Subgroups — C₂×C₁₃×#3258 #15747248

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3258	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#468	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#542	—	2	4	no	—
24	C₁₃×#542	C₂²	1	8	yes	—
25	C₁₃×#541	—	2	4	no	—
26	C₁₃×#541	C₂²	1	8	yes	complemented
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#126	—	2	1	no	—
30	C₂×C₁₃×#126	—	2	1	no	—
31	C₂×C₁₃×#126	—	2	1	no	—
32	C₂×C₁₃×#125	—	2	1	no	—
33	C₂×C₁₃×#125	—	2	1	no	—
34	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#123	—	2	1	no	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₁₃×#479	C₂²	1	8	yes	complemented
49	C₁₃×#478	C₂²	1	8	yes	complemented
50	C₁₃×#477	C₂²	1	8	yes	complemented
51	C₁₃×#475	C₂²	1	8	yes	complemented
52	C₁₃×#470	C₂²	1	8	yes	complemented
53	C₁₃×#468	C₂²	1	8	yes	—
54	C₁₃×#467	C₂²	1	8	yes	complemented
55	C₁₃×#465	C₂²	1	8	yes	—
56	C₁₃×#464	C₂²	1	8	yes	complemented
57	C₁₃×#464	C₂²	1	8	yes	complemented
58	C₁₃×#462	C₂²	1	8	yes	complemented
59	C₁₃×#461	C₂²	1	8	yes	complemented
60	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
64	C₁₃×#424	C₂²	1	8	yes	complemented
65	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	—	2	1	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×Q₁₆	—	4	2	no	—
86	C₂×C₁₃×Q₁₆	—	4	2	no	—
87	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	—	4	2	no	—
90	C₂×C₁₃×SD₁₆	—	4	2	no	—
91	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×M₁₆	—	4	2	no	—
94	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
95	C₂²×C₈×C₁₃	—	4	2	no	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
101	C₁₃×C₄⋊Q₈	—	2	2	no	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₁₃×#126	—	2	8	no	—
106	C₁₃×#126	—	2	8	no	—
107	C₁₃×#126	—	2	8	no	—
108	C₁₃×#125	—	2	8	no	—
109	C₁₃×#125	—	2	8	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	C₂³	1	4	yes	—
112	C₁₃×#124	—	2	8	no	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	C₂³	1	4	yes	—
115	C₁₃×#123	—	2	8	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	2	no	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₁₃×C₂²⋊Q₈	—	2	8	no	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	C₂³	1	4	yes	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
129	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
131	C₄×D₄×C₁₃	—	2	2	no	—
132	C₄×D₄×C₁₃	C₂³	1	4	yes	—
133	C₁₃×#117	D₄	1	4	yes	—
134	C₁₃×#117	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
147	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	—	2	1	no	—
162	C₂×C₄²×C₁₃	—	2	1	no	—
163	C₂×C₄²×C₁₃	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₁₃×#107	C₂³	1	4	yes	—
167	C₁₃×#107	C₂³	1	4	yes	—
168	C₁₃×#106	C₂³	1	4	yes	—
169	C₁₃×#106	C₂³	1	4	yes	—
170	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₁₃×#103	C₂³	1	4	yes	—
175	C₁₃×#103	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	4	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₂×#3258	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	—	2	1	no	—
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	4	no	—
189	C₂×Q₈×C₁₃	—	2	2	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	2	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	8	2	no	—
196	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	2	no	—
203	C₂×D₄×C₁₃	—	8	2	no	—
204	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	4	no	—
215	C₂²×C₄×C₁₃	—	8	2	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₁₃×Q₁₆	—	4	4	no	—
225	C₁₃×Q₁₆	—	4	4	no	—
226	C₁₃×SD₁₆	—	4	4	no	—
227	C₁₃×SD₁₆	—	4	4	no	—
228	C₁₃×M₁₆	—	4	4	no	—
229	C₂×C₈×C₁₃	—	2	2	no	—
230	C₂×C₈×C₁₃	—	2	2	no	—
231	C₂×C₈×C₁₃	—	2	2	no	—
232	C₂×C₈×C₁₃	—	2	2	no	—
233	C₂×C₈×C₁₃	—	4	4	no	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
254	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
255	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	4	no	—
261	C₁₃×C₂²⋊C₄	—	2	4	no	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
267	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	—	2	4	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	C₂×D₄	1	2	yes	—
272	C₄²×C₁₃	C₂×D₄	1	2	yes	—
273	C₄²×C₁₃	C₂⁴	1	2	yes	—
274	C₄²×C₁₃	C₂⁴	1	2	yes	—
275	C₂×#542	C₂×C₁₃	1	1	yes	characteristic
276	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#3258	C₂×C₁₃	1	16	yes	direct product factor
278	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
279	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
281	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂×#468	C₂×C₁₃	1	1	yes	characteristic
284	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂×#465	C₂×C₁₃	1	1	yes	characteristic
286	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
287	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
290	C₂×#424	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	4	2	no	—
296	C₂³×C₁₃	—	4	2	no	—
297	C₂³×C₁₃	—	4	2	no	—
298	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
299	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₁₃	—	2	2	no	—
301	Q₈×C₁₃	—	2	2	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	2	2	no	—
305	Q₈×C₁₃	—	2	2	no	—
306	Q₈×C₁₃	—	4	2	no	—
307	Q₈×C₁₃	—	4	2	no	—
308	Q₈×C₁₃	—	4	2	no	—
309	Q₈×C₁₃	—	8	4	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	2	no	—
312	D₄×C₁₃	—	4	2	no	—
313	D₄×C₁₃	—	8	4	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	4	2	no	—
330	C₂×C₄×C₁₃	—	4	2	no	—
331	C₂×C₄×C₁₃	—	4	2	no	—
332	C₂×C₄×C₁₃	—	4	2	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	2	no	—
335	C₂×C₄×C₁₃	—	4	2	no	—
336	C₂×C₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
345	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
346	C₈×C₁₃	—	2	2	no	—
347	C₈×C₁₃	—	2	2	no	—
348	C₈×C₁₃	—	2	2	no	—
349	C₈×C₁₃	—	2	2	no	—
350	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
354	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
355	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
356	#542	—	2	4	no	—
357	#542	C₂²×C₁₃	1	8	yes	—
358	#541	—	2	4	no	—
359	#541	C₂²×C₁₃	1	8	yes	complemented
360	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×#126	—	2	1	no	—
363	C₂×#126	—	2	1	no	—
364	C₂×#126	—	2	1	no	—
365	C₂×#125	—	2	1	no	—
366	C₂×#125	—	2	1	no	—
367	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#124	—	2	1	no	—
369	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#123	—	2	1	no	—
371	C₂×C₂²⋊Q₈	—	2	1	no	—
372	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
381	#479	C₂²×C₁₃	1	8	yes	complemented
382	#478	C₂²×C₁₃	1	8	yes	complemented
383	#477	C₂²×C₁₃	1	8	yes	complemented
384	#475	C₂²×C₁₃	1	8	yes	complemented
385	#470	C₂²×C₁₃	1	8	yes	complemented
386	#468	C₂²×C₁₃	1	8	yes	—
387	#467	C₂²×C₁₃	1	8	yes	complemented
388	#465	C₂²×C₁₃	1	8	yes	—
389	#464	C₂²×C₁₃	1	8	yes	complemented
390	#464	C₂²×C₁₃	1	8	yes	complemented
391	#462	C₂²×C₁₃	1	8	yes	complemented
392	#461	C₂²×C₁₃	1	8	yes	complemented
393	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
397	#424	C₂²×C₁₃	1	8	yes	complemented
398	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	4	4	no	—
414	C₂²×C₁₃	—	4	2	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	8	4	no	—
418	C₂²×C₁₃	#537	1	2	yes	—
419	C₂²×C₁₃	#577	1	2	yes	—
420	C₂²×C₁₃	#578	1	2	yes	—
421	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
422	C₄×C₁₃	—	2	2	no	—
423	C₄×C₁₃	—	2	2	no	—
424	C₄×C₁₃	—	2	2	no	—
425	C₄×C₁₃	—	2	2	no	—
426	C₄×C₁₃	—	2	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	2	no	—
429	C₄×C₁₃	—	4	2	no	—
430	C₄×C₁₃	—	4	2	no	—
431	C₄×C₁₃	—	4	2	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	#537	1	2	yes	—
435	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×Q₁₆	—	4	2	no	—
446	C₂×Q₁₆	—	4	2	no	—
447	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
448	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
449	C₂×SD₁₆	—	4	2	no	—
450	C₂×SD₁₆	—	4	2	no	—
451	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
452	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
453	C₂×M₁₆	—	4	2	no	—
454	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
455	C₂²×C₈	—	4	2	no	—
456	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
464	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
465	#126	—	2	8	no	—
466	#126	—	2	8	no	—
467	#126	—	2	8	no	—
468	#125	—	2	8	no	—
469	#125	—	2	8	no	—
470	#125	—	2	2	no	—
471	#125	C₂³×C₁₃	1	4	yes	—
472	#124	—	2	8	no	—
473	#124	—	2	2	no	—
474	#124	C₂³×C₁₃	1	4	yes	—
475	#123	—	2	8	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
481	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
482	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
483	#121	—	2	2	no	—
484	#121	C₂³×C₁₃	1	4	yes	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
489	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
490	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	C₂³×C₁₃	1	4	yes	—
493	#117	D₄×C₁₃	1	4	yes	—
494	#117	C₂³×C₁₃	1	4	yes	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	—	2	1	no	—
523	C₂×C₄²	—	2	1	no	—
524	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
526	#107	C₂³×C₁₃	1	4	yes	—
527	#107	C₂³×C₁₃	1	4	yes	—
528	#106	C₂³×C₁₃	1	4	yes	—
529	#106	C₂³×C₁₃	1	4	yes	—
530	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
531	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
532	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
533	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
534	#103	C₂³×C₁₃	1	4	yes	—
535	#103	C₂³×C₁₃	1	4	yes	—
536	#103	C₂³×C₁₃	1	4	yes	—
537	#103	C₂³×C₁₃	1	4	yes	—
538	#103	C₂³×C₁₃	1	4	yes	—
539	#103	C₂³×C₁₃	1	4	yes	—
540	#102	C₂³×C₁₃	1	4	yes	—
541	#102	C₂³×C₁₃	1	4	yes	—
542	C₂×C₁₃	—	4	2	no	—
543	C₂×C₁₃	—	8	2	no	—
544	C₂×C₁₃	#3258	1	4	yes	direct product factor
545	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
546	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
547	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
548	C₂⁴	—	2	1	no	—
549	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	8	2	no	—
561	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
562	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
563	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	8	2	no	—
569	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	8	2	no	—
581	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
589	Q₁₆	—	4	4	no	—
590	Q₁₆	—	4	4	no	—
591	SD₁₆	—	4	4	no	—
592	SD₁₆	—	4	4	no	—
593	M₁₆	—	4	4	no	—
594	C₂×C₈	—	2	2	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	4	4	no	—
599	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
600	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
601	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
602	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
619	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
620	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
632	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	C₂×D₄×C₁₃	1	2	yes	—
637	C₄²	C₂×D₄×C₁₃	1	2	yes	—
638	C₄²	C₂⁴×C₁₃	1	2	yes	—
639	C₄²	C₂⁴×C₁₃	1	2	yes	—
640	C₁₃	C₂×#3258	1	1	yes	characteristic, direct product factor, Sylow
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
649	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	8	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	8	4	no	—
687	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
694	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
695	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	8	4	no	—
708	C₂²	C₁₃×#537	1	2	yes	—
709	C₂²	C₁₃×#577	1	2	yes	—
710	C₂²	C₁₃×#578	1	2	yes	—
711	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₁₃×#537	1	2	yes	—
725	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
726	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	C₁₃×#3258	1	4	yes	direct product factor
730	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
731	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
732	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#541	C₂	semidirect
3. C₁₃×#3258	C₂	direct (N × H)
4. C₂×C₁₃×#479	C₂	semidirect
5. C₂×C₁₃×#477	C₂	semidirect
6. C₂×C₁₃×#475	C₂	semidirect
7. C₂×C₁₃×#478	C₂	semidirect
8. C₂×C₁₃×#470	C₂	semidirect
10. C₂×C₁₃×#467	C₂	semidirect
12. C₂×C₁₃×#464	C₂	semidirect
13. C₂×C₁₃×#464	C₂	semidirect
14. C₂×C₁₃×#462	C₂	semidirect
15. C₂×C₁₃×#461	C₂	semidirect
16. C₂×C₁₃×#424	C₂	semidirect
26. C₁₃×#541	C₂²	semidirect
48. C₁₃×#479	C₂²	semidirect
49. C₁₃×#478	C₂²	semidirect
50. C₁₃×#477	C₂²	semidirect
51. C₁₃×#475	C₂²	semidirect
52. C₁₃×#470	C₂²	semidirect
54. C₁₃×#467	C₂²	semidirect
56. C₁₃×#464	C₂²	semidirect
57. C₁₃×#464	C₂²	semidirect
58. C₁₃×#462	C₂²	semidirect
59. C₁₃×#461	C₂²	semidirect
64. C₁₃×#424	C₂²	semidirect
182. C₂×#3258	C₁₃	direct (N × H)
276. C₂×#541	C₂×C₁₃	semidirect
277. #3258	C₂×C₁₃	direct (N × H)
278. C₂×#479	C₂×C₁₃	semidirect
279. C₂×#477	C₂×C₁₃	semidirect
280. C₂×#475	C₂×C₁₃	semidirect
281. C₂×#478	C₂×C₁₃	semidirect
282. C₂×#470	C₂×C₁₃	semidirect
284. C₂×#467	C₂×C₁₃	semidirect
286. C₂×#464	C₂×C₁₃	semidirect
287. C₂×#464	C₂×C₁₃	semidirect
288. C₂×#462	C₂×C₁₃	semidirect
289. C₂×#461	C₂×C₁₃	semidirect
290. C₂×#424	C₂×C₁₃	semidirect
359. #541	C₂²×C₁₃	semidirect
381. #479	C₂²×C₁₃	semidirect
382. #478	C₂²×C₁₃	semidirect
383. #477	C₂²×C₁₃	semidirect
384. #475	C₂²×C₁₃	semidirect
385. #470	C₂²×C₁₃	semidirect
387. #467	C₂²×C₁₃	semidirect
389. #464	C₂²×C₁₃	semidirect
390. #464	C₂²×C₁₃	semidirect
391. #462	C₂²×C₁₃	semidirect
392. #461	C₂²×C₁₃	semidirect
397. #424	C₂²×C₁₃	semidirect
544. C₂×C₁₃	#3258	direct (N × H)
640. C₁₃	C₂×#3258	direct (N × H)
729. C₂	C₁₃×#3258	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×C₁₃×#542	2
C₂×C₁₃×#541	2
C₁₃×#3258	2
C₂×C₁₃×#479	2
C₂×C₁₃×#477	2
C₂×C₁₃×#475	2
C₂×C₁₃×#478	2
C₂×C₁₃×#470	2
C₂×C₁₃×#468	2
C₂×C₁₃×#467	2
C₂×C₁₃×#465	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#461	2
C₂×C₁₃×#424	2
C₂×#3258	13

Subgroups — C2×C13×#3258 #15747248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3258 #15747248