Subgroups — C₂×C₅×#5167 #14439015

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#216	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5167	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#497	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	—	2	2	no	—
18	C₅×#944	—	2	2	no	—
19	C₅×#944	C₂²	1	4	yes	complemented
20	C₂×C₅×#216	—	2	4	no	—
21	C₂×C₅×#216	C₂²	1	4	yes	complemented
22	C₅×#936	—	2	2	no	—
23	C₅×#936	C₂²	1	4	yes	—
24	C₂×C₅×#214	—	2	4	no	—
25	C₂×C₅×#214	C₂²	1	4	yes	—
26	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×Dic₁₂	—	2	4	no	—
30	C₂×C₅×Dic₁₂	C₂²	1	4	yes	complemented
31	C₅×#815	C₂²	1	4	yes	complemented
32	C₂×#5167	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×Q₁₆	—	3	1	no	—
34	C₂²×C₅×Q₁₆	—	3	1	no	—
35	C₂²×C₅×SD₁₆	—	3	1	no	—
36	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×C₅×#124	—	3	1	no	—
39	C₅×#497	—	3	8	no	—
40	C₂×C₅×#97	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	—	2	1	no	—
54	C₂²×C₅×Dic₃	D₄	1	2	yes	—
55	C₂×C₅×Dic₆	—	2	2	no	—
56	C₂×C₅×Dic₆	—	2	2	no	—
57	C₂×C₅×Dic₆	—	2	2	no	—
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	—	2	1	no	—
60	C₂×C₅×Dic₆	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₂×C₅×Dic₆	C₂³	1	2	yes	—
63	C₃×C₅×SD₁₆	—	2	8	no	—
64	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₅×#217	—	2	8	no	—
67	C₅×#216	—	2	8	no	—
68	C₅×#214	—	2	8	no	—
69	C₅×Dic₃⋊C₄	—	2	8	no	—
70	C₄×C₅×Dic₃	D₄	1	2	yes	—
71	C₄×C₅×Dic₃	C₂³	1	2	yes	—
72	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	—
73	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
74	C₅×Dic₁₂	—	2	8	no	—
75	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
76	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂²×#216	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#936	C₂×C₅	1	1	yes	characteristic
79	C₂²×#214	C₂×C₅	1	1	yes	characteristic
80	C₂²×Dic₁₂	C₂×C₅	1	1	yes	characteristic, complemented
81	#5167	C₂×C₅	1	8	yes	direct product factor
82	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
87	C₂×C₅×Q₁₆	—	3	4	no	—
88	C₂×C₅×Q₁₆	—	3	4	no	—
89	C₂×C₅×Q₁₆	—	6	4	no	—
90	C₂×C₅×Q₁₆	—	6	4	no	—
91	C₂×C₅×SD₁₆	—	2	4	no	—
92	C₂×C₅×SD₁₆	—	3	4	no	—
93	C₂×C₅×SD₁₆	—	6	4	no	—
94	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	—
95	C₂²×C₅×C₈	—	3	1	no	—
96	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
97	C₅×C₄⋊Q₈	—	3	4	no	—
98	C₅×C₄⋊Q₈	—	6	2	no	—
99	C₅×#124	—	3	4	no	—
100	C₅×#124	—	6	2	no	—
101	C₂×C₅×C₄⋊C₄	—	6	2	no	—
102	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₅×#97	—	3	4	no	—
105	C₂×#497	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	4	2	no	—
108	C₂³×C₃×C₅	—	4	4	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	4	2	no	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	4	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	4	2	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
122	C₂×C₅×Dic₃	—	2	4	no	—
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	4	2	no	—
126	C₂×C₅×Dic₃	—	4	2	no	—
127	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
128	C₅×Dic₆	—	2	2	no	—
129	C₅×Dic₆	—	2	2	no	—
130	C₅×Dic₆	—	2	2	no	—
131	C₅×Dic₆	—	2	2	no	—
132	C₅×Dic₆	—	4	2	no	—
133	C₅×Dic₆	—	4	2	no	—
134	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
135	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
136	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
138	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
139	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×SD₁₆	—	2	4	no	—
141	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
142	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
143	C₂×#217	—	2	2	no	—
144	#944	—	2	2	no	—
145	#944	C₂²×C₅	1	4	yes	complemented
146	C₂×#216	—	2	4	no	—
147	C₂×#216	C₂²×C₅	1	4	yes	complemented
148	#936	—	2	2	no	—
149	#936	C₂²×C₅	1	4	yes	—
150	C₂×#214	—	2	4	no	—
151	C₂×#214	C₂²×C₅	1	4	yes	—
152	C₂×Dic₃⋊C₄	—	2	2	no	—
153	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×Dic₁₂	—	2	4	no	—
156	C₂×Dic₁₂	C₂²×C₅	1	4	yes	complemented
157	#815	C₂²×C₅	1	4	yes	complemented
158	C₂⁴×C₅	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	2	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	3	2	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	6	1	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×Q₈	—	6	2	no	—
168	C₂×C₅×Q₈	—	6	2	no	—
169	C₂×C₅×Q₈	—	6	2	no	—
170	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
171	C₂×C₅×D₄	—	2	2	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	2	no	—
174	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	—	6	1	no	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×Q₁₆	—	6	8	no	—
181	C₅×Q₁₆	—	6	8	no	—
182	C₅×SD₁₆	—	2	8	no	—
183	C₅×SD₁₆	—	6	8	no	—
184	C₂×C₅×C₈	—	3	4	no	—
185	C₂×C₅×C₈	—	3	2	no	—
186	C₂×C₅×C₈	#67	1	4	yes	—
187	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
188	C₅×C₄⋊C₄	—	6	8	no	—
189	C₅×C₂²⋊C₄	—	6	8	no	—
190	C₄²×C₅	—	3	2	no	—
191	C₄²×C₅	—	3	2	no	—
192	C₂²×Q₁₆	—	3	1	no	—
193	C₂²×Q₁₆	—	3	1	no	—
194	C₂²×SD₁₆	—	3	1	no	—
195	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	—	3	1	no	—
197	C₂×#124	—	3	1	no	—
198	#497	—	3	8	no	—
199	C₂×#97	—	3	1	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	4	4	no	—
202	C₂²×C₃×C₅	—	8	4	no	—
203	C₂²×C₃×C₅	#127	1	2	yes	—
204	C₂²×C₃×C₅	#137	1	4	yes	—
205	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
206	C₃×C₄×C₅	—	4	2	no	—
207	C₃×C₄×C₅	#127	1	2	yes	—
208	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₅×Dic₃	—	2	4	no	—
211	C₅×Dic₃	—	4	2	no	—
212	C₅×Dic₃	—	4	2	no	—
213	C₂⁴×C₃	—	2	1	no	—
214	C₂×C₃×Q₈	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	2	no	—
216	C₂×C₃×Q₈	—	2	2	no	—
217	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
218	C₂×C₃×D₄	—	2	2	no	—
219	C₂×C₃×D₄	—	2	2	no	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×Dic₃	—	2	1	no	—
225	C₂²×Dic₃	—	2	1	no	—
226	C₂²×Dic₃	C₅×D₄	1	2	yes	—
227	C₂×Dic₆	—	2	2	no	—
228	C₂×Dic₆	—	2	2	no	—
229	C₂×Dic₆	—	2	2	no	—
230	C₂×Dic₆	—	2	2	no	—
231	C₂×Dic₆	—	2	1	no	—
232	C₂×Dic₆	—	2	1	no	—
233	C₂×Dic₆	C₂³×C₅	1	2	yes	—
234	C₂×Dic₆	C₂³×C₅	1	2	yes	—
235	C₃×SD₁₆	—	2	8	no	—
236	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
237	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
238	#217	—	2	8	no	—
239	#216	—	2	8	no	—
240	#214	—	2	8	no	—
241	Dic₃⋊C₄	—	2	8	no	—
242	C₄×Dic₃	C₅×D₄	1	2	yes	—
243	C₄×Dic₃	C₂³×C₅	1	2	yes	—
244	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	—
245	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
246	Dic₁₂	—	2	8	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	4	4	no	—
249	C₂³×C₅	—	4	2	no	—
250	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
251	C₅×Q₈	—	2	2	no	—
252	C₅×Q₈	—	2	2	no	—
253	C₅×Q₈	—	4	2	no	—
254	C₅×Q₈	—	6	2	no	—
255	C₅×Q₈	—	6	2	no	—
256	C₅×Q₈	—	6	2	no	—
257	C₅×Q₈	—	6	2	no	—
258	C₅×Q₈	—	12	2	no	—
259	C₅×Q₈	—	12	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	4	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	3	4	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	—	6	4	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	6	2	no	—
269	C₂×C₄×C₅	—	12	2	no	—
270	C₂×C₄×C₅	—	12	2	no	—
271	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₂×#67	1	2	yes	—
274	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
275	C₅×C₈	—	3	4	no	—
276	C₅×C₈	C₂×#67	1	4	yes	—
277	C₂²×Q₈	—	3	1	no	—
278	C₂²×Q₈	—	3	1	no	—
279	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
280	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×Q₁₆	—	3	4	no	—
282	C₂×Q₁₆	—	3	4	no	—
283	C₂×Q₁₆	—	6	4	no	—
284	C₂×Q₁₆	—	6	4	no	—
285	C₂×SD₁₆	—	2	4	no	—
286	C₂×SD₁₆	—	3	4	no	—
287	C₂×SD₁₆	—	6	4	no	—
288	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	—
289	C₂²×C₈	—	3	1	no	—
290	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
291	C₄⋊Q₈	—	3	4	no	—
292	C₄⋊Q₈	—	6	2	no	—
293	#124	—	3	4	no	—
294	#124	—	6	2	no	—
295	C₂×C₄⋊C₄	—	6	2	no	—
296	C₂×C₂²⋊C₄	—	6	2	no	—
297	C₂×C₄²	—	3	1	no	—
298	#97	—	3	4	no	—
299	C₂×C₃×C₅	—	8	2	no	—
300	C₂×C₃×C₅	#497	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#137	1	2	yes	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	4	2	no	—
305	C₂³×C₃	—	4	4	no	—
306	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×Q₈	—	4	2	no	—
310	C₃×D₄	—	2	2	no	—
311	C₃×D₄	—	2	2	no	—
312	C₃×D₄	—	4	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	4	2	no	—
315	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
318	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
319	C₂×Dic₃	—	2	4	no	—
320	C₂×Dic₃	—	2	2	no	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	4	2	no	—
323	C₂×Dic₃	—	4	2	no	—
324	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
325	Dic₆	—	2	2	no	—
326	Dic₆	—	2	2	no	—
327	Dic₆	—	2	2	no	—
328	Dic₆	—	2	2	no	—
329	Dic₆	—	4	2	no	—
330	Dic₆	—	4	2	no	—
331	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
332	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
333	C₂²×C₅	—	4	4	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	8	4	no	—
336	C₂²×C₅	#915	1	4	yes	—
337	C₂²×C₅	#940	1	2	yes	—
338	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	6	4	no	—
341	C₄×C₅	—	12	2	no	—
342	C₄×C₅	—	12	2	no	—
343	C₄×C₅	#940	1	2	yes	—
344	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
345	C₄×C₅	C₂²×#67	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	3	2	no	—
351	C₂×Q₈	—	3	2	no	—
352	C₂×Q₈	—	6	1	no	—
353	C₂×Q₈	—	6	1	no	—
354	C₂×Q₈	—	6	2	no	—
355	C₂×Q₈	—	6	2	no	—
356	C₂×Q₈	—	6	2	no	—
357	C₂×Q₈	—	6	2	no	—
358	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
368	Q₁₆	—	6	8	no	—
369	Q₁₆	—	6	8	no	—
370	SD₁₆	—	2	8	no	—
371	SD₁₆	—	6	8	no	—
372	C₂×C₈	—	3	4	no	—
373	C₂×C₈	—	3	2	no	—
374	C₂×C₈	C₅×#67	1	4	yes	—
375	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
376	C₄⋊C₄	—	6	8	no	—
377	C₂²⋊C₄	—	6	8	no	—
378	C₄²	—	3	2	no	—
379	C₄²	—	3	2	no	—
380	C₃×C₅	C₂×#497	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	4	4	no	—
383	C₂²×C₃	—	8	4	no	—
384	C₂²×C₃	C₅×#127	1	2	yes	—
385	C₂²×C₃	C₅×#137	1	4	yes	—
386	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
387	C₃×C₄	—	4	2	no	—
388	C₃×C₄	C₅×#127	1	2	yes	—
389	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
390	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
391	Dic₃	—	2	4	no	—
392	Dic₃	—	4	2	no	—
393	Dic₃	—	4	2	no	—
394	C₂×C₅	—	8	2	no	—
395	C₂×C₅	#5167	1	4	yes	direct product factor
396	C₂×C₅	C₂×#915	1	2	yes	—
397	C₂×C₅	C₂×#940	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	6	2	no	—
406	Q₈	—	6	2	no	—
407	Q₈	—	6	2	no	—
408	Q₈	—	6	2	no	—
409	Q₈	—	12	2	no	—
410	Q₈	—	12	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	3	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	6	4	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	2	no	—
420	C₂×C₄	—	12	2	no	—
421	C₂×C₄	—	12	2	no	—
422	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
423	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
424	C₂×C₄	C₂×C₅×#67	1	2	yes	—
425	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
426	C₈	—	3	4	no	—
427	C₈	C₂×C₅×#67	1	4	yes	—
428	C₂×C₃	—	8	2	no	—
429	C₂×C₃	C₅×#497	1	4	yes	complemented
430	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
431	C₂×C₃	C₂×C₅×#137	1	2	yes	—
432	C₅	C₂×#5167	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	4	no	—
436	C₂²	C₅×#915	1	4	yes	—
437	C₂²	C₅×#940	1	2	yes	—
438	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
439	C₄	—	4	2	no	—
440	C₄	—	6	4	no	—
441	C₄	—	12	2	no	—
442	C₄	—	12	2	no	—
443	C₄	C₅×#940	1	2	yes	—
444	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
445	C₄	C₂²×C₅×#67	1	1	yes	characteristic
446	C₃	C₂×C₅×#497	1	1	yes	characteristic, complemented, Sylow
447	C₂	—	8	2	no	—
448	C₂	C₅×#5167	1	4	yes	direct product factor
449	C₂	C₂×C₅×#915	1	2	yes	—
450	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#497
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#944	C₂	semidirect
3. C₂²×C₅×#216	C₂	semidirect
6. C₂²×C₅×Dic₁₂	C₂	semidirect
7. C₅×#5167	C₂	direct (N × H)
8. C₂×C₅×#815	C₂	semidirect
19. C₅×#944	C₂²	semidirect
21. C₂×C₅×#216	C₂²	semidirect
30. C₂×C₅×Dic₁₂	C₂²	semidirect
31. C₅×#815	C₂²	semidirect
32. C₂×#5167	C₅	direct (N × H)
76. C₂×#944	C₂×C₅	semidirect
77. C₂²×#216	C₂×C₅	semidirect
80. C₂²×Dic₁₂	C₂×C₅	semidirect
81. #5167	C₂×C₅	direct (N × H)
82. C₂×#815	C₂×C₅	semidirect
145. #944	C₂²×C₅	semidirect
147. C₂×#216	C₂²×C₅	semidirect
156. C₂×Dic₁₂	C₂²×C₅	semidirect
157. #815	C₂²×C₅	semidirect
300. C₂×C₃×C₅	#497	semidirect
380. C₃×C₅	C₂×#497	semidirect
395. C₂×C₅	#5167	direct (N × H)
429. C₂×C₃	C₅×#497	semidirect
432. C₅	C₂×#5167	direct (N × H)
446. C₃	C₂×C₅×#497	semidirect
448. C₂	C₅×#5167	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×SD₁₆	2
C₂×C₅×#944	2
C₂²×C₅×#216	2
C₂×C₅×#936	2
C₂²×C₅×#214	2
C₂²×C₅×Dic₁₂	2
C₅×#5167	2
C₂×C₅×#815	2
C₂×C₅×#497	3
C₂×#5167	5

Subgroups — C2×C5×#5167 #14439015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5167 #14439015