Subgroups — C₂×C₅×#4914 #14478329

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#919	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#828	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#826	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4914	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×D₄₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#509	—	3	1	no	maximal, Hall
10	C₂×C₅×#239	—	2	1	no	—
11	C₂×C₅×D₃×D₄	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#215	—	2	1	no	—
15	C₂×C₅×#213	—	2	1	no	—
16	C₅×#919	—	2	2	no	—
17	C₅×#919	C₂²	1	4	yes	complemented
18	C₅×D₃×D₈	—	2	2	no	—
19	C₅×D₃×D₈	C₂²	1	4	yes	complemented
20	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×SD₃₂	C₂²	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₅×#828	C₂²	1	4	yes	complemented
26	C₅×#826	C₂²	1	4	yes	complemented
27	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₅×D₄₈	C₂²	1	4	yes	complemented
29	C₅×#798	C₂²	1	4	yes	complemented
30	C₂×#4914	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₂²×C₅×D₈	—	3	1	no	—
33	C₅×#509	—	3	8	no	—
34	C₂×C₅×SD₃₂	—	3	1	no	—
35	C₂×C₅×SD₃₂	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×D₁₆	—	3	1	no	—
37	C₂×C₅×D₁₆	—	3	1	no	—
38	C₂×C₅×M₃₂	—	3	1	no	—
39	C₂³×C₅×D₃	—	4	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₅×#67	—	4	1	no	—
43	C₅×#239	—	2	4	no	—
44	C₅×#239	—	4	2	no	—
45	C₅×D₃×D₄	—	2	4	no	—
46	C₅×D₃×D₄	—	4	2	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	—	4	1	no	—
50	C₂×C₄×C₅×D₃	—	4	1	no	—
51	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	complemented
54	C₃×C₅×D₈	—	2	1	no	—
55	C₃×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#215	—	2	4	no	—
58	C₅×#213	—	2	4	no	—
59	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
60	C₅×D₂₄	—	2	1	no	—
61	C₅×D₂₄	—	2	1	no	—
62	C₅×D₂₄	C₂³	1	2	yes	—
63	C₅×D₂₄	C₂³	1	2	yes	complemented
64	C₅×D₃×C₈	D₄	1	2	yes	—
65	C₅×D₃×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₁₆	C₂³	1	2	yes	complemented
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	complemented
68	C₂×#919	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₃×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#828	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#826	C₂×C₅	1	1	yes	characteristic, complemented
73	#4914	C₂×C₅	1	8	yes	direct product factor
74	C₂×D₄₈	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#798	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	6	1	no	—
77	C₂²×C₅×D₄	—	6	1	no	—
78	C₅×#135	—	3	4	no	—
79	C₅×#135	—	6	2	no	—
80	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂×C₅×SD₁₆	—	6	1	no	—
82	C₂×C₅×D₈	—	3	4	no	—
83	C₂×C₅×D₈	—	3	1	no	—
84	C₂×C₅×D₈	—	3	1	no	—
85	C₂×C₅×D₈	—	6	2	no	—
86	C₂×C₅×D₈	—	6	1	no	—
87	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	—	3	1	no	—
89	C₅×SD₃₂	—	3	4	no	—
90	C₅×SD₃₂	C₂×D₃	1	4	yes	complemented
91	C₅×D₁₆	—	3	4	no	—
92	C₅×D₁₆	—	3	4	no	—
93	C₅×M₃₂	—	3	4	no	—
94	C₂×C₅×C₁₆	—	3	1	no	—
95	C₂×C₅×C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
96	C₂×#509	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	—	4	1	no	—
100	C₂²×C₅×D₃	—	4	4	no	—
101	C₂²×C₅×D₃	—	8	4	no	—
102	C₂²×C₅×D₃	D₈	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	4	1	no	—
105	C₃×C₅×D₄	—	2	2	no	—
106	C₃×C₅×D₄	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	4	1	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₅×#67	—	4	4	no	—
110	C₂×C₅×Dic₃	D₈	1	1	yes	characteristic
111	C₅×D₁₂	—	2	2	no	—
112	C₅×D₁₂	—	2	2	no	—
113	C₅×D₁₂	—	4	4	no	—
114	C₅×D₁₂	—	4	1	no	—
115	C₅×D₁₂	—	4	1	no	—
116	C₄×C₅×D₃	—	4	4	no	—
117	C₄×C₅×D₃	D₈	1	2	yes	—
118	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
122	C₂×#239	—	2	1	no	—
123	C₂×D₃×D₄	—	2	1	no	—
124	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
125	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
126	C₂×#215	—	2	1	no	—
127	C₂×#213	—	2	1	no	—
128	#919	—	2	2	no	—
129	#919	C₂²×C₅	1	4	yes	complemented
130	D₃×D₈	—	2	2	no	—
131	D₃×D₈	C₂²×C₅	1	4	yes	complemented
132	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×SD₃₂	C₂²×C₅	1	4	yes	complemented
136	C₂×C₃×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
137	#828	C₂²×C₅	1	4	yes	complemented
138	#826	C₂²×C₅	1	4	yes	complemented
139	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
140	D₄₈	C₂²×C₅	1	4	yes	complemented
141	#798	C₂²×C₅	1	4	yes	complemented
142	C₂⁴×C₅	—	12	1	no	—
143	C₅×#41	—	6	4	no	—
144	C₅×#41	—	12	2	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	6	4	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂×C₅×D₄	—	12	2	no	—
151	C₂×C₅×D₄	—	12	1	no	—
152	C₂×C₅×D₄	—	12	1	no	—
153	C₂²×C₄×C₅	—	3	1	no	—
154	C₂²×C₄×C₅	—	12	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	C₂²×D₃	1	2	yes	complemented
157	C₅×SD₁₆	—	6	4	no	—
158	C₅×D₈	—	2	1	no	—
159	C₅×D₈	—	3	2	no	—
160	C₅×D₈	—	3	2	no	—
161	C₅×D₈	—	6	4	no	—
162	C₅×D₈	—	6	1	no	—
163	C₅×D₈	—	6	1	no	—
164	C₅×D₈	C₂²×D₃	1	2	yes	—
165	C₂×C₅×C₈	—	3	1	no	—
166	C₂×C₅×C₈	—	3	2	no	—
167	C₂×C₅×C₈	—	3	2	no	—
168	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₅×C₁₆	—	3	2	no	—
170	C₅×C₁₆	C₂²×D₃	1	2	yes	complemented
171	C₂×#135	—	3	1	no	—
172	C₂²×D₈	—	3	1	no	—
173	#509	—	3	8	no	—
174	C₂×SD₃₂	—	3	1	no	—
175	C₂×SD₃₂	C₅×D₃	1	1	yes	characteristic, complemented
176	C₂×D₁₆	—	3	1	no	—
177	C₂×D₁₆	—	3	1	no	—
178	C₂×M₃₂	—	3	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	8	2	no	—
181	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
182	C₂×C₅×D₃	—	2	2	no	—
183	C₂×C₅×D₃	—	4	2	no	—
184	C₂×C₅×D₃	—	4	2	no	—
185	C₂×C₅×D₃	—	8	8	no	—
186	C₂×C₅×D₃	—	8	2	no	—
187	C₂×C₅×D₃	—	8	2	no	—
188	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₅×Dic₃	C₂×D₈	1	2	yes	—
193	C₂³×D₃	—	4	1	no	—
194	C₂×C₃×Q₈	—	2	1	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×#67	—	4	1	no	—
197	#239	—	2	4	no	—
198	#239	—	4	2	no	—
199	D₃×D₄	—	2	4	no	—
200	D₃×D₄	—	4	2	no	—
201	C₂×D₁₂	—	2	1	no	—
202	C₂×D₁₂	—	2	1	no	—
203	C₂×D₁₂	—	4	1	no	—
204	C₂×C₄×D₃	—	4	1	no	—
205	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
206	C₃×Q₁₆	—	2	1	no	—
207	C₃×Q₁₆	C₂³×C₅	1	2	yes	complemented
208	C₃×D₈	—	2	1	no	—
209	C₃×D₈	C₂³×C₅	1	2	yes	—
210	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
211	#215	—	2	4	no	—
212	#213	—	2	4	no	—
213	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
214	D₂₄	—	2	1	no	—
215	D₂₄	—	2	1	no	—
216	D₂₄	C₂³×C₅	1	2	yes	—
217	D₂₄	C₂³×C₅	1	2	yes	complemented
218	D₃×C₈	C₅×D₄	1	2	yes	—
219	D₃×C₈	C₂³×C₅	1	2	yes	—
220	C₃×C₁₆	C₂³×C₅	1	2	yes	complemented
221	C₃⋊C₁₆	C₂³×C₅	1	2	yes	complemented
222	C₂³×C₅	—	3	1	no	—
223	C₂³×C₅	—	4	1	no	—
224	C₂³×C₅	—	12	4	no	—
225	C₂³×C₅	—	12	1	no	—
226	C₂³×C₅	—	12	1	no	—
227	C₂³×C₅	—	24	4	no	—
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	—	6	2	no	—
233	C₅×D₄	—	6	2	no	—
234	C₅×D₄	—	12	4	no	—
235	C₅×D₄	—	12	4	no	—
236	C₅×D₄	—	12	1	no	—
237	C₅×D₄	—	12	1	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	2	no	—
240	C₂×C₄×C₅	—	3	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	12	4	no	—
243	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
244	C₅×C₈	—	3	2	no	—
245	C₅×C₈	D₃×D₄	1	1	yes	characteristic
246	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
247	C₂×#41	—	6	1	no	—
248	C₂²×D₄	—	6	1	no	—
249	#135	—	3	4	no	—
250	#135	—	6	2	no	—
251	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	—	6	1	no	—
253	C₂×D₈	—	3	4	no	—
254	C₂×D₈	—	3	1	no	—
255	C₂×D₈	—	3	1	no	—
256	C₂×D₈	—	6	2	no	—
257	C₂×D₈	—	6	1	no	—
258	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂²×C₈	—	3	1	no	—
260	SD₃₂	—	3	4	no	—
261	SD₃₂	C₂×C₅×D₃	1	4	yes	complemented
262	D₁₆	—	3	4	no	—
263	D₁₆	—	3	4	no	—
264	M₃₂	—	3	4	no	—
265	C₂×C₁₆	—	3	1	no	—
266	C₂×C₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
267	C₂×C₃×C₅	—	8	2	no	—
268	C₂×C₃×C₅	#509	1	2	yes	complemented
269	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
270	C₅×D₃	—	2	2	no	—
271	C₅×D₃	—	8	2	no	—
272	C₅×D₃	—	8	2	no	—
273	C₂³×C₃	—	4	1	no	—
274	C₂²×D₃	—	4	1	no	—
275	C₂²×D₃	—	4	1	no	—
276	C₂²×D₃	—	4	4	no	—
277	C₂²×D₃	—	8	4	no	—
278	C₂²×D₃	C₅×D₈	1	1	yes	characteristic
279	C₃×Q₈	—	2	2	no	—
280	C₃×Q₈	—	4	1	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	#67	—	4	4	no	—
286	C₂×Dic₃	C₅×D₈	1	1	yes	characteristic
287	D₁₂	—	2	2	no	—
288	D₁₂	—	2	2	no	—
289	D₁₂	—	4	4	no	—
290	D₁₂	—	4	1	no	—
291	D₁₂	—	4	1	no	—
292	C₄×D₃	—	4	4	no	—
293	C₄×D₃	C₅×D₈	1	2	yes	—
294	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
295	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
296	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
297	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
298	C₂²×C₅	—	3	2	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	6	2	no	—
301	C₂²×C₅	—	8	2	no	—
302	C₂²×C₅	—	12	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	—	24	8	no	—
305	C₂²×C₅	—	24	2	no	—
306	C₂²×C₅	—	24	2	no	—
307	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
308	C₄×C₅	—	3	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	D₃×D₈	1	1	yes	characteristic
311	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
312	C₂⁴	—	12	1	no	—
313	#41	—	6	4	no	—
314	#41	—	12	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	6	4	no	—
318	C₂×D₄	—	6	1	no	—
319	C₂×D₄	—	6	1	no	—
320	C₂×D₄	—	12	2	no	—
321	C₂×D₄	—	12	1	no	—
322	C₂×D₄	—	12	1	no	—
323	C₂²×C₄	—	3	1	no	—
324	C₂²×C₄	—	12	1	no	—
325	Q₁₆	—	2	1	no	—
326	Q₁₆	C₂²×C₅×D₃	1	2	yes	complemented
327	SD₁₆	—	6	4	no	—
328	D₈	—	2	1	no	—
329	D₈	—	3	2	no	—
330	D₈	—	3	2	no	—
331	D₈	—	6	4	no	—
332	D₈	—	6	1	no	—
333	D₈	—	6	1	no	—
334	D₈	C₂²×C₅×D₃	1	2	yes	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	—	3	2	no	—
337	C₂×C₈	—	3	2	no	—
338	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
339	C₁₆	—	3	2	no	—
340	C₁₆	C₂²×C₅×D₃	1	2	yes	complemented
341	C₃×C₅	C₂×#509	1	1	yes	characteristic, complemented, Hall
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	8	2	no	—
344	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
345	C₂×D₃	—	2	2	no	—
346	C₂×D₃	—	4	2	no	—
347	C₂×D₃	—	4	2	no	—
348	C₂×D₃	—	8	8	no	—
349	C₂×D₃	—	8	2	no	—
350	C₂×D₃	—	8	2	no	—
351	C₂×D₃	C₂×C₅×D₈	1	2	yes	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
354	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
355	Dic₃	C₂×C₅×D₈	1	2	yes	—
356	C₂×C₅	—	6	2	no	—
357	C₂×C₅	—	8	2	no	—
358	C₂×C₅	—	24	2	no	—
359	C₂×C₅	—	24	2	no	—
360	C₂×C₅	#4914	1	2	yes	direct product factor
361	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
362	C₂³	—	3	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	12	4	no	—
365	C₂³	—	12	1	no	—
366	C₂³	—	12	1	no	—
367	C₂³	—	24	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	6	2	no	—
373	D₄	—	6	2	no	—
374	D₄	—	12	4	no	—
375	D₄	—	12	4	no	—
376	D₄	—	12	1	no	—
377	D₄	—	12	1	no	—
378	C₂×C₄	—	3	1	no	—
379	C₂×C₄	—	3	2	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	12	4	no	—
383	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
384	C₈	—	3	2	no	—
385	C₈	C₅×D₃×D₄	1	1	yes	characteristic
386	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
387	C₂×C₃	—	8	2	no	—
388	C₂×C₃	C₅×#509	1	2	yes	complemented
389	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
390	D₃	—	2	2	no	—
391	D₃	—	8	2	no	—
392	D₃	—	8	2	no	—
393	C₅	C₂×#4914	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	3	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	6	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	12	2	no	—
399	C₂²	—	12	2	no	—
400	C₂²	—	24	8	no	—
401	C₂²	—	24	2	no	—
402	C₂²	—	24	2	no	—
403	C₂²	C₅×D₃×D₈	1	1	yes	characteristic
404	C₄	—	3	2	no	—
405	C₄	—	4	2	no	—
406	C₄	C₅×D₃×D₈	1	1	yes	characteristic
407	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
408	C₃	C₂×C₅×#509	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	6	2	no	—
410	C₂	—	8	2	no	—
411	C₂	—	24	2	no	—
412	C₂	—	24	2	no	—
413	C₂	C₅×#4914	1	2	yes	direct product factor
414	C₂	C₂×C₅×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×SD₃₂	C₂
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₅×SD₃₂	D₃
hypocenter	C₃	C₂×C₅×#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#919	C₂	semidirect
2. C₂×C₅×D₃×D₈	C₂	semidirect
3. C₂×C₃×C₅×SD₃₂	C₂	semidirect
4. C₂×C₅×#828	C₂	semidirect
5. C₂×C₅×#826	C₂	semidirect
6. C₅×#4914	C₂	direct (N × H)
7. C₂×C₅×D₄₈	C₂	semidirect
8. C₂×C₅×#798	C₂	semidirect
12. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₅×#919	C₂²	semidirect
19. C₅×D₃×D₈	C₂²	semidirect
21. C₂×C₅×D₂₄	C₂²	semidirect
23. C₃×C₅×SD₃₂	C₂²	semidirect
24. C₂×C₃×C₅×C₁₆	C₂²	semidirect
25. C₅×#828	C₂²	semidirect
26. C₅×#826	C₂²	semidirect
27. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
28. C₅×D₄₈	C₂²	semidirect
29. C₅×#798	C₂²	semidirect
30. C₂×#4914	C₅	direct (N × H)
35. C₂×C₅×SD₃₂	D₃	semidirect
53. C₃×C₅×Q₁₆	C₂³	semidirect
63. C₅×D₂₄	C₂³	semidirect
66. C₃×C₅×C₁₆	C₂³	semidirect
67. C₅×C₃⋊C₁₆	C₂³	semidirect
68. C₂×#919	C₂×C₅	semidirect
69. C₂×D₃×D₈	C₂×C₅	semidirect
70. C₂×C₃×SD₃₂	C₂×C₅	semidirect
71. C₂×#828	C₂×C₅	semidirect
72. C₂×#826	C₂×C₅	semidirect
73. #4914	C₂×C₅	direct (N × H)
74. C₂×D₄₈	C₂×C₅	semidirect
75. C₂×#798	C₂×C₅	semidirect
80. C₂×C₅×Q₁₆	C₂×D₃	semidirect
90. C₅×SD₃₂	C₂×D₃	semidirect
95. C₂×C₅×C₁₆	C₂×D₃	semidirect
124. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
129. #919	C₂²×C₅	semidirect
131. D₃×D₈	C₂²×C₅	semidirect
133. C₂×D₂₄	C₂²×C₅	semidirect
135. C₃×SD₃₂	C₂²×C₅	semidirect
136. C₂×C₃×C₁₆	C₂²×C₅	semidirect
137. #828	C₂²×C₅	semidirect
138. #826	C₂²×C₅	semidirect
139. C₂×C₃⋊C₁₆	C₂²×C₅	semidirect
140. D₄₈	C₂²×C₅	semidirect
141. #798	C₂²×C₅	semidirect
156. C₅×Q₁₆	C₂²×D₃	semidirect
170. C₅×C₁₆	C₂²×D₃	semidirect
175. C₂×SD₃₂	C₅×D₃	semidirect
207. C₃×Q₁₆	C₂³×C₅	semidirect
217. D₂₄	C₂³×C₅	semidirect
220. C₃×C₁₆	C₂³×C₅	semidirect
221. C₃⋊C₁₆	C₂³×C₅	semidirect
251. C₂×Q₁₆	C₂×C₅×D₃	semidirect
261. SD₃₂	C₂×C₅×D₃	semidirect
266. C₂×C₁₆	C₂×C₅×D₃	semidirect
268. C₂×C₃×C₅	#509	semidirect
326. Q₁₆	C₂²×C₅×D₃	semidirect
340. C₁₆	C₂²×C₅×D₃	semidirect
341. C₃×C₅	C₂×#509	semidirect
360. C₂×C₅	#4914	direct (N × H)
388. C₂×C₃	C₅×#509	semidirect
393. C₅	C₂×#4914	direct (N × H)
408. C₃	C₂×C₅×#509	semidirect
413. C₂	C₅×#4914	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×C₅×#919	2
C₂×C₅×D₃×D₈	2
C₂×C₃×C₅×SD₃₂	2
C₂×C₅×#828	2
C₂×C₅×#826	2
C₅×#4914	2
C₂×C₅×D₄₈	2
C₂×C₅×#798	2
C₂×C₅×#509	3
C₂×#4914	5

Subgroups — C2×C5×#4914 #14478329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4914 #14478329