Subgroups — C₂×C₁₁₃×#1783 #43288608

Order 28928.

5942 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	C₂⁴×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#100×C₁₁₃	C₂	1	4	yes	maximal, complemented
3	C₂×#407×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₁₁₃×#1783	C₂	1	8	yes	maximal, direct product factor
5	C₂⁶×C₁₁₃	C₄	1	2	yes	—
6	C₂³×D₄×C₁₁₃	—	2	16	no	—
7	C₂³×D₄×C₁₁₃	—	2	4	no	—
8	C₂³×D₄×C₁₁₃	—	2	4	no	—
9	C₂³×D₄×C₁₁₃	C₄	1	2	yes	—
10	C₂³×D₄×C₁₁₃	C₄	1	4	yes	—
11	C₂³×D₄×C₁₁₃	C₂²	1	4	yes	—
12	C₂³×D₄×C₁₁₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₁₃	C₂²	1	4	yes	complemented
15	C₂×#100×C₁₁₃	—	2	16	no	—
16	C₂×#100×C₁₁₃	C₂²	1	16	yes	complemented
17	#407×C₁₁₃	—	2	4	no	—
18	#407×C₁₁₃	C₂²	1	8	yes	complemented
19	C₂×C₂²⋊C₈×C₁₁₃	—	2	4	no	—
20	C₂⁵×C₁₁₃	—	2	16	no	—
21	C₂⁵×C₁₁₃	—	2	4	no	—
22	C₂⁵×C₁₁₃	—	2	4	no	—
23	C₂⁵×C₁₁₃	—	4	16	no	—
24	C₂⁵×C₁₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂⁵×C₁₁₃	C₂×C₄	1	8	yes	—
26	C₂⁵×C₁₁₃	C₂×C₄	1	4	yes	—
27	C₂²×D₄×C₁₁₃	—	2	64	no	—
28	C₂²×D₄×C₁₁₃	—	2	64	no	—
29	C₂²×D₄×C₁₁₃	—	2	16	no	—
30	C₂²×D₄×C₁₁₃	—	2	32	no	—
31	C₂²×D₄×C₁₁₃	—	2	32	no	—
32	C₂²×D₄×C₁₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₁₃	—	2	16	no	—
34	C₂²×D₄×C₁₁₃	—	2	4	no	—
35	C₂²×D₄×C₁₁₃	—	2	16	no	—
36	C₂²×D₄×C₁₁₃	—	2	8	no	—
37	C₂²×D₄×C₁₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₁₃	—	2	4	no	—
39	C₂²×D₄×C₁₁₃	C₂×C₄	1	8	yes	—
40	C₂²×D₄×C₁₁₃	C₂×C₄	1	4	yes	—
41	C₂²×D₄×C₁₁₃	D₄	1	16	yes	—
42	C₂²×D₄×C₁₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₁₃	—	2	8	no	—
44	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
47	C₂³×C₄×C₁₁₃	D₄	1	4	yes	—
48	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₁₃	—	2	4	no	—
51	C₂×M₁₆×C₁₁₃	—	2	16	no	—
52	C₂×M₁₆×C₁₁₃	C₂³	1	8	yes	complemented
53	C₂²×C₈×C₁₁₃	—	2	4	no	—
54	#100×C₁₁₃	—	2	32	no	—
55	C₂²⋊C₈×C₁₁₃	—	2	16	no	—
56	C₂⁴×C₁₁₃	—	2	8	no	—
57	C₂⁴×C₁₁₃	—	2	4	no	—
58	C₂⁴×C₁₁₃	—	2	32	no	—
59	C₂⁴×C₁₁₃	—	2	32	no	—
60	C₂⁴×C₁₁₃	—	2	32	no	—
61	C₂⁴×C₁₁₃	—	2	16	no	—
62	C₂⁴×C₁₁₃	—	2	8	no	—
63	C₂⁴×C₁₁₃	—	2	4	no	—
64	C₂⁴×C₁₁₃	—	2	4	no	—
65	C₂⁴×C₁₁₃	—	4	16	no	—
66	C₂⁴×C₁₁₃	—	4	32	no	—
67	C₂⁴×C₁₁₃	—	4	128	no	—
68	C₂⁴×C₁₁₃	—	4	16	no	—
69	C₂⁴×C₁₁₃	—	4	32	no	—
70	C₂⁴×C₁₁₃	—	4	16	no	—
71	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
72	C₂⁴×C₁₁₃	C₂²⋊C₄	1	2	yes	—
73	C₂⁴×C₁₁₃	C₂²⋊C₄	1	16	yes	—
74	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
75	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂⁴×C₁₁₃	C₂²×C₄	1	8	yes	—
77	C₂×D₄×C₁₁₃	—	2	32	no	—
78	C₂×D₄×C₁₁₃	—	2	32	no	—
79	C₂×D₄×C₁₁₃	—	2	128	no	—
80	C₂×D₄×C₁₁₃	—	2	128	no	—
81	C₂×D₄×C₁₁₃	—	2	32	no	—
82	C₂×D₄×C₁₁₃	—	2	16	no	—
83	C₂×D₄×C₁₁₃	—	2	8	no	—
84	C₂×D₄×C₁₁₃	—	2	8	no	—
85	C₂×D₄×C₁₁₃	—	2	32	no	—
86	C₂×D₄×C₁₁₃	—	2	32	no	—
87	C₂×D₄×C₁₁₃	—	2	8	no	—
88	C₂×D₄×C₁₁₃	—	2	8	no	—
89	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	16	yes	—
90	C₂×D₄×C₁₁₃	C₂×D₄	1	16	yes	—
91	C₂²×C₄×C₁₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₁₃	—	2	8	no	—
93	C₂²×C₄×C₁₁₃	—	2	16	no	—
94	C₂²×C₄×C₁₁₃	—	2	16	no	—
95	C₂²×C₄×C₁₁₃	—	2	8	no	—
96	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	8	yes	—
98	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₁₁₃	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₁₃	—	2	16	no	—
107	M₁₆×C₁₁₃	—	4	8	no	—
108	C₂×C₈×C₁₁₃	—	2	8	no	—
109	C₂×C₈×C₁₁₃	—	4	8	no	—
110	C₂³×C₁₁₃	—	2	32	no	—
111	C₂³×C₁₁₃	—	2	4	no	—
112	C₂³×C₁₁₃	—	2	4	no	—
113	C₂³×C₁₁₃	—	2	4	no	—
114	C₂³×C₁₁₃	—	2	4	no	—
115	C₂³×C₁₁₃	—	2	4	no	—
116	C₂³×C₁₁₃	—	2	8	no	—
117	C₂³×C₁₁₃	—	2	8	no	—
118	C₂³×C₁₁₃	—	2	64	no	—
119	C₂³×C₁₁₃	—	2	8	no	—
120	C₂³×C₁₁₃	—	2	8	no	—
121	C₂³×C₁₁₃	—	2	16	no	—
122	C₂³×C₁₁₃	—	2	16	no	—
123	C₂³×C₁₁₃	—	4	32	no	—
124	C₂³×C₁₁₃	—	4	16	no	—
125	C₂³×C₁₁₃	—	4	128	no	—
126	C₂³×C₁₁₃	—	4	128	no	—
127	C₂³×C₁₁₃	—	4	16	no	—
128	C₂³×C₁₁₃	—	4	32	no	—
129	C₂³×C₁₁₃	—	4	128	no	—
130	C₂³×C₁₁₃	—	4	32	no	—
131	C₂³×C₁₁₃	—	4	16	no	—
132	C₂³×C₁₁₃	—	4	32	no	—
133	C₂³×C₁₁₃	#100	1	8	yes	complemented
134	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
137	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	16	yes	—
138	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
140	D₄×C₁₁₃	—	2	64	no	—
141	D₄×C₁₁₃	—	2	32	no	—
142	D₄×C₁₁₃	—	2	32	no	—
143	C₂×C₄×C₁₁₃	—	2	4	no	—
144	C₂×C₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	4	no	—
146	C₂×C₄×C₁₁₃	—	2	16	no	—
147	C₂×C₄×C₁₁₃	—	2	16	no	—
148	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₁₃	#120	1	8	yes	—
152	C₂×C₄×C₁₁₃	#120	1	8	yes	—
153	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₂²×D₄	1	4	yes	—
155	C₈×C₁₁₃	—	4	8	no	—
156	C₂²×C₁₁₃	—	2	16	no	—
157	C₂²×C₁₁₃	—	2	16	no	—
158	C₂²×C₁₁₃	—	2	2	no	—
159	C₂²×C₁₁₃	—	2	4	no	—
160	C₂²×C₁₁₃	—	2	2	no	—
161	C₂²×C₁₁₃	—	2	4	no	—
162	C₂²×C₁₁₃	—	2	16	no	—
163	C₂²×C₁₁₃	—	2	8	no	—
164	C₂²×C₁₁₃	—	2	16	no	—
165	C₂²×C₁₁₃	—	4	16	no	—
166	C₂²×C₁₁₃	—	4	16	no	—
167	C₂²×C₁₁₃	—	4	32	no	—
168	C₂²×C₁₁₃	—	4	128	no	—
169	C₂²×C₁₁₃	—	4	16	no	—
170	C₂²×C₁₁₃	—	4	32	no	—
171	C₂²×C₁₁₃	#379	1	2	yes	—
172	C₂²×C₁₁₃	#379	1	2	yes	—
173	C₂²×C₁₁₃	C₂×#100	1	4	yes	—
174	C₂²×C₁₁₃	C₂×#100	1	8	yes	complemented
175	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	2	yes	—
176	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₁₁₃	—	2	4	no	—
178	C₄×C₁₁₃	#379	1	4	yes	—
179	C₄×C₁₁₃	C₂×#120	1	4	yes	—
180	C₂×#1783	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₁₁₃	—	2	2	no	—
182	C₂×C₁₁₃	—	2	2	no	—
183	C₂×C₁₁₃	—	2	8	no	—
184	C₂×C₁₁₃	—	4	16	no	—
185	C₂×C₁₁₃	#1783	1	4	yes	direct product factor
186	C₂×C₁₁₃	C₂×#379	1	1	yes	characteristic
187	C₂×C₁₁₃	C₂²×#100	1	2	yes	—
188	C₂⁴×D₄	C₂×C₁₁₃	1	1	yes	characteristic
189	C₂²×#100	C₂×C₁₁₃	1	4	yes	complemented
190	C₂×#407	C₂×C₁₁₃	1	2	yes	complemented
191	#1783	C₂×C₁₁₃	1	8	yes	direct product factor
192	C₁₁₃	C₂×#1783	1	1	yes	characteristic, direct product factor, Sylow
193	C₂⁶	C₄×C₁₁₃	1	2	yes	—
194	C₂³×D₄	—	2	16	no	—
195	C₂³×D₄	—	2	4	no	—
196	C₂³×D₄	—	2	4	no	—
197	C₂³×D₄	C₄×C₁₁₃	1	2	yes	—
198	C₂³×D₄	C₄×C₁₁₃	1	4	yes	—
199	C₂³×D₄	C₂²×C₁₁₃	1	4	yes	—
200	C₂³×D₄	C₂²×C₁₁₃	1	2	yes	—
201	C₂⁴×C₄	C₂²×C₁₁₃	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₁₁₃	1	4	yes	complemented
203	C₂×#100	—	2	16	no	—
204	C₂×#100	C₂²×C₁₁₃	1	16	yes	complemented
205	#407	—	2	4	no	—
206	#407	C₂²×C₁₁₃	1	8	yes	complemented
207	C₂×C₂²⋊C₈	—	2	4	no	—
208	C₂⁵	—	2	16	no	—
209	C₂⁵	—	2	4	no	—
210	C₂⁵	—	2	4	no	—
211	C₂⁵	—	4	16	no	—
212	C₂⁵	C₂×C₄×C₁₁₃	1	1	yes	characteristic
213	C₂⁵	C₂×C₄×C₁₁₃	1	8	yes	—
214	C₂⁵	C₂×C₄×C₁₁₃	1	4	yes	—
215	C₂²×D₄	—	2	64	no	—
216	C₂²×D₄	—	2	64	no	—
217	C₂²×D₄	—	2	16	no	—
218	C₂²×D₄	—	2	32	no	—
219	C₂²×D₄	—	2	32	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	16	no	—
223	C₂²×D₄	—	2	16	no	—
224	C₂²×D₄	—	2	4	no	—
225	C₂²×D₄	—	2	8	no	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₂×C₄×C₁₁₃	1	8	yes	—
228	C₂²×D₄	C₂×C₄×C₁₁₃	1	4	yes	—
229	C₂²×D₄	D₄×C₁₁₃	1	16	yes	—
230	C₂²×D₄	C₂³×C₁₁₃	1	4	yes	—
231	C₂³×C₄	—	2	8	no	—
232	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
234	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
235	C₂³×C₄	D₄×C₁₁₃	1	4	yes	—
236	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	2	16	no	—
240	C₂×M₁₆	C₂³×C₁₁₃	1	8	yes	complemented
241	C₂²×C₈	—	2	4	no	—
242	#100	—	2	32	no	—
243	C₂²⋊C₈	—	2	16	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	4	no	—
246	C₂⁴	—	2	32	no	—
247	C₂⁴	—	2	32	no	—
248	C₂⁴	—	2	32	no	—
249	C₂⁴	—	2	16	no	—
250	C₂⁴	—	2	8	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	4	16	no	—
254	C₂⁴	—	4	32	no	—
255	C₂⁴	—	4	128	no	—
256	C₂⁴	—	4	16	no	—
257	C₂⁴	—	4	32	no	—
258	C₂⁴	—	4	16	no	—
259	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
260	C₂⁴	C₂²⋊C₄×C₁₁₃	1	2	yes	—
261	C₂⁴	C₂²⋊C₄×C₁₁₃	1	16	yes	—
262	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
263	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
264	C₂⁴	C₂²×C₄×C₁₁₃	1	8	yes	—
265	C₂×D₄	—	2	32	no	—
266	C₂×D₄	—	2	32	no	—
267	C₂×D₄	—	2	128	no	—
268	C₂×D₄	—	2	128	no	—
269	C₂×D₄	—	2	32	no	—
270	C₂×D₄	—	2	16	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	8	no	—
273	C₂×D₄	—	2	32	no	—
274	C₂×D₄	—	2	32	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	16	yes	—
278	C₂×D₄	C₂×D₄×C₁₁₃	1	16	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	8	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
290	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₁₃	1	8	yes	—
292	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
294	M₁₆	—	2	16	no	—
295	M₁₆	—	4	8	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	4	8	no	—
298	C₂³	—	2	32	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	64	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	2	16	no	—
310	C₂³	—	2	16	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	16	no	—
313	C₂³	—	4	128	no	—
314	C₂³	—	4	128	no	—
315	C₂³	—	4	128	no	—
316	C₂³	—	4	32	no	—
317	C₂³	—	4	16	no	—
318	C₂³	—	4	32	no	—
319	C₂³	—	4	16	no	—
320	C₂³	—	4	32	no	—
321	C₂³	#100×C₁₁₃	1	8	yes	complemented
322	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
323	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
324	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
325	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	16	yes	—
326	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
327	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
328	D₄	—	2	64	no	—
329	D₄	—	2	32	no	—
330	D₄	—	2	32	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	16	no	—
335	C₂×C₄	—	2	16	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
339	C₂×C₄	#120×C₁₁₃	1	8	yes	—
340	C₂×C₄	#120×C₁₁₃	1	8	yes	—
341	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
342	C₂×C₄	C₂²×D₄×C₁₁₃	1	4	yes	—
343	C₈	—	4	8	no	—
344	C₂²	—	2	16	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	16	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	16	no	—
353	C₂²	—	4	16	no	—
354	C₂²	—	4	16	no	—
355	C₂²	—	4	32	no	—
356	C₂²	—	4	128	no	—
357	C₂²	—	4	32	no	—
358	C₂²	—	4	16	no	—
359	C₂²	#379×C₁₁₃	1	2	yes	—
360	C₂²	#379×C₁₁₃	1	2	yes	—
361	C₂²	C₂×#100×C₁₁₃	1	4	yes	—
362	C₂²	C₂×#100×C₁₁₃	1	8	yes	complemented
363	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	2	yes	—
364	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
365	C₄	—	2	4	no	—
366	C₄	#379×C₁₁₃	1	4	yes	—
367	C₄	C₂×#120×C₁₁₃	1	4	yes	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	—	2	8	no	—
371	C₂	—	4	16	no	—
372	C₂	C₁₁₃×#1783	1	4	yes	direct product factor
373	C₂	C₂×#379×C₁₁₃	1	1	yes	characteristic
374	C₂	C₂²×#100×C₁₁₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂⁴×D₄×C₁₁₃	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂⁴×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#100×C₁₁₃	C₂	semidirect
3. C₂×#407×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1783	C₂	direct (N × H)
14. C₂²×M₁₆×C₁₁₃	C₂²	semidirect
16. C₂×#100×C₁₁₃	C₂²	semidirect
18. #407×C₁₁₃	C₂²	semidirect
52. C₂×M₁₆×C₁₁₃	C₂³	semidirect
133. C₂³×C₁₁₃	#100	semidirect
174. C₂²×C₁₁₃	C₂×#100	semidirect
180. C₂×#1783	C₁₁₃	direct (N × H)
185. C₂×C₁₁₃	#1783	direct (N × H)
189. C₂²×#100	C₂×C₁₁₃	semidirect
190. C₂×#407	C₂×C₁₁₃	semidirect
191. #1783	C₂×C₁₁₃	direct (N × H)
192. C₁₁₃	C₂×#1783	direct (N × H)
202. C₂²×M₁₆	C₂²×C₁₁₃	semidirect
204. C₂×#100	C₂²×C₁₁₃	semidirect
206. #407	C₂²×C₁₁₃	semidirect
240. C₂×M₁₆	C₂³×C₁₁₃	semidirect
321. C₂³	#100×C₁₁₃	semidirect
362. C₂²	C₂×#100×C₁₁₃	semidirect
372. C₂	C₁₁₃×#1783	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×D₄×C₁₁₃	2
C₂²×#100×C₁₁₃	2
C₂×#407×C₁₁₃	2
C₁₁₃×#1783	2
C₂×#1783	113

Subgroups — C2×C113×#1783 #43288608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1783 #43288608