Subgroups — C₂×C₅×#5196 #14417839

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#948	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#837	C₂	1	2	yes	maximal, complemented
4	C₅×#5196	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#443	—	3	1	no	maximal, Hall
8	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
9	C₃×C₅×#135	C₄	1	4	yes	complemented
10	C₃×C₅×#135	C₂²	1	4	yes	—
11	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×SD₁₆	C₄	1	2	yes	complemented
13	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#948	—	2	4	no	—
16	C₅×#948	C₂²	1	8	yes	complemented
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	—	2	2	no	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₅×#837	C₂²	1	8	yes	complemented
23	C₅×#819	C₂²	1	4	yes	complemented
24	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
25	C₂×#5196	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#135	D₃	1	1	yes	characteristic
27	C₂×C₅×#131	—	3	2	no	—
28	C₅×#443	—	3	8	no	—
29	C₂×C₅×#108	—	3	1	no	—
30	C₂×C₅×#104	—	3	2	no	—
31	C₂×C₄×C₅×C₈	—	3	1	no	—
32	C₃×C₅×#41	—	2	2	no	—
33	C₃×C₅×#41	—	2	2	no	—
34	C₃×C₅×#41	C₂×C₄	1	4	yes	—
35	C₃×C₅×#41	C₂³	1	4	yes	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
43	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
44	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₄×C₅×Dic₃	—	2	1	no	—
50	C₄×C₅×Dic₃	C₂³	1	2	yes	—
51	C₅×#208	—	2	2	no	—
52	C₅×#208	—	2	8	no	—
53	C₅×#208	C₂³	1	4	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	8	no	—
56	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
58	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
59	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
60	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
61	C₂×#948	C₂×C₅	1	2	yes	complemented
62	C₂×#837	C₂×C₅	1	2	yes	complemented
63	#5196	C₂×C₅	1	8	yes	direct product factor
64	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	C₂×D₃	1	2	yes	—
67	C₅×#135	Dic₃	1	4	yes	complemented
68	C₅×#135	C₂×D₃	1	4	yes	—
69	C₂×C₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
70	C₂×C₅×SD₁₆	Dic₃	1	2	yes	complemented
71	C₂×C₅×D₈	Dic₃	1	1	yes	characteristic, complemented
72	C₅×#131	—	3	8	no	—
73	C₅×#131	—	6	4	no	—
74	C₂×C₅×M₁₆	—	3	2	no	—
75	C₂×C₅×M₁₆	—	6	2	no	—
76	C₂²×C₅×C₈	—	3	1	no	—
77	C₂²×C₅×C₈	—	6	2	no	—
78	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₄²×C₅	—	3	1	no	—
80	C₅×#108	—	3	4	no	—
81	C₅×#104	—	3	8	no	—
82	C₄×C₅×C₈	—	3	4	no	—
83	C₂×#443	—	3	1	no	Sylow
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	#41	1	1	yes	characteristic
86	C₃×C₅×Q₈	—	2	2	no	—
87	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	2	2	no	—
91	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₅×C₃⋊C₈	—	2	4	no	—
106	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
107	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
108	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
109	C₃×#135	C₄×C₅	1	4	yes	complemented
110	C₃×#135	C₂²×C₅	1	4	yes	—
111	C₂×C₃×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×SD₁₆	C₄×C₅	1	2	yes	complemented
113	C₂×C₃×D₈	C₄×C₅	1	1	yes	characteristic, complemented
114	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
115	#948	—	2	4	no	—
116	#948	C₂²×C₅	1	8	yes	complemented
117	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
118	C₂×#208	—	2	2	no	—
119	C₂×#208	C₂²×C₅	1	2	yes	—
120	C₂²×C₃⋊C₈	—	2	2	no	—
121	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
122	#837	C₂²×C₅	1	8	yes	complemented
123	#819	C₂²×C₅	1	4	yes	complemented
124	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
125	C₅×#41	—	2	2	no	—
126	C₅×#41	—	2	2	no	—
127	C₅×#41	C₂×Dic₃	1	4	yes	—
128	C₅×#41	C₂²×D₃	1	4	yes	—
129	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
132	C₂²×C₄×C₅	—	2	2	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₅×Q₁₆	C₂×Dic₃	1	4	yes	complemented
136	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
137	C₅×D₈	C₂×Dic₃	1	4	yes	complemented
138	C₅×M₁₆	—	3	4	no	—
139	C₅×M₁₆	—	6	8	no	—
140	C₅×M₁₆	—	6	2	no	—
141	C₂×C₅×C₈	—	3	2	no	—
142	C₂×C₅×C₈	—	3	1	no	—
143	C₂×C₅×C₈	—	3	1	no	—
144	C₂×C₅×C₈	—	3	2	no	—
145	C₂×C₅×C₈	—	6	8	no	—
146	C₂×C₅×C₈	—	6	2	no	—
147	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
150	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
151	C₄²×C₅	—	3	2	no	—
152	C₄²×C₅	—	6	1	no	—
153	C₂×#135	C₅×D₃	1	1	yes	characteristic
154	C₂×#131	—	3	2	no	—
155	#443	—	3	8	no	—
156	C₂×#108	—	3	1	no	—
157	C₂×#104	—	3	2	no	—
158	C₂×C₄×C₈	—	3	1	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
164	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₅×Dic₃	—	2	4	no	—
171	C₃×#41	—	2	2	no	—
172	C₃×#41	—	2	2	no	—
173	C₃×#41	C₂×C₄×C₅	1	4	yes	—
174	C₃×#41	C₂³×C₅	1	4	yes	—
175	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
176	C₂×C₃×D₄	—	2	2	no	—
177	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
180	C₂²×Dic₃	—	2	1	no	—
181	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
182	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
183	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
184	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
186	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
187	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
188	C₄×Dic₃	—	2	1	no	—
189	C₄×Dic₃	C₂³×C₅	1	2	yes	—
190	#208	—	2	2	no	—
191	#208	—	2	8	no	—
192	#208	C₂³×C₅	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	2	8	no	—
195	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
196	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
197	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
198	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
199	C₂³×C₅	—	2	2	no	—
200	C₂³×C₅	#237	1	1	yes	characteristic
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
203	C₅×D₄	—	2	4	no	—
204	C₅×D₄	—	2	4	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	C₂²×Dic₃	1	4	yes	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	6	4	no	—
211	C₂×C₄×C₅	—	6	2	no	—
212	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	#237	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
218	C₅×C₈	—	3	2	no	—
219	C₅×C₈	—	3	2	no	—
220	C₅×C₈	—	6	4	no	—
221	C₅×C₈	C₂²×Dic₃	1	2	yes	—
222	C₅×C₈	C₂²×Dic₃	1	2	yes	—
223	C₂×#41	C₂×C₅×D₃	1	2	yes	—
224	#135	C₅×Dic₃	1	4	yes	complemented
225	#135	C₂×C₅×D₃	1	4	yes	—
226	C₂×Q₁₆	C₅×Dic₃	1	1	yes	characteristic, complemented
227	C₂×SD₁₆	C₅×Dic₃	1	2	yes	complemented
228	C₂×D₈	C₅×Dic₃	1	1	yes	characteristic, complemented
229	#131	—	3	8	no	—
230	#131	—	6	4	no	—
231	C₂×M₁₆	—	3	2	no	—
232	C₂×M₁₆	—	6	2	no	—
233	C₂²×C₈	—	3	1	no	—
234	C₂²×C₈	—	6	2	no	—
235	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
236	C₂×C₄²	—	3	1	no	—
237	#108	—	3	4	no	—
238	#104	—	3	8	no	—
239	C₄×C₈	—	3	4	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	2	1	no	—
242	C₂×C₃×C₅	—	4	4	no	—
243	C₂×C₃×C₅	#443	1	2	yes	complemented
244	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	C₅×#41	1	1	yes	characteristic
247	C₃×Q₈	—	2	2	no	—
248	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	4	no	—
251	C₃×D₄	—	2	2	no	—
252	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
262	C₂×Dic₃	—	2	4	no	—
263	C₂×Dic₃	—	2	2	no	—
264	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
265	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
266	C₃⋊C₈	—	2	4	no	—
267	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
268	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	4	no	—
271	C₂²×C₅	—	4	4	no	—
272	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
273	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
274	C₂²×C₅	C₂×#237	1	1	yes	characteristic
275	C₄×C₅	—	2	4	no	—
276	C₄×C₅	—	6	4	no	—
277	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
278	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
279	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
280	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	C₂×C₅×Dic₃	1	4	yes	—
284	#41	C₂²×C₅×D₃	1	4	yes	—
285	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	6	1	no	—
290	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
291	Q₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
292	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
293	D₈	C₂×C₅×Dic₃	1	4	yes	complemented
294	M₁₆	—	3	4	no	—
295	M₁₆	—	6	8	no	—
296	M₁₆	—	6	2	no	—
297	C₂×C₈	—	3	1	no	—
298	C₂×C₈	—	3	1	no	—
299	C₂×C₈	—	3	2	no	—
300	C₂×C₈	—	3	2	no	—
301	C₂×C₈	—	6	8	no	—
302	C₂×C₈	—	6	2	no	—
303	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
304	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
305	C₂×C₈	C₂×C₅×Dic₃	1	2	yes	—
306	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
307	C₄²	—	3	2	no	—
308	C₄²	—	6	1	no	—
309	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	4	4	no	—
313	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
318	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
319	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
321	Dic₃	—	2	4	no	—
322	C₂×C₅	—	2	1	no	—
323	C₂×C₅	—	2	1	no	—
324	C₂×C₅	—	4	4	no	—
325	C₂×C₅	#5196	1	2	yes	direct product factor
326	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	C₅×#237	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
331	D₄	—	2	4	no	—
332	D₄	—	2	4	no	—
333	D₄	—	2	2	no	—
334	D₄	C₂²×C₅×Dic₃	1	4	yes	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
341	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
342	C₂×C₄	C₅×#237	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
345	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₈	—	3	2	no	—
347	C₈	—	3	2	no	—
348	C₈	—	6	4	no	—
349	C₈	C₂²×C₅×Dic₃	1	2	yes	—
350	C₈	C₂²×C₅×Dic₃	1	2	yes	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	4	4	no	—
354	C₂×C₃	C₅×#443	1	2	yes	complemented
355	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
356	C₅	C₂×#5196	1	1	yes	characteristic, direct product factor, Sylow
357	C₂²	—	2	2	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	4	4	no	—
360	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
361	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
362	C₂²	C₂×C₅×#237	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	6	4	no	—
365	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
366	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
367	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
368	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
369	C₃	C₂×C₅×#443	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	4	4	no	—
373	C₂	C₅×#5196	1	2	yes	direct product factor
374	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₄×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₂×C₅×#443
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#837	C₂	semidirect
4. C₅×#5196	C₂	direct (N × H)
5. C₂×C₅×#819	C₂	semidirect
6. C₂×C₅×C₈×Dic₃	C₂	semidirect
9. C₃×C₅×#135	C₄	semidirect
11. C₂×C₃×C₅×Q₁₆	C₄	semidirect
12. C₂×C₃×C₅×SD₁₆	C₄	semidirect
13. C₂×C₃×C₅×D₈	C₄	semidirect
16. C₅×#948	C₂²	semidirect
22. C₅×#837	C₂²	semidirect
23. C₅×#819	C₂²	semidirect
24. C₅×C₈×Dic₃	C₂²	semidirect
25. C₂×#5196	C₅	direct (N × H)
42. C₃×C₅×Q₁₆	C₂×C₄	semidirect
43. C₃×C₅×SD₁₆	C₂×C₄	semidirect
44. C₃×C₅×D₈	C₂×C₄	semidirect
61. C₂×#948	C₂×C₅	semidirect
62. C₂×#837	C₂×C₅	semidirect
63. #5196	C₂×C₅	direct (N × H)
64. C₂×#819	C₂×C₅	semidirect
65. C₂×C₈×Dic₃	C₂×C₅	semidirect
67. C₅×#135	Dic₃	semidirect
69. C₂×C₅×Q₁₆	Dic₃	semidirect
70. C₂×C₅×SD₁₆	Dic₃	semidirect
71. C₂×C₅×D₈	Dic₃	semidirect
109. C₃×#135	C₄×C₅	semidirect
111. C₂×C₃×Q₁₆	C₄×C₅	semidirect
112. C₂×C₃×SD₁₆	C₄×C₅	semidirect
113. C₂×C₃×D₈	C₄×C₅	semidirect
116. #948	C₂²×C₅	semidirect
122. #837	C₂²×C₅	semidirect
123. #819	C₂²×C₅	semidirect
124. C₈×Dic₃	C₂²×C₅	semidirect
135. C₅×Q₁₆	C₂×Dic₃	semidirect
136. C₅×SD₁₆	C₂×Dic₃	semidirect
137. C₅×D₈	C₂×Dic₃	semidirect
181. C₃×Q₁₆	C₂×C₄×C₅	semidirect
182. C₃×SD₁₆	C₂×C₄×C₅	semidirect
183. C₃×D₈	C₂×C₄×C₅	semidirect
224. #135	C₅×Dic₃	semidirect
226. C₂×Q₁₆	C₅×Dic₃	semidirect
227. C₂×SD₁₆	C₅×Dic₃	semidirect
228. C₂×D₈	C₅×Dic₃	semidirect
243. C₂×C₃×C₅	#443	semidirect
291. Q₁₆	C₂×C₅×Dic₃	semidirect
292. SD₁₆	C₂×C₅×Dic₃	semidirect
293. D₈	C₂×C₅×Dic₃	semidirect
309. C₃×C₅	C₂×#443	semidirect
325. C₂×C₅	#5196	direct (N × H)
354. C₂×C₃	C₅×#443	semidirect
356. C₅	C₂×#5196	direct (N × H)
369. C₃	C₂×C₅×#443	semidirect
373. C₂	C₅×#5196	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×#135	2
C₂×C₅×#948	2
C₂×C₅×#837	2
C₅×#5196	2
C₂×C₅×#819	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#443	3
C₂×#5196	5

Subgroups — C2×C5×#5196 #14417839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5196 #14417839