Subgroups — C₂×#11750941 #14413828

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91761	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91104	C₂	1	1	yes	maximal, characteristic
4	C₂×#91104	C₂	1	1	yes	maximal, characteristic
5	C₂×#91099	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750941	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65129	—	3	1	no	maximal, Hall
10	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×#6714	C₄	1	1	yes	characteristic
15	C₂×#6714	C₄	1	1	yes	characteristic
16	C₂×#6712	C₄	1	1	yes	characteristic
17	C₂×#6712	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
21	#91761	C₄	1	4	yes	—
22	#91761	C₂²	1	4	yes	—
23	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
24	#91104	C₂²	1	4	yes	—
25	#91104	C₂²	1	4	yes	—
26	#91099	C₂²	1	4	yes	complemented
27	C₈×Dic₁₅	C₂²	1	4	yes	complemented
28	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
29	C₂×#4840	—	5	1	no	maximal, Hall
30	C₂×#4018	—	3	1	no	—
31	C₂×C₅×C₄⋊C₈	D₃	1	1	yes	characteristic, complemented
32	C₂×#3952	—	3	1	no	—
33	C₂×#3952	—	3	1	no	—
34	C₂×#3947	—	3	1	no	—
35	C₂×C₈×Dic₅	—	3	1	no	—
36	C₂×C₄⋊#168	—	3	1	no	—
37	#65129	—	3	8	no	—
38	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₅	—	2	2	no	—
46	C₂×C₄×D₁₅	—	2	2	no	—
47	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
48	C₂×C₄×D₁₅	C₂³	1	2	yes	—
49	C₂×C₃×C₅×C₈	—	2	2	no	—
50	C₂×C₃×C₅×C₈	—	2	2	no	—
51	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂³	1	2	yes	—
55	#6714	C₂×C₄	1	4	yes	—
56	#6714	C₂×C₄	1	4	yes	—
57	#6712	C₂×C₄	1	4	yes	—
58	#6712	C₂×C₄	1	4	yes	—
59	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₅	C₂³	1	2	yes	—
61	C₂×C₃⋊#168	—	2	2	no	—
62	C₂×C₃⋊#168	—	2	2	no	—
63	C₂×C₃⋊#168	C₂³	1	2	yes	—
64	C₂×C₃⋊#168	C₂³	1	2	yes	—
65	C₂×#872	—	5	1	no	—
66	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic, complemented
67	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
68	C₂×(C₂×D₃)⋊C₈	—	5	1	no	—
69	C₂×#815	—	5	1	no	—
70	C₂×C₈×Dic₃	—	5	1	no	—
71	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
72	#4840	—	5	8	no	—
73	C₂²×C₄×D₅	—	3	1	no	—
74	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	C₂×#685	—	3	1	no	—
78	C₂×#685	—	3	1	no	—
79	C₂×#683	—	3	1	no	—
80	C₂×#683	—	3	1	no	—
81	C₂×C₄×Dic₅	—	3	1	no	—
82	C₂²×#168	—	3	1	no	—
83	C₂²×#168	—	3	1	no	—
84	#4018	—	3	4	no	—
85	#4018	—	3	4	no	—
86	C₅×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
87	#3952	—	3	4	no	—
88	#3952	—	3	4	no	—
89	#3947	—	3	4	no	—
90	C₈×Dic₅	—	3	4	no	—
91	C₄⋊#168	—	3	4	no	—
92	C₂×#433	—	15	1	no	Sylow
93	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×D₁₅	—	2	2	no	—
95	C₂²×D₁₅	—	2	2	no	—
96	C₂²×D₁₅	—	2	2	no	—
97	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	2	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×Dic₁₅	—	2	2	no	—
107	C₂×Dic₁₅	—	2	2	no	—
108	C₂×Dic₁₅	—	2	2	no	—
109	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
110	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
111	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
112	C₄×D₁₅	—	2	4	no	—
113	C₄×D₁₅	—	2	2	no	—
114	C₄×D₁₅	—	2	2	no	—
115	C₃×C₅×C₈	—	2	2	no	—
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃⋊#168	—	2	2	no	—
118	C₃⋊#168	—	2	2	no	—
119	C₂²×C₄×D₃	—	5	1	no	—
120	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
123	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
124	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
125	C₂×Dic₃⋊C₄	—	5	1	no	—
126	C₂×Dic₃⋊C₄	—	5	1	no	—
127	C₂×C₄×Dic₃	—	5	1	no	—
128	C₂²×C₃⋊C₈	—	5	1	no	—
129	C₂²×C₃⋊C₈	—	5	1	no	—
130	#872	—	5	4	no	—
131	#872	—	5	4	no	—
132	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
133	(C₂×D₃)⋊C₈	—	5	4	no	—
134	(C₂×D₃)⋊C₈	—	5	4	no	—
135	#815	—	5	4	no	—
136	C₈×Dic₃	—	5	4	no	—
137	C₄⋊(C₃⋊C₈)	—	5	4	no	—
138	C₂³×D₅	—	3	1	no	—
139	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
142	C₂²×Dic₅	—	3	1	no	—
143	C₂²×Dic₅	—	3	1	no	—
144	C₂²×Dic₅	—	3	1	no	—
145	C₂×C₄×D₅	—	3	2	no	—
146	C₂×C₄×D₅	—	3	2	no	—
147	C₂×C₄×D₅	—	6	2	no	—
148	C₂×C₄×D₅	—	6	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
152	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
153	C₄²×C₅	C₄×D₃	1	2	yes	—
154	C₄²×C₅	C₂²×D₃	1	2	yes	—
155	#685	—	3	4	no	—
156	#685	—	3	4	no	—
157	#683	—	3	4	no	—
158	#683	—	3	4	no	—
159	C₄×Dic₅	—	3	2	no	—
160	C₄×Dic₅	—	3	2	no	—
161	C₂×#168	—	3	2	no	—
162	C₂×#168	—	3	2	no	—
163	C₂×#168	—	6	2	no	—
164	C₂×#168	—	6	2	no	—
165	C₂×#117	—	15	1	no	—
166	#433	—	15	8	no	—
167	C₂×C₄⋊C₈	—	15	1	no	—
168	C₂×C₄⋊C₈	D₁₅	1	1	yes	characteristic, complemented
169	C₂×C₂²⋊C₈	—	15	1	no	—
170	C₂×C₂²⋊C₈	—	15	1	no	—
171	C₂×#97	—	15	1	no	—
172	C₂×C₄×C₈	—	15	1	no	—
173	C₂²×C₃×C₅	#117	1	2	yes	—
174	C₂²×C₃×C₅	#131	1	2	yes	—
175	C₂²×C₃×C₅	#131	1	2	yes	—
176	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₂×D₁₅	—	2	2	no	—
178	C₂×D₁₅	—	2	2	no	—
179	C₂×D₁₅	—	2	2	no	—
180	C₂×D₁₅	—	4	4	no	—
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	—	2	2	no	—
183	C₃×C₄×C₅	#117	1	2	yes	—
184	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
186	Dic₁₅	—	2	2	no	—
187	Dic₁₅	—	2	2	no	—
188	Dic₁₅	—	2	2	no	—
189	C₂³×D₃	—	5	1	no	—
190	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
193	C₂²×Dic₃	—	5	1	no	—
194	C₂²×Dic₃	—	5	1	no	—
195	C₂²×Dic₃	—	5	1	no	—
196	C₂×C₄×D₃	—	5	2	no	—
197	C₂×C₄×D₃	—	5	2	no	—
198	C₂×C₄×D₃	—	10	2	no	—
199	C₂×C₄×D₃	—	10	2	no	—
200	C₂×C₃×C₈	—	2	2	no	—
201	C₂×C₃×C₈	—	2	2	no	—
202	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
203	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
204	C₃×C₄²	C₄×D₅	1	2	yes	—
205	C₃×C₄²	C₂²×D₅	1	2	yes	—
206	(C₂×D₃)⋊C₄	—	5	4	no	—
207	(C₂×D₃)⋊C₄	—	5	4	no	—
208	Dic₃⋊C₄	—	5	4	no	—
209	Dic₃⋊C₄	—	5	4	no	—
210	C₄×Dic₃	—	5	2	no	—
211	C₄×Dic₃	—	5	2	no	—
212	C₂×C₃⋊C₈	—	5	2	no	—
213	C₂×C₃⋊C₈	—	5	2	no	—
214	C₂×C₃⋊C₈	—	10	2	no	—
215	C₂×C₃⋊C₈	—	10	2	no	—
216	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
217	C₂²×D₅	—	3	2	no	—
218	C₂²×D₅	—	6	2	no	—
219	C₂²×D₅	—	6	2	no	—
220	C₂²×D₅	—	6	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
224	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
225	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂×C₄×C₅	#237	1	2	yes	—
227	C₂×C₄×C₅	#239	1	2	yes	—
228	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
229	C₂×Dic₅	—	3	2	no	—
230	C₂×Dic₅	—	3	2	no	—
231	C₂×Dic₅	—	3	2	no	—
232	C₂×Dic₅	—	6	2	no	—
233	C₂×Dic₅	—	6	2	no	—
234	C₂×Dic₅	—	6	2	no	—
235	C₄×D₅	—	6	4	no	—
236	C₄×D₅	—	6	2	no	—
237	C₄×D₅	—	6	2	no	—
238	C₅×C₈	—	2	2	no	—
239	C₅×C₈	—	2	2	no	—
240	#168	—	6	2	no	—
241	#168	—	6	2	no	—
242	C₂³×C₄	—	15	1	no	—
243	C₂²×C₈	—	15	1	no	—
244	C₂²×C₈	—	15	1	no	—
245	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
246	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
247	#117	—	15	4	no	—
248	#117	—	15	4	no	—
249	C₂×C₄⋊C₄	—	15	1	no	—
250	C₂×C₄⋊C₄	—	15	1	no	—
251	C₂×C₂²⋊C₄	—	15	1	no	—
252	C₂×C₂²⋊C₄	—	15	1	no	—
253	C₂×C₄²	—	15	1	no	—
254	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
255	C₄⋊C₈	—	15	4	no	—
256	C₄⋊C₈	C₂×D₁₅	1	4	yes	complemented
257	C₂²⋊C₈	—	15	4	no	—
258	C₂²⋊C₈	—	15	4	no	—
259	#97	—	15	4	no	—
260	C₄×C₈	—	15	4	no	—
261	C₂×C₃×C₅	#433	1	4	yes	complemented
262	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
265	D₁₅	—	4	2	no	—
266	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
267	C₂²×D₃	—	5	2	no	—
268	C₂²×D₃	—	10	2	no	—
269	C₂²×D₃	—	10	2	no	—
270	C₂²×D₃	—	10	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	#711	1	2	yes	—
277	C₂×C₃×C₄	#713	1	2	yes	—
278	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
279	C₂×Dic₃	—	5	2	no	—
280	C₂×Dic₃	—	5	2	no	—
281	C₂×Dic₃	—	5	2	no	—
282	C₂×Dic₃	—	10	2	no	—
283	C₂×Dic₃	—	10	2	no	—
284	C₂×Dic₃	—	10	2	no	—
285	C₄×D₃	—	10	2	no	—
286	C₄×D₃	—	10	2	no	—
287	C₄×D₃	—	10	4	no	—
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	2	2	no	—
290	C₃⋊C₈	—	10	2	no	—
291	C₃⋊C₈	—	10	2	no	—
292	C₂²×C₅	#892	1	2	yes	—
293	C₂²×C₅	#901	1	2	yes	—
294	C₂²×C₅	#907	1	2	yes	—
295	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
296	C₂×D₅	—	6	2	no	—
297	C₂×D₅	—	6	2	no	—
298	C₂×D₅	—	6	2	no	—
299	C₂×D₅	—	12	4	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	#892	1	2	yes	—
303	C₄×C₅	C₂×#237	1	1	yes	characteristic
304	C₄×C₅	C₂×#239	1	1	yes	characteristic
305	Dic₅	—	6	2	no	—
306	Dic₅	—	6	2	no	—
307	Dic₅	—	6	2	no	—
308	C₂⁴	—	15	1	no	—
309	C₂²×C₄	—	15	1	no	—
310	C₂²×C₄	—	15	1	no	—
311	C₂²×C₄	—	15	1	no	—
312	C₂²×C₄	—	15	2	no	—
313	C₂²×C₄	—	15	2	no	—
314	C₂²×C₄	—	30	2	no	—
315	C₂²×C₄	—	30	2	no	—
316	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
317	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	15	2	no	—
322	C₂×C₈	—	15	2	no	—
323	C₂×C₈	—	30	2	no	—
324	C₂×C₈	—	30	2	no	—
325	C₂×C₈	C₂²×D₁₅	1	2	yes	—
326	C₂×C₈	C₂²×D₁₅	1	2	yes	—
327	C₄⋊C₄	—	15	4	no	—
328	C₄⋊C₄	—	15	4	no	—
329	C₂²⋊C₄	—	15	4	no	—
330	C₂²⋊C₄	—	15	4	no	—
331	C₄²	—	15	2	no	—
332	C₄²	—	15	2	no	—
333	C₄²	C₄×D₁₅	1	2	yes	—
334	C₄²	C₂²×D₁₅	1	2	yes	—
335	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	#4038	1	2	yes	—
337	C₂²×C₃	#4047	1	2	yes	—
338	C₂²×C₃	#4053	1	2	yes	—
339	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
340	C₂×D₃	—	10	2	no	—
341	C₂×D₃	—	10	2	no	—
342	C₂×D₃	—	10	2	no	—
343	C₂×D₃	—	20	4	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	#4038	1	2	yes	—
347	C₃×C₄	C₂×#711	1	1	yes	characteristic
348	C₃×C₄	C₂×#713	1	1	yes	characteristic
349	Dic₃	—	10	2	no	—
350	Dic₃	—	10	2	no	—
351	Dic₃	—	10	2	no	—
352	C₂×C₅	#4840	1	4	yes	complemented
353	C₂×C₅	C₂×#892	1	1	yes	characteristic
354	C₂×C₅	C₂×#901	1	1	yes	characteristic
355	C₂×C₅	C₂×#907	1	1	yes	characteristic
356	D₅	—	12	2	no	—
357	C₂³	—	15	2	no	—
358	C₂³	—	30	2	no	—
359	C₂³	—	30	2	no	—
360	C₂³	—	30	2	no	—
361	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	15	2	no	—
365	C₂×C₄	—	15	2	no	—
366	C₂×C₄	—	15	2	no	—
367	C₂×C₄	—	30	2	no	—
368	C₂×C₄	—	30	2	no	—
369	C₂×C₄	—	30	2	no	—
370	C₂×C₄	—	30	4	no	—
371	C₂×C₄	—	30	2	no	—
372	C₂×C₄	—	30	2	no	—
373	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
374	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
375	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
376	C₂×C₄	#6819	1	2	yes	—
377	C₂×C₄	#6821	1	2	yes	—
378	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	30	2	no	—
382	C₈	—	30	2	no	—
383	C₂×C₃	#65129	1	4	yes	complemented
384	C₂×C₃	C₂×#4038	1	1	yes	characteristic
385	C₂×C₃	C₂×#4047	1	1	yes	characteristic
386	C₂×C₃	C₂×#4053	1	1	yes	characteristic
387	D₃	—	20	2	no	—
388	C₅	C₂×#4840	1	1	yes	characteristic, complemented, Sylow
389	C₂²	—	30	2	no	—
390	C₂²	—	30	2	no	—
391	C₂²	—	30	2	no	—
392	C₂²	—	60	4	no	—
393	C₂²	#91781	1	2	yes	—
394	C₂²	#91790	1	2	yes	—
395	C₂²	#91796	1	2	yes	—
396	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	30	2	no	—
400	C₄	—	30	2	no	—
401	C₄	—	30	2	no	—
402	C₄	#91781	1	2	yes	—
403	C₄	C₂×#6819	1	1	yes	characteristic
404	C₄	C₂×#6821	1	1	yes	characteristic
405	C₃	C₂×#65129	1	1	yes	characteristic, complemented, Sylow
406	C₂	—	60	2	no	—
407	C₂	#11750941	1	4	yes	direct product factor
408	C₂	C₂×#91781	1	1	yes	characteristic
409	C₂	C₂×#91790	1	1	yes	characteristic
410	C₂	C₂×#91796	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄⋊C₈	D₁₅
hypocenter	C₃×C₅	C₂×#433
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
5. C₂×#91099	C₂	semidirect
6. C₂×C₈×Dic₁₅	C₂	semidirect
7. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
8. #11750941	C₂	direct (N × H)
23. C₃×C₅×C₄⋊C₈	C₂²	semidirect
26. #91099	C₂²	semidirect
27. C₈×Dic₁₅	C₂²	semidirect
28. C₄⋊(C₃⋊#168)	C₂²	semidirect
31. C₂×C₅×C₄⋊C₈	D₃	semidirect
66. C₂×C₃×C₄⋊C₈	D₅	semidirect
86. C₅×C₄⋊C₈	C₂×D₃	semidirect
132. C₃×C₄⋊C₈	C₂×D₅	semidirect
168. C₂×C₄⋊C₈	D₁₅	semidirect
256. C₄⋊C₈	C₂×D₁₅	semidirect
261. C₂×C₃×C₅	#433	semidirect
335. C₃×C₅	C₂×#433	semidirect
352. C₂×C₅	#4840	semidirect
383. C₂×C₃	#65129	semidirect
388. C₅	C₂×#4840	semidirect
405. C₃	C₂×#65129	semidirect
407. C₂	#11750941	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×#91761	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×#91104	2
C₂×#91099	2
C₂×C₈×Dic₁₅	2
C₂×C₄⋊(C₃⋊#168)	2
#11750941	2
C₂×#65129	3
C₂×#4840	5

Subgroups — C2×#11750941 #14413828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11750941 #14413828