Subgroups — C₁₁₃×#17685 #43285705

Order 28928.

1152 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×#3500	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#2970	C₂	1	2	yes	maximal, complemented
3	C₁₁₃×#1536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁₃×#1533	C₂	1	2	yes	maximal, complemented
5	C₁₁₃×#1530	C₂	1	4	yes	maximal, complemented
6	C₁₁₃×#1527	C₂	1	2	yes	maximal, complemented
7	C₁₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#329×C₁₁₃	C₂	1	2	yes	maximal, complemented
9	C₂×2₋¹⁺⁴×C₁₁₃	C₄	1	1	yes	characteristic
10	C₂×H(5,𝔽₂)×C₁₁₃	C₄	1	1	yes	characteristic
11	#548×C₁₁₃	—	2	2	no	—
12	#546×C₁₁₃	—	2	2	no	—
13	#546×C₁₁₃	—	2	4	no	—
14	#536×C₁₁₃	C₄	1	1	yes	characteristic
15	#536×C₁₁₃	C₄	1	2	yes	—
16	#535×C₁₁₃	C₄	1	1	yes	characteristic
17	#535×C₁₁₃	C₄	1	2	yes	—
18	#532×C₁₁₃	C₂²	1	1	yes	characteristic
19	#532×C₁₁₃	C₂²	1	2	yes	—
20	C₂×#124×C₁₁₃	C₂²	1	2	yes	—
21	C₂×#124×C₁₁₃	C₂²	1	1	yes	characteristic
22	C₄×#41×C₁₁₃	C₂²	1	1	yes	characteristic
23	#446×C₁₁₃	—	2	2	no	—
24	#435×C₁₁₃	—	2	4	no	—
25	C₈×D₄×C₁₁₃	—	2	2	no	—
26	#432×C₁₁₃	C₂²	1	2	yes	complemented
27	#432×C₁₁₃	C₂²	1	4	yes	complemented
28	C₄×M₁₆×C₁₁₃	C₂²	1	2	yes	complemented
29	C₂×#97×C₁₁₃	C₂²	1	4	yes	complemented
30	#329×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
31	#329×C₁₁₃	C₂²	1	4	yes	complemented
32	#329×C₁₁₃	C₂²	1	2	yes	complemented
33	#329×C₁₁₃	C₂²	1	2	yes	complemented
34	#329×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
35	#329×C₁₁₃	C₂²	1	4	yes	complemented
36	#329×C₁₁₃	C₂²	1	2	yes	complemented
37	2₋¹⁺⁴×C₁₁₃	—	4	4	no	—
38	H(5,𝔽₂)×C₁₁₃	—	4	4	no	—
39	C₂×#41×C₁₁₃	—	2	1	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂×#41×C₁₁₃	—	2	1	no	—
42	C₂×#41×C₁₁₃	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#41×C₁₁₃	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×M₁₆×C₁₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₁₃	—	2	4	no	—
56	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
58	#127×C₁₁₃	C₂×C₄	1	1	yes	characteristic
59	#127×C₁₁₃	C₂×C₄	1	2	yes	—
60	#124×C₁₁₃	—	2	2	no	—
61	#124×C₁₁₃	—	2	4	no	—
62	#124×C₁₁₃	C₂×C₄	1	2	yes	—
63	#124×C₁₁₃	C₂×C₄	1	2	yes	—
64	#124×C₁₁₃	C₂×C₄	1	2	yes	—
65	#124×C₁₁₃	C₂³	1	1	yes	characteristic
66	#124×C₁₁₃	C₂³	1	2	yes	—
67	#124×C₁₁₃	C₂³	1	1	yes	characteristic
68	#123×C₁₁₃	—	2	2	no	—
69	#123×C₁₁₃	—	2	4	no	—
70	C₂²⋊Q₈×C₁₁₃	—	2	4	no	—
71	C₂²⋊Q₈×C₁₁₃	—	2	2	no	—
72	#121×C₁₁₃	—	2	4	no	—
73	#121×C₁₁₃	—	2	2	no	—
74	#121×C₁₁₃	—	2	4	no	—
75	#121×C₁₁₃	—	2	2	no	—
76	#120×C₁₁₃	—	2	2	no	—
77	#120×C₁₁₃	—	2	4	no	—
78	C₄×Q₈×C₁₁₃	D₄	1	2	yes	—
79	C₄×D₄×C₁₁₃	—	2	2	no	—
80	C₄×D₄×C₁₁₃	—	2	4	no	—
81	C₄×D₄×C₁₁₃	D₄	1	2	yes	—
82	C₄×D₄×C₁₁₃	D₄	1	4	yes	—
83	#117×C₁₁₃	C₂×C₄	1	1	yes	characteristic
84	#117×C₁₁₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₁₃	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₁₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₁₁₃	—	2	2	no	—
90	C₄⋊C₈×C₁₁₃	—	2	4	no	—
91	C₂²⋊C₈×C₁₁₃	—	2	4	no	—
92	C₂²⋊C₈×C₁₁₃	—	2	2	no	—
93	#97×C₁₁₃	—	2	4	no	—
94	#97×C₁₁₃	C₂³	1	2	yes	—
95	#97×C₁₁₃	C₂³	1	4	yes	—
96	#97×C₁₁₃	C₂³	1	2	yes	—
97	C₄×C₈×C₁₁₃	—	2	2	no	—
98	C₂⁴×C₁₁₃	—	2	1	no	—
99	C₂⁴×C₁₁₃	—	2	2	no	—
100	#41×C₁₁₃	—	2	4	no	—
101	#41×C₁₁₃	—	4	4	no	—
102	#41×C₁₁₃	—	4	4	no	—
103	#41×C₁₁₃	—	4	2	no	—
104	#41×C₁₁₃	—	4	2	no	—
105	#41×C₁₁₃	—	4	8	no	—
106	#41×C₁₁₃	—	4	4	no	—
107	#41×C₁₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₁₃	—	4	2	no	—
111	C₂×Q₈×C₁₁₃	—	4	4	no	—
112	C₂×Q₈×C₁₁₃	—	4	4	no	—
113	C₂×Q₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₁₃	C₂²×C₄	1	2	yes	—
115	C₂×Q₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×Q₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₁₁₃	—	2	1	no	—
118	C₂×D₄×C₁₁₃	—	2	2	no	—
119	C₂×D₄×C₁₁₃	—	2	1	no	—
120	C₂×D₄×C₁₁₃	—	2	2	no	—
121	C₂×D₄×C₁₁₃	—	2	2	no	—
122	C₂×D₄×C₁₁₃	—	2	1	no	—
123	C₂×D₄×C₁₁₃	—	2	2	no	—
124	C₂×D₄×C₁₁₃	—	2	4	no	—
125	C₂×D₄×C₁₁₃	—	4	4	no	—
126	C₂×D₄×C₁₁₃	—	4	2	no	—
127	C₂×D₄×C₁₁₃	—	4	8	no	—
128	C₂×D₄×C₁₁₃	—	4	4	no	—
129	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
130	C₂×D₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
144	M₁₆×C₁₁₃	—	4	4	no	—
145	C₂×C₈×C₁₁₃	—	2	2	no	—
146	C₂×C₈×C₁₁₃	—	2	2	no	—
147	C₂×C₈×C₁₁₃	—	2	4	no	—
148	C₂×C₈×C₁₁₃	—	4	8	no	—
149	C₄⋊C₄×C₁₁₃	—	2	2	no	—
150	C₄⋊C₄×C₁₁₃	—	2	4	no	—
151	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
152	C₄⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
153	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
154	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
155	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
156	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
157	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
158	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
159	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
160	C₂²⋊C₄×C₁₁₃	C₂²⋊C₄	1	4	yes	—
161	C₄²×C₁₁₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₁₃	C₂×D₄	1	4	yes	—
165	C₄²×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂³×C₁₁₃	—	2	2	no	—
167	C₂³×C₁₁₃	—	2	1	no	—
168	C₂³×C₁₁₃	—	2	1	no	—
169	C₂³×C₁₁₃	—	4	2	no	—
170	C₂³×C₁₁₃	—	4	4	no	—
171	C₂³×C₁₁₃	—	8	4	no	—
172	C₂³×C₁₁₃	—	8	2	no	—
173	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
175	Q₈×C₁₁₃	—	2	2	no	—
176	Q₈×C₁₁₃	—	4	2	no	—
177	Q₈×C₁₁₃	—	4	1	no	—
178	Q₈×C₁₁₃	—	4	1	no	—
179	Q₈×C₁₁₃	—	4	4	no	—
180	Q₈×C₁₁₃	—	4	2	no	—
181	D₄×C₁₁₃	—	2	4	no	—
182	D₄×C₁₁₃	—	4	1	no	—
183	D₄×C₁₁₃	—	4	2	no	—
184	D₄×C₁₁₃	—	4	1	no	—
185	D₄×C₁₁₃	—	4	4	no	—
186	D₄×C₁₁₃	—	4	2	no	—
187	D₄×C₁₁₃	—	4	2	no	—
188	D₄×C₁₁₃	—	4	4	no	—
189	D₄×C₁₁₃	—	4	4	no	—
190	D₄×C₁₁₃	—	4	2	no	—
191	D₄×C₁₁₃	—	8	4	no	—
192	D₄×C₁₁₃	—	8	2	no	—
193	D₄×C₁₁₃	#100	1	4	yes	—
194	C₂×C₄×C₁₁₃	—	2	4	no	—
195	C₂×C₄×C₁₁₃	—	2	2	no	—
196	C₂×C₄×C₁₁₃	—	2	2	no	—
197	C₂×C₄×C₁₁₃	—	2	1	no	—
198	C₂×C₄×C₁₁₃	—	2	1	no	—
199	C₂×C₄×C₁₁₃	—	4	4	no	—
200	C₂×C₄×C₁₁₃	—	4	2	no	—
201	C₂×C₄×C₁₁₃	—	4	4	no	—
202	C₂×C₄×C₁₁₃	—	4	4	no	—
203	C₂×C₄×C₁₁₃	—	4	2	no	—
204	C₂×C₄×C₁₁₃	—	4	4	no	—
205	C₂×C₄×C₁₁₃	—	4	2	no	—
206	C₂×C₄×C₁₁₃	—	4	2	no	—
207	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	4	yes	—
209	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
213	C₈×C₁₁₃	—	2	4	no	—
214	C₈×C₁₁₃	—	4	4	no	—
215	C₈×C₁₁₃	—	4	2	no	—
216	C₂²×C₁₁₃	—	2	4	no	—
217	C₂²×C₁₁₃	—	2	1	no	—
218	C₂²×C₁₁₃	—	2	2	no	—
219	C₂²×C₁₁₃	—	4	1	no	—
220	C₂²×C₁₁₃	—	4	2	no	—
221	C₂²×C₁₁₃	—	4	1	no	—
222	C₂²×C₁₁₃	—	4	2	no	—
223	C₂²×C₁₁₃	—	4	2	no	—
224	C₂²×C₁₁₃	—	4	4	no	—
225	C₂²×C₁₁₃	—	16	4	no	—
226	C₂²×C₁₁₃	—	16	2	no	—
227	C₂²×C₁₁₃	C₂×#100	1	4	yes	—
228	C₂²×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₁₁₃	—	2	1	no	—
230	C₄×C₁₁₃	—	2	2	no	—
231	C₄×C₁₁₃	—	2	2	no	—
232	C₄×C₁₁₃	—	2	4	no	—
233	C₄×C₁₁₃	—	2	2	no	—
234	C₄×C₁₁₃	—	4	1	no	—
235	C₄×C₁₁₃	—	4	2	no	—
236	C₄×C₁₁₃	—	4	1	no	—
237	C₄×C₁₁₃	C₂×#100	1	2	yes	—
238	#17685	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂×C₁₁₃	—	2	4	no	—
240	C₂×C₁₁₃	—	4	1	no	—
241	C₂×C₁₁₃	—	8	1	no	—
242	C₂×C₁₁₃	—	8	1	no	—
243	C₂×C₁₁₃	—	8	2	no	—
244	C₂×C₁₁₃	C₂²×#100	1	1	yes	characteristic
245	C₂×C₁₁₃	#2901	1	2	yes	—
246	#3500	C₂×C₁₁₃	1	1	yes	characteristic
247	#2970	C₂×C₁₁₃	1	2	yes	complemented
248	#1536	C₂×C₁₁₃	1	1	yes	characteristic, complemented
249	#1533	C₂×C₁₁₃	1	2	yes	complemented
250	#1530	C₂×C₁₁₃	1	4	yes	complemented
251	#1527	C₂×C₁₁₃	1	2	yes	complemented
252	#1525	C₂×C₁₁₃	1	1	yes	characteristic, complemented
253	C₂×#329	C₂×C₁₁₃	1	2	yes	complemented
254	C₁₁₃	#17685	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×2₋¹⁺⁴	C₄×C₁₁₃	1	1	yes	characteristic
256	C₂×H(5,𝔽₂)	C₄×C₁₁₃	1	1	yes	characteristic
257	#548	—	2	2	no	—
258	#546	—	2	2	no	—
259	#546	—	2	4	no	—
260	#536	C₄×C₁₁₃	1	1	yes	characteristic
261	#536	C₄×C₁₁₃	1	2	yes	—
262	#535	C₄×C₁₁₃	1	1	yes	characteristic
263	#535	C₄×C₁₁₃	1	2	yes	—
264	#532	C₂²×C₁₁₃	1	1	yes	characteristic
265	#532	C₂²×C₁₁₃	1	2	yes	—
266	C₂×#124	C₂²×C₁₁₃	1	2	yes	—
267	C₂×#124	C₂²×C₁₁₃	1	1	yes	characteristic
268	C₄×#41	C₂²×C₁₁₃	1	1	yes	characteristic
269	#446	—	2	2	no	—
270	#435	—	2	4	no	—
271	C₈×D₄	—	2	2	no	—
272	#432	C₂²×C₁₁₃	1	2	yes	complemented
273	#432	C₂²×C₁₁₃	1	4	yes	complemented
274	C₄×M₁₆	C₂²×C₁₁₃	1	2	yes	complemented
275	C₂×#97	C₂²×C₁₁₃	1	4	yes	complemented
276	#329	C₂²×C₁₁₃	1	2	yes	complemented
277	#329	C₂²×C₁₁₃	1	2	yes	complemented
278	#329	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
279	#329	C₂²×C₁₁₃	1	4	yes	complemented
280	#329	C₂²×C₁₁₃	1	2	yes	complemented
281	#329	C₂²×C₁₁₃	1	1	yes	characteristic, complemented
282	#329	C₂²×C₁₁₃	1	4	yes	complemented
283	2₋¹⁺⁴	—	4	4	no	—
284	H(5,𝔽₂)	—	4	4	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	1	no	—
288	C₂×#41	C₂×C₄×C₁₁₃	1	2	yes	—
289	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
290	C₂×#41	C₂×C₄×C₁₁₃	1	2	yes	—
291	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
292	C₂×#41	C₂×C₄×C₁₁₃	1	1	yes	characteristic
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
295	C₂²×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
299	C₂²×D₄	C₂×C₄×C₁₁₃	1	1	yes	characteristic
300	C₂×M₁₆	—	2	2	no	—
301	C₂²×C₈	—	2	4	no	—
302	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
303	C₄⋊Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
304	#127	C₂×C₄×C₁₁₃	1	1	yes	characteristic
305	#127	C₂×C₄×C₁₁₃	1	2	yes	—
306	#124	—	2	2	no	—
307	#124	—	2	4	no	—
308	#124	C₂×C₄×C₁₁₃	1	2	yes	—
309	#124	C₂×C₄×C₁₁₃	1	2	yes	—
310	#124	C₂×C₄×C₁₁₃	1	2	yes	—
311	#124	C₂³×C₁₁₃	1	1	yes	characteristic
312	#124	C₂³×C₁₁₃	1	2	yes	—
313	#124	C₂³×C₁₁₃	1	1	yes	characteristic
314	#123	—	2	2	no	—
315	#123	—	2	4	no	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	#121	—	2	4	no	—
319	#121	—	2	2	no	—
320	#121	—	2	4	no	—
321	#121	—	2	2	no	—
322	#120	—	2	2	no	—
323	#120	—	2	4	no	—
324	C₄×Q₈	D₄×C₁₁₃	1	2	yes	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	D₄×C₁₁₃	1	2	yes	—
328	C₄×D₄	D₄×C₁₁₃	1	4	yes	—
329	#117	C₂×C₄×C₁₁₃	1	1	yes	characteristic
330	#117	C₂×C₄×C₁₁₃	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₄²	C₂³×C₁₁₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	2	4	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	#97	—	2	4	no	—
340	#97	C₂³×C₁₁₃	1	2	yes	—
341	#97	C₂³×C₁₁₃	1	4	yes	—
342	#97	C₂³×C₁₁₃	1	2	yes	—
343	C₄×C₈	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	2	no	—
346	#41	—	2	4	no	—
347	#41	—	4	4	no	—
348	#41	—	4	4	no	—
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	#41	—	4	8	no	—
352	#41	—	4	4	no	—
353	#41	—	4	4	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
360	C₂×Q₈	C₂²×C₄×C₁₁₃	1	2	yes	—
361	C₂×Q₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
362	C₂×Q₈	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
376	C₂×D₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
377	C₂×D₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
378	C₂×D₄	C₂²×C₄×C₁₁₃	1	2	yes	—
379	C₂×D₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	C₂²×C₄×C₁₁₃	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₁₃	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₁₁₃	1	2	yes	—
390	M₁₆	—	4	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	4	8	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
398	C₄⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	2	yes	—
406	C₂²⋊C₄	C₂²⋊C₄×C₁₁₃	1	4	yes	—
407	C₄²	C₂²×C₄×C₁₁₃	1	2	yes	—
408	C₄²	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
409	C₄²	C₂×D₄×C₁₁₃	1	2	yes	—
410	C₄²	C₂×D₄×C₁₁₃	1	4	yes	—
411	C₄²	C₂⁴×C₁₁₃	1	1	yes	characteristic
412	C₂³	—	2	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	8	4	no	—
418	C₂³	—	8	2	no	—
419	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
420	C₂³	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
421	Q₈	—	2	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	4	no	—
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	1	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	4	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	4	no	—
438	D₄	—	8	2	no	—
439	D₄	#100×C₁₁₃	1	4	yes	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	4	yes	—
455	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₁₁₃	1	2	yes	—
459	C₈	—	2	4	no	—
460	C₈	—	4	4	no	—
461	C₈	—	4	2	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	16	4	no	—
472	C₂²	—	16	2	no	—
473	C₂²	C₂×#100×C₁₁₃	1	4	yes	—
474	C₂²	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	1	no	—
483	C₄	C₂×#100×C₁₁₃	1	2	yes	—
484	C₂	—	2	4	no	—
485	C₂	—	4	1	no	—
486	C₂	—	8	1	no	—
487	C₂	—	8	2	no	—
488	C₂	—	8	1	no	—
489	C₂	C₂²×#100×C₁₁₃	1	1	yes	characteristic
490	C₂	C₁₁₃×#2901	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₁₃
prime radical	C₁₁₃×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄×#41×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁₃×#2970	C₂	semidirect
3. C₁₁₃×#1536	C₂	semidirect
4. C₁₁₃×#1533	C₂	semidirect
5. C₁₁₃×#1530	C₂	semidirect
6. C₁₁₃×#1527	C₂	semidirect
7. C₁₁₃×#1525	C₂	semidirect
8. C₂×#329×C₁₁₃	C₂	semidirect
26. #432×C₁₁₃	C₂²	semidirect
27. #432×C₁₁₃	C₂²	semidirect
28. C₄×M₁₆×C₁₁₃	C₂²	semidirect
29. C₂×#97×C₁₁₃	C₂²	semidirect
30. #329×C₁₁₃	C₂²	semidirect
31. #329×C₁₁₃	C₂²	semidirect
32. #329×C₁₁₃	C₂²	semidirect
33. #329×C₁₁₃	C₂²	semidirect
34. #329×C₁₁₃	C₂²	semidirect
35. #329×C₁₁₃	C₂²	semidirect
36. #329×C₁₁₃	C₂²	semidirect
238. #17685	C₁₁₃	direct (N × H)
247. #2970	C₂×C₁₁₃	semidirect
248. #1536	C₂×C₁₁₃	semidirect
249. #1533	C₂×C₁₁₃	semidirect
250. #1530	C₂×C₁₁₃	semidirect
251. #1527	C₂×C₁₁₃	semidirect
252. #1525	C₂×C₁₁₃	semidirect
253. C₂×#329	C₂×C₁₁₃	semidirect
254. C₁₁₃	#17685	direct (N × H)
272. #432	C₂²×C₁₁₃	semidirect
273. #432	C₂²×C₁₁₃	semidirect
274. C₄×M₁₆	C₂²×C₁₁₃	semidirect
275. C₂×#97	C₂²×C₁₁₃	semidirect
276. #329	C₂²×C₁₁₃	semidirect
277. #329	C₂²×C₁₁₃	semidirect
278. #329	C₂²×C₁₁₃	semidirect
279. #329	C₂²×C₁₁₃	semidirect
280. #329	C₂²×C₁₁₃	semidirect
281. #329	C₂²×C₁₁₃	semidirect
282. #329	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×#3500	2
C₁₁₃×#2970	2
C₁₁₃×#1536	2
C₁₁₃×#1533	2
C₁₁₃×#1530	2
C₁₁₃×#1527	2
C₁₁₃×#1525	2
C₂×#329×C₁₁₃	2
#17685	113

Subgroups — C113×#17685 #43285705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#17685 #43285705