Subgroups — C₁₁₃×#3545 #28388341

Order 14464.

1060 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#563×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#562×C₁₁₃	C₂	1	2	yes	maximal, complemented
3	H(3,𝔽₄)×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#555×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	#551×C₁₁₃	C₂	1	2	yes	maximal, complemented
6	#551×C₁₁₃	C₂	1	4	yes	maximal, complemented
7	#546×C₁₁₃	C₂	1	4	yes	maximal, complemented
8	#542×C₁₁₃	C₂	1	4	yes	maximal, complemented
9	#538×C₁₁₃	C₂	1	4	yes	maximal, complemented
10	#536×C₁₁₃	C₂	1	2	yes	maximal, complemented
11	#534×C₁₁₃	C₂	1	2	yes	maximal, complemented
12	#529×C₁₁₃	C₂	1	2	yes	maximal, complemented
13	C₂×#124×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#41×C₁₁₃	C₂²	1	2	yes	—
15	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
18	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
19	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
20	#126×C₁₁₃	C₂²	1	4	yes	complemented
21	#126×C₁₁₃	C₂²	1	4	yes	complemented
22	#126×C₁₁₃	C₂²	1	4	yes	complemented
23	#125×C₁₁₃	C₂²	1	2	yes	complemented
24	#124×C₁₁₃	C₂²	1	1	yes	characteristic
25	#124×C₁₁₃	C₂²	1	1	yes	characteristic
26	#124×C₁₁₃	C₂²	1	4	yes	complemented
27	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
28	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
29	#124×C₁₁₃	C₂²	1	2	yes	complemented
30	#124×C₁₁₃	C₂²	1	2	yes	complemented
31	#124×C₁₁₃	C₂²	1	2	yes	complemented
32	#124×C₁₁₃	C₂²	1	4	yes	complemented
33	#124×C₁₁₃	C₂²	1	4	yes	complemented
34	#123×C₁₁₃	C₂²	1	2	yes	—
35	#123×C₁₁₃	C₂²	1	4	yes	complemented
36	#123×C₁₁₃	C₂²	1	2	yes	complemented
37	#123×C₁₁₃	C₂²	1	4	yes	complemented
38	#123×C₁₁₃	C₂²	1	4	yes	complemented
39	#123×C₁₁₃	C₂²	1	4	yes	complemented
40	#123×C₁₁₃	C₂²	1	4	yes	complemented
41	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
42	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
43	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
44	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
45	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
46	#121×C₁₁₃	C₂²	1	2	yes	—
47	#121×C₁₁₃	C₂²	1	4	yes	—
48	#121×C₁₁₃	C₂²	1	4	yes	complemented
49	#121×C₁₁₃	C₂²	1	4	yes	complemented
50	#121×C₁₁₃	C₂²	1	4	yes	complemented
51	#120×C₁₁₃	C₂²	1	4	yes	—
52	#120×C₁₁₃	C₂²	1	2	yes	—
53	#120×C₁₁₃	C₂²	1	2	yes	complemented
54	#120×C₁₁₃	C₂²	1	4	yes	complemented
55	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
56	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
57	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
58	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
59	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
60	#117×C₁₁₃	C₂²	1	4	yes	complemented
61	#117×C₁₁₃	C₂²	1	2	yes	complemented
62	#117×C₁₁₃	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	complemented
64	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	4	yes	complemented
66	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
68	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
69	#41×C₁₁₃	—	4	4	no	—
70	C₂×Q₈×C₁₁₃	—	4	2	no	—
71	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
72	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
74	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
75	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₁₁₃	—	4	2	no	—
77	C₂×D₄×C₁₁₃	—	4	4	no	—
78	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
79	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
80	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
81	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
82	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
84	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
85	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
86	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
89	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
91	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
92	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
93	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
94	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
95	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
96	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
97	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
98	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
99	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
100	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
101	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
102	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
103	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
104	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
105	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
106	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
107	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
108	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
113	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
114	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
115	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
116	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
117	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
118	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₄²×C₁₁₃	C₂³	1	2	yes	—
120	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
121	C₄²×C₁₁₃	C₂³	1	2	yes	—
122	C₄²×C₁₁₃	C₂³	1	4	yes	—
123	C₄²×C₁₁₃	C₂³	1	2	yes	—
124	C₂³×C₁₁₃	—	2	4	no	—
125	C₂³×C₁₁₃	—	4	2	no	—
126	C₂³×C₁₁₃	—	4	4	no	—
127	C₂³×C₁₁₃	—	4	4	no	—
128	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
129	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
130	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
131	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	Q₈×C₁₁₃	—	4	1	no	—
133	Q₈×C₁₁₃	—	4	2	no	—
134	Q₈×C₁₁₃	—	4	1	no	—
135	Q₈×C₁₁₃	—	4	2	no	—
136	Q₈×C₁₁₃	—	4	2	no	—
137	D₄×C₁₁₃	—	2	8	no	—
138	D₄×C₁₁₃	—	4	1	no	—
139	D₄×C₁₁₃	—	4	2	no	—
140	D₄×C₁₁₃	—	4	1	no	—
141	D₄×C₁₁₃	—	4	4	no	—
142	D₄×C₁₁₃	—	4	4	no	—
143	D₄×C₁₁₃	—	4	4	no	—
144	D₄×C₁₁₃	—	4	2	no	—
145	D₄×C₁₁₃	—	4	2	no	—
146	C₂×C₄×C₁₁₃	—	2	2	no	—
147	C₂×C₄×C₁₁₃	—	2	4	no	—
148	C₂×C₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	4	2	no	—
150	C₂×C₄×C₁₁₃	—	4	4	no	—
151	C₂×C₄×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	4	4	no	—
153	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
156	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₁₁₃	—	2	2	no	—
163	C₂²×C₁₁₃	—	2	4	no	—
164	C₂²×C₁₁₃	—	2	2	no	—
165	C₂²×C₁₁₃	—	2	2	no	—
166	C₂²×C₁₁₃	—	2	4	no	—
167	C₂²×C₁₁₃	—	2	4	no	—
168	C₂²×C₁₁₃	—	2	4	no	—
169	C₂²×C₁₁₃	—	2	4	no	—
170	C₂²×C₁₁₃	—	8	4	no	—
171	C₂²×C₁₁₃	—	8	4	no	—
172	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
174	C₄×C₁₁₃	—	2	2	no	—
175	C₄×C₁₁₃	—	2	1	no	—
176	C₄×C₁₁₃	—	2	1	no	—
177	C₄×C₁₁₃	—	2	2	no	—
178	C₄×C₁₁₃	—	2	4	no	—
179	C₄×C₁₁₃	—	2	2	no	—
180	C₄×C₁₁₃	—	2	4	no	—
181	C₄×C₁₁₃	—	2	2	no	—
182	C₄×C₁₁₃	—	2	4	no	—
183	C₂×C₁₁₃	—	2	2	no	—
184	C₂×C₁₁₃	—	4	4	no	—
185	C₂×C₁₁₃	—	4	2	no	—
186	C₂×C₁₁₃	—	4	2	no	—
187	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₁₁₃	#585	1	2	yes	—
189	#3545	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₁₁₃	#3545	1	1	yes	characteristic, direct product factor, Sylow
191	#563	C₂×C₁₁₃	1	1	yes	characteristic, complemented
192	#562	C₂×C₁₁₃	1	2	yes	complemented
193	H(3,𝔽₄)	C₂×C₁₁₃	1	1	yes	characteristic, complemented
194	#555	C₂×C₁₁₃	1	2	yes	complemented
195	#551	C₂×C₁₁₃	1	2	yes	complemented
196	#551	C₂×C₁₁₃	1	4	yes	complemented
197	#546	C₂×C₁₁₃	1	4	yes	complemented
198	#542	C₂×C₁₁₃	1	4	yes	complemented
199	#538	C₂×C₁₁₃	1	4	yes	complemented
200	#536	C₂×C₁₁₃	1	2	yes	complemented
201	#534	C₂×C₁₁₃	1	2	yes	complemented
202	#529	C₂×C₁₁₃	1	2	yes	complemented
203	C₂×#124	C₂×C₁₁₃	1	1	yes	characteristic, complemented
204	C₂×#41	C₂²×C₁₁₃	1	2	yes	—
205	C₂²×Q₈	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
206	C₂²×D₄	C₂²×C₁₁₃	1	1	yes	characteristic
207	C₂²×D₄	C₂²×C₁₁₃	1	2	yes	complemented
208	C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
209	C₄⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
210	#126	C₂²×C₁₁₃	1	4	yes	complemented
211	#126	C₂²×C₁₁₃	1	4	yes	complemented
212	#126	C₂²×C₁₁₃	1	4	yes	complemented
213	#125	C₂²×C₁₁₃	1	2	yes	complemented
214	#124	C₂²×C₁₁₃	1	1	yes	characteristic
215	#124	C₂²×C₁₁₃	1	1	yes	characteristic
216	#124	C₂²×C₁₁₃	1	4	yes	complemented
217	#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
218	#124	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
219	#124	C₂²×C₁₁₃	1	2	yes	complemented
220	#124	C₂²×C₁₁₃	1	2	yes	complemented
221	#124	C₂²×C₁₁₃	1	2	yes	complemented
222	#124	C₂²×C₁₁₃	1	4	yes	complemented
223	#124	C₂²×C₁₁₃	1	4	yes	complemented
224	#123	C₂²×C₁₁₃	1	2	yes	—
225	#123	C₂²×C₁₁₃	1	4	yes	complemented
226	#123	C₂²×C₁₁₃	1	2	yes	complemented
227	#123	C₂²×C₁₁₃	1	4	yes	complemented
228	#123	C₂²×C₁₁₃	1	4	yes	complemented
229	#123	C₂²×C₁₁₃	1	4	yes	complemented
230	#123	C₂²×C₁₁₃	1	4	yes	complemented
231	C₂²⋊Q₈	C₂²×C₁₁₃	1	2	yes	complemented
232	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	complemented
233	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	complemented
234	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	complemented
235	C₂²⋊Q₈	C₂²×C₁₁₃	1	4	yes	complemented
236	#121	C₂²×C₁₁₃	1	2	yes	—
237	#121	C₂²×C₁₁₃	1	4	yes	—
238	#121	C₂²×C₁₁₃	1	4	yes	complemented
239	#121	C₂²×C₁₁₃	1	4	yes	complemented
240	#121	C₂²×C₁₁₃	1	4	yes	complemented
241	#120	C₂²×C₁₁₃	1	4	yes	—
242	#120	C₂²×C₁₁₃	1	2	yes	—
243	#120	C₂²×C₁₁₃	1	2	yes	complemented
244	#120	C₂²×C₁₁₃	1	4	yes	complemented
245	C₄×Q₈	C₂²×C₁₁₃	1	2	yes	complemented
246	C₄×D₄	C₂²×C₁₁₃	1	2	yes	complemented
247	C₄×D₄	C₂²×C₁₁₃	1	4	yes	complemented
248	C₄×D₄	C₂²×C₁₁₃	1	4	yes	complemented
249	C₄×D₄	C₂²×C₁₁₃	1	4	yes	complemented
250	#117	C₂²×C₁₁₃	1	4	yes	complemented
251	#117	C₂²×C₁₁₃	1	2	yes	complemented
252	#117	C₂²×C₁₁₃	1	4	yes	complemented
253	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	complemented
254	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	2	yes	complemented
255	C₂×C₂²⋊C₄	C₂²×C₁₁₃	1	4	yes	complemented
256	C₂×C₄²	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
257	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
258	C₂⁴	C₂³×C₁₁₃	1	2	yes	—
259	#41	—	4	4	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
262	C₂×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
263	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
264	C₂×Q₈	C₂³×C₁₁₃	1	2	yes	—
265	C₂×Q₈	C₂³×C₁₁₃	1	1	yes	characteristic
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	C₂³×C₁₁₃	1	4	yes	—
269	C₂×D₄	C₂³×C₁₁₃	1	4	yes	—
270	C₂×D₄	C₂³×C₁₁₃	1	4	yes	—
271	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
272	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
273	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
274	C₂×D₄	C₂³×C₁₁₃	1	2	yes	—
275	C₂×D₄	C₂³×C₁₁₃	1	4	yes	—
276	C₂×D₄	C₂³×C₁₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
279	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
280	C₂²×C₄	C₂³×C₁₁₃	1	4	yes	—
281	C₂²×C₄	C₂³×C₁₁₃	1	4	yes	—
282	C₂²×C₄	C₂³×C₁₁₃	1	4	yes	—
283	C₂²×C₄	C₂³×C₁₁₃	1	2	yes	—
284	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
285	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
286	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
287	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
288	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
289	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
290	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
291	C₄⋊C₄	C₂³×C₁₁₃	1	2	yes	—
292	C₄⋊C₄	C₂³×C₁₁₃	1	4	yes	—
293	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
294	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
295	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
296	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
297	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
298	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
299	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
300	C₂²⋊C₄	C₂³×C₁₁₃	1	2	yes	—
301	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
302	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
303	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
304	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
307	C₂²⋊C₄	C₂³×C₁₁₃	1	4	yes	—
308	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
309	C₄²	C₂³×C₁₁₃	1	2	yes	—
310	C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
311	C₄²	C₂³×C₁₁₃	1	2	yes	—
312	C₄²	C₂³×C₁₁₃	1	4	yes	—
313	C₄²	C₂³×C₁₁₃	1	2	yes	—
314	C₂³	—	2	4	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
319	C₂³	C₂⁴×C₁₁₃	1	4	yes	—
320	C₂³	C₂⁴×C₁₁₃	1	2	yes	—
321	C₂³	C₂⁴×C₁₁₃	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	D₄	—	2	8	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
344	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
345	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
346	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
347	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
350	C₂×C₄	C₂⁴×C₁₁₃	1	4	yes	—
351	C₂×C₄	C₂⁴×C₁₁₃	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	H(5,𝔽₂)×C₁₁₃	1	2	yes	—
363	C₂²	C₂⁵×C₁₁₃	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	4	no	—
373	C₂	—	2	2	no	—
374	C₂	—	4	2	no	—
375	C₂	—	4	4	no	—
376	C₂	—	4	2	no	—
377	C₂	C₂×H(5,𝔽₂)×C₁₁₃	1	1	yes	characteristic
378	C₂	#585×C₁₁₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. #563×C₁₁₃	C₂	semidirect
2. #562×C₁₁₃	C₂	semidirect
3. H(3,𝔽₄)×C₁₁₃	C₂	semidirect
4. #555×C₁₁₃	C₂	semidirect
5. #551×C₁₁₃	C₂	semidirect
6. #551×C₁₁₃	C₂	semidirect
7. #546×C₁₁₃	C₂	semidirect
8. #542×C₁₁₃	C₂	semidirect
9. #538×C₁₁₃	C₂	semidirect
10. #536×C₁₁₃	C₂	semidirect
11. #534×C₁₁₃	C₂	semidirect
12. #529×C₁₁₃	C₂	semidirect
13. C₂×#124×C₁₁₃	C₂	semidirect
15. C₂²×Q₈×C₁₁₃	C₂²	semidirect
17. C₂²×D₄×C₁₁₃	C₂²	semidirect
18. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
19. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
20. #126×C₁₁₃	C₂²	semidirect
21. #126×C₁₁₃	C₂²	semidirect
22. #126×C₁₁₃	C₂²	semidirect
23. #125×C₁₁₃	C₂²	semidirect
26. #124×C₁₁₃	C₂²	semidirect
27. #124×C₁₁₃	C₂²	semidirect
28. #124×C₁₁₃	C₂²	semidirect
29. #124×C₁₁₃	C₂²	semidirect
30. #124×C₁₁₃	C₂²	semidirect
31. #124×C₁₁₃	C₂²	semidirect
32. #124×C₁₁₃	C₂²	semidirect
33. #124×C₁₁₃	C₂²	semidirect
35. #123×C₁₁₃	C₂²	semidirect
36. #123×C₁₁₃	C₂²	semidirect
37. #123×C₁₁₃	C₂²	semidirect
38. #123×C₁₁₃	C₂²	semidirect
39. #123×C₁₁₃	C₂²	semidirect
40. #123×C₁₁₃	C₂²	semidirect
41. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
42. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
43. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
44. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
45. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
48. #121×C₁₁₃	C₂²	semidirect
49. #121×C₁₁₃	C₂²	semidirect
50. #121×C₁₁₃	C₂²	semidirect
53. #120×C₁₁₃	C₂²	semidirect
54. #120×C₁₁₃	C₂²	semidirect
55. C₄×Q₈×C₁₁₃	C₂²	semidirect
56. C₄×D₄×C₁₁₃	C₂²	semidirect
57. C₄×D₄×C₁₁₃	C₂²	semidirect
58. C₄×D₄×C₁₁₃	C₂²	semidirect
59. C₄×D₄×C₁₁₃	C₂²	semidirect
60. #117×C₁₁₃	C₂²	semidirect
61. #117×C₁₁₃	C₂²	semidirect
62. #117×C₁₁₃	C₂²	semidirect
63. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
64. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
66. C₂×C₄²×C₁₁₃	C₂²	semidirect
189. #3545	C₁₁₃	direct (N × H)
190. C₁₁₃	#3545	direct (N × H)
191. #563	C₂×C₁₁₃	semidirect
192. #562	C₂×C₁₁₃	semidirect
193. H(3,𝔽₄)	C₂×C₁₁₃	semidirect
194. #555	C₂×C₁₁₃	semidirect
195. #551	C₂×C₁₁₃	semidirect
196. #551	C₂×C₁₁₃	semidirect
197. #546	C₂×C₁₁₃	semidirect
198. #542	C₂×C₁₁₃	semidirect
199. #538	C₂×C₁₁₃	semidirect
200. #536	C₂×C₁₁₃	semidirect
201. #534	C₂×C₁₁₃	semidirect
202. #529	C₂×C₁₁₃	semidirect
203. C₂×#124	C₂×C₁₁₃	semidirect
205. C₂²×Q₈	C₂²×C₁₁₃	semidirect
207. C₂²×D₄	C₂²×C₁₁₃	semidirect
208. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
209. C₄⋊Q₈	C₂²×C₁₁₃	semidirect
210. #126	C₂²×C₁₁₃	semidirect
211. #126	C₂²×C₁₁₃	semidirect
212. #126	C₂²×C₁₁₃	semidirect
213. #125	C₂²×C₁₁₃	semidirect
216. #124	C₂²×C₁₁₃	semidirect
217. #124	C₂²×C₁₁₃	semidirect
218. #124	C₂²×C₁₁₃	semidirect
219. #124	C₂²×C₁₁₃	semidirect
220. #124	C₂²×C₁₁₃	semidirect
221. #124	C₂²×C₁₁₃	semidirect
222. #124	C₂²×C₁₁₃	semidirect
223. #124	C₂²×C₁₁₃	semidirect
225. #123	C₂²×C₁₁₃	semidirect
226. #123	C₂²×C₁₁₃	semidirect
227. #123	C₂²×C₁₁₃	semidirect
228. #123	C₂²×C₁₁₃	semidirect
229. #123	C₂²×C₁₁₃	semidirect
230. #123	C₂²×C₁₁₃	semidirect
231. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
232. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
233. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
234. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
235. C₂²⋊Q₈	C₂²×C₁₁₃	semidirect
238. #121	C₂²×C₁₁₃	semidirect
239. #121	C₂²×C₁₁₃	semidirect
240. #121	C₂²×C₁₁₃	semidirect
243. #120	C₂²×C₁₁₃	semidirect
244. #120	C₂²×C₁₁₃	semidirect
245. C₄×Q₈	C₂²×C₁₁₃	semidirect
246. C₄×D₄	C₂²×C₁₁₃	semidirect
247. C₄×D₄	C₂²×C₁₁₃	semidirect
248. C₄×D₄	C₂²×C₁₁₃	semidirect
249. C₄×D₄	C₂²×C₁₁₃	semidirect
250. #117	C₂²×C₁₁₃	semidirect
251. #117	C₂²×C₁₁₃	semidirect
252. #117	C₂²×C₁₁₃	semidirect
253. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
254. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
255. C₂×C₂²⋊C₄	C₂²×C₁₁₃	semidirect
256. C₂×C₄²	C₂²×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#563×C₁₁₃	2
#562×C₁₁₃	2
H(3,𝔽₄)×C₁₁₃	2
#555×C₁₁₃	2
#551×C₁₁₃	2
#546×C₁₁₃	2
#542×C₁₁₃	2
#538×C₁₁₃	2
#536×C₁₁₃	2
#534×C₁₁₃	2
#529×C₁₁₃	2
C₂×#124×C₁₁₃	2
#3545	113

Subgroups — C113×#3545 #28388341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#3545 #28388341