Subgroups — C₁₁₃×#18179 #43286199

Order 28928.

1250 conjugacy classes of subgroups.

The subgroup lattice has 406 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
2	C₁₁₃×#3112	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#2398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1607	C₂	1	4	yes	maximal, complemented
5	C₁₁₃×#1601	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1505	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×#121×C₁₁₃	—	2	2	no	—
16	C₂×C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
18	#480×C₁₁₃	C₂²	1	4	yes	complemented
19	#477×C₁₁₃	—	2	2	no	—
20	#460×C₁₁₃	—	2	2	no	—
21	#448×C₁₁₃	C₂²	1	4	yes	complemented
22	#440×C₁₁₃	—	2	4	no	—
23	#432×C₁₁₃	C₂²	1	2	yes	complemented
24	#400×C₁₁₃	—	2	1	no	—
25	#397×C₁₁₃	C₂²	1	2	yes	complemented
26	#394×C₁₁₃	—	2	1	no	—
27	#393×C₁₁₃	C₂²	1	2	yes	complemented
28	C₄×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
29	#376×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	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁₃	D₄	1	2	yes	—
41	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
42	C₄⋊Q₈×C₁₁₃	D₄	1	2	yes	—
43	#127×C₁₁₃	D₄	1	2	yes	—
44	#124×C₁₁₃	—	2	2	no	—
45	#123×C₁₁₃	—	2	8	no	—
46	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
47	#121×C₁₁₃	—	2	4	no	—
48	#121×C₁₁₃	—	2	4	no	—
49	#121×C₁₁₃	—	2	4	no	—
50	#121×C₁₁₃	—	2	2	no	—
51	#121×C₁₁₃	—	2	4	no	—
52	#121×C₁₁₃	C₂³	1	4	yes	—
53	#120×C₁₁₃	—	2	8	no	—
54	C₄×Q₈×C₁₁₃	—	2	2	no	—
55	C₄×Q₈×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	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₁₃	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
71	#107×C₁₁₃	—	2	4	no	—
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	2	no	—
79	#95×C₁₁₃	—	2	2	no	—
80	#95×C₁₁₃	C₂³	1	2	yes	—
81	C₂⁴×C₁₁₃	—	2	4	no	—
82	C₂⁴×C₁₁₃	C₂×D₄	1	2	yes	—
83	#41×C₁₁₃	—	4	8	no	—
84	#41×C₁₁₃	—	4	16	no	—
85	C₂×Q₈×C₁₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₁₃	—	4	2	no	—
88	C₂×D₄×C₁₁₃	—	2	4	no	—
89	C₂×D₄×C₁₁₃	—	2	8	no	—
90	C₂×D₄×C₁₁₃	—	2	4	no	—
91	C₂×D₄×C₁₁₃	—	2	4	no	—
92	C₂×D₄×C₁₁₃	—	2	2	no	—
93	C₂×D₄×C₁₁₃	—	2	2	no	—
94	C₂×D₄×C₁₁₃	—	2	2	no	—
95	C₂×D₄×C₁₁₃	—	4	16	no	—
96	C₂×D₄×C₁₁₃	—	4	8	no	—
97	C₂×D₄×C₁₁₃	—	4	8	no	—
98	C₂×D₄×C₁₁₃	—	8	4	no	—
99	C₂×D₄×C₁₁₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₁₁₃	—	4	8	no	—
113	C₂×C₈×C₁₁₃	—	2	4	no	—
114	C₄⋊C₄×C₁₁₃	—	2	4	no	—
115	C₄⋊C₄×C₁₁₃	—	2	2	no	—
116	C₄⋊C₄×C₁₁₃	—	2	2	no	—
117	C₄⋊C₄×C₁₁₃	—	2	2	no	—
118	C₄⋊C₄×C₁₁₃	—	4	2	no	—
119	C₄⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
120	C₂²⋊C₄×C₁₁₃	—	2	8	no	—
121	C₂²⋊C₄×C₁₁₃	—	2	4	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	C₄²×C₁₁₃	—	4	2	no	—
127	C₄²×C₁₁₃	—	4	1	no	—
128	C₄²×C₁₁₃	—	4	1	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	4	no	—
134	C₂³×C₁₁₃	—	4	2	no	—
135	C₂³×C₁₁₃	—	4	2	no	—
136	C₂³×C₁₁₃	—	4	8	no	—
137	C₂³×C₁₁₃	—	8	4	no	—
138	C₂³×C₁₁₃	—	8	4	no	—
139	C₂³×C₁₁₃	AGL(1,ℤ/8)	1	4	yes	—
140	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₁₃	—	2	4	no	—
142	Q₈×C₁₁₃	—	4	2	no	—
143	Q₈×C₁₁₃	—	4	4	no	—
144	D₄×C₁₁₃	—	2	8	no	—
145	D₄×C₁₁₃	—	4	4	no	—
146	D₄×C₁₁₃	—	4	4	no	—
147	D₄×C₁₁₃	—	4	16	no	—
148	D₄×C₁₁₃	—	4	8	no	—
149	D₄×C₁₁₃	—	4	4	no	—
150	D₄×C₁₁₃	—	8	4	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	2	4	no	—
156	C₂×C₄×C₁₁₃	—	4	1	no	—
157	C₂×C₄×C₁₁₃	—	4	8	no	—
158	C₂×C₄×C₁₁₃	—	4	8	no	—
159	C₂×C₄×C₁₁₃	—	4	1	no	—
160	C₂×C₄×C₁₁₃	—	4	1	no	—
161	C₂×C₄×C₁₁₃	—	4	4	no	—
162	C₂×C₄×C₁₁₃	—	4	2	no	—
163	C₂×C₄×C₁₁₃	—	4	2	no	—
164	C₂×C₄×C₁₁₃	—	4	2	no	—
165	C₂×C₄×C₁₁₃	—	4	1	no	—
166	C₂×C₄×C₁₁₃	—	4	2	no	—
167	C₂×C₄×C₁₁₃	—	4	2	no	—
168	C₂×C₄×C₁₁₃	—	8	2	no	—
169	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	#120	1	2	yes	—
171	C₂×C₄×C₁₁₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
173	C₈×C₁₁₃	—	4	4	no	—
174	C₂²×C₁₁₃	—	2	1	no	—
175	C₂²×C₁₁₃	—	2	1	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	—	4	4	no	—
178	C₂²×C₁₁₃	—	4	2	no	—
179	C₂²×C₁₁₃	—	4	2	no	—
180	C₂²×C₁₁₃	—	4	4	no	—
181	C₂²×C₁₁₃	—	4	4	no	—
182	C₂²×C₁₁₃	—	4	4	no	—
183	C₂²×C₁₁₃	—	8	2	no	—
184	C₂²×C₁₁₃	—	16	8	no	—
185	C₂²×C₁₁₃	C₂×#120	1	1	yes	characteristic
186	C₂²×C₁₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
187	C₄×C₁₁₃	—	2	2	no	—
188	C₄×C₁₁₃	—	2	1	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	4	4	no	—
191	C₄×C₁₁₃	—	4	2	no	—
192	C₄×C₁₁₃	—	4	2	no	—
193	C₄×C₁₁₃	—	8	2	no	—
194	C₄×C₁₁₃	—	8	1	no	—
195	C₄×C₁₁₃	#455	1	2	yes	—
196	#18179	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₁₁₃	—	2	2	no	—
198	C₂×C₁₁₃	—	4	4	no	—
199	C₂×C₁₁₃	—	8	4	no	—
200	C₂×C₁₁₃	#3003	1	1	yes	characteristic
201	C₂×C₁₁₃	C₂×#455	1	1	yes	characteristic
202	C₂×C₁₁₃	#3025	1	1	yes	characteristic
203	#3496	C₂×C₁₁₃	1	1	yes	characteristic
204	#3112	C₂×C₁₁₃	1	2	yes	complemented
205	#2398	C₂×C₁₁₃	1	1	yes	characteristic, complemented
206	#1607	C₂×C₁₁₃	1	4	yes	complemented
207	#1601	C₂×C₁₁₃	1	4	yes	complemented
208	#1505	C₂×C₁₁₃	1	2	yes	complemented
209	#1466	C₂×C₁₁₃	1	1	yes	characteristic, complemented
210	C₁₁₃	#18179	1	1	yes	characteristic, direct product factor, Sylow
211	C₂×H(5,𝔽₂)	—	2	1	no	—
212	#547	—	2	2	no	—
213	#546	—	2	4	no	—
214	D₄²	—	2	2	no	—
215	#537	—	2	1	no	—
216	#534	C₂²×C₁₁₃	1	4	yes	—
217	#532	C₂²×C₁₁₃	1	2	yes	—
218	C₂×#121	—	2	2	no	—
219	C₂×C₄×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
220	C₂×C₄×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
221	#480	C₂²×C₁₁₃	1	4	yes	complemented
222	#477	—	2	2	no	—
223	#460	—	2	2	no	—
224	#448	C₂²×C₁₁₃	1	4	yes	complemented
225	#440	—	2	4	no	—
226	#432	C₂²×C₁₁₃	1	2	yes	complemented
227	#400	—	2	1	no	—
228	#397	C₂²×C₁₁₃	1	2	yes	complemented
229	#394	—	2	1	no	—
230	#393	C₂²×C₁₁₃	1	2	yes	complemented
231	C₄×C₂²⋊C₄	—	2	2	no	—
232	#376	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
233	#327	C₂²×C₁₁₃	1	8	yes	complemented
234	#323	C₂²×C₁₁₃	1	4	yes	complemented
235	H(5,𝔽₂)	—	4	8	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	2	no	—
238	C₂²×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	D₄×C₁₁₃	1	1	yes	characteristic
243	C₂³×C₄	D₄×C₁₁₃	1	2	yes	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₄⋊Q₈	D₄×C₁₁₃	1	2	yes	—
246	#127	D₄×C₁₁₃	1	2	yes	—
247	#124	—	2	2	no	—
248	#123	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	4	no	—
252	#121	—	2	4	no	—
253	#121	—	2	2	no	—
254	#121	—	2	4	no	—
255	#121	C₂³×C₁₁₃	1	4	yes	—
256	#120	—	2	8	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	D₄×C₁₁₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₁₁₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
274	#107	—	2	4	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#103	—	2	4	no	—
277	#102	—	2	4	no	—
278	C₂²⋊C₈	C₂³×C₁₁₃	1	4	yes	—
279	#97	—	2	2	no	—
280	#95	—	2	1	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	C₂³×C₁₁₃	1	2	yes	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	C₂×D₄×C₁₁₃	1	2	yes	—
286	#41	—	4	8	no	—
287	#41	—	4	16	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	8	4	no	—
302	C₂×D₄	C₂×D₄×C₁₁₃	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
315	SD₁₆	—	4	8	no	—
316	C₂×C₈	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	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	—	2	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₄²	—	4	2	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
333	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	8	no	—
340	C₂³	—	8	4	no	—
341	C₂³	—	8	4	no	—
342	C₂³	AGL(1,ℤ/8)×C₁₁₃	1	4	yes	—
343	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	4	no	—
347	D₄	—	2	8	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	16	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	4	no	—
353	D₄	—	8	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
373	C₂×C₄	#120×C₁₁₃	1	2	yes	—
374	C₂×C₄	#120×C₁₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
376	C₈	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	16	8	no	—
388	C₂²	C₂×#120×C₁₁₃	1	1	yes	characteristic
389	C₂²	C₂×AGL(1,ℤ/8)×C₁₁₃	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	#455×C₁₁₃	1	2	yes	—
399	C₂	—	2	2	no	—
400	C₂	—	4	4	no	—
401	C₂	—	8	4	no	—
402	C₂	C₁₁₃×#3003	1	1	yes	characteristic
403	C₂	C₂×#455×C₁₁₃	1	1	yes	characteristic
404	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×#3496	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
2. C₁₁₃×#3112	C₂	semidirect
3. C₁₁₃×#2398	C₂	semidirect
4. C₁₁₃×#1607	C₂	semidirect
5. C₁₁₃×#1601	C₂	semidirect
6. C₁₁₃×#1505	C₂	semidirect
7. C₁₁₃×#1466	C₂	semidirect
16. C₂×C₄×Q₈×C₁₁₃	C₂²	semidirect
18. #480×C₁₁₃	C₂²	semidirect
21. #448×C₁₁₃	C₂²	semidirect
23. #432×C₁₁₃	C₂²	semidirect
25. #397×C₁₁₃	C₂²	semidirect
27. #393×C₁₁₃	C₂²	semidirect
29. #376×C₁₁₃	C₂²	semidirect
30. #327×C₁₁₃	C₂²	semidirect
31. #323×C₁₁₃	C₂²	semidirect
196. #18179	C₁₁₃	direct (N × H)
204. #3112	C₂×C₁₁₃	semidirect
205. #2398	C₂×C₁₁₃	semidirect
206. #1607	C₂×C₁₁₃	semidirect
207. #1601	C₂×C₁₁₃	semidirect
208. #1505	C₂×C₁₁₃	semidirect
209. #1466	C₂×C₁₁₃	semidirect
210. C₁₁₃	#18179	direct (N × H)
219. C₂×C₄×Q₈	C₂²×C₁₁₃	semidirect
221. #480	C₂²×C₁₁₃	semidirect
224. #448	C₂²×C₁₁₃	semidirect
226. #432	C₂²×C₁₁₃	semidirect
228. #397	C₂²×C₁₁₃	semidirect
230. #393	C₂²×C₁₁₃	semidirect
232. #376	C₂²×C₁₁₃	semidirect
233. #327	C₂²×C₁₁₃	semidirect
234. #323	C₂²×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×#3112	2
C₁₁₃×#2398	2
C₁₁₃×#1607	2
C₁₁₃×#1601	2
C₁₁₃×#1505	2
C₁₁₃×#1466	2
#18179	113

Subgroups — C113×#18179 #43286199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#18179 #43286199