Subgroups — C₂×C₅×#4949 #14331997

Order 1920.

1816 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×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#217	C₂	1	2	yes	maximal
3	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4949	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#399	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
12	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂×C₅×#217	—	2	8	no	—
16	C₂×C₅×#217	C₂²	1	8	yes	—
17	C₂×C₅×C₄⋊Dic₃	—	2	4	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	complemented
19	C₂×C₅×Dic₃⋊C₄	—	2	8	no	—
20	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
21	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
22	C₂×#4949	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
24	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
25	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
26	C₂²×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic
27	C₅×#399	—	3	8	no	—
28	C₂×C₅×#95	—	3	1	no	—
29	C₂⁴×C₃×C₅	—	2	4	no	—
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂⁴×C₃×C₅	—	2	2	no	—
32	C₂⁴×C₃×C₅	—	2	4	no	—
33	C₂⁴×C₃×C₅	Q₈	1	4	yes	—
34	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₅×Dic₃	—	2	4	no	—
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₂²×C₅×Dic₃	—	2	4	no	—
45	C₂²×C₅×Dic₃	—	2	4	no	—
46	C₂²×C₅×Dic₃	—	2	4	no	—
47	C₂²×C₅×Dic₃	D₄	1	8	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
50	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
51	C₅×#217	—	2	16	no	—
52	C₅×C₄⋊Dic₃	—	2	8	no	—
53	C₅×Dic₃⋊C₄	—	2	16	no	—
54	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
55	C₂²×#217	C₂×C₅	1	2	yes	—
56	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂²×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
58	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic, complemented
59	#4949	C₂×C₅	1	8	yes	direct product factor
60	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂³×C₄×C₅	—	3	2	no	—
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	—	3	8	no	—
66	C₂×C₅×C₄⋊C₄	—	3	4	no	—
67	C₂×C₅×C₄⋊C₄	—	6	8	no	—
68	C₂×C₅×C₄⋊C₄	—	6	4	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
71	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
72	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	—
73	C₅×#95	—	3	4	no	—
74	C₂×#399	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	16	no	—
76	C₂³×C₃×C₅	—	2	8	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	—	4	8	no	—
82	C₂³×C₃×C₅	—	4	4	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
86	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
87	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
88	C₂³×C₃×C₅	#41	1	2	yes	—
89	C₂³×C₃×C₅	#41	1	4	yes	—
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	—	2	8	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	4	4	no	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
97	C₂×C₅×Dic₃	—	2	16	no	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	2	4	no	—
100	C₂×C₅×Dic₃	—	2	4	no	—
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	—	2	4	no	—
103	C₂×C₅×Dic₃	—	4	8	no	—
104	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
105	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
106	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
108	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
109	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
112	C₂×#217	—	2	8	no	—
113	C₂×#217	C₂²×C₅	1	8	yes	—
114	C₂×C₄⋊Dic₃	—	2	4	no	—
115	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	complemented
116	C₂×Dic₃⋊C₄	—	2	8	no	—
117	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	complemented
118	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
119	C₂⁴×C₅	—	2	2	no	—
120	C₂⁴×C₅	—	2	4	no	—
121	C₂⁴×C₅	—	2	4	no	—
122	C₂⁴×C₅	—	2	2	no	—
123	C₂⁴×C₅	Dic₆	1	4	yes	—
124	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
125	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	3	8	no	—
130	C₂²×C₄×C₅	—	3	4	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	4	no	—
133	C₂²×C₄×C₅	—	6	4	no	—
134	C₂²×C₄×C₅	—	6	4	no	—
135	C₂²×C₄×C₅	—	6	4	no	—
136	C₂²×C₄×C₅	—	6	4	no	—
137	C₂²×C₄×C₅	#67	1	4	yes	—
138	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
139	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
140	C₅×C₄⋊C₄	—	6	16	no	—
141	C₅×C₄⋊C₄	—	6	8	no	—
142	C₅×C₂²⋊C₄	—	2	8	no	—
143	C₅×C₂²⋊C₄	—	6	16	no	—
144	C₂²×C₄⋊C₄	—	3	2	no	—
145	C₂²×C₄⋊C₄	—	3	1	no	—
146	C₂²×C₂²⋊C₄	—	3	2	no	—
147	C₂²×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic
148	#399	—	3	8	no	—
149	C₂×#95	—	3	1	no	—
150	C₂²×C₃×C₅	—	2	8	no	—
151	C₂²×C₃×C₅	—	2	4	no	—
152	C₂²×C₃×C₅	—	4	4	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	16	no	—
156	C₂²×C₃×C₅	C₂²⋊Q₈	1	8	yes	—
157	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
158	C₂²×C₃×C₅	#123	1	8	yes	—
159	C₂²×C₃×C₅	#123	1	4	yes	—
160	C₂²×C₃×C₅	#127	1	4	yes	—
161	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
165	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
166	C₃×C₄×C₅	—	2	4	no	—
167	C₃×C₄×C₅	—	4	2	no	—
168	C₅×Dic₃	—	2	8	no	—
169	C₅×Dic₃	—	4	4	no	—
170	C₂⁴×C₃	—	2	4	no	—
171	C₂⁴×C₃	—	2	2	no	—
172	C₂⁴×C₃	—	2	2	no	—
173	C₂⁴×C₃	—	2	4	no	—
174	C₂⁴×C₃	C₅×Q₈	1	4	yes	—
175	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
176	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
183	C₂²×Dic₃	—	2	4	no	—
184	C₂²×Dic₃	—	2	4	no	—
185	C₂²×Dic₃	—	2	4	no	—
186	C₂²×Dic₃	—	2	4	no	—
187	C₂²×Dic₃	—	2	4	no	—
188	C₂²×Dic₃	C₅×D₄	1	8	yes	—
189	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
190	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
191	C₃×C₂²⋊C₄	—	2	8	no	—
192	#217	—	2	16	no	—
193	C₄⋊Dic₃	—	2	8	no	—
194	Dic₃⋊C₄	—	2	16	no	—
195	C₂³×C₅	—	2	16	no	—
196	C₂³×C₅	—	2	8	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	2	4	no	—
199	C₂³×C₅	—	2	4	no	—
200	C₂³×C₅	—	2	2	no	—
201	C₂³×C₅	—	4	8	no	—
202	C₂³×C₅	—	4	4	no	—
203	C₂³×C₅	—	4	4	no	—
204	C₂³×C₅	C₂×Dic₆	1	4	yes	—
205	C₂³×C₅	C₂×Dic₆	1	2	yes	—
206	C₂³×C₅	#235	1	2	yes	—
207	C₂³×C₅	D₃×D₄	1	4	yes	—
208	C₂³×C₅	#237	1	4	yes	—
209	C₂³×C₅	C₂×#67	1	2	yes	—
210	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	3	8	no	—
216	C₂×C₄×C₅	—	4	4	no	—
217	C₂×C₄×C₅	—	6	16	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	—	6	4	no	—
221	C₂×C₄×C₅	—	6	4	no	—
222	C₂×C₄×C₅	—	6	4	no	—
223	C₂×C₄×C₅	—	12	8	no	—
224	C₂×C₄×C₅	C₂×#67	1	4	yes	—
225	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
226	C₂³×C₄	—	3	2	no	—
227	C₂³×C₄	—	3	2	no	—
228	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	—	3	8	no	—
231	C₂×C₄⋊C₄	—	3	4	no	—
232	C₂×C₄⋊C₄	—	6	8	no	—
233	C₂×C₄⋊C₄	—	6	4	no	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	3	8	no	—
236	C₂×C₂²⋊C₄	—	6	8	no	—
237	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	—
238	#95	—	3	4	no	—
239	C₂×C₃×C₅	—	4	4	no	—
240	C₂×C₃×C₅	#399	1	8	yes	complemented
241	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	2	yes	—
242	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#123	1	2	yes	—
244	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
246	C₂³×C₃	—	2	16	no	—
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	2	no	—
250	C₂³×C₃	—	2	2	no	—
251	C₂³×C₃	—	2	4	no	—
252	C₂³×C₃	—	4	8	no	—
253	C₂³×C₃	—	4	4	no	—
254	C₂³×C₃	—	4	4	no	—
255	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
256	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
257	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
258	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
259	C₂³×C₃	C₅×#41	1	2	yes	—
260	C₂³×C₃	C₅×#41	1	4	yes	—
261	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
262	C₂×C₃×C₄	—	2	8	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	4	4	no	—
267	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
268	C₂×Dic₃	—	2	16	no	—
269	C₂×Dic₃	—	2	4	no	—
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	2	4	no	—
273	C₂×Dic₃	—	2	4	no	—
274	C₂×Dic₃	—	4	8	no	—
275	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
276	C₂²×C₅	—	2	8	no	—
277	C₂²×C₅	—	2	4	no	—
278	C₂²×C₅	—	4	16	no	—
279	C₂²×C₅	—	4	4	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	#878	1	8	yes	—
283	C₂²×C₅	#883	1	8	yes	—
284	C₂²×C₅	#924	1	4	yes	—
285	C₂²×C₅	#935	1	4	yes	—
286	C₂²×C₅	#940	1	4	yes	—
287	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
288	C₂²×C₅	C₂×#235	1	1	yes	characteristic
289	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
290	C₂²×C₅	C₂×#237	1	2	yes	—
291	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
292	C₄×C₅	—	2	4	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	6	8	no	—
295	C₄×C₅	—	12	4	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	C₅×Dic₆	1	4	yes	—
301	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
302	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	3	8	no	—
307	C₂²×C₄	—	3	4	no	—
308	C₂²×C₄	—	3	4	no	—
309	C₂²×C₄	—	6	4	no	—
310	C₂²×C₄	—	6	4	no	—
311	C₂²×C₄	—	6	4	no	—
312	C₂²×C₄	—	6	4	no	—
313	C₂²×C₄	—	6	4	no	—
314	C₂²×C₄	C₅×#67	1	4	yes	—
315	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
316	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
317	C₄⋊C₄	—	6	16	no	—
318	C₄⋊C₄	—	6	8	no	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	6	16	no	—
321	C₃×C₅	C₂×#399	1	1	yes	characteristic, complemented, Hall
322	C₂²×C₃	—	2	8	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	4	16	no	—
325	C₂²×C₃	—	4	4	no	—
326	C₂²×C₃	—	4	2	no	—
327	C₂²×C₃	—	4	2	no	—
328	C₂²×C₃	C₅×C₂²⋊Q₈	1	8	yes	—
329	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
330	C₂²×C₃	C₅×#123	1	8	yes	—
331	C₂²×C₃	C₅×#123	1	4	yes	—
332	C₂²×C₃	C₅×#127	1	4	yes	—
333	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
334	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
336	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
337	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	4	2	no	—
340	Dic₃	—	2	8	no	—
341	Dic₃	—	4	4	no	—
342	C₂×C₅	—	4	4	no	—
343	C₂×C₅	#4949	1	8	yes	direct product factor
344	C₂×C₅	C₂×#878	1	2	yes	—
345	C₂×C₅	C₂×#883	1	2	yes	—
346	C₂×C₅	C₂×#924	1	1	yes	characteristic
347	C₂×C₅	C₂×#935	1	1	yes	characteristic
348	C₂×C₅	C₂×#940	1	1	yes	characteristic
349	C₂³	—	2	16	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₅×Dic₆	1	4	yes	—
359	C₂³	C₂×C₅×Dic₆	1	2	yes	—
360	C₂³	C₅×#235	1	2	yes	—
361	C₂³	C₅×D₃×D₄	1	4	yes	—
362	C₂³	C₅×#237	1	4	yes	—
363	C₂³	C₂×C₅×#67	1	2	yes	—
364	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	3	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	6	16	no	—
372	C₂×C₄	—	6	4	no	—
373	C₂×C₄	—	6	4	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	—	6	4	no	—
377	C₂×C₄	—	12	8	no	—
378	C₂×C₄	C₂×C₅×#67	1	4	yes	—
379	C₂×C₃	—	4	4	no	—
380	C₂×C₃	C₅×#399	1	8	yes	complemented
381	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	2	yes	—
382	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₃	C₂×C₅×#123	1	2	yes	—
384	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
385	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
386	C₅	C₂×#4949	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	2	8	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	4	16	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₅×#878	1	8	yes	—
394	C₂²	C₅×#883	1	8	yes	—
395	C₂²	C₅×#924	1	4	yes	—
396	C₂²	C₅×#935	1	4	yes	—
397	C₂²	C₅×#940	1	4	yes	—
398	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
399	C₂²	C₂×C₅×#235	1	1	yes	characteristic
400	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
401	C₂²	C₂×C₅×#237	1	2	yes	—
402	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	6	8	no	—
406	C₄	—	12	4	no	—
407	C₃	C₂×C₅×#399	1	1	yes	characteristic, complemented, Sylow
408	C₂	—	4	4	no	—
409	C₂	C₅×#4949	1	8	yes	direct product factor
410	C₂	C₂×C₅×#878	1	2	yes	—
411	C₂	C₂×C₅×#883	1	2	yes	—
412	C₂	C₂×C₅×#924	1	1	yes	characteristic
413	C₂	C₂×C₅×#935	1	1	yes	characteristic
414	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator, cosocle	C₂³×C₃	C₂⁴×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁵×C₃×C₅	C₂²
hypercenter	C₂²×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#399
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
4. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
5. C₂×C₅×C₃⋊#95	C₂	semidirect
6. C₅×#4949	C₂	direct (N × H)
18. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
20. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
21. C₅×C₃⋊#95	C₂²	semidirect
22. C₂×#4949	C₅	direct (N × H)
56. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
57. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
58. C₂×C₃⋊#95	C₂×C₅	semidirect
59. #4949	C₂×C₅	direct (N × H)
115. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
117. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
118. C₃⋊#95	C₂²×C₅	semidirect
240. C₂×C₃×C₅	#399	semidirect
321. C₃×C₅	C₂×#399	semidirect
343. C₂×C₅	#4949	direct (N × H)
380. C₂×C₃	C₅×#399	semidirect
386. C₅	C₂×#4949	direct (N × H)
407. C₃	C₂×C₅×#399	semidirect
409. C₂	C₅×#4949	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×C₂²⋊C₄	2
C₂²×C₅×#217	2
C₂²×C₅×C₄⋊Dic₃	2
C₂²×C₅×Dic₃⋊C₄	2
C₂×C₅×C₃⋊#95	2
C₅×#4949	2
C₂×C₅×#399	3
C₂×#4949	5

Subgroups — C2×C5×#4949 #14331997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4949 #14331997