Subgroups — C₂×C₅×#5683 #14495251

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#947	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#937	C₂	1	2	yes	maximal, complemented
4	C₅×#5683	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#885	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#882	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#875	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×H(3,𝔽₄)	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	2	yes	complemented
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₅×Dic₆	C₂²	1	2	yes	complemented
16	C₃×C₅×#124	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×#217	C₂²	1	2	yes	complemented
20	C₅×#947	C₂²	1	16	yes	complemented
21	C₅×#937	C₂²	1	16	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
26	C₅×#885	C₂²	1	32	yes	complemented
27	C₅×#882	C₂²	1	32	yes	complemented
28	C₅×#875	C₂²	1	16	yes	complemented
29	C₂×#5683	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₅×H(3,𝔽₄)	—	3	16	no	—
31	C₂×C₅×#124	—	3	2	no	—
32	C₂×C₅×#124	—	3	4	no	—
33	C₂×C₅×#124	—	3	2	no	—
34	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
35	C₂×C₅×#120	—	3	2	no	—
36	C₂×C₅×#120	—	3	4	no	—
37	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
38	C₂³×C₅×D₃	—	4	4	no	—
39	C₂³×C₅×D₃	—	4	8	no	—
40	C₂³×C₅×D₃	C₂³	1	4	yes	—
41	C₂³×C₅×D₃	C₂³	1	8	yes	complemented
42	C₂×C₃×C₅×Q₈	—	4	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
44	C₂×C₃×C₅×D₄	—	4	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂×C₅×#67	—	4	8	no	—
50	C₂×C₅×#67	C₂³	1	16	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
52	C₂×C₅×D₁₂	—	4	4	no	—
53	C₂×C₅×D₁₂	—	4	4	no	—
54	C₂×C₅×D₁₂	C₂³	1	8	yes	—
55	C₂×C₅×D₁₂	C₂³	1	8	yes	—
56	C₂×C₅×Dic₆	—	4	4	no	—
57	C₂×C₅×Dic₆	C₂³	1	8	yes	complemented
58	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	complemented
59	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
60	C₅×#217	C₂³	1	8	yes	complemented
61	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
62	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
63	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
64	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
65	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×#947	C₂×C₅	1	2	yes	complemented
67	C₂×#937	C₂×C₅	1	2	yes	complemented
68	#5683	C₂×C₅	1	16	yes	direct product factor
69	C₂×#885	C₂×C₅	1	4	yes	complemented
70	C₂×#882	C₂×C₅	1	4	yes	complemented
71	C₂×#875	C₂×C₅	1	2	yes	complemented
72	C₂⁵×C₅	—	3	2	no	—
73	C₂²×C₅×Q₈	—	3	2	no	—
74	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
75	C₂²×C₅×D₄	—	3	4	no	—
76	C₂²×C₅×D₄	—	3	2	no	—
77	C₂²×C₅×D₄	—	3	2	no	—
78	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
79	C₅×#124	—	3	16	no	—
80	C₅×#124	—	3	32	no	—
81	C₅×#124	—	3	16	no	—
82	C₅×#124	C₂×D₃	1	8	yes	complemented
83	C₅×#120	—	3	16	no	—
84	C₅×#120	—	3	32	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
87	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
89	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
90	C₂×C₄²×C₅	—	3	2	no	—
91	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
92	C₂×H(3,𝔽₄)	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	8	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	8	no	—
98	C₂²×C₅×D₃	—	2	8	no	—
99	C₂²×C₅×D₃	—	2	8	no	—
100	C₂²×C₅×D₃	—	4	8	no	—
101	C₂²×C₅×D₃	—	4	16	no	—
102	C₂²×C₅×D₃	—	4	32	no	—
103	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
104	C₃×C₅×Q₈	—	4	4	no	—
105	C₃×C₅×D₄	—	4	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
112	C₅×#67	—	4	16	no	—
113	C₂×C₅×Dic₃	—	2	8	no	—
114	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
115	C₅×D₁₂	—	4	8	no	—
116	C₅×D₁₂	—	4	8	no	—
117	C₅×Dic₆	—	4	8	no	—
118	C₂⁴×D₃	C₂²×C₅	1	2	yes	complemented
119	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
120	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
121	C₂²×#67	C₂²×C₅	1	4	yes	—
122	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
123	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
124	C₂²×Dic₆	C₂²×C₅	1	2	yes	complemented
125	C₃×#124	C₂²×C₅	1	8	yes	complemented
126	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
127	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
128	C₂×#217	C₂²×C₅	1	2	yes	complemented
129	#947	C₂²×C₅	1	16	yes	complemented
130	#937	C₂²×C₅	1	16	yes	complemented
131	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
132	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
133	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
134	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
135	#885	C₂²×C₅	1	32	yes	complemented
136	#882	C₂²×C₅	1	32	yes	complemented
137	#875	C₂²×C₅	1	16	yes	complemented
138	C₂⁴×C₅	—	3	4	no	—
139	C₂⁴×C₅	—	3	8	no	—
140	C₂⁴×C₅	—	12	4	no	—
141	C₂⁴×C₅	—	12	8	no	—
142	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
143	C₂×C₅×Q₈	—	3	8	no	—
144	C₂×C₅×Q₈	—	4	2	no	—
145	C₂×C₅×Q₈	—	12	4	no	—
146	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
147	C₂×C₅×D₄	—	3	16	no	—
148	C₂×C₅×D₄	—	3	8	no	—
149	C₂×C₅×D₄	—	3	8	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	—	12	4	no	—
152	C₂×C₅×D₄	—	12	4	no	—
153	C₂×C₅×D₄	—	12	8	no	—
154	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
155	C₂²×C₄×C₅	—	3	4	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
159	C₅×C₂²⋊C₄	—	3	8	no	—
160	C₅×C₂²⋊C₄	—	3	16	no	—
161	C₅×C₂²⋊C₄	—	3	16	no	—
162	C₅×C₂²⋊C₄	—	3	16	no	—
163	C₅×C₂²⋊C₄	C₂²×D₃	1	16	yes	complemented
164	C₄²×C₅	—	3	8	no	—
165	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
166	H(3,𝔽₄)	—	3	16	no	—
167	C₂×#124	—	3	2	no	—
168	C₂×#124	—	3	4	no	—
169	C₂×#124	—	3	2	no	—
170	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
171	C₂×#120	—	3	2	no	—
172	C₂×#120	—	3	4	no	—
173	C₂²×C₃×C₅	—	2	8	no	—
174	C₂²×C₃×C₅	—	2	4	no	—
175	C₂²×C₃×C₅	—	4	8	no	—
176	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
177	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
178	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	8	no	—
180	C₂×C₅×D₃	—	2	8	no	—
181	C₂×C₅×D₃	—	2	8	no	—
182	C₂×C₅×D₃	—	4	32	no	—
183	C₂×C₅×D₃	—	4	16	no	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	2	4	no	—
186	C₃×C₄×C₅	—	2	2	no	—
187	C₅×Dic₃	—	2	8	no	—
188	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
189	C₂³×D₃	—	4	4	no	—
190	C₂³×D₃	—	4	8	no	—
191	C₂³×D₃	C₂³×C₅	1	4	yes	—
192	C₂³×D₃	C₂³×C₅	1	8	yes	complemented
193	C₂×C₃×Q₈	—	4	2	no	—
194	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
195	C₂×C₃×D₄	—	4	2	no	—
196	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
197	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
198	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
200	C₂×#67	—	4	8	no	—
201	C₂×#67	C₂³×C₅	1	16	yes	—
202	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
203	C₂×D₁₂	—	4	4	no	—
204	C₂×D₁₂	—	4	4	no	—
205	C₂×D₁₂	C₂³×C₅	1	8	yes	—
206	C₂×D₁₂	C₂³×C₅	1	8	yes	—
207	C₂×Dic₆	—	4	4	no	—
208	C₂×Dic₆	C₂³×C₅	1	8	yes	complemented
209	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	complemented
210	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
211	#217	C₂³×C₅	1	8	yes	complemented
212	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
213	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
214	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
215	C₄×Dic₃	C₂³×C₅	1	8	yes	complemented
216	C₂³×C₅	—	2	4	no	—
217	C₂³×C₅	—	2	8	no	—
218	C₂³×C₅	—	3	8	no	—
219	C₂³×C₅	—	6	8	no	—
220	C₂³×C₅	—	6	8	no	—
221	C₂³×C₅	—	6	8	no	—
222	C₂³×C₅	—	12	8	no	—
223	C₂³×C₅	—	12	16	no	—
224	C₂³×C₅	—	12	32	no	—
225	C₂³×C₅	C₂³×D₃	1	4	yes	—
226	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
227	C₅×Q₈	—	4	4	no	—
228	C₅×Q₈	—	12	8	no	—
229	C₅×D₄	—	4	4	no	—
230	C₅×D₄	—	12	8	no	—
231	C₅×D₄	—	12	8	no	—
232	C₅×D₄	—	12	16	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	3	8	no	—
237	C₂×C₄×C₅	—	6	8	no	—
238	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
239	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
240	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
241	C₂⁵	—	3	2	no	—
242	C₂²×Q₈	—	3	2	no	—
243	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
244	C₂²×D₄	—	3	4	no	—
245	C₂²×D₄	—	3	2	no	—
246	C₂²×D₄	—	3	2	no	—
247	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
248	#124	—	3	16	no	—
249	#124	—	3	32	no	—
250	#124	—	3	16	no	—
251	#124	C₂×C₅×D₃	1	8	yes	complemented
252	#120	—	3	16	no	—
253	#120	—	3	32	no	—
254	C₂×C₂²⋊C₄	—	3	2	no	—
255	C₂×C₂²⋊C₄	—	3	4	no	—
256	C₂×C₂²⋊C₄	—	3	4	no	—
257	C₂×C₂²⋊C₄	—	3	4	no	—
258	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
259	C₂×C₄²	—	3	2	no	—
260	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
261	C₂×C₃×C₅	—	4	4	no	—
262	C₂×C₃×C₅	H(3,𝔽₄)	1	4	yes	complemented
263	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
265	C₅×D₃	—	4	8	no	—
266	C₂³×C₃	—	2	8	no	—
267	C₂³×C₃	—	2	4	no	—
268	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
269	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
270	C₂²×D₃	—	2	8	no	—
271	C₂²×D₃	—	2	8	no	—
272	C₂²×D₃	—	2	8	no	—
273	C₂²×D₃	—	4	8	no	—
274	C₂²×D₃	—	4	16	no	—
275	C₂²×D₃	—	4	32	no	—
276	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
277	C₃×Q₈	—	4	4	no	—
278	C₃×D₄	—	4	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	2	4	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
283	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
284	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
285	#67	—	4	16	no	—
286	C₂×Dic₃	—	2	8	no	—
287	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
288	D₁₂	—	4	8	no	—
289	D₁₂	—	4	8	no	—
290	Dic₆	—	4	8	no	—
291	C₂²×C₅	—	2	4	no	—
292	C₂²×C₅	—	2	8	no	—
293	C₂²×C₅	—	4	8	no	—
294	C₂²×C₅	—	6	8	no	—
295	C₂²×C₅	—	6	8	no	—
296	C₂²×C₅	—	6	8	no	—
297	C₂²×C₅	—	12	32	no	—
298	C₂²×C₅	—	12	16	no	—
299	C₂²×C₅	#1004	1	2	yes	—
300	C₂²×C₅	#1009	1	4	yes	—
301	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	2	4	no	—
304	C₄×C₅	—	2	4	no	—
305	C₄×C₅	—	6	8	no	—
306	C₂⁴	—	3	4	no	—
307	C₂⁴	—	3	8	no	—
308	C₂⁴	—	12	4	no	—
309	C₂⁴	—	12	8	no	—
310	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
311	C₂×Q₈	—	3	8	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	12	4	no	—
314	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
315	C₂×D₄	—	3	16	no	—
316	C₂×D₄	—	3	8	no	—
317	C₂×D₄	—	3	8	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	12	4	no	—
320	C₂×D₄	—	12	4	no	—
321	C₂×D₄	—	12	8	no	—
322	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
323	C₂²×C₄	—	3	4	no	—
324	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
327	C₂²⋊C₄	—	3	8	no	—
328	C₂²⋊C₄	—	3	16	no	—
329	C₂²⋊C₄	—	3	16	no	—
330	C₂²⋊C₄	—	3	16	no	—
331	C₂²⋊C₄	C₂²×C₅×D₃	1	16	yes	complemented
332	C₄²	—	3	8	no	—
333	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
334	C₃×C₅	C₂×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Hall
335	C₂²×C₃	—	2	8	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	4	8	no	—
338	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
339	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
340	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
341	C₂×D₃	—	2	8	no	—
342	C₂×D₃	—	2	8	no	—
343	C₂×D₃	—	2	8	no	—
344	C₂×D₃	—	4	32	no	—
345	C₂×D₃	—	4	16	no	—
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	2	4	no	—
348	C₃×C₄	—	2	2	no	—
349	Dic₃	—	2	8	no	—
350	C₂×C₅	—	4	4	no	—
351	C₂×C₅	—	12	8	no	—
352	C₂×C₅	#5683	1	4	yes	direct product factor
353	C₂×C₅	C₂×#1004	1	1	yes	characteristic
354	C₂×C₅	C₂×#1009	1	2	yes	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	3	8	no	—
358	C₂³	—	6	8	no	—
359	C₂³	—	6	8	no	—
360	C₂³	—	6	8	no	—
361	C₂³	—	12	8	no	—
362	C₂³	—	12	16	no	—
363	C₂³	—	12	32	no	—
364	C₂³	C₂³×C₅×D₃	1	4	yes	—
365	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	Q₈	—	12	8	no	—
368	D₄	—	4	4	no	—
369	D₄	—	12	8	no	—
370	D₄	—	12	8	no	—
371	D₄	—	12	16	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	3	8	no	—
376	C₂×C₄	—	6	8	no	—
377	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
378	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
379	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
380	C₂×C₃	—	4	4	no	—
381	C₂×C₃	C₅×H(3,𝔽₄)	1	4	yes	complemented
382	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
384	D₃	—	4	8	no	—
385	C₅	C₂×#5683	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	6	8	no	—
390	C₂²	—	6	8	no	—
391	C₂²	—	6	8	no	—
392	C₂²	—	12	32	no	—
393	C₂²	—	12	16	no	—
394	C₂²	C₅×#1004	1	2	yes	—
395	C₂²	C₅×#1009	1	4	yes	—
396	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	6	8	no	—
401	C₃	C₂×C₅×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	4	4	no	—
403	C₂	—	12	8	no	—
404	C₂	C₅×#5683	1	4	yes	direct product factor
405	C₂	C₂×C₅×#1004	1	1	yes	characteristic
406	C₂	C₂×C₅×#1009	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₅×#947	C₂	semidirect
3. C₂×C₅×#937	C₂	semidirect
4. C₅×#5683	C₂	direct (N × H)
5. C₂×C₅×#885	C₂	semidirect
6. C₂×C₅×#882	C₂	semidirect
7. C₂×C₅×#875	C₂	semidirect
9. C₂⁴×C₅×D₃	C₂²	semidirect
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
15. C₂²×C₅×Dic₆	C₂²	semidirect
16. C₃×C₅×#124	C₂²	semidirect
17. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
18. C₂×C₃×C₄²×C₅	C₂²	semidirect
19. C₂×C₅×#217	C₂²	semidirect
20. C₅×#947	C₂²	semidirect
21. C₅×#937	C₂²	semidirect
22. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
23. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
24. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
25. C₂×C₄×C₅×Dic₃	C₂²	semidirect
26. C₅×#885	C₂²	semidirect
27. C₅×#882	C₂²	semidirect
28. C₅×#875	C₂²	semidirect
29. C₂×#5683	C₅	direct (N × H)
34. C₂×C₅×#124	D₃	semidirect
41. C₂³×C₅×D₃	C₂³	semidirect
43. C₂×C₃×C₅×Q₈	C₂³	semidirect
57. C₂×C₅×Dic₆	C₂³	semidirect
58. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
59. C₃×C₄²×C₅	C₂³	semidirect
60. C₅×#217	C₂³	semidirect
61. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
62. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
63. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
64. C₄×C₅×Dic₃	C₂³	semidirect
65. C₂×C₃×#124	C₂×C₅	semidirect
66. C₂×#947	C₂×C₅	semidirect
67. C₂×#937	C₂×C₅	semidirect
68. #5683	C₂×C₅	direct (N × H)
69. C₂×#885	C₂×C₅	semidirect
70. C₂×#882	C₂×C₅	semidirect
71. C₂×#875	C₂×C₅	semidirect
74. C₂²×C₅×Q₈	C₂×D₃	semidirect
82. C₅×#124	C₂×D₃	semidirect
89. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
91. C₂×C₄²×C₅	C₂×D₃	semidirect
118. C₂⁴×D₃	C₂²×C₅	semidirect
119. C₂²×C₃×Q₈	C₂²×C₅	semidirect
124. C₂²×Dic₆	C₂²×C₅	semidirect
125. C₃×#124	C₂²×C₅	semidirect
126. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
127. C₂×C₃×C₄²	C₂²×C₅	semidirect
128. C₂×#217	C₂²×C₅	semidirect
129. #947	C₂²×C₅	semidirect
130. #937	C₂²×C₅	semidirect
131. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
132. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
133. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
134. C₂×C₄×Dic₃	C₂²×C₅	semidirect
135. #885	C₂²×C₅	semidirect
136. #882	C₂²×C₅	semidirect
137. #875	C₂²×C₅	semidirect
146. C₂×C₅×Q₈	C₂²×D₃	semidirect
163. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
165. C₄²×C₅	C₂²×D₃	semidirect
170. C₂×#124	C₅×D₃	semidirect
192. C₂³×D₃	C₂³×C₅	semidirect
194. C₂×C₃×Q₈	C₂³×C₅	semidirect
208. C₂×Dic₆	C₂³×C₅	semidirect
209. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
210. C₃×C₄²	C₂³×C₅	semidirect
211. #217	C₂³×C₅	semidirect
212. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
213. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
214. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
215. C₄×Dic₃	C₂³×C₅	semidirect
243. C₂²×Q₈	C₂×C₅×D₃	semidirect
251. #124	C₂×C₅×D₃	semidirect
258. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
260. C₂×C₄²	C₂×C₅×D₃	semidirect
262. C₂×C₃×C₅	H(3,𝔽₄)	semidirect
314. C₂×Q₈	C₂²×C₅×D₃	semidirect
331. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
333. C₄²	C₂²×C₅×D₃	semidirect
334. C₃×C₅	C₂×H(3,𝔽₄)	semidirect
352. C₂×C₅	#5683	direct (N × H)
381. C₂×C₃	C₅×H(3,𝔽₄)	semidirect
385. C₅	C₂×#5683	direct (N × H)
401. C₃	C₂×C₅×H(3,𝔽₄)	semidirect
404. C₂	C₅×#5683	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×C₃×C₅×#124	2
C₂×C₅×#947	2
C₂×C₅×#937	2
C₅×#5683	2
C₂×C₅×#885	2
C₂×C₅×#882	2
C₂×C₅×#875	2
C₂×C₅×H(3,𝔽₄)	3
C₂×#5683	5

Subgroups — C2×C5×#5683 #14495251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5683 #14495251