Subgroups — C₂×C₅×#1953 #11943903

Order 1280.

858 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#430	C₂	1	2	yes	maximal
2	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₅×#1953	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#344	C₂	1	2	yes	maximal
7	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₅×#430	—	2	4	no	—
13	C₅×#430	C₂²	1	8	yes	—
14	C₂×C₅×#108	—	2	4	no	—
15	C₂×C₅×#108	—	2	1	no	—
16	C₂×C₅×#108	—	2	1	no	—
17	C₂×C₅×#108	—	2	2	no	—
18	C₂×C₅×#108	C₄	1	4	yes	complemented
19	C₂×C₅×#108	C₄	1	4	yes	complemented
20	C₂×C₅×#108	C₂²	1	4	yes	—
21	C₂×C₅×#108	C₂²	1	4	yes	—
22	C₅×#405	—	2	2	no	—
23	C₅×#405	C₂²	1	4	yes	—
24	C₂×C₅×#97	—	2	1	no	—
25	C₂×C₄×C₅×C₈	—	2	1	no	—
26	C₅×#344	C₂²	1	8	yes	—
27	C₂×#1953	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂×C₅×M₁₆	—	2	1	no	—
30	C₂×C₅×M₁₆	—	2	2	no	—
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	2	no	—
33	C₂×C₅×M₁₆	—	2	1	no	—
34	C₂×C₅×M₁₆	—	2	1	no	—
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	—	2	2	no	—
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	2	2	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
41	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
42	C₂×C₅×M₁₆	D₄	1	2	yes	—
43	C₂×C₅×M₁₆	D₄	1	2	yes	—
44	C₂×C₅×M₁₆	C₂³	1	4	yes	—
45	C₂×C₅×M₁₆	C₂³	1	4	yes	—
46	C₂×C₅×M₁₆	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	—	2	1	no	—
48	C₂²×C₅×C₈	—	2	2	no	—
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
51	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	D₄	1	2	yes	—
55	C₂²×C₅×C₈	Q₈	1	2	yes	—
56	C₂²×C₅×C₈	Q₈	1	2	yes	—
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₅×#117	—	2	1	no	—
59	C₅×#117	—	2	1	no	—
60	C₅×#117	Q₈	1	2	yes	—
61	C₅×#117	C₂³	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	Q₈	1	2	yes	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₅×#108	—	2	16	no	—
66	C₅×#108	—	2	4	no	—
67	C₅×#108	—	2	4	no	—
68	C₅×#108	C₂×C₄	1	16	yes	complemented
69	C₅×#97	—	2	4	no	—
70	C₄×C₅×C₈	—	2	4	no	—
71	C₂×#430	C₂×C₅	1	2	yes	—
72	C₂²×#108	C₂×C₅	1	1	yes	characteristic
73	C₂²×#108	C₂×C₅	1	1	yes	characteristic
74	C₂×#405	C₂×C₅	1	1	yes	characteristic
75	#1953	C₂×C₅	1	8	yes	direct product factor
76	C₂×#344	C₂×C₅	1	2	yes	—
77	C₂⁴×C₅	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₅	—	2	2	no	—
79	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₅	#41	1	1	yes	characteristic
89	C₂²×C₄×C₅	#41	1	1	yes	characteristic
90	C₂²×C₄×C₅	#41	1	1	yes	characteristic
91	C₂²×C₄×C₅	#41	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₅×M₁₆	—	2	4	no	—
94	C₅×M₁₆	—	2	4	no	—
95	C₅×M₁₆	—	2	2	no	—
96	C₅×M₁₆	—	2	2	no	—
97	C₅×M₁₆	—	2	4	no	—
98	C₅×M₁₆	—	2	2	no	—
99	C₅×M₁₆	—	2	4	no	—
100	C₅×M₁₆	—	2	4	no	—
101	C₅×M₁₆	—	4	2	no	—
102	C₅×M₁₆	—	4	2	no	—
103	C₅×M₁₆	C₂²×C₄	1	8	yes	—
104	C₅×M₁₆	C₂×D₄	1	4	yes	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	4	no	—
111	C₂×C₅×C₈	—	2	4	no	—
112	C₂×C₅×C₈	—	4	2	no	—
113	C₂×C₅×C₈	—	4	2	no	—
114	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
115	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
116	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
117	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
118	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
119	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
120	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
121	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
122	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
123	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₂²⋊C₄	—	2	2	no	—
127	C₅×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
131	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
132	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
133	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×#117	C₂²×C₅	1	1	yes	characteristic
135	#430	—	2	4	no	—
136	#430	C₂²×C₅	1	8	yes	—
137	C₂×#108	—	2	4	no	—
138	C₂×#108	—	2	1	no	—
139	C₂×#108	—	2	1	no	—
140	C₂×#108	—	2	2	no	—
141	C₂×#108	C₄×C₅	1	4	yes	complemented
142	C₂×#108	C₄×C₅	1	4	yes	complemented
143	C₂×#108	C₂²×C₅	1	4	yes	—
144	C₂×#108	C₂²×C₅	1	4	yes	—
145	#405	—	2	2	no	—
146	#405	C₂²×C₅	1	4	yes	—
147	C₂×#97	—	2	1	no	—
148	C₂×C₄×C₈	—	2	1	no	—
149	#344	C₂²×C₅	1	8	yes	—
150	C₂³×C₅	—	4	2	no	—
151	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
152	C₂³×C₅	C₄×Q₈	1	1	yes	characteristic
153	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
156	C₂³×C₅	C₄⋊Q₈	1	1	yes	characteristic
157	C₂³×C₅	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₅	—	2	4	no	—
159	C₂×C₄×C₅	—	4	4	no	—
160	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅	#121	1	1	yes	characteristic
171	C₂×C₄×C₅	#121	1	1	yes	characteristic
172	C₂×C₄×C₅	#121	1	1	yes	characteristic
173	C₂×C₄×C₅	#121	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₅	#125	1	1	yes	characteristic
177	C₂×C₄×C₅	#125	1	1	yes	characteristic
178	C₂×C₄×C₅	#125	1	1	yes	characteristic
179	C₂×C₄×C₅	#125	1	1	yes	characteristic
180	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
188	C₅×C₈	—	2	8	no	—
189	C₅×C₈	—	2	4	no	—
190	C₅×C₈	—	4	4	no	—
191	C₅×C₈	C₂×C₄⋊C₄	1	4	yes	—
192	C₅×C₈	C₂×C₄⋊C₄	1	4	yes	—
193	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
194	C₂×M₁₆	—	2	1	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	2	2	no	—
198	C₂×M₁₆	—	2	1	no	—
199	C₂×M₁₆	—	2	1	no	—
200	C₂×M₁₆	—	2	2	no	—
201	C₂×M₁₆	—	2	2	no	—
202	C₂×M₁₆	—	2	2	no	—
203	C₂×M₁₆	—	2	2	no	—
204	C₂×M₁₆	—	2	2	no	—
205	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
206	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
207	C₂×M₁₆	C₅×D₄	1	2	yes	—
208	C₂×M₁₆	C₅×D₄	1	2	yes	—
209	C₂×M₁₆	C₂³×C₅	1	4	yes	—
210	C₂×M₁₆	C₂³×C₅	1	4	yes	—
211	C₂×M₁₆	C₂³×C₅	1	2	yes	—
212	C₂²×C₈	—	2	1	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
216	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
217	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
218	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
219	C₂²×C₈	C₅×D₄	1	2	yes	—
220	C₂²×C₈	C₅×Q₈	1	2	yes	—
221	C₂²×C₈	C₅×Q₈	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	#117	—	2	1	no	—
224	#117	—	2	1	no	—
225	#117	C₅×Q₈	1	2	yes	—
226	#117	C₂³×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	C₅×Q₈	1	2	yes	—
229	C₂×C₄²	—	2	1	no	—
230	#108	—	2	16	no	—
231	#108	—	2	4	no	—
232	#108	—	2	4	no	—
233	#108	C₂×C₄×C₅	1	16	yes	complemented
234	#97	—	2	4	no	—
235	C₄×C₈	—	2	4	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	2	no	—
239	C₂²×C₅	—	4	1	no	—
240	C₂²×C₅	—	4	1	no	—
241	C₂²×C₅	—	4	1	no	—
242	C₂²×C₅	—	4	1	no	—
243	C₂²×C₅	#389	1	1	yes	characteristic
244	C₂²×C₅	#389	1	1	yes	characteristic
245	C₂²×C₅	#389	1	1	yes	characteristic
246	C₂²×C₅	#389	1	1	yes	characteristic
247	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₂²×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	#389	1	1	yes	characteristic
252	C₄×C₅	#389	1	1	yes	characteristic
253	C₄×C₅	#389	1	1	yes	characteristic
254	C₄×C₅	#389	1	1	yes	characteristic
255	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
256	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₅	C₂×#121	1	1	yes	characteristic
258	C₄×C₅	C₂×#125	1	1	yes	characteristic
259	C₂⁴	C₂×C₅×Q₈	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
270	C₂²×C₄	C₅×#41	1	1	yes	characteristic
271	C₂²×C₄	C₅×#41	1	1	yes	characteristic
272	C₂²×C₄	C₅×#41	1	1	yes	characteristic
273	C₂²×C₄	C₅×#41	1	1	yes	characteristic
274	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
275	M₁₆	—	2	4	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	2	4	no	—
280	M₁₆	—	2	2	no	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	4	2	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	C₂²×C₄×C₅	1	8	yes	—
286	M₁₆	C₂×C₅×D₄	1	4	yes	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
297	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
298	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
299	C₂×C₈	C₅×C₄⋊C₄	1	2	yes	—
300	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
301	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
302	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
303	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
304	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	C₂×C₅×Q₈	1	4	yes	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₂×C₅	—	2	1	no	—
313	C₂×C₅	—	2	1	no	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	2	1	no	—
318	C₂×C₅	#1953	1	2	yes	direct product factor
319	C₂×C₅	C₂×#389	1	1	yes	characteristic
320	C₂³	—	4	2	no	—
321	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
322	C₂³	C₄×C₅×Q₈	1	1	yes	characteristic
323	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
324	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
325	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
326	C₂³	C₅×C₄⋊Q₈	1	1	yes	characteristic
327	C₂³	C₂²×C₅×Q₈	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
335	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
336	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
337	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
338	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
339	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
340	C₂×C₄	C₅×#121	1	1	yes	characteristic
341	C₂×C₄	C₅×#121	1	1	yes	characteristic
342	C₂×C₄	C₅×#121	1	1	yes	characteristic
343	C₂×C₄	C₅×#121	1	1	yes	characteristic
344	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
345	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
346	C₂×C₄	C₅×#125	1	1	yes	characteristic
347	C₂×C₄	C₅×#125	1	1	yes	characteristic
348	C₂×C₄	C₅×#125	1	1	yes	characteristic
349	C₂×C₄	C₅×#125	1	1	yes	characteristic
350	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
351	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
352	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₈	—	2	4	no	—
360	C₈	—	4	4	no	—
361	C₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
362	C₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
363	C₅	C₂×#1953	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	C₅×#389	1	1	yes	characteristic
372	C₂²	C₅×#389	1	1	yes	characteristic
373	C₂²	C₅×#389	1	1	yes	characteristic
374	C₂²	C₅×#389	1	1	yes	characteristic
375	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
376	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂²	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
378	C₄	—	4	4	no	—
379	C₄	C₅×#389	1	1	yes	characteristic
380	C₄	C₅×#389	1	1	yes	characteristic
381	C₄	C₅×#389	1	1	yes	characteristic
382	C₄	C₅×#389	1	1	yes	characteristic
383	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
384	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
385	C₄	C₂×C₅×#121	1	1	yes	characteristic
386	C₄	C₂×C₅×#125	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	C₅×#1953	1	2	yes	direct product factor
394	C₂	C₂×C₅×#389	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	#389
prime radical	C₂⁴×C₅	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1953	C₂	direct (N × H)
18. C₂×C₅×#108	C₄	semidirect
19. C₂×C₅×#108	C₄	semidirect
27. C₂×#1953	C₅	direct (N × H)
68. C₅×#108	C₂×C₄	semidirect
75. #1953	C₂×C₅	direct (N × H)
141. C₂×#108	C₄×C₅	semidirect
142. C₂×#108	C₄×C₅	semidirect
233. #108	C₂×C₄×C₅	semidirect
318. C₂×C₅	#1953	direct (N × H)
363. C₅	C₂×#1953	direct (N × H)
393. C₂	C₅×#1953	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×C₅×#430	2
C₂²×C₅×#108	2
C₂×C₅×#405	2
C₅×#1953	2
C₂×C₅×#344	2
C₂×#1953	5

Subgroups — C2×C5×#1953 #11943903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1953 #11943903