²×D₃	—	10	2	no	—
127	(C₂×D₃)⋊C₈	—	5	4	no	—
128	(C₂×D₃)⋊C₈	Dic₅	1	4	yes	complemented
129	C₈×Dic₃	—	10	2	no	—
130	C₈×Dic₃	—	10	2	no	—
131	C₂⁴×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	2	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	1	no	—
137	C₂²×C₄×C₅	—	6	1	no	—
138	C₂²×C₄×C₅	—	6	1	no	—
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₂²×Dic₅	—	3	2	no	—
141	C₂²×Dic₅	—	3	8	no	—
142	C₂²×Dic₅	—	6	4	no	—
143	C₂²×Dic₅	—	6	4	no	—
144	C₂²×Dic₅	C₄×D₃	1	2	yes	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	C₄×D₃	1	2	yes	complemented
151	C₄×Dic₅	—	2	1	no	—
152	C₄×Dic₅	—	2	1	no	—
153	C₄×Dic₅	—	3	2	no	—
154	C₄×Dic₅	—	3	2	no	—
155	C₄×Dic₅	—	6	4	no	—
156	C₂×#168	—	2	1	no	—
157	C₂×#168	—	2	1	no	—
158	C₂×#168	—	3	2	no	—
159	C₂×#168	—	6	1	no	—
160	C₂×#168	—	6	1	no	—
161	C₂×#168	C₄×D₃	1	2	yes	complemented
162	C₂²×C₄²	—	15	1	no	—
163	C₂×C₂²⋊C₈	—	3	1	no	—
164	C₂×C₂²⋊C₈	—	15	1	no	—
165	C₂×C₄×C₈	—	15	1	no	—
166	C₂×C₄×C₈	—	15	1	no	—
167	#336	—	5	1	no	—
168	#336	—	15	1	no	—
169	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	#117	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
173	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
174	C₂×C₅×D₃	—	2	2	no	—
175	C₂×C₅×D₃	—	2	2	no	—
176	C₂×C₅×D₃	—	2	4	no	—
177	C₂×C₅×D₃	—	2	4	no	—
178	C₂×C₅×D₃	C₄×C₈	1	4	yes	complemented
179	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
180	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
181	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
182	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
183	Dic₁₅	C₂²⋊C₈	1	8	yes	complemented
184	C₃×Dic₅	—	2	4	no	—
185	C₅×Dic₃	—	2	2	no	—
186	C₂³×D₃	C₄×D₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
189	C₂²×Dic₃	—	5	2	no	—
190	C₂²×Dic₃	C₄×D₅	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	1	no	—
192	C₂×C₄×D₃	—	2	1	no	—
193	C₂×C₄×D₃	—	2	1	no	—
194	C₂×C₄×D₃	—	2	1	no	—
195	C₂×C₄×D₃	—	5	8	no	—
196	C₂×C₄×D₃	—	10	4	no	—
197	C₂×C₄×D₃	—	10	4	no	—
198	C₂×C₄×D₃	C₄×D₅	1	2	yes	—
199	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
200	C₂×C₃×C₈	—	2	1	no	—
201	C₂×C₃×C₈	—	2	1	no	—
202	C₂×C₃×C₈	—	5	2	no	—
203	C₂×C₃×C₈	—	10	1	no	—
204	C₂×C₃×C₈	—	10	1	no	—
205	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	complemented
206	C₃×C₄²	—	10	1	no	—
207	C₃×C₄²	—	10	1	no	—
208	C₄×Dic₃	—	5	2	no	—
209	C₄×Dic₃	—	5	2	no	—
210	C₄×Dic₃	—	10	4	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂×C₃⋊C₈	—	2	1	no	—
213	C₂×C₃⋊C₈	—	5	2	no	—
214	C₂×C₃⋊C₈	—	10	1	no	—
215	C₂×C₃⋊C₈	—	10	1	no	—
216	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	complemented
217	C₂³×C₅	—	3	2	no	—
218	C₂³×C₅	—	3	4	no	—
219	C₂³×C₅	—	6	1	no	—
220	C₂³×C₅	—	6	1	no	—
221	C₂³×C₅	—	6	2	no	—
222	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
223	C₂×C₄×C₅	—	3	2	no	—
224	C₂×C₄×C₅	—	6	1	no	—
225	C₂×C₄×C₅	—	6	1	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	6	2	no	—
228	C₂×C₄×C₅	—	6	2	no	—
229	C₂×C₄×C₅	—	6	2	no	—
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	#237	1	1	yes	characteristic
235	C₂×C₄×C₅	#239	1	1	yes	characteristic
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	2	2	no	—
238	C₂×Dic₅	—	3	4	no	—
239	C₂×Dic₅	—	3	4	no	—
240	C₂×Dic₅	—	3	4	no	—
241	C₂×Dic₅	—	6	16	no	—
242	C₂×Dic₅	D₃×C₈	1	4	yes	—
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	6	2	no	—
245	#168	—	2	2	no	—
246	#168	—	6	2	no	—
247	C₂³×C₄	—	3	1	no	—
248	C₂³×C₄	—	15	2	no	—
249	C₂²×C₈	—	3	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	15	1	no	—
252	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	15	1	no	—
255	C₂×C₄²	—	15	2	no	—
256	C₂×C₄²	—	30	2	no	—
257	C₂×C₄²	—	30	2	no	—
258	C₂²⋊C₈	—	3	4	no	—
259	C₂²⋊C₈	—	15	4	no	—
260	C₄×C₈	—	30	2	no	—
261	C₄×C₈	—	30	2	no	—
262	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂×C₄×C₈	1	1	yes	characteristic
264	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	2	yes	—
266	C₂×C₃×C₅	#431	1	2	yes	—
267	C₅×D₃	—	2	4	no	—
268	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
269	C₂²×D₃	—	2	1	no	—
270	C₂²×D₃	—	2	1	no	—
271	C₂²×D₃	—	2	2	no	—
272	C₂²×D₃	C₈×D₅	1	4	yes	—
273	C₂²×D₃	C₄×Dic₅	1	2	yes	—
274	C₂×C₃×C₄	—	5	4	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
278	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
279	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	#711	1	1	yes	characteristic
281	C₂×C₃×C₄	#711	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
283	C₂×Dic₃	—	2	1	no	—
284	C₂×Dic₃	—	2	1	no	—
285	C₂×Dic₃	—	5	4	no	—
286	C₂×Dic₃	—	5	4	no	—
287	C₂×Dic₃	—	5	4	no	—
288	C₂×Dic₃	C₄×Dic₅	1	2	yes	—
289	C₄×D₃	—	2	2	no	—
290	C₄×D₃	—	2	2	no	—
291	C₄×D₃	—	2	2	no	—
292	C₄×D₃	—	2	2	no	—
293	C₄×D₃	—	10	16	no	—
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	10	2	no	—
296	C₃⋊C₈	—	2	2	no	—
297	C₃⋊C₈	—	10	2	no	—
298	C₂²×C₅	—	3	4	no	—
299	C₂²×C₅	—	6	2	no	—
300	C₂²×C₅	—	6	2	no	—
301	C₂²×C₅	—	6	4	no	—
302	C₂²×C₅	—	6	4	no	—
303	C₂²×C₅	C₄²×D₃	1	1	yes	characteristic
304	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₅	#892	1	1	yes	characteristic
306	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
307	C₂²×C₅	D₃×M₁₆	1	2	yes	—
308	C₄×C₅	—	6	2	no	—
309	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
310	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
311	C₄×C₅	#893	1	1	yes	characteristic
312	C₄×C₅	#893	1	1	yes	characteristic
313	Dic₅	—	2	4	no	—
314	Dic₅	—	3	8	no	—
315	C₂⁴	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
317	C₂²×C₄	—	3	2	no	—
318	C₂²×C₄	—	3	2	no	—
319	C₂²×C₄	—	5	2	no	—
320	C₂²×C₄	—	6	1	no	—
321	C₂²×C₄	—	6	1	no	—
322	C₂²×C₄	—	6	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	C₂²×C₄	—	15	8	no	—
325	C₂²×C₄	—	15	2	no	—
326	C₂²×C₄	—	30	4	no	—
327	C₂²×C₄	—	30	4	no	—
328	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	3	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	6	1	no	—
334	C₂×C₈	—	6	1	no	—
335	C₂×C₈	—	10	1	no	—
336	C₂×C₈	—	10	1	no	—
337	C₂×C₈	—	15	2	no	—
338	C₂×C₈	—	30	1	no	—
339	C₂×C₈	—	30	1	no	—
340	C₂×C₈	D₃×Dic₅	1	2	yes	complemented
341	C₄²	—	10	1	no	—
342	C₄²	—	10	1	no	—
343	C₄²	—	15	2	no	—
344	C₄²	—	15	2	no	—
345	C₄²	—	30	4	no	—
346	C₃×C₅	C₄×C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	#4023	1	1	yes	characteristic
348	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₃	C₂×C₈×D₅	1	2	yes	—
350	C₂²×C₃	D₅×M₁₆	1	2	yes	—
351	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
352	C₂×D₃	—	2	2	no	—
353	C₂×D₃	—	2	2	no	—
354	C₂×D₃	—	2	4	no	—
355	C₂×D₃	—	2	4	no	—
356	C₂×D₃	C₈×Dic₅	1	4	yes	complemented
357	C₃×C₄	—	10	4	no	—
358	C₃×C₄	#4027	1	1	yes	characteristic
359	C₃×C₄	#4027	1	1	yes	characteristic
360	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
361	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
362	Dic₃	—	2	2	no	—
363	Dic₃	—	5	8	no	—
364	C₂×C₅	—	6	4	no	—
365	C₂×C₅	#4666	1	1	yes	characteristic
366	C₂×C₅	C₄×D₃×C₈	1	1	yes	characteristic
367	C₂×C₅	#4707	1	1	yes	characteristic
368	C₂×C₅	D₃×C₂²⋊C₈	1	2	yes	—
369	C₂×C₅	#4833	1	2	yes	—
370	C₂³	—	3	2	no	—
371	C₂³	—	3	4	no	—
372	C₂³	—	6	1	no	—
373	C₂³	—	6	1	no	—
374	C₂³	—	6	2	no	—
375	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	5	4	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	6	1	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	6	2	no	—
382	C₂×C₄	—	6	2	no	—
383	C₂×C₄	—	6	2	no	—
384	C₂×C₄	—	10	2	no	—
385	C₂×C₄	—	10	2	no	—
386	C₂×C₄	—	15	4	no	—
387	C₂×C₄	—	15	4	no	—
388	C₂×C₄	—	15	4	no	—
389	C₂×C₄	—	30	16	no	—
390	C₂×C₄	#6768	1	1	yes	characteristic
391	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
392	C₂×C₄	#6777	1	1	yes	characteristic
393	C₂×C₄	#6780	1	1	yes	characteristic
394	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
395	C₂×C₄	#6790	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	6	2	no	—
398	C₈	—	10	2	no	—
399	C₈	—	30	2	no	—
400	C₂×C₃	#65007	1	2	yes	—
401	C₂×C₃	D₅×C₂²⋊C₈	1	2	yes	—
402	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
403	C₂×C₃	C₂×C₈×Dic₅	1	1	yes	characteristic
404	C₂×C₃	M₁₆×Dic₅	1	1	yes	characteristic
405	D₃	—	2	4	no	—
406	C₅	#68599	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	3	4	no	—
408	C₂²	—	6	4	no	—
409	C₂²	—	6	2	no	—
410	C₂²	—	6	2	no	—
411	C₂²	—	6	4	no	—
412	C₂²	D₃×C₈×D₅	1	2	yes	—
413	C₂²	#91246	1	2	yes	—
414	C₂²	C₄×D₃×Dic₅	1	1	yes	characteristic
415	C₂²	#91400	1	1	yes	characteristic
416	C₂²	#91473	1	1	yes	characteristic
417	C₄	—	6	2	no	—
418	C₄	—	10	4	no	—
419	C₄	—	15	8	no	—
420	C₄	#91406	1	1	yes	characteristic
421	C₄	#91435	1	1	yes	characteristic
422	C₄	#91442	1	1	yes	characteristic
423	C₄	#67⋊Dic₅	1	1	yes	characteristic
424	C₃	Dic₅×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
425	C₂	—	6	4	no	—
426	C₂	D₃×C₈×Dic₅	1	1	yes	characteristic
427	C₂	#11747581	1	2	yes	—
428	C₂	#11747602	1	1	yes	characteristic
429	C₂	#11748100	1	2	yes	—
430	C₂	#11748886	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Dic₁₅	C₂	semidirect
5. C₂×#90951	C₂	semidirect
6. C₃×#64770	C₂	semidirect
7. #11745966	C₂	semidirect
21. C₅×(C₂×D₃)⋊C₈	C₄	semidirect
22. (C₂×D₃)⋊#168	C₄	semidirect
31. #64770	D₃	semidirect
45. C₂×D₃×Dic₅	C₈	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
53. C₂×C₃⋊#168	C₂×C₄	semidirect
56. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
61. C₂×C₃×#168	C₂×C₄	semidirect
128. (C₂×D₃)⋊C₈	Dic₅	semidirect
150. C₂×C₅×C₈	C₄×D₃	semidirect
161. C₂×#168	C₄×D₃	semidirect
178. C₂×C₅×D₃	C₄×C₈	semidirect
183. Dic₁₅	C₂²⋊C₈	semidirect
205. C₂×C₃×C₈	C₂×Dic₅	semidirect
216. C₂×C₃⋊C₈	C₂×Dic₅	semidirect
340. C₂×C₈	D₃×Dic₅	semidirect
346. C₃×C₅	C₄×C₂²⋊C₈	semidirect
356. C₂×D₃	C₈×Dic₅	semidirect
406. C₅	#68599	semidirect
424. C₃	Dic₅×C₂²⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×Dic₅	2
C₂×C₈×Dic₁₅	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×(C₂×D₃)⋊#168	2
C₂×#90951	2
C₃×#64770	2
#11745966	2
Dic₅×C₂²⋊C₈	3
#68599	5