Subgroups — C₁₁₃×#15194 #43283214

Order 28928.

1370 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₁₁₃	C₂	1	2	yes	maximal
2	C₂×#389×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₁₃×#1445	C₂	1	2	yes	maximal
5	C₁₁₃×#1444	C₂	1	2	yes	maximal
6	C₁₁₃×#1441	C₂	1	4	yes	maximal
7	C₁₁₃×C₄⋊#95	C₂	1	2	yes	maximal
8	C₁₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
18	#389×C₁₁₃	—	2	8	no	—
19	#389×C₁₁₃	—	2	4	no	—
20	C₄×C₄⋊C₄×C₁₁₃	—	2	4	no	—
21	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
22	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
23	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
24	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
25	C₂×#95×C₁₁₃	C₂²	1	2	yes	—
26	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
27	C₂×#95×C₁₁₃	C₂²	1	4	yes	—
28	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₁₃	C₂³	1	4	yes	—
33	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₁₃	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₁₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
50	C₂×C₄⋊C₄×C₁₁₃	—	4	4	no	—
51	C₂×C₄⋊C₄×C₁₁₃	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₁₃	Q₈	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₁₃	Q₈	1	8	yes	—
54	C₂×C₄²×C₁₁₃	—	2	4	no	—
55	C₂×C₄²×C₁₁₃	—	2	4	no	—
56	C₂×C₄²×C₁₁₃	—	2	4	no	—
57	C₂×C₄²×C₁₁₃	—	2	4	no	—
58	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
59	#95×C₁₁₃	—	2	4	no	—
60	#95×C₁₁₃	—	2	8	no	—
61	#95×C₁₁₃	—	2	4	no	—
62	#95×C₁₁₃	—	2	4	no	—
63	#95×C₁₁₃	—	4	2	no	—
64	#95×C₁₁₃	—	4	4	no	—
65	#95×C₁₁₃	—	4	4	no	—
66	C₂⁴×C₁₁₃	C₂⁴	1	1	yes	characteristic
67	C₂²×C₄×C₁₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₁₃	—	2	4	no	—
74	C₂²×C₄×C₁₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₁₃	—	2	1	no	—
86	C₂²×C₄×C₁₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₁₁₃	C₂×Q₈	1	8	yes	—
107	C₂²×C₄×C₁₁₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₁₃	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
110	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
111	C₂²×C₄×C₁₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₁₃	#41	1	4	yes	—
113	C₄⋊C₄×C₁₁₃	—	2	8	no	—
114	C₄⋊C₄×C₁₁₃	—	2	8	no	—
115	C₄⋊C₄×C₁₁₃	—	2	8	no	—
116	C₄⋊C₄×C₁₁₃	—	2	16	no	—
117	C₄⋊C₄×C₁₁₃	—	4	16	no	—
118	C₄⋊C₄×C₁₁₃	—	4	8	no	—
119	C₄⋊C₄×C₁₁₃	—	4	4	no	—
120	C₄²×C₁₁₃	—	2	8	no	—
121	C₄²×C₁₁₃	—	4	8	no	—
122	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
123	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
124	C₂³×C₁₁₃	C₂²×Q₈	1	2	yes	—
125	C₂³×C₁₁₃	C₂²×Q₈	1	1	yes	characteristic
126	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
127	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
128	C₂³×C₁₁₃	C₂×#41	1	1	yes	characteristic
129	C₂³×C₁₁₃	C₂×#41	1	2	yes	—
130	C₂³×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
131	C₂³×C₁₁₃	H(5,𝔽₂)	1	1	yes	characteristic
132	C₂³×C₁₁₃	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂×C₄×C₁₁₃	—	2	2	no	—
134	C₂×C₄×C₁₁₃	—	2	2	no	—
135	C₂×C₄×C₁₁₃	—	2	4	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	4	no	—
140	C₂×C₄×C₁₁₃	—	2	2	no	—
141	C₂×C₄×C₁₁₃	—	2	4	no	—
142	C₂×C₄×C₁₁₃	—	2	2	no	—
143	C₂×C₄×C₁₁₃	—	2	2	no	—
144	C₂×C₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	8	no	—
146	C₂×C₄×C₁₁₃	—	2	4	no	—
147	C₂×C₄×C₁₁₃	—	2	4	no	—
148	C₂×C₄×C₁₁₃	—	2	8	no	—
149	C₂×C₄×C₁₁₃	—	2	8	no	—
150	C₂×C₄×C₁₁₃	—	2	4	no	—
151	C₂×C₄×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	4	2	no	—
153	C₂×C₄×C₁₁₃	—	4	2	no	—
154	C₂×C₄×C₁₁₃	—	4	4	no	—
155	C₂×C₄×C₁₁₃	—	4	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	4	no	—
160	C₂×C₄×C₁₁₃	—	4	2	no	—
161	C₂×C₄×C₁₁₃	—	4	4	no	—
162	C₂×C₄×C₁₁₃	—	4	2	no	—
163	C₂×C₄×C₁₁₃	—	4	4	no	—
164	C₂×C₄×C₁₁₃	—	4	2	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	4	2	no	—
168	C₂×C₄×C₁₁₃	—	4	2	no	—
169	C₂×C₄×C₁₁₃	—	4	2	no	—
170	C₂×C₄×C₁₁₃	—	4	2	no	—
171	C₂×C₄×C₁₁₃	—	4	4	no	—
172	C₂×C₄×C₁₁₃	—	4	4	no	—
173	C₂×C₄×C₁₁₃	#121	1	4	yes	—
174	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₁₁₃	C₂²⋊Q₈	1	8	yes	—
176	C₂×C₄×C₁₁₃	#123	1	4	yes	—
177	C₂×C₄×C₁₁₃	#125	1	8	yes	—
178	C₂×C₄×C₁₁₃	C₄⋊Q₈	1	4	yes	—
179	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
180	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂²×C₁₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
182	C₂²×C₁₁₃	C₂×#123	1	1	yes	characteristic
183	C₂²×C₁₁₃	#525	1	1	yes	characteristic
184	C₂²×C₁₁₃	C₂×#125	1	2	yes	—
185	C₂²×C₁₁₃	#529	1	2	yes	—
186	C₂²×C₁₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
187	C₂²×C₁₁₃	#533	1	2	yes	—
188	C₂²×C₁₁₃	#535	1	1	yes	characteristic
189	C₂²×C₁₁₃	#537	1	1	yes	characteristic
190	C₂²×C₁₁₃	#540	1	2	yes	—
191	C₂²×C₁₁₃	#542	1	2	yes	—
192	C₂²×C₁₁₃	#546	1	2	yes	—
193	C₂²×C₁₁₃	D₄×Q₈	1	1	yes	characteristic
194	C₂²×C₁₁₃	#550	1	1	yes	characteristic
195	C₂²×C₁₁₃	#553	1	2	yes	—
196	C₂²×C₁₁₃	#554	1	2	yes	—
197	C₂²×C₁₁₃	#554	1	2	yes	—
198	C₂²×C₁₁₃	#554	1	1	yes	characteristic
199	C₂²×C₁₁₃	#556	1	1	yes	characteristic
200	C₂²×C₁₁₃	#557	1	2	yes	—
201	C₂²×C₁₁₃	Q₈²	1	2	yes	—
202	C₄×C₁₁₃	—	2	4	no	—
203	C₄×C₁₁₃	—	4	2	no	—
204	C₄×C₁₁₃	—	4	8	no	—
205	C₄×C₁₁₃	—	4	4	no	—
206	C₄×C₁₁₃	—	4	4	no	—
207	C₄×C₁₁₃	—	4	4	no	—
208	C₄×C₁₁₃	—	8	2	no	—
209	C₄×C₁₁₃	#398	1	8	yes	—
210	#15194	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₁₁₃	C₂×#398	1	1	yes	characteristic
212	C₂×C₁₁₃	#2451	1	2	yes	—
213	C₂×C₁₁₃	#2454	1	2	yes	—
214	C₂×C₁₁₃	#2507	1	2	yes	—
215	C₂×C₁₁₃	#2509	1	2	yes	—
216	C₂×C₁₁₃	#2535	1	1	yes	characteristic
217	C₂×C₁₁₃	#2538	1	1	yes	characteristic
218	C₂×C₁₁₃	#2567	1	1	yes	characteristic
219	C₂×C₁₁₃	#2584	1	1	yes	characteristic
220	C₂×C₁₁₃	#2624	1	1	yes	characteristic
221	C₂×C₁₁₃	#2855	1	1	yes	characteristic
222	C₂×#389	C₂×C₁₁₃	1	1	yes	characteristic
223	C₂×#389	C₂×C₁₁₃	1	2	yes	—
224	C₂×C₄×C₄⋊C₄	C₂×C₁₁₃	1	1	yes	characteristic
225	#1445	C₂×C₁₁₃	1	2	yes	—
226	#1444	C₂×C₁₁₃	1	2	yes	—
227	#1441	C₂×C₁₁₃	1	4	yes	—
228	C₄⋊#95	C₂×C₁₁₃	1	2	yes	—
229	C₄⋊#95	C₂×C₁₁₃	1	1	yes	characteristic
230	C₁₁₃	#15194	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	4	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
236	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₁₁₃	1	2	yes	—
238	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
240	#389	—	2	8	no	—
241	#389	—	2	4	no	—
242	C₄×C₄⋊C₄	—	2	4	no	—
243	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
244	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
245	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
246	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
247	C₂×#95	C₂²×C₁₁₃	1	2	yes	—
248	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
249	C₂×#95	C₂²×C₁₁₃	1	4	yes	—
250	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₁₁₃	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	8	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	8	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	4	4	no	—
272	C₂×C₄⋊C₄	—	4	4	no	—
273	C₂×C₄⋊C₄	D₄×C₁₁₃	1	4	yes	—
274	C₂×C₄⋊C₄	Q₈×C₁₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	Q₈×C₁₁₃	1	8	yes	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	—	2	4	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
281	#95	—	2	4	no	—
282	#95	—	2	8	no	—
283	#95	—	2	4	no	—
284	#95	—	2	4	no	—
285	#95	—	4	2	no	—
286	#95	—	4	4	no	—
287	#95	—	4	4	no	—
288	C₂⁴	C₂⁴×C₁₁₃	1	1	yes	characteristic
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
324	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
327	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
328	C₂²×C₄	C₂×Q₈×C₁₁₃	1	8	yes	—
329	C₂²×C₄	C₂×Q₈×C₁₁₃	1	2	yes	—
330	C₂²×C₄	C₂×Q₈×C₁₁₃	1	4	yes	—
331	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
332	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
333	C₂²×C₄	#41×C₁₁₃	1	2	yes	—
334	C₂²×C₄	#41×C₁₁₃	1	4	yes	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	16	no	—
339	C₄⋊C₄	—	4	16	no	—
340	C₄⋊C₄	—	4	8	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄²	—	2	8	no	—
343	C₄²	—	4	8	no	—
344	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
345	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
346	C₂³	C₂²×Q₈×C₁₁₃	1	2	yes	—
347	C₂³	C₂²×Q₈×C₁₁₃	1	1	yes	characteristic
348	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
349	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
350	C₂³	C₂×#41×C₁₁₃	1	1	yes	characteristic
351	C₂³	C₂×#41×C₁₁₃	1	2	yes	—
352	C₂³	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
353	C₂³	H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
354	C₂³	2₋¹⁺⁴×C₁₁₃	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	#121×C₁₁₃	1	4	yes	—
396	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	4	yes	—
397	C₂×C₄	C₂²⋊Q₈×C₁₁₃	1	8	yes	—
398	C₂×C₄	#123×C₁₁₃	1	4	yes	—
399	C₂×C₄	#125×C₁₁₃	1	8	yes	—
400	C₂×C₄	C₄⋊Q₈×C₁₁₃	1	4	yes	—
401	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
402	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	1	yes	characteristic
403	C₂²	C₂×C₂²⋊Q₈×C₁₁₃	1	2	yes	—
404	C₂²	C₂×#123×C₁₁₃	1	1	yes	characteristic
405	C₂²	#525×C₁₁₃	1	1	yes	characteristic
406	C₂²	C₂×#125×C₁₁₃	1	2	yes	—
407	C₂²	#529×C₁₁₃	1	2	yes	—
408	C₂²	C₂×C₄⋊Q₈×C₁₁₃	1	1	yes	characteristic
409	C₂²	#533×C₁₁₃	1	2	yes	—
410	C₂²	#535×C₁₁₃	1	1	yes	characteristic
411	C₂²	#537×C₁₁₃	1	1	yes	characteristic
412	C₂²	#540×C₁₁₃	1	2	yes	—
413	C₂²	#542×C₁₁₃	1	2	yes	—
414	C₂²	#546×C₁₁₃	1	2	yes	—
415	C₂²	D₄×Q₈×C₁₁₃	1	1	yes	characteristic
416	C₂²	#550×C₁₁₃	1	1	yes	characteristic
417	C₂²	#553×C₁₁₃	1	2	yes	—
418	C₂²	#554×C₁₁₃	1	1	yes	characteristic
419	C₂²	#554×C₁₁₃	1	2	yes	—
420	C₂²	#554×C₁₁₃	1	2	yes	—
421	C₂²	#556×C₁₁₃	1	1	yes	characteristic
422	C₂²	#557×C₁₁₃	1	2	yes	—
423	C₂²	Q₈²×C₁₁₃	1	2	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	8	no	—
430	C₄	—	8	2	no	—
431	C₄	#398×C₁₁₃	1	8	yes	—
432	C₂	C₂×#398×C₁₁₃	1	1	yes	characteristic
433	C₂	C₁₁₃×#2451	1	2	yes	—
434	C₂	C₁₁₃×#2454	1	2	yes	—
435	C₂	C₁₁₃×#2507	1	2	yes	—
436	C₂	C₁₁₃×#2509	1	2	yes	—
437	C₂	C₁₁₃×#2535	1	1	yes	characteristic
438	C₂	C₁₁₃×#2538	1	1	yes	characteristic
439	C₂	C₁₁₃×#2567	1	1	yes	characteristic
440	C₂	C₁₁₃×#2584	1	1	yes	characteristic
441	C₂	C₁₁₃×#2624	1	1	yes	characteristic
442	C₂	C₁₁₃×#2855	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
210. #15194	C₁₁₃	direct (N × H)
230. C₁₁₃	#15194	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×#389×C₁₁₃	2
C₂×C₄×C₄⋊C₄×C₁₁₃	2
C₁₁₃×#1445	2
C₁₁₃×#1444	2
C₁₁₃×#1441	2
C₁₁₃×C₄⋊#95	2
#15194	113

Subgroups — C113×#15194 #43283214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#15194 #43283214