Subgroups — C₁₁₃×#18358 #43286378

Order 28928.

1284 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁₃×#3213	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1601	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1595	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₁₁₃	—	2	1	no	—
9	#547×C₁₁₃	—	2	2	no	—
10	#546×C₁₁₃	—	2	4	no	—
11	D₄²×C₁₁₃	—	2	2	no	—
12	#537×C₁₁₃	—	2	1	no	—
13	#534×C₁₁₃	C₂²	1	4	yes	—
14	#532×C₁₁₃	C₂²	1	2	yes	—
15	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×#121×C₁₁₃	—	2	2	no	—
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	#496×C₁₁₃	—	2	2	no	—
19	#489×C₁₁₃	—	2	2	no	—
20	#463×C₁₁₃	—	2	4	no	—
21	#448×C₁₁₃	C₂²	1	4	yes	complemented
22	#447×C₁₁₃	C₂²	1	4	yes	complemented
23	#432×C₁₁₃	C₂²	1	2	yes	complemented
24	#397×C₁₁₃	—	2	1	no	—
25	#393×C₁₁₃	C₂²	1	2	yes	complemented
26	#392×C₁₁₃	—	2	1	no	—
27	#392×C₁₁₃	C₂²	1	2	yes	complemented
28	#386×C₁₁₃	—	2	2	no	—
29	#383×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
30	#327×C₁₁₃	C₂²	1	8	yes	complemented
31	#323×C₁₁₃	C₂²	1	4	yes	complemented
32	H(5,𝔽₂)×C₁₁₃	—	4	8	no	—
33	C₂×#41×C₁₁₃	—	2	4	no	—
34	C₂×#41×C₁₁₃	—	2	2	no	—
35	C₂²×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₁₃	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
43	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
44	C₂×D₈×C₁₁₃	—	2	4	no	—
45	C₄⋊Q₈×C₁₁₃	D₄	1	2	yes	complemented
46	#127×C₁₁₃	D₄	1	2	yes	complemented
47	#124×C₁₁₃	—	2	2	no	—
48	#124×C₁₁₃	—	2	2	no	—
49	#124×C₁₁₃	—	2	2	no	—
50	#123×C₁₁₃	—	2	8	no	—
51	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
52	#121×C₁₁₃	—	2	4	no	—
53	#121×C₁₁₃	—	2	4	no	—
54	#121×C₁₁₃	—	2	4	no	—
55	#121×C₁₁₃	—	2	2	no	—
56	#121×C₁₁₃	—	2	4	no	—
57	#121×C₁₁₃	C₂³	1	4	yes	—
58	#120×C₁₁₃	—	2	8	no	—
59	C₄×D₄×C₁₁₃	—	2	2	no	—
60	C₄×D₄×C₁₁₃	—	2	2	no	—
61	C₄×D₄×C₁₁₃	—	2	2	no	—
62	C₄×D₄×C₁₁₃	D₄	1	4	yes	complemented
63	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₁₁₃	—	2	2	no	—
73	#103×C₁₁₃	—	2	4	no	—
74	#102×C₁₁₃	—	2	4	no	—
75	C₂²⋊C₈×C₁₁₃	C₂³	1	4	yes	—
76	#97×C₁₁₃	—	2	2	no	—
77	#95×C₁₁₃	—	2	1	no	—
78	#95×C₁₁₃	—	2	1	no	—
79	#95×C₁₁₃	—	2	2	no	—
80	#95×C₁₁₃	C₂³	1	2	yes	—
81	C₂⁴×C₁₁₃	—	2	4	no	—
82	C₂⁴×C₁₁₃	—	2	1	no	—
83	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
84	#41×C₁₁₃	—	4	8	no	—
85	#41×C₁₁₃	—	4	16	no	—
86	C₂×Q₈×C₁₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₁₃	—	8	1	no	—
89	C₂×D₄×C₁₁₃	—	2	4	no	—
90	C₂×D₄×C₁₁₃	—	2	8	no	—
91	C₂×D₄×C₁₁₃	—	2	4	no	—
92	C₂×D₄×C₁₁₃	—	2	4	no	—
93	C₂×D₄×C₁₁₃	—	2	2	no	—
94	C₂×D₄×C₁₁₃	—	2	2	no	—
95	C₂×D₄×C₁₁₃	—	2	2	no	—
96	C₂×D₄×C₁₁₃	—	2	2	no	—
97	C₂×D₄×C₁₁₃	—	4	16	no	—
98	C₂×D₄×C₁₁₃	—	4	8	no	—
99	C₂×D₄×C₁₁₃	—	4	8	no	—
100	C₂×D₄×C₁₁₃	—	4	4	no	—
101	C₂×D₄×C₁₁₃	—	8	1	no	—
102	C₂×D₄×C₁₁₃	—	8	4	no	—
103	C₂×D₄×C₁₁₃	—	8	2	no	—
104	C₂×D₄×C₁₁₃	—	8	2	no	—
105	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₁₃	—	8	2	no	—
113	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
117	SD₁₆×C₁₁₃	—	8	4	no	—
118	D₈×C₁₁₃	—	8	4	no	—
119	C₂×C₈×C₁₁₃	—	2	4	no	—
120	C₄⋊C₄×C₁₁₃	—	2	4	no	—
121	C₄⋊C₄×C₁₁₃	—	2	2	no	—
122	C₄⋊C₄×C₁₁₃	—	2	2	no	—
123	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
125	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
126	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
127	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
128	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
129	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
130	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
131	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
132	C₂²⋊C₄×C₁₁₃	—	8	2	no	—
133	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
134	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	2	2	no	—
137	C₂³×C₁₁₃	—	2	4	no	—
138	C₂³×C₁₁₃	—	4	2	no	—
139	C₂³×C₁₁₃	—	4	2	no	—
140	C₂³×C₁₁₃	—	4	8	no	—
141	C₂³×C₁₁₃	—	4	1	no	—
142	C₂³×C₁₁₃	—	4	1	no	—
143	C₂³×C₁₁₃	—	4	2	no	—
144	C₂³×C₁₁₃	—	4	1	no	—
145	C₂³×C₁₁₃	—	4	2	no	—
146	C₂³×C₁₁₃	—	8	4	no	—
147	C₂³×C₁₁₃	—	8	4	no	—
148	C₂³×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
149	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₁₃	—	4	4	no	—
151	Q₈×C₁₁₃	—	4	4	no	—
152	D₄×C₁₁₃	—	2	8	no	—
153	D₄×C₁₁₃	—	4	4	no	—
154	D₄×C₁₁₃	—	4	4	no	—
155	D₄×C₁₁₃	—	4	4	no	—
156	D₄×C₁₁₃	—	4	4	no	—
157	D₄×C₁₁₃	—	4	16	no	—
158	D₄×C₁₁₃	—	4	8	no	—
159	D₄×C₁₁₃	—	8	4	no	—
160	D₄×C₁₁₃	—	8	8	no	—
161	C₂×C₄×C₁₁₃	—	2	2	no	—
162	C₂×C₄×C₁₁₃	—	2	2	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	4	1	no	—
165	C₂×C₄×C₁₁₃	—	4	1	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	4	8	no	—
168	C₂×C₄×C₁₁₃	—	4	8	no	—
169	C₂×C₄×C₁₁₃	—	4	2	no	—
170	C₂×C₄×C₁₁₃	—	4	2	no	—
171	C₂×C₄×C₁₁₃	—	4	2	no	—
172	C₂×C₄×C₁₁₃	—	4	2	no	—
173	C₂×C₄×C₁₁₃	—	4	1	no	—
174	C₂×C₄×C₁₁₃	—	4	2	no	—
175	C₂×C₄×C₁₁₃	—	8	2	no	—
176	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₁₁₃	#120	1	2	yes	—
179	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
180	C₈×C₁₁₃	—	4	4	no	—
181	C₂²×C₁₁₃	—	2	1	no	—
182	C₂²×C₁₁₃	—	2	1	no	—
183	C₂²×C₁₁₃	—	2	4	no	—
184	C₂²×C₁₁₃	—	4	4	no	—
185	C₂²×C₁₁₃	—	4	2	no	—
186	C₂²×C₁₁₃	—	4	2	no	—
187	C₂²×C₁₁₃	—	4	4	no	—
188	C₂²×C₁₁₃	—	4	4	no	—
189	C₂²×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	8	2	no	—
191	C₂²×C₁₁₃	—	8	2	no	—
192	C₂²×C₁₁₃	—	8	2	no	—
193	C₂²×C₁₁₃	—	8	1	no	—
194	C₂²×C₁₁₃	—	8	1	no	—
195	C₂²×C₁₁₃	—	8	1	no	—
196	C₂²×C₁₁₃	—	16	8	no	—
197	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
198	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	—	2	1	no	—
201	C₄×C₁₁₃	—	2	1	no	—
202	C₄×C₁₁₃	—	2	2	no	—
203	C₄×C₁₁₃	—	4	4	no	—
204	C₄×C₁₁₃	—	4	2	no	—
205	C₄×C₁₁₃	—	8	2	no	—
206	C₄×C₁₁₃	—	8	1	no	—
207	#18358	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₁₁₃	—	2	2	no	—
209	C₂×C₁₁₃	—	4	4	no	—
210	C₂×C₁₁₃	—	8	4	no	—
211	C₂×C₁₁₃	—	16	1	no	—
212	C₂×C₁₁₃	#3003	1	1	yes	characteristic
213	C₂×C₁₁₃	#3019	1	1	yes	characteristic
214	C₂×C₁₁₃	#3027	1	1	yes	characteristic
215	#3496	C₂×C₁₁₃	1	1	yes	characteristic, complemented
216	#3213	C₂×C₁₁₃	1	2	yes	complemented
217	#2631	C₂×C₁₁₃	1	1	yes	characteristic, complemented
218	#1601	C₂×C₁₁₃	1	4	yes	complemented
219	#1595	C₂×C₁₁₃	1	4	yes	complemented
220	#1514	C₂×C₁₁₃	1	2	yes	complemented
221	#1466	C₂×C₁₁₃	1	1	yes	characteristic, complemented
222	C₁₁₃	#18358	1	1	yes	characteristic, direct product factor, Sylow
223	C₂×H(5,𝔽₂)	—	2	1	no	—
224	#547	—	2	2	no	—
225	#546	—	2	4	no	—
226	D₄²	—	2	2	no	—
227	#537	—	2	1	no	—
228	#534	C₂²×C₁₁₃	1	4	yes	—
229	#532	C₂²×C₁₁₃	1	2	yes	—
230	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
231	C₂×#121	—	2	2	no	—
232	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
233	#496	—	2	2	no	—
234	#489	—	2	2	no	—
235	#463	—	2	4	no	—
236	#448	C₂²×C₁₁₃	1	4	yes	complemented
237	#447	C₂²×C₁₁₃	1	4	yes	complemented
238	#432	C₂²×C₁₁₃	1	2	yes	complemented
239	#397	—	2	1	no	—
240	#393	C₂²×C₁₁₃	1	2	yes	complemented
241	#392	—	2	1	no	—
242	#392	C₂²×C₁₁₃	1	2	yes	complemented
243	#386	—	2	2	no	—
244	#383	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
245	#327	C₂²×C₁₁₃	1	8	yes	complemented
246	#323	C₂²×C₁₁₃	1	4	yes	complemented
247	H(5,𝔽₂)	—	4	8	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	2	no	—
250	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
251	C₂²×D₄	—	2	4	no	—
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
256	C₂²×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
258	C₂×SD₁₆	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₄⋊Q₈	D₄×C₁₁₃	1	2	yes	complemented
261	#127	D₄×C₁₁₃	1	2	yes	complemented
262	#124	—	2	2	no	—
263	#124	—	2	2	no	—
264	#124	—	2	2	no	—
265	#123	—	2	8	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	#121	—	2	4	no	—
268	#121	—	2	4	no	—
269	#121	—	2	4	no	—
270	#121	—	2	2	no	—
271	#121	—	2	4	no	—
272	#121	C₂³×C₁₁₃	1	4	yes	—
273	#120	—	2	8	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	D₄×C₁₁₃	1	4	yes	complemented
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
287	C₄⋊C₈	—	2	2	no	—
288	#103	—	2	4	no	—
289	#102	—	2	4	no	—
290	C₂²⋊C₈	C₂³×C₁₁₃	1	4	yes	—
291	#97	—	2	2	no	—
292	#95	—	2	1	no	—
293	#95	—	2	1	no	—
294	#95	—	2	2	no	—
295	#95	C₂³×C₁₁₃	1	2	yes	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
299	#41	—	4	8	no	—
300	#41	—	4	16	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	8	1	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	16	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	4	no	—
316	C₂×D₄	—	8	1	no	—
317	C₂×D₄	—	8	4	no	—
318	C₂×D₄	—	8	2	no	—
319	C₂×D₄	—	8	2	no	—
320	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	8	2	no	—
328	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
332	SD₁₆	—	8	4	no	—
333	D₈	—	8	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	8	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
349	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	4	no	—
362	C₂³	—	8	4	no	—
363	C₂³	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
364	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
365	Q₈	—	4	4	no	—
366	Q₈	—	4	4	no	—
367	D₄	—	2	8	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	16	no	—
373	D₄	—	4	8	no	—
374	D₄	—	8	4	no	—
375	D₄	—	8	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
392	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
393	C₂×C₄	#120×C₁₁₃	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
395	C₈	—	4	4	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	16	8	no	—
412	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
413	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₂	—	2	2	no	—
423	C₂	—	4	4	no	—
424	C₂	—	8	4	no	—
425	C₂	—	16	1	no	—
426	C₂	C₁₁₃×#3003	1	1	yes	characteristic
427	C₂	C₁₁₃×#3019	1	1	yes	characteristic
428	C₂	C₁₁₃×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
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×#3496	C₂	semidirect
2. C₁₁₃×#3213	C₂	semidirect
3. C₁₁₃×#2631	C₂	semidirect
4. C₁₁₃×#1601	C₂	semidirect
5. C₁₁₃×#1595	C₂	semidirect
6. C₁₁₃×#1514	C₂	semidirect
7. C₁₁₃×#1466	C₂	semidirect
15. C₂×#124×C₁₁₃	C₂²	semidirect
21. #448×C₁₁₃	C₂²	semidirect
22. #447×C₁₁₃	C₂²	semidirect
23. #432×C₁₁₃	C₂²	semidirect
25. #393×C₁₁₃	C₂²	semidirect
27. #392×C₁₁₃	C₂²	semidirect
29. #383×C₁₁₃	C₂²	semidirect
30. #327×C₁₁₃	C₂²	semidirect
31. #323×C₁₁₃	C₂²	semidirect
45. C₄⋊Q₈×C₁₁₃	D₄	semidirect
46. #127×C₁₁₃	D₄	semidirect
62. C₄×D₄×C₁₁₃	D₄	semidirect
207. #18358	C₁₁₃	direct (N × H)
215. #3496	C₂×C₁₁₃	semidirect
216. #3213	C₂×C₁₁₃	semidirect
217. #2631	C₂×C₁₁₃	semidirect
218. #1601	C₂×C₁₁₃	semidirect
219. #1595	C₂×C₁₁₃	semidirect
220. #1514	C₂×C₁₁₃	semidirect
221. #1466	C₂×C₁₁₃	semidirect
222. C₁₁₃	#18358	direct (N × H)
230. C₂×#124	C₂²×C₁₁₃	semidirect
236. #448	C₂²×C₁₁₃	semidirect
237. #447	C₂²×C₁₁₃	semidirect
238. #432	C₂²×C₁₁₃	semidirect
240. #393	C₂²×C₁₁₃	semidirect
242. #392	C₂²×C₁₁₃	semidirect
244. #383	C₂²×C₁₁₃	semidirect
245. #327	C₂²×C₁₁₃	semidirect
246. #323	C₂²×C₁₁₃	semidirect
260. C₄⋊Q₈	D₄×C₁₁₃	semidirect
261. #127	D₄×C₁₁₃	semidirect
277. C₄×D₄	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×#3496	2
C₁₁₃×#3213	2
C₁₁₃×#2631	2
C₁₁₃×#1601	2
C₁₁₃×#1595	2
C₁₁₃×#1514	2
C₁₁₃×#1466	2
#18358	113

Subgroups — C113×#18358 #43286378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#18358 #43286378