Subgroups — C₂×C₁₁₃×#1857 #43288874

Order 28928.

1402 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#519×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#428×C₁₁₃	C₂	1	2	yes	maximal
3	C₂²×#101×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#391×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₁₃×#1857	C₂	1	8	yes	maximal, direct product factor
6	C₂×#339×C₁₁₃	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₁₁₃	C₂²	1	2	yes	—
9	#519×C₁₁₃	—	2	2	no	—
10	#519×C₁₁₃	—	2	4	no	—
11	#519×C₁₁₃	C₂²	1	4	yes	—
12	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
13	C₂×C₄×Q₈×C₁₁₃	—	2	2	no	—
14	C₂×#117×C₁₁₃	—	2	2	no	—
15	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
18	#428×C₁₁₃	—	2	4	no	—
19	#428×C₁₁₃	C₂²	1	8	yes	—
20	C₂×#107×C₁₁₃	—	2	2	no	—
21	C₂×#106×C₁₁₃	—	2	2	no	—
22	C₂×#101×C₁₁₃	C₄	1	8	yes	complemented
23	C₂×#101×C₁₁₃	C₂²	1	4	yes	—
24	#391×C₁₁₃	—	2	2	no	—
25	#391×C₁₁₃	C₂²	1	4	yes	—
26	C₂×#95×C₁₁₃	—	2	2	no	—
27	#339×C₁₁₃	C₂²	1	8	yes	—
28	C₂²×Q₈×C₁₁₃	—	2	2	no	—
29	C₂²×Q₈×C₁₁₃	—	2	2	no	—
30	C₂²×Q₈×C₁₁₃	—	2	4	no	—
31	C₂²×Q₈×C₁₁₃	C₂×C₄	1	4	yes	—
32	C₂²×Q₈×C₁₁₃	D₄	1	2	yes	—
33	C₂²×Q₈×C₁₁₃	Q₈	1	4	yes	—
34	C₂²×Q₈×C₁₁₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₁₃	—	2	1	no	—
36	C₂³×C₄×C₁₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₁₃	—	2	2	no	—
40	C₂×M₁₆×C₁₁₃	—	2	4	no	—
41	C₂×M₁₆×C₁₁₃	C₂×C₄	1	8	yes	—
42	C₂×M₁₆×C₁₁₃	C₂³	1	4	yes	—
43	C₂²×C₈×C₁₁₃	—	2	2	no	—
44	C₄×Q₈×C₁₁₃	—	2	8	no	—
45	C₄×Q₈×C₁₁₃	—	2	8	no	—
46	C₄×Q₈×C₁₁₃	—	2	8	no	—
47	C₄×Q₈×C₁₁₃	—	2	8	no	—
48	#117×C₁₁₃	—	2	8	no	—
49	#117×C₁₁₃	—	2	8	no	—
50	#117×C₁₁₃	—	2	2	no	—
51	#117×C₁₁₃	—	2	2	no	—
52	#117×C₁₁₃	D₄	1	4	yes	—
53	#117×C₁₁₃	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₁₃	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₁₃	—	2	4	no	—
64	C₂×C₄²×C₁₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₁₃	—	2	4	no	—
66	C₂×C₄²×C₁₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
68	#107×C₁₁₃	—	2	8	no	—
69	#106×C₁₁₃	—	2	8	no	—
70	#101×C₁₁₃	C₂×C₄	1	16	yes	complemented
71	#95×C₁₁₃	—	2	8	no	—
72	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₁₁₃	—	2	8	no	—
74	C₂×Q₈×C₁₁₃	—	2	8	no	—
75	C₂×Q₈×C₁₁₃	—	2	4	no	—
76	C₂×Q₈×C₁₁₃	—	2	8	no	—
77	C₂×Q₈×C₁₁₃	—	2	8	no	—
78	C₂×Q₈×C₁₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₁₃	—	2	4	no	—
80	C₂×Q₈×C₁₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₁₃	C₄⋊C₄	1	8	yes	—
82	C₂×Q₈×C₁₁₃	C₂²×C₄	1	4	yes	—
83	C₂×Q₈×C₁₁₃	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₁₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₁₃	—	4	4	no	—
95	C₂²×C₄×C₁₁₃	—	4	1	no	—
96	C₂²×C₄×C₁₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₁₃	C₄⋊C₄	1	8	yes	—
98	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
105	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₁₁₃	—	2	8	no	—
107	M₁₆×C₁₁₃	—	2	4	no	—
108	M₁₆×C₁₁₃	C₂²×C₄	1	8	yes	—
109	C₂×C₈×C₁₁₃	—	2	8	no	—
110	C₂×C₈×C₁₁₃	—	2	4	no	—
111	C₄⋊C₄×C₁₁₃	—	2	8	no	—
112	C₄⋊C₄×C₁₁₃	—	2	8	no	—
113	C₄⋊C₄×C₁₁₃	—	2	2	no	—
114	C₄⋊C₄×C₁₁₃	—	2	2	no	—
115	C₄⋊C₄×C₁₁₃	—	2	4	no	—
116	C₄⋊C₄×C₁₁₃	—	4	2	no	—
117	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
118	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
119	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
120	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
121	C₄²×C₁₁₃	—	2	16	no	—
122	C₄²×C₁₁₃	—	2	4	no	—
123	C₄²×C₁₁₃	—	2	4	no	—
124	C₄²×C₁₁₃	—	2	4	no	—
125	C₄²×C₁₁₃	—	4	2	no	—
126	C₂³×C₁₁₃	—	2	2	no	—
127	C₂³×C₁₁₃	—	2	2	no	—
128	C₂³×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
129	C₂³×C₁₁₃	#120	1	1	yes	characteristic
130	C₂³×C₁₁₃	#120	1	1	yes	characteristic
131	C₂³×C₁₁₃	#123	1	2	yes	—
132	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₁₃	—	2	8	no	—
134	Q₈×C₁₁₃	—	2	8	no	—
135	Q₈×C₁₁₃	—	2	16	no	—
136	C₂×C₄×C₁₁₃	—	2	4	no	—
137	C₂×C₄×C₁₁₃	—	2	4	no	—
138	C₂×C₄×C₁₁₃	—	2	8	no	—
139	C₂×C₄×C₁₁₃	—	2	8	no	—
140	C₂×C₄×C₁₁₃	—	2	4	no	—
141	C₂×C₄×C₁₁₃	—	2	4	no	—
142	C₂×C₄×C₁₁₃	—	2	4	no	—
143	C₂×C₄×C₁₁₃	—	4	8	no	—
144	C₂×C₄×C₁₁₃	—	4	2	no	—
145	C₂×C₄×C₁₁₃	—	4	2	no	—
146	C₂×C₄×C₁₁₃	—	4	4	no	—
147	C₂×C₄×C₁₁₃	—	4	4	no	—
148	C₂×C₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	8	2	no	—
151	C₂×C₄×C₁₁₃	—	8	2	no	—
152	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	8	yes	—
153	C₂×C₄×C₁₁₃	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
155	C₂×C₄×C₁₁₃	C₄×D₄	1	4	yes	—
156	C₂×C₄×C₁₁₃	#120	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
158	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₁₃	#123	1	2	yes	—
160	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂×#41	1	2	yes	—
164	C₈×C₁₁₃	—	2	8	no	—
165	C₂²×C₁₁₃	—	2	4	no	—
166	C₂²×C₁₁₃	—	2	4	no	—
167	C₂²×C₁₁₃	—	2	1	no	—
168	C₂²×C₁₁₃	—	2	1	no	—
169	C₂²×C₁₁₃	—	2	1	no	—
170	C₂²×C₁₁₃	—	2	1	no	—
171	C₂²×C₁₁₃	#385	1	2	yes	—
172	C₂²×C₁₁₃	#385	1	2	yes	—
173	C₂²×C₁₁₃	#454	1	2	yes	—
174	C₂²×C₁₁₃	#456	1	2	yes	—
175	C₂²×C₁₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
177	C₂²×C₁₁₃	C₂×#123	1	1	yes	characteristic
178	C₄×C₁₁₃	—	2	8	no	—
179	C₄×C₁₁₃	—	4	4	no	—
180	C₄×C₁₁₃	—	4	4	no	—
181	C₄×C₁₁₃	—	4	4	no	—
182	C₄×C₁₁₃	—	8	2	no	—
183	C₄×C₁₁₃	#385	1	4	yes	—
184	C₄×C₁₁₃	C₂×C₄×D₄	1	2	yes	—
185	C₄×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
186	C₂×#1857	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂×C₁₁₃	—	2	1	no	—
188	C₂×C₁₁₃	—	2	1	no	—
189	C₂×C₁₁₃	—	2	2	no	—
190	C₂×C₁₁₃	#1857	1	4	yes	direct product factor
191	C₂×C₁₁₃	C₂×#385	1	1	yes	characteristic
192	C₂×C₁₁₃	C₂×#454	1	1	yes	characteristic
193	C₂×C₁₁₃	C₂×#456	1	1	yes	characteristic
194	C₂×#519	C₂×C₁₁₃	1	1	yes	characteristic
195	C₂×#428	C₂×C₁₁₃	1	2	yes	—
196	C₂²×#101	C₂×C₁₁₃	1	1	yes	characteristic
197	C₂×#391	C₂×C₁₁₃	1	1	yes	characteristic
198	#1857	C₂×C₁₁₃	1	8	yes	direct product factor
199	C₂×#339	C₂×C₁₁₃	1	2	yes	—
200	C₁₁₃	C₂×#1857	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₁₁₃	1	2	yes	—
203	#519	—	2	2	no	—
204	#519	—	2	4	no	—
205	#519	C₂²×C₁₁₃	1	4	yes	—
206	C₂×C₄×Q₈	—	2	2	no	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×#117	—	2	2	no	—
209	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
212	#428	—	2	4	no	—
213	#428	C₂²×C₁₁₃	1	8	yes	—
214	C₂×#107	—	2	2	no	—
215	C₂×#106	—	2	2	no	—
216	C₂×#101	C₄×C₁₁₃	1	8	yes	complemented
217	C₂×#101	C₂²×C₁₁₃	1	4	yes	—
218	#391	—	2	2	no	—
219	#391	C₂²×C₁₁₃	1	4	yes	—
220	C₂×#95	—	2	2	no	—
221	#339	C₂²×C₁₁₃	1	8	yes	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	C₂×C₄×C₁₁₃	1	4	yes	—
226	C₂²×Q₈	D₄×C₁₁₃	1	2	yes	—
227	C₂²×Q₈	Q₈×C₁₁₃	1	4	yes	—
228	C₂²×Q₈	C₂³×C₁₁₃	1	2	yes	—
229	C₂³×C₄	—	2	1	no	—
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	C₂×C₄×C₁₁₃	1	8	yes	—
236	C₂×M₁₆	C₂³×C₁₁₃	1	4	yes	—
237	C₂²×C₈	—	2	2	no	—
238	C₄×Q₈	—	2	8	no	—
239	C₄×Q₈	—	2	8	no	—
240	C₄×Q₈	—	2	8	no	—
241	C₄×Q₈	—	2	8	no	—
242	#117	—	2	8	no	—
243	#117	—	2	8	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	D₄×C₁₁₃	1	4	yes	—
247	#117	C₂³×C₁₁₃	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	D₄×C₁₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	4	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
262	#107	—	2	8	no	—
263	#106	—	2	8	no	—
264	#101	C₂×C₄×C₁₁₃	1	16	yes	complemented
265	#95	—	2	8	no	—
266	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	8	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	C₄⋊C₄×C₁₁₃	1	8	yes	—
276	C₂×Q₈	C₂²×C₄×C₁₁₃	1	4	yes	—
277	C₂×Q₈	C₂×Q₈×C₁₁₃	1	4	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₄⋊C₄×C₁₁₃	1	8	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
298	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
299	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
300	M₁₆	—	2	8	no	—
301	M₁₆	—	2	4	no	—
302	M₁₆	C₂²×C₄×C₁₁₃	1	8	yes	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
312	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₄²	—	2	16	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	4	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
323	C₂³	#120×C₁₁₃	1	1	yes	characteristic
324	C₂³	#120×C₁₁₃	1	1	yes	characteristic
325	C₂³	#123×C₁₁₃	1	2	yes	—
326	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
327	Q₈	—	2	8	no	—
328	Q₈	—	2	8	no	—
329	Q₈	—	2	16	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	8	yes	—
347	C₂×C₄	C₂×C₄⋊C₄×C₁₁₃	1	2	yes	—
348	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
349	C₂×C₄	C₄×D₄×C₁₁₃	1	4	yes	—
350	C₂×C₄	#120×C₁₁₃	1	2	yes	—
351	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
352	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
353	C₂×C₄	#123×C₁₁₃	1	2	yes	—
354	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
356	C₂×C₄	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₁₃	1	2	yes	—
358	C₈	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	#385×C₁₁₃	1	2	yes	—
366	C₂²	#385×C₁₁₃	1	2	yes	—
367	C₂²	#454×C₁₁₃	1	2	yes	—
368	C₂²	#456×C₁₁₃	1	2	yes	—
369	C₂²	C₂²×C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
370	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
371	C₂²	C₂×#123×C₁₁₃	1	1	yes	characteristic
372	C₄	—	2	8	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	4	no	—
376	C₄	—	8	2	no	—
377	C₄	#385×C₁₁₃	1	4	yes	—
378	C₄	C₂×C₄×D₄×C₁₁₃	1	2	yes	—
379	C₄	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	2	no	—
383	C₂	C₁₁₃×#1857	1	4	yes	direct product factor
384	C₂	C₂×#385×C₁₁₃	1	1	yes	characteristic
385	C₂	C₂×#454×C₁₁₃	1	1	yes	characteristic
386	C₂	C₂×#456×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁₃	#120
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₂⁴×C₁₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁₃ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₁₃×#1857	C₂	direct (N × H)
22. C₂×#101×C₁₁₃	C₄	semidirect
70. #101×C₁₁₃	C₂×C₄	semidirect
186. C₂×#1857	C₁₁₃	direct (N × H)
190. C₂×C₁₁₃	#1857	direct (N × H)
198. #1857	C₂×C₁₁₃	direct (N × H)
200. C₁₁₃	C₂×#1857	direct (N × H)
216. C₂×#101	C₄×C₁₁₃	semidirect
264. #101	C₂×C₄×C₁₁₃	semidirect
383. C₂	C₁₁₃×#1857	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×#519×C₁₁₃	2
C₂×#428×C₁₁₃	2
C₂²×#101×C₁₁₃	2
C₂×#391×C₁₁₃	2
C₁₁₃×#1857	2
C₂×#339×C₁₁₃	2
C₂×#1857	113

Subgroups — C2×C113×#1857 #43288874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1857 #43288874