Subgroups — C₁₁₃×#18180 #43286200

Order 28928.

1106 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#3110	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#2397	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1614	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1596	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1506	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	#554×C₁₁₃	—	2	2	no	—
9	#554×C₁₁₃	—	2	4	no	—
10	D₄×Q₈×C₁₁₃	—	2	2	no	—
11	#544×C₁₁₃	—	2	1	no	—
12	#543×C₁₁₃	C₂²	1	4	yes	—
13	#533×C₁₁₃	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
15	#518×C₁₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₁₃	—	2	2	no	—
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
19	#484×C₁₁₃	C₂²	1	4	yes	—
20	#474×C₁₁₃	—	2	2	no	—
21	#461×C₁₁₃	—	2	2	no	—
22	#450×C₁₁₃	C₂²	1	4	yes	—
23	#440×C₁₁₃	—	2	4	no	—
24	#432×C₁₁₃	C₂²	1	2	yes	—
25	#399×C₁₁₃	—	2	1	no	—
26	#399×C₁₁₃	C₂²	1	2	yes	—
27	#392×C₁₁₃	—	2	1	no	—
28	#392×C₁₁₃	C₂²	1	2	yes	—
29	#376×C₁₁₃	C₂²	1	1	yes	characteristic
30	#328×C₁₁₃	C₂²	1	8	yes	—
31	#323×C₁₁₃	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₁₃	—	2	2	no	—
33	C₂²×D₄×C₁₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₁₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
38	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
39	C₄⋊Q₈×C₁₁₃	—	2	4	no	—
40	C₄⋊Q₈×C₁₁₃	D₄	1	2	yes	complemented
41	C₄⋊Q₈×C₁₁₃	D₄	1	2	yes	complemented
42	#125×C₁₁₃	—	2	4	no	—
43	#125×C₁₁₃	—	2	2	no	—
44	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
45	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
46	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
47	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
48	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
49	C₂²⋊Q₈×C₁₁₃	—	2	8	no	—
50	C₂²⋊Q₈×C₁₁₃	C₂³	1	4	yes	—
51	C₄×Q₈×C₁₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₁₃	D₄	1	4	yes	complemented
53	C₄×D₄×C₁₁₃	—	2	4	no	—
54	C₄×D₄×C₁₁₃	—	2	4	no	—
55	C₄×D₄×C₁₁₃	—	2	2	no	—
56	C₄×D₄×C₁₁₃	—	2	2	no	—
57	C₄×D₄×C₁₁₃	—	2	2	no	—
58	C₄×D₄×C₁₁₃	—	2	2	no	—
59	C₄×D₄×C₁₁₃	—	4	8	no	—
60	#117×C₁₁₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
73	#107×C₁₁₃	—	2	4	no	—
74	C₄⋊C₈×C₁₁₃	—	2	2	no	—
75	#103×C₁₁₃	—	2	4	no	—
76	#102×C₁₁₃	—	2	4	no	—
77	C₂²⋊C₈×C₁₁₃	C₂³	1	4	yes	—
78	#97×C₁₁₃	—	2	2	no	—
79	#95×C₁₁₃	—	2	1	no	—
80	#95×C₁₁₃	C₂³	1	2	yes	—
81	C₂⁴×C₁₁₃	—	2	1	no	—
82	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
83	C₂×Q₈×C₁₁₃	—	2	4	no	—
84	C₂×Q₈×C₁₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₁₃	—	8	4	no	—
86	C₂×Q₈×C₁₁₃	C₂×D₄	1	4	yes	—
87	C₂×D₄×C₁₁₃	—	2	4	no	—
88	C₂×D₄×C₁₁₃	—	2	2	no	—
89	C₂×D₄×C₁₁₃	—	2	2	no	—
90	C₂×D₄×C₁₁₃	—	4	4	no	—
91	C₂×D₄×C₁₁₃	—	4	2	no	—
92	C₂×D₄×C₁₁₃	—	4	4	no	—
93	C₂×D₄×C₁₁₃	—	4	4	no	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₁₃	—	4	4	no	—
101	C₂²×C₄×C₁₁₃	—	4	4	no	—
102	C₂²×C₄×C₁₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
108	SD₁₆×C₁₁₃	—	4	8	no	—
109	C₂×C₈×C₁₁₃	—	2	4	no	—
110	C₄⋊C₄×C₁₁₃	—	2	4	no	—
111	C₄⋊C₄×C₁₁₃	—	2	8	no	—
112	C₄⋊C₄×C₁₁₃	—	2	2	no	—
113	C₄⋊C₄×C₁₁₃	—	2	4	no	—
114	C₄⋊C₄×C₁₁₃	—	2	2	no	—
115	C₄⋊C₄×C₁₁₃	—	2	2	no	—
116	C₄⋊C₄×C₁₁₃	—	2	2	no	—
117	C₄⋊C₄×C₁₁₃	—	2	4	no	—
118	C₄⋊C₄×C₁₁₃	—	2	2	no	—
119	C₄⋊C₄×C₁₁₃	—	4	4	no	—
120	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
121	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
122	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
123	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
124	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
125	C₂²⋊C₄×C₁₁₃	—	4	4	no	—
126	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
127	C₄²×C₁₁₃	—	2	4	no	—
128	C₄²×C₁₁₃	—	2	4	no	—
129	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	2	2	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	—	4	2	no	—
137	C₂³×C₁₁₃	—	4	1	no	—
138	C₂³×C₁₁₃	—	4	1	no	—
139	C₂³×C₁₁₃	—	4	2	no	—
140	C₂³×C₁₁₃	#137	1	4	yes	—
141	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₁₁₃	—	4	4	no	—
143	Q₈×C₁₁₃	—	4	4	no	—
144	Q₈×C₁₁₃	—	8	4	no	—
145	D₄×C₁₁₃	—	2	8	no	—
146	D₄×C₁₁₃	—	2	4	no	—
147	D₄×C₁₁₃	—	4	2	no	—
148	D₄×C₁₁₃	—	4	16	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	no	—
151	C₂×C₄×C₁₁₃	—	2	4	no	—
152	C₂×C₄×C₁₁₃	—	2	4	no	—
153	C₂×C₄×C₁₁₃	—	2	4	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	4	1	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	—	4	4	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	—	4	2	no	—
161	C₂×C₄×C₁₁₃	—	4	1	no	—
162	C₂×C₄×C₁₁₃	—	8	2	no	—
163	C₂×C₄×C₁₁₃	—	8	2	no	—
164	C₂×C₄×C₁₁₃	—	8	4	no	—
165	C₂×C₄×C₁₁₃	—	8	4	no	—
166	C₂×C₄×C₁₁₃	—	8	2	no	—
167	C₂×C₄×C₁₁₃	#120	1	2	yes	—
168	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
171	C₈×C₁₁₃	—	4	4	no	—
172	C₂²×C₁₁₃	—	2	1	no	—
173	C₂²×C₁₁₃	—	2	1	no	—
174	C₂²×C₁₁₃	—	2	4	no	—
175	C₂²×C₁₁₃	—	4	4	no	—
176	C₂²×C₁₁₃	—	4	4	no	—
177	C₂²×C₁₁₃	—	4	2	no	—
178	C₂²×C₁₁₃	—	4	2	no	—
179	C₂²×C₁₁₃	—	4	2	no	—
180	C₂²×C₁₁₃	—	8	2	no	—
181	C₂²×C₁₁₃	—	8	2	no	—
182	C₂²×C₁₁₃	—	8	1	no	—
183	C₂²×C₁₁₃	—	8	1	no	—
184	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
185	C₂²×C₁₁₃	C₂×#137	1	2	yes	—
186	C₄×C₁₁₃	—	2	2	no	—
187	C₄×C₁₁₃	—	2	1	no	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	4	4	no	—
190	C₄×C₁₁₃	—	4	2	no	—
191	C₄×C₁₁₃	—	4	4	no	—
192	C₄×C₁₁₃	—	4	4	no	—
193	C₄×C₁₁₃	—	8	1	no	—
194	C₄×C₁₁₃	#453	1	2	yes	—
195	#18180	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂×C₁₁₃	—	2	2	no	—
197	C₂×C₁₁₃	—	4	4	no	—
198	C₂×C₁₁₃	—	8	2	no	—
199	C₂×C₁₁₃	#3004	1	1	yes	characteristic
200	C₂×C₁₁₃	C₂×#453	1	1	yes	characteristic
201	C₂×C₁₁₃	#3025	1	1	yes	characteristic
202	#3501	C₂×C₁₁₃	1	1	yes	characteristic, complemented
203	#3110	C₂×C₁₁₃	1	2	yes	complemented
204	#2397	C₂×C₁₁₃	1	1	yes	characteristic
205	#1614	C₂×C₁₁₃	1	4	yes	complemented
206	#1596	C₂×C₁₁₃	1	4	yes	complemented
207	#1506	C₂×C₁₁₃	1	2	yes	complemented
208	#1466	C₂×C₁₁₃	1	1	yes	characteristic, complemented
209	C₁₁₃	#18180	1	1	yes	characteristic, direct product factor, Sylow
210	#554	—	2	2	no	—
211	#554	—	2	4	no	—
212	D₄×Q₈	—	2	2	no	—
213	#544	—	2	1	no	—
214	#543	C₂²×C₁₁₃	1	4	yes	—
215	#533	C₂²×C₁₁₃	1	2	yes	—
216	C₂×C₂²⋊Q₈	—	2	2	no	—
217	#518	—	2	1	no	—
218	C₂×C₄×D₄	—	2	2	no	—
219	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
221	#484	C₂²×C₁₁₃	1	4	yes	—
222	#474	—	2	2	no	—
223	#461	—	2	2	no	—
224	#450	C₂²×C₁₁₃	1	4	yes	—
225	#440	—	2	4	no	—
226	#432	C₂²×C₁₁₃	1	2	yes	—
227	#399	—	2	1	no	—
228	#399	C₂²×C₁₁₃	1	2	yes	—
229	#392	—	2	1	no	—
230	#392	C₂²×C₁₁₃	1	2	yes	—
231	#376	C₂²×C₁₁₃	1	1	yes	characteristic
232	#328	C₂²×C₁₁₃	1	8	yes	—
233	#323	C₂²×C₁₁₃	1	4	yes	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
240	C₂×SD₁₆	—	2	4	no	—
241	C₄⋊Q₈	—	2	4	no	—
242	C₄⋊Q₈	D₄×C₁₁₃	1	2	yes	complemented
243	C₄⋊Q₈	D₄×C₁₁₃	1	2	yes	complemented
244	#125	—	2	4	no	—
245	#125	—	2	2	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	4	no	—
248	C₂²⋊Q₈	—	2	8	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	8	no	—
252	C₂²⋊Q₈	C₂³×C₁₁₃	1	4	yes	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	D₄×C₁₁₃	1	4	yes	complemented
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	4	8	no	—
262	#117	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	—	2	4	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
275	#107	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	#103	—	2	4	no	—
278	#102	—	2	4	no	—
279	C₂²⋊C₈	C₂³×C₁₁₃	1	4	yes	—
280	#97	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	C₂³×C₁₁₃	1	2	yes	—
283	C₂⁴	—	2	1	no	—
284	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	8	4	no	—
288	C₂×Q₈	C₂×D₄×C₁₁₃	1	4	yes	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
310	SD₁₆	—	4	8	no	—
311	C₂×C₈	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
332	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	#137×C₁₁₃	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	8	4	no	—
347	D₄	—	2	8	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	16	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	4	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	#120×C₁₁₃	1	2	yes	—
370	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
371	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	1	no	—
386	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
387	C₂²	C₂×#137×C₁₁₃	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	1	no	—
396	C₄	#453×C₁₁₃	1	2	yes	—
397	C₂	—	2	2	no	—
398	C₂	—	4	4	no	—
399	C₂	—	8	2	no	—
400	C₂	C₁₁₃×#3004	1	1	yes	characteristic
401	C₂	C₂×#453×C₁₁₃	1	1	yes	characteristic
402	C₂	C₁₁₃×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
prime radical	C₁₁₃×#2397	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁₃×#3501	C₂	semidirect
2. C₁₁₃×#3110	C₂	semidirect
4. C₁₁₃×#1614	C₂	semidirect
5. C₁₁₃×#1596	C₂	semidirect
6. C₁₁₃×#1506	C₂	semidirect
7. C₁₁₃×#1466	C₂	semidirect
40. C₄⋊Q₈×C₁₁₃	D₄	semidirect
41. C₄⋊Q₈×C₁₁₃	D₄	semidirect
52. C₄×Q₈×C₁₁₃	D₄	semidirect
195. #18180	C₁₁₃	direct (N × H)
202. #3501	C₂×C₁₁₃	semidirect
203. #3110	C₂×C₁₁₃	semidirect
205. #1614	C₂×C₁₁₃	semidirect
206. #1596	C₂×C₁₁₃	semidirect
207. #1506	C₂×C₁₁₃	semidirect
208. #1466	C₂×C₁₁₃	semidirect
209. C₁₁₃	#18180	direct (N × H)
242. C₄⋊Q₈	D₄×C₁₁₃	semidirect
243. C₄⋊Q₈	D₄×C₁₁₃	semidirect
254. C₄×Q₈	D₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁₃×#3501	2
C₁₁₃×#3110	2
C₁₁₃×#2397	2
C₁₁₃×#1614	2
C₁₁₃×#1596	2
C₁₁₃×#1506	2
C₁₁₃×#1466	2
#18180	113

Subgroups — C113×#18180 #43286200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#18180 #43286200