Subgroups — C₁₁₃×#22234 #43290254

Order 28928.

714 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁₃×#1962	C₂	1	1	yes	maximal, characteristic
6	C₁₁₃×#1929	C₂	1	4	yes	maximal, complemented
7	C₁₁₃×#1866	C₂	1	4	yes	maximal, complemented
8	C₁₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₁₁₃	C₂²	1	2	yes	—
11	#533×C₁₁₃	C₂²	1	1	yes	characteristic
12	#532×C₁₁₃	C₂²	1	1	yes	characteristic
13	#488×C₁₁₃	C₄	1	4	yes	complemented
14	#487×C₁₁₃	C₄	1	1	yes	characteristic, complemented
15	#487×C₁₁₃	C₄	1	1	yes	characteristic, complemented
16	#486×C₁₁₃	C₄	1	1	yes	characteristic, complemented
17	#486×C₁₁₃	C₄	1	1	yes	characteristic, complemented
18	#446×C₁₁₃	—	2	1	no	—
19	#446×C₁₁₃	—	2	1	no	—
20	C₈×Q₈×C₁₁₃	—	2	1	no	—
21	C₈×Q₈×C₁₁₃	—	2	1	no	—
22	#436×C₁₁₃	—	2	1	no	—
23	#436×C₁₁₃	—	2	1	no	—
24	C₈×D₄×C₁₁₃	—	2	1	no	—
25	C₈×D₄×C₁₁₃	—	2	1	no	—
26	C₂×#108×C₁₁₃	C₂²	1	4	yes	—
27	#424×C₁₁₃	C₂²	1	2	yes	—
28	#423×C₁₁₃	C₂²	1	1	yes	characteristic
29	#423×C₁₁₃	C₂²	1	1	yes	characteristic
30	C₂×#104×C₁₁₃	C₂²	1	4	yes	—
31	#416×C₁₁₃	C₂²	1	4	yes	—
32	#408×C₁₁₃	C₂²	1	2	yes	—
33	#405×C₁₁₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
36	C₄³×C₁₁₃	C₂²	1	1	yes	characteristic
37	#339×C₁₁₃	C₂²	1	4	yes	—
38	#336×C₁₁₃	C₂²	1	2	yes	—
39	#336×C₁₁₃	C₂²	1	2	yes	—
40	C₂×#41×C₁₁₃	C₂³	1	2	yes	—
41	#131×C₁₁₃	—	4	4	no	—
42	C₂×M₁₆×C₁₁₃	—	2	2	no	—
43	C₂×M₁₆×C₁₁₃	C₂³	1	2	yes	—
44	C₂×M₁₆×C₁₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
52	#127×C₁₁₃	C₂×C₄	1	1	yes	characteristic
53	#125×C₁₁₃	C₂×C₄	1	2	yes	—
54	#124×C₁₁₃	C₂×C₄	1	2	yes	—
55	C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
56	C₂²⋊Q₈×C₁₁₃	—	2	1	no	—
57	#121×C₁₁₃	—	2	1	no	—
58	#121×C₁₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₁₃	—	2	1	no	—
60	C₄×Q₈×C₁₁₃	—	2	1	no	—
61	C₄×D₄×C₁₁₃	—	2	1	no	—
62	C₄×D₄×C₁₁₃	—	2	1	no	—
63	#117×C₁₁₃	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
67	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
68	#108×C₁₁₃	—	4	4	no	—
69	C₄⋊C₈×C₁₁₃	—	2	2	no	—
70	C₄⋊C₈×C₁₁₃	—	2	2	no	—
71	C₄⋊C₈×C₁₁₃	—	2	1	no	—
72	C₄⋊C₈×C₁₁₃	—	2	1	no	—
73	C₄⋊C₈×C₁₁₃	—	2	1	no	—
74	C₄⋊C₈×C₁₁₃	—	2	1	no	—
75	#104×C₁₁₃	—	4	4	no	—
76	#103×C₁₁₃	C₂×C₄	1	4	yes	—
77	#103×C₁₁₃	C₂×C₄	1	4	yes	—
78	#102×C₁₁₃	C₂×C₄	1	4	yes	—
79	#102×C₁₁₃	C₂×C₄	1	4	yes	—
80	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
81	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
82	#97×C₁₁₃	—	2	2	no	—
83	C₄×C₈×C₁₁₃	—	2	2	no	—
84	C₄×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
91	#41×C₁₁₃	—	2	4	no	—
92	#41×C₁₁₃	—	2	4	no	—
93	C₂×Q₈×C₁₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₁₃	—	2	2	no	—
97	C₂×D₄×C₁₁₃	—	2	1	no	—
98	C₂×D₄×C₁₁₃	—	2	1	no	—
99	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₁₁₃	—	2	4	no	—
106	M₁₆×C₁₁₃	—	2	4	no	—
107	M₁₆×C₁₁₃	—	4	4	no	—
108	C₂×C₈×C₁₁₃	—	2	2	no	—
109	C₂×C₈×C₁₁₃	—	2	2	no	—
110	C₂×C₈×C₁₁₃	—	2	2	no	—
111	C₂×C₈×C₁₁₃	—	2	2	no	—
112	C₂×C₈×C₁₁₃	—	2	2	no	—
113	C₂×C₈×C₁₁₃	—	2	2	no	—
114	C₂×C₈×C₁₁₃	—	4	4	no	—
115	C₂×C₈×C₁₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₁₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁₃	C₂×D₄	1	1	yes	characteristic
121	C₄⋊C₄×C₁₁₃	—	2	1	no	—
122	C₄⋊C₄×C₁₁₃	—	2	1	no	—
123	C₄⋊C₄×C₁₁₃	—	2	2	no	—
124	C₄⋊C₄×C₁₁₃	—	2	2	no	—
125	C₄⋊C₄×C₁₁₃	—	2	1	no	—
126	C₄⋊C₄×C₁₁₃	—	2	1	no	—
127	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
130	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
131	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
132	C₄²×C₁₁₃	—	2	4	no	—
133	C₄²×C₁₁₃	—	2	2	no	—
134	C₄²×C₁₁₃	—	2	2	no	—
135	C₄²×C₁₁₃	—	2	2	no	—
136	C₄²×C₁₁₃	—	4	2	no	—
137	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₁₁₃	—	2	2	no	—
142	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
143	Q₈×C₁₁₃	—	2	4	no	—
144	Q₈×C₁₁₃	—	4	2	no	—
145	Q₈×C₁₁₃	—	4	2	no	—
146	D₄×C₁₁₃	—	2	4	no	—
147	D₄×C₁₁₃	—	4	4	no	—
148	D₄×C₁₁₃	—	4	2	no	—
149	D₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	4	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	2	2	no	—
156	C₂×C₄×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
167	C₂×C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
168	C₈×C₁₁₃	—	2	2	no	—
169	C₈×C₁₁₃	—	2	2	no	—
170	C₈×C₁₁₃	—	2	1	no	—
171	C₈×C₁₁₃	—	2	1	no	—
172	C₈×C₁₁₃	—	2	1	no	—
173	C₈×C₁₁₃	—	2	1	no	—
174	C₈×C₁₁₃	—	4	2	no	—
175	C₈×C₁₁₃	—	4	2	no	—
176	C₂²×C₁₁₃	—	2	1	no	—
177	C₂²×C₁₁₃	—	2	1	no	—
178	C₂²×C₁₁₃	—	4	2	no	—
179	C₂²×C₁₁₃	—	4	2	no	—
180	C₂²×C₁₁₃	—	4	2	no	—
181	C₂²×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₁₁₃	#542	1	2	yes	—
183	C₄×C₁₁₃	—	2	1	no	—
184	C₄×C₁₁₃	—	2	1	no	—
185	C₄×C₁₁₃	—	4	4	no	—
186	C₄×C₁₁₃	—	4	2	no	—
187	C₄×C₁₁₃	—	4	2	no	—
188	C₄×C₁₁₃	—	4	2	no	—
189	C₄×C₁₁₃	#443	1	2	yes	—
190	C₄×C₁₁₃	#444	1	2	yes	—
191	C₄×C₁₁₃	#520	1	2	yes	—
192	C₄×C₁₁₃	#535	1	1	yes	characteristic
193	C₄×C₁₁₃	#536	1	1	yes	characteristic
194	#22234	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₁₁₃	—	2	2	no	—
196	C₂×C₁₁₃	—	8	2	no	—
197	C₂×C₁₁₃	#2326	1	1	yes	characteristic
198	C₂×C₁₁₃	C₂×#443	1	1	yes	characteristic
199	C₂×C₁₁₃	C₂×#444	1	1	yes	characteristic
200	#3131	C₂×C₁₁₃	1	1	yes	characteristic
201	#2960	C₂×C₁₁₃	1	1	yes	characteristic, complemented
202	#2931	C₂×C₁₁₃	1	1	yes	characteristic
203	#1994	C₂×C₁₁₃	1	1	yes	characteristic, complemented
204	#1962	C₂×C₁₁₃	1	1	yes	characteristic
205	#1929	C₂×C₁₁₃	1	4	yes	complemented
206	#1866	C₂×C₁₁₃	1	4	yes	complemented
207	#1848	C₂×C₁₁₃	1	1	yes	characteristic, complemented
208	#1744	C₂×C₁₁₃	1	1	yes	characteristic, complemented
209	C₁₁₃	#22234	1	1	yes	characteristic, direct product factor, Sylow
210	C₂×#131	C₂²×C₁₁₃	1	2	yes	—
211	#533	C₂²×C₁₁₃	1	1	yes	characteristic
212	#532	C₂²×C₁₁₃	1	1	yes	characteristic
213	#488	C₄×C₁₁₃	1	4	yes	complemented
214	#487	C₄×C₁₁₃	1	1	yes	characteristic, complemented
215	#487	C₄×C₁₁₃	1	1	yes	characteristic, complemented
216	#486	C₄×C₁₁₃	1	1	yes	characteristic, complemented
217	#486	C₄×C₁₁₃	1	1	yes	characteristic, complemented
218	#446	—	2	1	no	—
219	#446	—	2	1	no	—
220	C₈×Q₈	—	2	1	no	—
221	C₈×Q₈	—	2	1	no	—
222	#436	—	2	1	no	—
223	#436	—	2	1	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	C₂×#108	C₂²×C₁₁₃	1	4	yes	—
227	#424	C₂²×C₁₁₃	1	2	yes	—
228	#423	C₂²×C₁₁₃	1	1	yes	characteristic
229	#423	C₂²×C₁₁₃	1	1	yes	characteristic
230	C₂×#104	C₂²×C₁₁₃	1	4	yes	—
231	#416	C₂²×C₁₁₃	1	4	yes	—
232	#408	C₂²×C₁₁₃	1	2	yes	—
233	#405	C₂²×C₁₁₃	1	2	yes	—
234	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
236	C₄³	C₂²×C₁₁₃	1	1	yes	characteristic
237	#339	C₂²×C₁₁₃	1	4	yes	—
238	#336	C₂²×C₁₁₃	1	2	yes	—
239	#336	C₂²×C₁₁₃	1	2	yes	—
240	C₂×#41	C₂³×C₁₁₃	1	2	yes	—
241	#131	—	4	4	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	C₂³×C₁₁₃	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₁₃	1	2	yes	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₁₃	1	1	yes	characteristic
249	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
250	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
251	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
252	#127	C₂×C₄×C₁₁₃	1	1	yes	characteristic
253	#125	C₂×C₄×C₁₁₃	1	2	yes	—
254	#124	C₂×C₄×C₁₁₃	1	2	yes	—
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	—	2	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	#117	C₂³×C₁₁₃	1	2	yes	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
267	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
268	#108	—	4	4	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	#104	—	4	4	no	—
276	#103	C₂×C₄×C₁₁₃	1	4	yes	—
277	#103	C₂×C₄×C₁₁₃	1	4	yes	—
278	#102	C₂×C₄×C₁₁₃	1	4	yes	—
279	#102	C₂×C₄×C₁₁₃	1	4	yes	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
285	C₄×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
286	C₄×C₈	C₂×C₄×C₁₁₃	1	2	yes	—
287	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
288	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
289	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
290	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
305	M₁₆	—	2	4	no	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	4	no	—
315	C₂×C₈	C₂²×C₄×C₁₁₃	1	2	yes	—
316	C₂×C₈	C₂²×C₄×C₁₁₃	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₁₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
328	C₄⋊C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	4	2	no	—
337	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
338	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₁₁₃	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
366	C₂×C₄	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
367	C₂×C₄	2₋¹⁺⁴×C₁₁₃	1	2	yes	—
368	C₈	—	2	2	no	—
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
382	C₂²	#542×C₁₁₃	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	#443×C₁₁₃	1	2	yes	—
390	C₄	#444×C₁₁₃	1	2	yes	—
391	C₄	#520×C₁₁₃	1	2	yes	—
392	C₄	#535×C₁₁₃	1	1	yes	characteristic
393	C₄	#536×C₁₁₃	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	C₁₁₃×#2326	1	1	yes	characteristic
397	C₂	C₂×#443×C₁₁₃	1	1	yes	characteristic
398	C₂	C₂×#444×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	C₂×C₄×D₄
prime radical	#532×C₁₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂×C₄×C₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#2960	C₂	semidirect
4. C₁₁₃×#1994	C₂	semidirect
6. C₁₁₃×#1929	C₂	semidirect
7. C₁₁₃×#1866	C₂	semidirect
8. C₁₁₃×#1848	C₂	semidirect
9. C₁₁₃×#1744	C₂	semidirect
13. #488×C₁₁₃	C₄	semidirect
14. #487×C₁₁₃	C₄	semidirect
15. #487×C₁₁₃	C₄	semidirect
16. #486×C₁₁₃	C₄	semidirect
17. #486×C₁₁₃	C₄	semidirect
194. #22234	C₁₁₃	direct (N × H)
201. #2960	C₂×C₁₁₃	semidirect
203. #1994	C₂×C₁₁₃	semidirect
205. #1929	C₂×C₁₁₃	semidirect
206. #1866	C₂×C₁₁₃	semidirect
207. #1848	C₂×C₁₁₃	semidirect
208. #1744	C₂×C₁₁₃	semidirect
209. C₁₁₃	#22234	direct (N × H)
213. #488	C₄×C₁₁₃	semidirect
214. #487	C₄×C₁₁₃	semidirect
215. #487	C₄×C₁₁₃	semidirect
216. #486	C₄×C₁₁₃	semidirect
217. #486	C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁₃×#3131	2
C₁₁₃×#2960	2
C₁₁₃×#2931	2
C₁₁₃×#1994	2
C₁₁₃×#1962	2
C₁₁₃×#1929	2
C₁₁₃×#1866	2
C₁₁₃×#1848	2
C₁₁₃×#1744	2
#22234	113

Subgroups — C113×#22234 #43290254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#22234 #43290254