Subgroups — C₂×C₁₁₃×#1976 #43289263

Order 28928.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₁₁₃	C₂	1	2	yes	maximal, complemented
4	C₂×#410×C₁₁₃	C₂	1	2	yes	maximal, complemented
5	C₂×#405×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁₃×#1976	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#41×C₁₁₃	C₂²	1	2	yes	—
8	C₂×#135×C₁₁₃	—	2	1	no	—
9	C₂×#135×C₁₁₃	—	2	1	no	—
10	C₂×#135×C₁₁₃	—	2	2	no	—
11	C₂×#135×C₁₁₃	—	2	1	no	—
12	C₂×#135×C₁₁₃	—	2	1	no	—
13	C₂×#135×C₁₁₃	—	2	2	no	—
14	C₂×#135×C₁₁₃	C₄	1	4	yes	complemented
15	C₂×#135×C₁₁₃	C₂²	1	4	yes	—
16	C₂²×Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
17	C₂²×SD₁₆×C₁₁₃	C₄	1	2	yes	complemented
18	C₂²×D₈×C₁₁₃	C₄	1	1	yes	characteristic, complemented
19	C₂²×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₁₃	C₂²	1	2	yes	—
22	C₂×#117×C₁₁₃	C₂²	1	1	yes	characteristic
23	#427×C₁₁₃	—	2	2	no	—
24	#427×C₁₁₃	C₂²	1	4	yes	complemented
25	C₂×#107×C₁₁₃	—	2	1	no	—
26	C₂×#106×C₁₁₃	—	2	1	no	—
27	#421×C₁₁₃	—	2	4	no	—
28	#421×C₁₁₃	C₂²	1	8	yes	complemented
29	C₂×#104×C₁₁₃	—	2	4	no	—
30	#410×C₁₁₃	—	2	4	no	—
31	#410×C₁₁₃	C₂²	1	8	yes	complemented
32	C₂×#99×C₁₁₃	—	2	4	no	—
33	#405×C₁₁₃	—	2	2	no	—
34	#405×C₁₁₃	C₂²	1	4	yes	complemented
35	C₂×#97×C₁₁₃	—	2	1	no	—
36	C₂×C₄×C₈×C₁₁₃	—	2	1	no	—
37	C₂×#41×C₁₁₃	—	2	2	no	—
38	C₂×#41×C₁₁₃	—	2	2	no	—
39	C₂×#41×C₁₁₃	—	2	2	no	—
40	C₂×#41×C₁₁₃	—	2	2	no	—
41	C₂×#41×C₁₁₃	—	2	2	no	—
42	C₂×#41×C₁₁₃	—	2	2	no	—
43	C₂×#41×C₁₁₃	—	2	2	no	—
44	C₂×#41×C₁₁₃	—	2	2	no	—
45	C₂×#41×C₁₁₃	—	2	2	no	—
46	C₂×#41×C₁₁₃	—	2	2	no	—
47	C₂×#41×C₁₁₃	C₂×C₄	1	4	yes	—
48	C₂×#41×C₁₁₃	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₁₃	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
54	#135×C₁₁₃	—	2	4	no	—
55	#135×C₁₁₃	—	2	4	no	—
56	#135×C₁₁₃	—	2	4	no	—
57	#135×C₁₁₃	—	2	4	no	—
58	#135×C₁₁₃	—	2	4	no	—
59	#135×C₁₁₃	—	2	4	no	—
60	#135×C₁₁₃	—	2	4	no	—
61	#135×C₁₁₃	—	2	4	no	—
62	C₂×Q₁₆×C₁₁₃	—	2	1	no	—
63	C₂×Q₁₆×C₁₁₃	—	2	1	no	—
64	C₂×Q₁₆×C₁₁₃	—	2	2	no	—
65	C₂×Q₁₆×C₁₁₃	C₂×C₄	1	4	yes	complemented
66	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
67	C₂×SD₁₆×C₁₁₃	—	2	2	no	—
68	C₂×SD₁₆×C₁₁₃	—	2	4	no	—
69	C₂×SD₁₆×C₁₁₃	C₂×C₄	1	8	yes	complemented
70	C₂×D₈×C₁₁₃	—	2	1	no	—
71	C₂×D₈×C₁₁₃	—	2	1	no	—
72	C₂×D₈×C₁₁₃	—	2	2	no	—
73	C₂×D₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
74	C₂×M₁₆×C₁₁₃	—	2	1	no	—
75	C₂×M₁₆×C₁₁₃	—	2	1	no	—
76	C₂×M₁₆×C₁₁₃	—	2	1	no	—
77	C₂×M₁₆×C₁₁₃	D₄	1	2	yes	—
78	C₂×M₁₆×C₁₁₃	D₄	1	2	yes	—
79	C₂×M₁₆×C₁₁₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₁₁₃	D₄	1	2	yes	—
87	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₁₁₃	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₁₁₃	D₄	1	2	yes	—
90	C₂²×C₈×C₁₁₃	C₂³	1	2	yes	—
91	#117×C₁₁₃	—	2	1	no	—
92	#117×C₁₁₃	—	2	1	no	—
93	#117×C₁₁₃	—	2	2	no	—
94	#117×C₁₁₃	—	2	2	no	—
95	#117×C₁₁₃	—	2	2	no	—
96	#117×C₁₁₃	D₄	1	2	yes	—
97	#117×C₁₁₃	C₂³	1	4	yes	—
98	#117×C₁₁₃	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₁₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₁₁₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₁₁₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₁₃	D₄	1	2	yes	—
103	C₂×C₄²×C₁₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₁₃	—	2	2	no	—
105	#107×C₁₁₃	—	2	4	no	—
106	#106×C₁₁₃	—	2	4	no	—
107	#104×C₁₁₃	—	2	16	no	—
108	#99×C₁₁₃	—	2	16	no	—
109	#97×C₁₁₃	—	2	4	no	—
110	C₄×C₈×C₁₁₃	—	2	4	no	—
111	C₂⁴×C₁₁₃	—	2	2	no	—
112	C₂⁴×C₁₁₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₁₁₃	—	2	4	no	—
114	#41×C₁₁₃	—	2	4	no	—
115	#41×C₁₁₃	—	2	4	no	—
116	#41×C₁₁₃	—	2	4	no	—
117	#41×C₁₁₃	—	2	4	no	—
118	#41×C₁₁₃	—	2	4	no	—
119	#41×C₁₁₃	—	2	4	no	—
120	#41×C₁₁₃	—	2	4	no	—
121	#41×C₁₁₃	—	4	2	no	—
122	#41×C₁₁₃	—	4	2	no	—
123	#41×C₁₁₃	—	4	2	no	—
124	#41×C₁₁₃	—	4	2	no	—
125	#41×C₁₁₃	—	4	2	no	—
126	#41×C₁₁₃	—	4	2	no	—
127	#41×C₁₁₃	—	4	2	no	—
128	#41×C₁₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₁₃	C₂²×C₄	1	4	yes	—
135	C₂×D₄×C₁₁₃	—	2	4	no	—
136	C₂×D₄×C₁₁₃	—	2	4	no	—
137	C₂×D₄×C₁₁₃	—	2	2	no	—
138	C₂×D₄×C₁₁₃	—	2	2	no	—
139	C₂×D₄×C₁₁₃	—	2	2	no	—
140	C₂×D₄×C₁₁₃	—	2	2	no	—
141	C₂×D₄×C₁₁₃	—	2	2	no	—
142	C₂×D₄×C₁₁₃	—	4	2	no	—
143	C₂×D₄×C₁₁₃	—	4	2	no	—
144	C₂×D₄×C₁₁₃	—	4	2	no	—
145	C₂×D₄×C₁₁₃	—	4	2	no	—
146	C₂×D₄×C₁₁₃	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
168	C₂²×C₄×C₁₁₃	#41	1	1	yes	characteristic
169	C₂²×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
170	Q₁₆×C₁₁₃	—	2	4	no	—
171	Q₁₆×C₁₁₃	—	2	4	no	—
172	SD₁₆×C₁₁₃	—	2	8	no	—
173	SD₁₆×C₁₁₃	—	2	8	no	—
174	D₈×C₁₁₃	—	2	4	no	—
175	D₈×C₁₁₃	—	2	4	no	—
176	M₁₆×C₁₁₃	—	2	2	no	—
177	M₁₆×C₁₁₃	—	2	2	no	—
178	M₁₆×C₁₁₃	—	2	2	no	—
179	M₁₆×C₁₁₃	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₁₁₃	—	2	2	no	—
181	C₂×C₈×C₁₁₃	—	2	2	no	—
182	C₂×C₈×C₁₁₃	—	2	2	no	—
183	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
189	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
190	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
191	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
192	C₂×C₈×C₁₁₃	C₂²⋊C₄	1	2	yes	—
193	C₂×C₈×C₁₁₃	C₂²×C₄	1	2	yes	—
194	C₂×C₈×C₁₁₃	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
197	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₁₁₃	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₁₁₃	—	2	2	no	—
200	C₄⋊C₄×C₁₁₃	—	2	2	no	—
201	C₄⋊C₄×C₁₁₃	—	2	4	no	—
202	C₄⋊C₄×C₁₁₃	—	4	2	no	—
203	C₂²⋊C₄×C₁₁₃	—	2	2	no	—
204	C₂²⋊C₄×C₁₁₃	—	2	4	no	—
205	C₂²⋊C₄×C₁₁₃	—	4	2	no	—
206	C₂²⋊C₄×C₁₁₃	C₂×D₄	1	4	yes	—
207	C₄²×C₁₁₃	—	2	2	no	—
208	C₄²×C₁₁₃	—	2	2	no	—
209	C₄²×C₁₁₃	—	2	4	no	—
210	C₄²×C₁₁₃	—	4	2	no	—
211	C₂³×C₁₁₃	—	2	4	no	—
212	C₂³×C₁₁₃	—	4	2	no	—
213	C₂³×C₁₁₃	—	4	2	no	—
214	C₂³×C₁₁₃	—	4	2	no	—
215	C₂³×C₁₁₃	—	8	4	no	—
216	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
217	C₂³×C₁₁₃	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₁₁₃	#121	1	1	yes	characteristic
219	C₂³×C₁₁₃	#121	1	1	yes	characteristic
220	C₂³×C₁₁₃	#127	1	1	yes	characteristic
221	C₂³×C₁₁₃	#127	1	1	yes	characteristic
222	C₂³×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
223	Q₈×C₁₁₃	—	2	4	no	—
224	Q₈×C₁₁₃	—	2	4	no	—
225	Q₈×C₁₁₃	—	4	2	no	—
226	Q₈×C₁₁₃	—	4	2	no	—
227	D₄×C₁₁₃	—	2	4	no	—
228	D₄×C₁₁₃	—	2	4	no	—
229	D₄×C₁₁₃	—	4	4	no	—
230	D₄×C₁₁₃	—	4	4	no	—
231	D₄×C₁₁₃	—	4	4	no	—
232	D₄×C₁₁₃	—	4	4	no	—
233	D₄×C₁₁₃	—	4	2	no	—
234	D₄×C₁₁₃	—	4	2	no	—
235	C₂×C₄×C₁₁₃	—	2	4	no	—
236	C₂×C₄×C₁₁₃	—	2	4	no	—
237	C₂×C₄×C₁₁₃	—	4	4	no	—
238	C₂×C₄×C₁₁₃	—	4	2	no	—
239	C₂×C₄×C₁₁₃	—	4	2	no	—
240	C₂×C₄×C₁₁₃	—	4	4	no	—
241	C₂×C₄×C₁₁₃	—	4	4	no	—
242	C₂×C₄×C₁₁₃	—	4	4	no	—
243	C₂×C₄×C₁₁₃	—	4	4	no	—
244	C₂×C₄×C₁₁₃	—	4	4	no	—
245	C₂×C₄×C₁₁₃	—	8	4	no	—
246	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
258	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
259	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₁₃	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
263	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
264	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
265	C₂×C₄×C₁₁₃	#124	1	1	yes	characteristic
266	C₂×C₄×C₁₁₃	#127	1	1	yes	characteristic
267	C₂×C₄×C₁₁₃	#127	1	1	yes	characteristic
268	C₂×C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
274	C₈×C₁₁₃	—	2	4	no	—
275	C₈×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
276	C₈×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
277	C₈×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
278	C₈×C₁₁₃	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂²×C₁₁₃	—	2	2	no	—
280	C₂²×C₁₁₃	—	2	2	no	—
281	C₂²×C₁₁₃	—	2	2	no	—
282	C₂²×C₁₁₃	—	4	1	no	—
283	C₂²×C₁₁₃	—	4	1	no	—
284	C₂²×C₁₁₃	—	4	1	no	—
285	C₂²×C₁₁₃	—	4	1	no	—
286	C₂²×C₁₁₃	—	4	4	no	—
287	C₂²×C₁₁₃	—	8	4	no	—
288	C₂²×C₁₁₃	—	8	4	no	—
289	C₂²×C₁₁₃	—	8	4	no	—
290	C₂²×C₁₁₃	#390	1	1	yes	characteristic
291	C₂²×C₁₁₃	#390	1	1	yes	characteristic
292	C₂²×C₁₁₃	#390	1	1	yes	characteristic
293	C₂²×C₁₁₃	#390	1	1	yes	characteristic
294	C₂²×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₁₁₃	C₂×#121	1	1	yes	characteristic
296	C₂²×C₁₁₃	C₂×#127	1	1	yes	characteristic
297	C₄×C₁₁₃	—	4	4	no	—
298	C₄×C₁₁₃	—	4	4	no	—
299	C₄×C₁₁₃	—	8	4	no	—
300	C₄×C₁₁₃	#390	1	1	yes	characteristic
301	C₄×C₁₁₃	#390	1	1	yes	characteristic
302	C₄×C₁₁₃	#390	1	1	yes	characteristic
303	C₄×C₁₁₃	#390	1	1	yes	characteristic
304	C₄×C₁₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₁₁₃	C₂×#121	1	1	yes	characteristic
307	C₄×C₁₁₃	C₂×#124	1	1	yes	characteristic
308	C₂×#1976	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂×C₁₁₃	—	2	1	no	—
310	C₂×C₁₁₃	—	2	1	no	—
311	C₂×C₁₁₃	—	2	1	no	—
312	C₂×C₁₁₃	—	2	1	no	—
313	C₂×C₁₁₃	—	2	1	no	—
314	C₂×C₁₁₃	—	2	1	no	—
315	C₂×C₁₁₃	—	8	4	no	—
316	C₂×C₁₁₃	#1976	1	2	yes	direct product factor
317	C₂×C₁₁₃	C₂×#390	1	1	yes	characteristic
318	C₂²×#135	C₂×C₁₁₃	1	1	yes	characteristic
319	C₂×#427	C₂×C₁₁₃	1	1	yes	characteristic, complemented
320	C₂×#421	C₂×C₁₁₃	1	2	yes	complemented
321	C₂×#410	C₂×C₁₁₃	1	2	yes	complemented
322	C₂×#405	C₂×C₁₁₃	1	1	yes	characteristic, complemented
323	#1976	C₂×C₁₁₃	1	8	yes	direct product factor
324	C₁₁₃	C₂×#1976	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²×#41	C₂²×C₁₁₃	1	2	yes	—
326	C₂×#135	—	2	1	no	—
327	C₂×#135	—	2	1	no	—
328	C₂×#135	—	2	2	no	—
329	C₂×#135	—	2	1	no	—
330	C₂×#135	—	2	1	no	—
331	C₂×#135	—	2	2	no	—
332	C₂×#135	C₄×C₁₁₃	1	4	yes	complemented
333	C₂×#135	C₂²×C₁₁₃	1	4	yes	—
334	C₂²×Q₁₆	C₄×C₁₁₃	1	1	yes	characteristic, complemented
335	C₂²×SD₁₆	C₄×C₁₁₃	1	2	yes	complemented
336	C₂²×D₈	C₄×C₁₁₃	1	1	yes	characteristic, complemented
337	C₂²×M₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
338	C₂³×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
339	C₂×#117	C₂²×C₁₁₃	1	2	yes	—
340	C₂×#117	C₂²×C₁₁₃	1	1	yes	characteristic
341	#427	—	2	2	no	—
342	#427	C₂²×C₁₁₃	1	4	yes	complemented
343	C₂×#107	—	2	1	no	—
344	C₂×#106	—	2	1	no	—
345	#421	—	2	4	no	—
346	#421	C₂²×C₁₁₃	1	8	yes	complemented
347	C₂×#104	—	2	4	no	—
348	#410	—	2	4	no	—
349	#410	C₂²×C₁₁₃	1	8	yes	complemented
350	C₂×#99	—	2	4	no	—
351	#405	—	2	2	no	—
352	#405	C₂²×C₁₁₃	1	4	yes	complemented
353	C₂×#97	—	2	1	no	—
354	C₂×C₄×C₈	—	2	1	no	—
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	2	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	2	2	no	—
365	C₂×#41	C₂×C₄×C₁₁₃	1	4	yes	—
366	C₂×#41	C₂³×C₁₁₃	1	4	yes	—
367	C₂²×Q₈	C₂×C₄×C₁₁₃	1	2	yes	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	C₂×C₄×C₁₁₃	1	2	yes	—
370	C₂³×C₄	—	2	2	no	—
371	C₂³×C₄	C₂³×C₁₁₃	1	1	yes	characteristic
372	#135	—	2	4	no	—
373	#135	—	2	4	no	—
374	#135	—	2	4	no	—
375	#135	—	2	4	no	—
376	#135	—	2	4	no	—
377	#135	—	2	4	no	—
378	#135	—	2	4	no	—
379	#135	—	2	4	no	—
380	C₂×Q₁₆	—	2	1	no	—
381	C₂×Q₁₆	—	2	1	no	—
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	C₂×C₄×C₁₁₃	1	4	yes	complemented
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	4	no	—
387	C₂×SD₁₆	C₂×C₄×C₁₁₃	1	8	yes	complemented
388	C₂×D₈	—	2	1	no	—
389	C₂×D₈	—	2	1	no	—
390	C₂×D₈	—	2	2	no	—
391	C₂×D₈	C₂×C₄×C₁₁₃	1	4	yes	complemented
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	D₄×C₁₁₃	1	2	yes	—
396	C₂×M₁₆	D₄×C₁₁₃	1	2	yes	—
397	C₂×M₁₆	C₂³×C₁₁₃	1	2	yes	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
401	C₂²×C₈	C₂×C₄×C₁₁₃	1	2	yes	—
402	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
403	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
404	C₂²×C₈	D₄×C₁₁₃	1	2	yes	—
405	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
406	C₂²×C₈	D₄×C₁₁₃	1	1	yes	characteristic
407	C₂²×C₈	D₄×C₁₁₃	1	2	yes	—
408	C₂²×C₈	C₂³×C₁₁₃	1	2	yes	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	D₄×C₁₁₃	1	2	yes	—
415	#117	C₂³×C₁₁₃	1	4	yes	—
416	#117	C₂³×C₁₁₃	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	D₄×C₁₁₃	1	2	yes	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	2	no	—
423	#107	—	2	4	no	—
424	#106	—	2	4	no	—
425	#104	—	2	16	no	—
426	#99	—	2	16	no	—
427	#97	—	2	4	no	—
428	C₄×C₈	—	2	4	no	—
429	C₂⁴	—	2	2	no	—
430	C₂⁴	C₂×D₄×C₁₁₃	1	1	yes	characteristic
431	#41	—	2	4	no	—
432	#41	—	2	4	no	—
433	#41	—	2	4	no	—
434	#41	—	2	4	no	—
435	#41	—	2	4	no	—
436	#41	—	2	4	no	—
437	#41	—	2	4	no	—
438	#41	—	2	4	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	4	2	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	C₂²×C₄×C₁₁₃	1	4	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	C₂²×C₄×C₁₁₃	1	4	yes	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₁₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₁₃	1	1	yes	characteristic
483	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
484	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
485	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
486	C₂²×C₄	#41×C₁₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₁₁₃	1	1	yes	characteristic
488	Q₁₆	—	2	4	no	—
489	Q₁₆	—	2	4	no	—
490	SD₁₆	—	2	8	no	—
491	SD₁₆	—	2	8	no	—
492	D₈	—	2	4	no	—
493	D₈	—	2	4	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	C₂×D₄×C₁₁₃	1	4	yes	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
502	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
503	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
504	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
506	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
507	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
508	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
509	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
510	C₂×C₈	C₂²⋊C₄×C₁₁₃	1	2	yes	—
511	C₂×C₈	C₂²×C₄×C₁₁₃	1	2	yes	—
512	C₂×C₈	C₂²×C₄×C₁₁₃	1	2	yes	—
513	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
514	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₁₁₃	1	2	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	4	2	no	—
524	C₂²⋊C₄	C₂×D₄×C₁₁₃	1	4	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	4	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	4	2	no	—
533	C₂³	—	8	4	no	—
534	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
535	C₂³	C₄×D₄×C₁₁₃	1	1	yes	characteristic
536	C₂³	#121×C₁₁₃	1	1	yes	characteristic
537	C₂³	#121×C₁₁₃	1	1	yes	characteristic
538	C₂³	#127×C₁₁₃	1	1	yes	characteristic
539	C₂³	#127×C₁₁₃	1	1	yes	characteristic
540	C₂³	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
541	Q₈	—	2	4	no	—
542	Q₈	—	2	4	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	2	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	4	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	8	4	no	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
568	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
569	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
570	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
571	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
572	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
573	C₂×C₄	C₄×D₄×C₁₁₃	1	1	yes	characteristic
574	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
575	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
576	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
577	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
578	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
579	C₂×C₄	#121×C₁₁₃	1	1	yes	characteristic
580	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
581	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
582	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
583	C₂×C₄	#124×C₁₁₃	1	1	yes	characteristic
584	C₂×C₄	#127×C₁₁₃	1	1	yes	characteristic
585	C₂×C₄	#127×C₁₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×C₄×C₁₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₄×C₁₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₁₃	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
594	C₈	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
595	C₈	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
596	C₈	C₂×C₂²⋊C₄×C₁₁₃	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	8	4	no	—
607	C₂²	—	8	4	no	—
608	C₂²	#390×C₁₁₃	1	1	yes	characteristic
609	C₂²	#390×C₁₁₃	1	1	yes	characteristic
610	C₂²	#390×C₁₁₃	1	1	yes	characteristic
611	C₂²	#390×C₁₁₃	1	1	yes	characteristic
612	C₂²	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
613	C₂²	C₂×#121×C₁₁₃	1	1	yes	characteristic
614	C₂²	C₂×#127×C₁₁₃	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	4	4	no	—
617	C₄	—	8	4	no	—
618	C₄	#390×C₁₁₃	1	1	yes	characteristic
619	C₄	#390×C₁₁₃	1	1	yes	characteristic
620	C₄	#390×C₁₁₃	1	1	yes	characteristic
621	C₄	#390×C₁₁₃	1	1	yes	characteristic
622	C₄	C₂²×C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
623	C₄	C₂×C₄×D₄×C₁₁₃	1	1	yes	characteristic
624	C₄	C₂×#121×C₁₁₃	1	1	yes	characteristic
625	C₄	C₂×#124×C₁₁₃	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	4	no	—
633	C₂	C₁₁₃×#1976	1	2	yes	direct product factor
634	C₂	C₂×#390×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁₃	#121
commutator	C₂×C₄	C₂³×C₄×C₁₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁₃
socle	C₂²×C₁₁₃	#390
prime radical	C₂²×#135×C₁₁₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₂³×C₄×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#427×C₁₁₃	C₂	semidirect
3. C₂×#421×C₁₁₃	C₂	semidirect
4. C₂×#410×C₁₁₃	C₂	semidirect
5. C₂×#405×C₁₁₃	C₂	semidirect
6. C₁₁₃×#1976	C₂	direct (N × H)
14. C₂×#135×C₁₁₃	C₄	semidirect
16. C₂²×Q₁₆×C₁₁₃	C₄	semidirect
17. C₂²×SD₁₆×C₁₁₃	C₄	semidirect
18. C₂²×D₈×C₁₁₃	C₄	semidirect
24. #427×C₁₁₃	C₂²	semidirect
28. #421×C₁₁₃	C₂²	semidirect
31. #410×C₁₁₃	C₂²	semidirect
34. #405×C₁₁₃	C₂²	semidirect
65. C₂×Q₁₆×C₁₁₃	C₂×C₄	semidirect
69. C₂×SD₁₆×C₁₁₃	C₂×C₄	semidirect
73. C₂×D₈×C₁₁₃	C₂×C₄	semidirect
308. C₂×#1976	C₁₁₃	direct (N × H)
316. C₂×C₁₁₃	#1976	direct (N × H)
319. C₂×#427	C₂×C₁₁₃	semidirect
320. C₂×#421	C₂×C₁₁₃	semidirect
321. C₂×#410	C₂×C₁₁₃	semidirect
322. C₂×#405	C₂×C₁₁₃	semidirect
323. #1976	C₂×C₁₁₃	direct (N × H)
324. C₁₁₃	C₂×#1976	direct (N × H)
332. C₂×#135	C₄×C₁₁₃	semidirect
334. C₂²×Q₁₆	C₄×C₁₁₃	semidirect
335. C₂²×SD₁₆	C₄×C₁₁₃	semidirect
336. C₂²×D₈	C₄×C₁₁₃	semidirect
342. #427	C₂²×C₁₁₃	semidirect
346. #421	C₂²×C₁₁₃	semidirect
349. #410	C₂²×C₁₁₃	semidirect
352. #405	C₂²×C₁₁₃	semidirect
383. C₂×Q₁₆	C₂×C₄×C₁₁₃	semidirect
387. C₂×SD₁₆	C₂×C₄×C₁₁₃	semidirect
391. C₂×D₈	C₂×C₄×C₁₁₃	semidirect
633. C₂	C₁₁₃×#1976	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₁₁₃	2
C₂×#427×C₁₁₃	2
C₂×#421×C₁₁₃	2
C₂×#410×C₁₁₃	2
C₂×#405×C₁₁₃	2
C₁₁₃×#1976	2
C₂×#1976	113

Subgroups — C2×C113×#1976 #43289263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁₃×#1976 #43289263