Subgroups — C₂×C₅×#5192 #14429427

Order 1920.

896 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	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#942	C₂	1	2	yes	maximal
3	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#836	C₂	1	2	yes	maximal, complemented
5	C₅×#5192	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#473	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
11	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#216	—	2	2	no	—
16	C₅×#942	—	2	4	no	—
17	C₅×#942	C₂²	1	8	yes	—
18	C₂×C₅×#215	—	2	2	no	—
19	C₂×C₅×#208	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	2	yes	—
21	C₅×#901	—	2	2	no	—
22	C₅×#901	C₂²	1	4	yes	—
23	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
24	C₂×C₅×D₃×C₈	—	2	1	no	—
25	C₅×#836	C₂²	1	8	yes	complemented
26	C₅×#819	C₂²	1	4	yes	complemented
27	C₂×#5192	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#137	—	3	2	no	—
29	C₂²×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#131	—	3	1	no	—
31	C₅×#473	—	3	8	no	—
32	C₂×C₅×#108	—	3	1	no	—
33	C₂×C₅×#101	—	3	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×#67	—	2	1	no	—
43	C₅×#235	—	2	1	no	—
44	C₅×#235	—	2	1	no	—
45	C₅×#235	D₄	1	2	yes	—
46	C₅×#235	C₂³	1	2	yes	—
47	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
50	C₃×C₅×Q₁₆	—	2	4	no	—
51	C₃×C₅×Q₁₆	—	2	4	no	—
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₅×#216	—	2	8	no	—
57	C₅×#215	—	2	8	no	—
58	C₅×#208	—	2	1	no	—
59	C₅×#208	—	2	2	no	—
60	C₅×#208	C₂³	1	2	yes	—
61	C₅×#208	C₂³	1	4	yes	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
65	C₅×D₃×C₈	—	2	4	no	—
66	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#942	C₂×C₅	1	2	yes	—
68	C₂×#901	C₂×C₅	1	1	yes	characteristic
69	C₂×#836	C₂×C₅	1	2	yes	complemented
70	#5192	C₂×C₅	1	8	yes	direct product factor
71	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₅×#41	—	3	1	no	—
73	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
74	C₅×#137	—	3	8	no	—
75	C₅×#137	—	6	4	no	—
76	C₂×C₅×Q₁₆	—	2	1	no	—
77	C₂×C₅×Q₁₆	—	2	1	no	—
78	C₂×C₅×Q₁₆	—	2	2	no	—
79	C₂×C₅×Q₁₆	—	6	2	no	—
80	C₂×C₅×Q₁₆	C₂×D₃	1	4	yes	complemented
81	C₂×C₅×SD₁₆	—	6	2	no	—
82	C₅×#131	—	3	4	no	—
83	C₅×#131	—	6	2	no	—
84	C₂×C₅×M₁₆	—	3	1	no	—
85	C₂×C₅×M₁₆	—	3	2	no	—
86	C₂×C₅×M₁₆	—	6	1	no	—
87	C₂²×C₅×C₈	—	6	1	no	—
88	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₅×#108	—	3	4	no	—
90	C₅×#101	—	3	8	no	—
91	C₂×#473	—	3	1	no	Sylow
92	C₂³×C₃×C₅	#41	1	1	yes	characteristic
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₃×C₅×Q₈	—	2	4	no	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₃×C₅×Q₈	—	4	2	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	4	2	no	—
100	C₂×C₃×C₄×C₅	—	4	2	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₅×#67	—	2	2	no	—
108	C₅×#67	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₅×D₁₂	—	2	1	no	—
111	C₅×D₁₂	C₂×D₄	1	2	yes	—
112	C₄×C₅×D₃	—	2	2	no	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₅×Dic₆	—	2	1	no	—
115	C₅×Dic₆	C₂×D₄	1	2	yes	—
116	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
117	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
118	C₅×C₃⋊C₈	—	2	2	no	—
119	C₅×C₃⋊C₈	—	2	4	no	—
120	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
121	C₂×#235	C₂²×C₅	1	1	yes	characteristic
122	C₂×C₃×Q₁₆	—	2	1	no	—
123	C₂×C₃×Q₁₆	—	2	1	no	—
124	C₂×C₃×Q₁₆	—	2	2	no	—
125	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×#216	—	2	2	no	—
128	#942	—	2	4	no	—
129	#942	C₂²×C₅	1	8	yes	—
130	C₂×#215	—	2	2	no	—
131	C₂×#208	C₂²×C₅	1	1	yes	characteristic
132	C₂×#208	C₂²×C₅	1	2	yes	—
133	#901	—	2	2	no	—
134	#901	C₂²×C₅	1	4	yes	—
135	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
136	C₂×D₃×C₈	—	2	1	no	—
137	#836	C₂²×C₅	1	8	yes	complemented
138	#819	C₂²×C₅	1	4	yes	complemented
139	C₅×#41	—	3	2	no	—
140	C₅×#41	—	3	2	no	—
141	C₅×#41	—	6	1	no	—
142	C₅×#41	—	6	1	no	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	—	2	2	no	—
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	—	3	1	no	—
149	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
150	C₂×C₅×D₄	—	3	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂²×C₄×C₅	—	2	2	no	—
153	C₂²×C₄×C₅	—	6	1	no	—
154	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
155	C₅×Q₁₆	—	2	4	no	—
156	C₅×Q₁₆	—	2	4	no	—
157	C₅×Q₁₆	—	6	8	no	—
158	C₅×SD₁₆	—	6	8	no	—
159	C₅×M₁₆	—	3	2	no	—
160	C₅×M₁₆	—	3	4	no	—
161	C₅×M₁₆	—	6	2	no	—
162	C₅×M₁₆	—	6	1	no	—
163	C₅×M₁₆	—	6	4	no	—
164	C₂×C₅×C₈	—	6	2	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	—	6	4	no	—
167	C₂×C₅×C₈	#67	1	1	yes	characteristic
168	C₂×C₅×C₈	#67	1	1	yes	characteristic
169	C₂×C₅×C₈	#67	1	2	yes	—
170	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
171	C₂×#137	—	3	2	no	—
172	C₂²×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
173	C₂×#131	—	3	1	no	—
174	#473	—	3	8	no	—
175	C₂×#108	—	3	1	no	—
176	C₂×#101	—	3	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	#121	1	1	yes	characteristic
179	C₂²×C₃×C₅	#121	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	4	2	no	—
183	C₃×C₄×C₅	—	4	4	no	—
184	C₃×C₄×C₅	#121	1	1	yes	characteristic
185	C₃×C₄×C₅	#121	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×Dic₃	—	2	2	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	2	2	no	—
192	C₂×C₃×Q₈	—	2	2	no	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₂×#67	—	2	1	no	—
198	#235	—	2	1	no	—
199	#235	—	2	1	no	—
200	#235	C₅×D₄	1	2	yes	—
201	#235	C₂³×C₅	1	2	yes	—
202	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
205	C₃×Q₁₆	—	2	4	no	—
206	C₃×Q₁₆	—	2	4	no	—
207	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
208	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
209	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
210	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
211	#216	—	2	8	no	—
212	#215	—	2	8	no	—
213	#208	—	2	1	no	—
214	#208	—	2	2	no	—
215	#208	C₂³×C₅	1	4	yes	—
216	#208	C₂³×C₅	1	2	yes	—
217	C₂×C₃⋊C₈	—	2	1	no	—
218	C₂×C₃⋊C₈	—	2	2	no	—
219	ΓL(1,𝔽₂₅)	—	2	4	no	—
220	D₃×C₈	—	2	4	no	—
221	C₂³×C₅	—	6	1	no	—
222	C₂³×C₅	#237	1	1	yes	characteristic
223	C₅×Q₈	—	2	4	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	3	2	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	4	2	no	—
228	C₅×Q₈	—	6	1	no	—
229	C₅×D₄	—	3	2	no	—
230	C₅×D₄	—	6	2	no	—
231	C₅×D₄	—	6	2	no	—
232	C₅×D₄	—	6	1	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	#237	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
245	C₅×C₈	—	6	4	no	—
246	C₅×C₈	—	6	2	no	—
247	C₅×C₈	C₂×#67	1	2	yes	—
248	C₅×C₈	C₂×#67	1	2	yes	—
249	C₂×#41	—	3	1	no	—
250	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
251	#137	—	3	8	no	—
252	#137	—	6	4	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	6	2	no	—
257	C₂×Q₁₆	C₂×C₅×D₃	1	4	yes	complemented
258	C₂×SD₁₆	—	6	2	no	—
259	#131	—	3	4	no	—
260	#131	—	6	2	no	—
261	C₂×M₁₆	—	3	1	no	—
262	C₂×M₁₆	—	3	2	no	—
263	C₂×M₁₆	—	6	1	no	—
264	C₂²×C₈	—	6	1	no	—
265	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
266	#108	—	3	4	no	—
267	#101	—	3	8	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	#473	1	2	yes	complemented
271	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
272	C₅×D₃	—	4	2	no	—
273	C₂³×C₃	C₅×#41	1	1	yes	characteristic
274	C₂²×D₃	—	2	1	no	—
275	C₃×Q₈	—	2	4	no	—
276	C₃×Q₈	—	2	4	no	—
277	C₃×Q₈	—	4	2	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	4	2	no	—
281	C₂×C₃×C₄	—	4	2	no	—
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	#67	—	2	2	no	—
289	#67	—	2	2	no	—
290	C₂×Dic₃	—	2	1	no	—
291	D₁₂	—	2	1	no	—
292	D₁₂	C₂×C₅×D₄	1	2	yes	—
293	C₄×D₃	—	2	2	no	—
294	C₄×D₃	—	2	2	no	—
295	Dic₆	—	2	1	no	—
296	Dic₆	C₂×C₅×D₄	1	2	yes	—
297	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
298	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
299	C₃⋊C₈	—	2	2	no	—
300	C₃⋊C₈	—	2	4	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	2	no	—
304	C₂²×C₅	#938	1	1	yes	characteristic
305	C₂²×C₅	#938	1	1	yes	characteristic
306	C₂²×C₅	C₂×#237	1	1	yes	characteristic
307	C₄×C₅	—	4	4	no	—
308	C₄×C₅	—	6	2	no	—
309	C₄×C₅	#938	1	1	yes	characteristic
310	C₄×C₅	#938	1	1	yes	characteristic
311	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
312	C₄×C₅	C₂²×#67	1	1	yes	characteristic
313	#41	—	3	2	no	—
314	#41	—	3	2	no	—
315	#41	—	6	1	no	—
316	#41	—	6	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	3	1	no	—
323	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	6	1	no	—
328	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	Q₁₆	—	2	4	no	—
331	Q₁₆	—	6	8	no	—
332	SD₁₆	—	6	8	no	—
333	M₁₆	—	3	2	no	—
334	M₁₆	—	3	4	no	—
335	M₁₆	—	6	2	no	—
336	M₁₆	—	6	1	no	—
337	M₁₆	—	6	4	no	—
338	C₂×C₈	—	6	2	no	—
339	C₂×C₈	—	6	1	no	—
340	C₂×C₈	—	6	4	no	—
341	C₂×C₈	C₅×#67	1	1	yes	characteristic
342	C₂×C₈	C₅×#67	1	1	yes	characteristic
343	C₂×C₈	C₅×#67	1	2	yes	—
344	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	C₅×#121	1	1	yes	characteristic
348	C₂²×C₃	C₅×#121	1	1	yes	characteristic
349	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
350	C₂×D₃	—	2	2	no	—
351	C₂×D₃	—	4	2	no	—
352	C₃×C₄	—	4	4	no	—
353	C₃×C₄	C₅×#121	1	1	yes	characteristic
354	C₃×C₄	C₅×#121	1	1	yes	characteristic
355	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
357	Dic₃	—	2	2	no	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	12	2	no	—
361	C₂×C₅	#5192	1	2	yes	direct product factor
362	C₂×C₅	C₂×#938	1	1	yes	characteristic
363	C₂³	—	6	1	no	—
364	C₂³	C₅×#237	1	1	yes	characteristic
365	Q₈	—	2	4	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	3	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	6	1	no	—
371	D₄	—	3	2	no	—
372	D₄	—	6	2	no	—
373	D₄	—	6	2	no	—
374	D₄	—	6	1	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	6	1	no	—
379	C₂×C₄	—	6	2	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
382	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
383	C₂×C₄	C₅×#237	1	1	yes	characteristic
384	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
385	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
386	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
387	C₈	—	6	4	no	—
388	C₈	—	6	2	no	—
389	C₈	C₂×C₅×#67	1	2	yes	—
390	C₈	C₂×C₅×#67	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	C₅×#473	1	2	yes	complemented
394	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
395	D₃	—	4	2	no	—
396	C₅	C₂×#5192	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	6	2	no	—
399	C₂²	—	12	2	no	—
400	C₂²	C₅×#938	1	1	yes	characteristic
401	C₂²	C₅×#938	1	1	yes	characteristic
402	C₂²	C₂×C₅×#237	1	1	yes	characteristic
403	C₄	—	4	4	no	—
404	C₄	—	6	2	no	—
405	C₄	C₅×#938	1	1	yes	characteristic
406	C₄	C₅×#938	1	1	yes	characteristic
407	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
408	C₄	C₂²×C₅×#67	1	1	yes	characteristic
409	C₃	C₂×C₅×#473	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	12	2	no	—
413	C₂	C₅×#5192	1	2	yes	direct product factor
414	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#938
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₂²×C₅×Q₁₆	D₃
hypocenter	C₃	C₂×C₅×#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₂×C₅×#836	C₂	semidirect
5. C₅×#5192	C₂	direct (N × H)
6. C₂×C₅×#819	C₂	semidirect
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
25. C₅×#836	C₂²	semidirect
26. C₅×#819	C₂²	semidirect
27. C₂×#5192	C₅	direct (N × H)
29. C₂²×C₅×Q₁₆	D₃	semidirect
66. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
69. C₂×#836	C₂×C₅	semidirect
70. #5192	C₂×C₅	direct (N × H)
71. C₂×#819	C₂×C₅	semidirect
80. C₂×C₅×Q₁₆	C₂×D₃	semidirect
125. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
137. #836	C₂²×C₅	semidirect
138. #819	C₂²×C₅	semidirect
172. C₂²×Q₁₆	C₅×D₃	semidirect
257. C₂×Q₁₆	C₂×C₅×D₃	semidirect
270. C₂×C₃×C₅	#473	semidirect
345. C₃×C₅	C₂×#473	semidirect
361. C₂×C₅	#5192	direct (N × H)
393. C₂×C₃	C₅×#473	semidirect
396. C₅	C₂×#5192	direct (N × H)
409. C₃	C₂×C₅×#473	semidirect
413. C₂	C₅×#5192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×Q₁₆	2
C₂×C₅×#942	2
C₂×C₅×#901	2
C₂×C₅×#836	2
C₅×#5192	2
C₂×C₅×#819	2
C₂×C₅×#473	3
C₂×#5192	5

Subgroups — C2×C5×#5192 #14429427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5192 #14429427