Subgroups — C₁₁₃×#20721 #43288741

Order 28928.

1350 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#431×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1818	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1797	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1780	C₂	1	2	yes	maximal
7	C₁₁₃×#1750	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₄×#41×C₁₁₃	—	2	4	no	—
10	C₄×#41×C₁₁₃	—	2	4	no	—
11	C₂×C₄×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₁₁₃	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₁₁₃	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₁₃	C₄	1	1	yes	characteristic
17	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₁₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
21	#432×C₁₁₃	—	2	4	no	—
22	#431×C₁₁₃	—	2	4	no	—
23	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₁₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	8	yes	—
26	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₁₁₃	C₂²	1	2	yes	—
28	C₂×#97×C₁₁₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₁₃	C₂²	1	2	yes	—
30	#336×C₁₁₃	C₂²	1	8	yes	—
31	C₂×#41×C₁₁₃	—	2	2	no	—
32	C₂×#41×C₁₁₃	—	2	2	no	—
33	C₂×#41×C₁₁₃	—	2	8	no	—
34	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₁₃	C₂³	1	4	yes	—
45	C₄×Q₈×C₁₁₃	—	2	4	no	—
46	C₄×Q₈×C₁₁₃	—	2	4	no	—
47	C₄×D₄×C₁₁₃	—	2	8	no	—
48	C₄×D₄×C₁₁₃	—	2	8	no	—
49	C₄×D₄×C₁₁₃	—	2	4	no	—
50	C₄×D₄×C₁₁₃	—	2	4	no	—
51	#117×C₁₁₃	—	2	2	no	—
52	#117×C₁₁₃	—	2	2	no	—
53	#117×C₁₁₃	—	2	4	no	—
54	#117×C₁₁₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₁₃	—	2	4	no	—
63	C₂×C₄²×C₁₁₃	—	2	4	no	—
64	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
69	C₂×C₄²×C₁₁₃	D₄	1	4	yes	—
70	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₁₃	—	2	4	no	—
74	C₄⋊C₈×C₁₁₃	—	2	4	no	—
75	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
76	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
77	C₂²⋊C₈×C₁₁₃	—	2	16	no	—
78	#97×C₁₁₃	—	2	4	no	—
79	C₄×C₈×C₁₁₃	—	2	4	no	—
80	C₂⁴×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂⁴×C₁₁₃	C₂²×C₄	1	2	yes	—
82	#41×C₁₁₃	—	2	16	no	—
83	#41×C₁₁₃	—	2	16	no	—
84	C₂×Q₈×C₁₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₁₃	—	2	4	no	—
86	C₂×D₄×C₁₁₃	—	2	4	no	—
87	C₂×D₄×C₁₁₃	—	2	4	no	—
88	C₂×D₄×C₁₁₃	—	2	4	no	—
89	C₂×D₄×C₁₁₃	—	2	2	no	—
90	C₂×D₄×C₁₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₁₃	—	2	4	no	—
92	C₂²×C₄×C₁₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₁₃	—	2	8	no	—
99	C₂²×C₄×C₁₁₃	—	4	2	no	—
100	C₂²×C₄×C₁₁₃	—	4	4	no	—
101	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₁₃	#41	1	8	yes	—
114	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₁₁₃	—	2	4	no	—
116	C₂×C₈×C₁₁₃	—	2	4	no	—
117	C₂×C₈×C₁₁₃	—	2	8	no	—
118	C₂×C₈×C₁₁₃	—	2	8	no	—
119	C₄⋊C₄×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	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
124	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
125	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
126	C₄²×C₁₁₃	—	2	4	no	—
127	C₄²×C₁₁₃	—	2	4	no	—
128	C₄²×C₁₁₃	—	2	2	no	—
129	C₄²×C₁₁₃	—	2	2	no	—
130	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₁₁₃	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
133	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
134	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
135	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
136	C₂³×C₁₁₃	—	2	2	no	—
137	C₂³×C₁₁₃	—	2	2	no	—
138	C₂³×C₁₁₃	—	2	2	no	—
139	C₂³×C₁₁₃	—	2	2	no	—
140	C₂³×C₁₁₃	—	2	4	no	—
141	C₂³×C₁₁₃	—	2	2	no	—
142	C₂³×C₁₁₃	—	2	4	no	—
143	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₁₁₃	#117	1	4	yes	—
145	C₂³×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
146	Q₈×C₁₁₃	—	2	8	no	—
147	D₄×C₁₁₃	—	2	8	no	—
148	D₄×C₁₁₃	—	2	16	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	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	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	2	8	no	—
158	C₂×C₄×C₁₁₃	—	2	8	no	—
159	C₂×C₄×C₁₁₃	—	2	8	no	—
160	C₂×C₄×C₁₁₃	—	2	2	no	—
161	C₂×C₄×C₁₁₃	—	2	2	no	—
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	8	no	—
166	C₂×C₄×C₁₁₃	—	4	8	no	—
167	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₁₃	#117	1	4	yes	—
173	C₂×C₄×C₁₁₃	#131	1	4	yes	—
174	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁₃	C₂×#41	1	4	yes	—
177	C₈×C₁₁₃	—	4	4	no	—
178	C₈×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	2	2	no	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	8	no	—
182	C₂²×C₁₁₃	—	2	2	no	—
183	C₂²×C₁₁₃	—	2	4	no	—
184	C₂²×C₁₁₃	—	4	2	no	—
185	C₂²×C₁₁₃	—	4	2	no	—
186	C₂²×C₁₁₃	—	4	4	no	—
187	C₂²×C₁₁₃	—	4	4	no	—
188	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₁₁₃	C₂×#117	1	2	yes	—
190	C₂²×C₁₁₃	C₂×#131	1	2	yes	—
191	C₂²×C₁₁₃	#568	1	2	yes	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	—	2	2	no	—
194	C₄×C₁₁₃	—	2	2	no	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	4	no	—
197	C₄×C₁₁₃	—	4	2	no	—
198	C₄×C₁₁₃	—	4	2	no	—
199	C₄×C₁₁₃	#408	1	4	yes	—
200	C₄×C₁₁₃	#525	1	2	yes	—
201	C₄×C₁₁₃	#525	1	2	yes	—
202	#20721	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₁₁₃	—	4	2	no	—
204	C₂×C₁₁₃	—	4	4	no	—
205	C₂×C₁₁₃	#2280	1	1	yes	characteristic
206	C₂×C₁₁₃	C₂×#408	1	1	yes	characteristic
207	C₂×C₁₁₃	#2879	1	1	yes	characteristic
208	C₂×C₁₁₃	#2925	1	4	yes	—
209	C₂×C₄×#41	C₂×C₁₁₃	1	1	yes	characteristic
210	C₂×#432	C₂×C₁₁₃	1	1	yes	characteristic, complemented
211	C₂×#431	C₂×C₁₁₃	1	1	yes	characteristic, complemented
212	#1818	C₂×C₁₁₃	1	2	yes	complemented
213	#1797	C₂×C₁₁₃	1	4	yes	complemented
214	#1780	C₂×C₁₁₃	1	2	yes	—
215	#1750	C₂×C₁₁₃	1	4	yes	complemented
216	C₁₁₃	#20721	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×#41	C₂²×C₁₁₃	1	1	yes	characteristic
218	C₄×#41	—	2	4	no	—
219	C₄×#41	—	2	4	no	—
220	C₂×C₄×Q₈	C₄×C₁₁₃	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₄×C₁₁₃	1	1	yes	characteristic
222	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
223	C₂×C₄×D₄	C₄×C₁₁₃	1	2	yes	—
224	C₂×C₄×D₄	C₄×C₁₁₃	1	1	yes	characteristic
225	C₂×C₄×D₄	C₄×C₁₁₃	1	1	yes	characteristic
226	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
227	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
228	C₂²×C₄²	C₂²×C₁₁₃	1	2	yes	—
229	C₂²×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic
230	#432	—	2	4	no	—
231	#431	—	2	4	no	—
232	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₁₁₃	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	8	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
236	C₂×C₂²⋊C₈	C₂²×C₁₁₃	1	2	yes	—
237	C₂×#97	C₂²×C₁₁₃	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₁₁₃	1	2	yes	—
239	#336	C₂²×C₁₁₃	1	8	yes	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	—	2	8	no	—
243	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
244	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
245	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
246	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
247	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
248	C₂³×C₄	C₂×C₄×C₁₁₃	1	2	yes	—
249	C₂³×C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₁₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
253	C₂²×C₈	C₂³×C₁₁₃	1	4	yes	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×D₄	—	2	8	no	—
257	C₄×D₄	—	2	8	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	—	2	4	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	4	no	—
263	#117	—	2	4	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₁₁₃	1	2	yes	—
271	C₂×C₄²	—	2	4	no	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
274	C₂×C₄²	C₂×C₄×C₁₁₃	1	2	yes	—
275	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
276	C₂×C₄²	C₂×C₄×C₁₁₃	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
278	C₂×C₄²	D₄×C₁₁₃	1	4	yes	—
279	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	2	4	no	—
284	C₂²⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	C₂²⋊C₈	—	2	16	no	—
287	#97	—	2	4	no	—
288	C₄×C₈	—	2	4	no	—
289	C₂⁴	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
290	C₂⁴	C₂²×C₄×C₁₁₃	1	2	yes	—
291	#41	—	2	16	no	—
292	#41	—	2	16	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
311	C₂²×C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
322	C₂²×C₄	#41×C₁₁₃	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	—	2	8	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
340	C₄²	C₂²⋊C₄×C₁₁₃	1	4	yes	—
341	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
342	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
343	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
344	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
353	C₂³	#117×C₁₁₃	1	4	yes	—
354	C₂³	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	16	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	8	no	—
375	C₂×C₄	—	4	8	no	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
381	C₂×C₄	#117×C₁₁₃	1	4	yes	—
382	C₂×C₄	#131×C₁₁₃	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₁₁₃	1	4	yes	—
386	C₈	—	4	4	no	—
387	C₈	—	4	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
398	C₂²	C₂×#117×C₁₁₃	1	2	yes	—
399	C₂²	C₂×#131×C₁₁₃	1	2	yes	—
400	C₂²	#568×C₁₁₃	1	2	yes	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	#408×C₁₁₃	1	4	yes	—
409	C₄	#525×C₁₁₃	1	2	yes	—
410	C₄	#525×C₁₁₃	1	2	yes	—
411	C₂	—	4	2	no	—
412	C₂	—	4	4	no	—
413	C₂	C₁₁₃×#2280	1	1	yes	characteristic
414	C₂	C₂×#408×C₁₁₃	1	1	yes	characteristic
415	C₂	C₁₁₃×#2879	1	1	yes	characteristic
416	C₂	C₁₁₃×#2925	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂³×C₁₁₃	C₂³×C₄
prime radical	C₂²×#41×C₁₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₁₁₃	C₂	semidirect
3. C₂×#431×C₁₁₃	C₂	semidirect
4. C₁₁₃×#1818	C₂	semidirect
5. C₁₁₃×#1797	C₂	semidirect
7. C₁₁₃×#1750	C₂	semidirect
202. #20721	C₁₁₃	direct (N × H)
210. C₂×#432	C₂×C₁₁₃	semidirect
211. C₂×#431	C₂×C₁₁₃	semidirect
212. #1818	C₂×C₁₁₃	semidirect
213. #1797	C₂×C₁₁₃	semidirect
215. #1750	C₂×C₁₁₃	semidirect
216. C₁₁₃	#20721	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×C₄×#41×C₁₁₃	2
C₂×#432×C₁₁₃	2
C₂×#431×C₁₁₃	2
C₁₁₃×#1818	2
C₁₁₃×#1797	2
C₁₁₃×#1780	2
C₁₁₃×#1750	2
#20721	113

Subgroups — C113×#20721 #43288741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#20721 #43288741