Subgroups — C₁₃×#34929 #15721268

Order 3328.

2308 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2556	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2506	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2492	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2452	C₂	1	2	yes	maximal
10	C₁₃×#2429	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2293	C₂	1	2	yes	maximal
16	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#533	—	2	16	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#125	C₂²	1	4	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	4	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#400	C₂²	1	4	yes	—
39	C₁₃×#399	C₂²	1	4	yes	—
40	C₁₃×#398	C₂²	1	4	yes	—
41	C₁₃×#398	C₂²	1	4	yes	—
42	C₁₃×#396	C₂²	1	4	yes	—
43	C₁₃×#396	C₂²	1	4	yes	—
44	C₁₃×#395	C₂²	1	4	yes	—
45	C₁₃×#393	C₂²	1	4	yes	—
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	4	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#390	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	2	yes	—
51	C₁₃×#389	C₂²	1	2	yes	—
52	C₁₃×#389	C₂²	1	2	yes	—
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	2	yes	—
57	C₁₃×#389	C₂²	1	2	yes	—
58	C₁₃×#389	C₂²	1	4	yes	—
59	C₁₃×#388	C₂²	1	4	yes	—
60	C₁₃×#388	C₂²	1	4	yes	—
61	C₁₃×#387	C₂²	1	4	yes	—
62	C₁₃×#385	C₂²	1	4	yes	—
63	C₁₃×#384	C₂²	1	2	yes	—
64	C₁₃×#384	C₂²	1	1	yes	characteristic
65	C₁₃×#380	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄³×C₁₃	C₂²	1	1	yes	characteristic
83	C₄³×C₁₃	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	—	2	8	no	—
92	C₁₃×C₄⋊Q₈	—	2	8	no	—
93	C₁₃×C₄⋊Q₈	—	2	8	no	—
94	C₁₃×C₄⋊Q₈	—	2	4	no	—
95	C₁₃×#125	—	2	16	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	—	2	16	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₄×Q₈×C₁₃	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	16	no	—
102	C₄×Q₈×C₁₃	—	2	8	no	—
103	C₄×Q₈×C₁₃	—	2	4	no	—
104	C₄×Q₈×C₁₃	D₄	1	8	yes	complemented
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
108	C₁₃×#117	—	2	16	no	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	—	2	8	no	—
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#95	C₂³	1	2	yes	—
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	2	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	#34929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₁₃	—	2	8	no	—
171	C₂×Q₈×C₁₃	—	2	4	no	—
172	C₂×Q₈×C₁₃	—	2	2	no	—
173	C₂×Q₈×C₁₃	—	2	2	no	—
174	C₂×Q₈×C₁₃	—	2	4	no	—
175	C₂×Q₈×C₁₃	—	2	8	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	—	4	4	no	—
178	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
182	C₂²×C₄×C₁₃	—	2	4	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	4	2	no	—
190	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	—	2	8	no	—
208	C₁₃×C₄⋊C₄	—	2	8	no	—
209	C₁₃×C₄⋊C₄	—	2	8	no	—
210	C₁₃×C₄⋊C₄	—	2	8	no	—
211	C₁₃×C₄⋊C₄	—	2	8	no	—
212	C₁₃×C₄⋊C₄	—	2	8	no	—
213	C₁₃×C₄⋊C₄	—	2	4	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	2	8	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	4	no	—
222	C₁₃×C₄⋊C₄	—	2	4	no	—
223	C₁₃×C₄⋊C₄	—	4	2	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
226	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
227	C₁₃×C₄⋊C₄	#41	1	4	yes	—
228	C₁₃×C₄⋊C₄	#41	1	4	yes	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	—	2	8	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	4	no	—
233	C₁₃×C₂²⋊C₄	—	2	8	no	—
234	C₁₃×C₂²⋊C₄	—	4	4	no	—
235	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	—	2	4	no	—
239	C₄²×C₁₃	—	2	8	no	—
240	C₄²×C₁₃	—	2	2	no	—
241	C₄²×C₁₃	—	2	4	no	—
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	—	2	4	no	—
245	C₄²×C₁₃	—	2	2	no	—
246	C₄²×C₁₃	—	2	4	no	—
247	C₄²×C₁₃	—	4	1	no	—
248	C₄²×C₁₃	—	4	2	no	—
249	C₄²×C₁₃	C₂×D₄	1	4	yes	—
250	C₄²×C₁₃	C₂×D₄	1	8	yes	—
251	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
252	C₄²×C₁₃	#41	1	4	yes	—
253	C₂×#533	C₂×C₁₃	1	2	yes	complemented
254	#2556	C₂×C₁₃	1	4	yes	complemented
255	#2551	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2546	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2542	C₂×C₁₃	1	1	yes	characteristic
258	#2538	C₂×C₁₃	1	1	yes	characteristic
259	#2506	C₂×C₁₃	1	2	yes	complemented
260	#2492	C₂×C₁₃	1	2	yes	complemented
261	#2452	C₂×C₁₃	1	2	yes	—
262	#2429	C₂×C₁₃	1	2	yes	complemented
263	#2396	C₂×C₁₃	1	4	yes	complemented
264	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
265	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
267	#2293	C₂×C₁₃	1	2	yes	—
268	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
269	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	2	2	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	—	2	2	no	—
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
277	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
278	Q₈×C₁₃	—	2	8	no	—
279	Q₈×C₁₃	—	4	16	no	—
280	Q₈×C₁₃	—	4	8	no	—
281	D₄×C₁₃	—	2	8	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	16	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	4	8	no	—
315	C₂×C₄×C₁₃	—	4	8	no	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
323	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
324	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
325	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
326	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
327	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
328	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
329	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
330	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
332	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
333	#533	—	2	16	no	—
334	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
335	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
337	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
338	C₂×#125	C₂²×C₁₃	1	4	yes	—
339	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
340	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
341	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
342	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
343	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
344	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
345	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#117	C₂²×C₁₃	1	4	yes	—
352	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
353	#400	C₂²×C₁₃	1	4	yes	—
354	#399	C₂²×C₁₃	1	4	yes	—
355	#398	C₂²×C₁₃	1	4	yes	—
356	#398	C₂²×C₁₃	1	4	yes	—
357	#396	C₂²×C₁₃	1	4	yes	—
358	#396	C₂²×C₁₃	1	4	yes	—
359	#395	C₂²×C₁₃	1	4	yes	—
360	#393	C₂²×C₁₃	1	4	yes	—
361	#391	C₂²×C₁₃	1	2	yes	—
362	#391	C₂²×C₁₃	1	4	yes	—
363	#391	C₂²×C₁₃	1	2	yes	—
364	#390	C₂²×C₁₃	1	2	yes	—
365	#390	C₂²×C₁₃	1	2	yes	—
366	#389	C₂²×C₁₃	1	4	yes	—
367	#389	C₂²×C₁₃	1	2	yes	—
368	#389	C₂²×C₁₃	1	2	yes	—
369	#389	C₂²×C₁₃	1	2	yes	—
370	#389	C₂²×C₁₃	1	2	yes	—
371	#389	C₂²×C₁₃	1	2	yes	—
372	#389	C₂²×C₁₃	1	2	yes	—
373	#389	C₂²×C₁₃	1	2	yes	—
374	#388	C₂²×C₁₃	1	4	yes	—
375	#388	C₂²×C₁₃	1	4	yes	—
376	#387	C₂²×C₁₃	1	4	yes	—
377	#385	C₂²×C₁₃	1	4	yes	—
378	#384	C₂²×C₁₃	1	2	yes	—
379	#384	C₂²×C₁₃	1	1	yes	characteristic
380	#380	C₂²×C₁₃	1	2	yes	—
381	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
383	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
384	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
385	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
386	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
387	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
389	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
392	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
393	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
396	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
397	C₄³	C₂²×C₁₃	1	1	yes	characteristic
398	C₄³	C₂²×C₁₃	1	2	yes	—
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	4	no	—
402	C₂²×C₁₃	—	4	2	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	2	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
407	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
408	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
412	C₂²×C₁₃	#585	1	1	yes	characteristic
413	C₄×C₁₃	—	2	4	no	—
414	C₄×C₁₃	—	2	2	no	—
415	C₄×C₁₃	—	2	4	no	—
416	C₄×C₁₃	—	2	2	no	—
417	C₄×C₁₃	—	2	4	no	—
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	4	no	—
421	C₄×C₁₃	—	4	2	no	—
422	C₄×C₁₃	—	4	4	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	4	no	—
425	C₄×C₁₃	—	4	1	no	—
426	C₄×C₁₃	#532	1	4	yes	—
427	C₄×C₁₃	#533	1	4	yes	complemented
428	C₄×C₁₃	D₄×Q₈	1	4	yes	—
429	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
430	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
431	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
434	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
435	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
436	C₄⋊Q₈	—	2	8	no	—
437	C₄⋊Q₈	—	2	8	no	—
438	C₄⋊Q₈	—	2	8	no	—
439	C₄⋊Q₈	—	2	4	no	—
440	#125	—	2	16	no	—
441	C₂²⋊Q₈	—	2	8	no	—
442	C₂²⋊Q₈	—	2	8	no	—
443	C₂²⋊Q₈	—	2	16	no	—
444	C₂²⋊Q₈	—	2	8	no	—
445	C₄×Q₈	—	2	4	no	—
446	C₄×Q₈	—	2	16	no	—
447	C₄×Q₈	—	2	8	no	—
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	D₄×C₁₃	1	8	yes	complemented
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
453	#117	—	2	16	no	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂×C₄²	—	2	8	no	—
484	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
485	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
497	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
501	#95	C₂³×C₁₃	1	2	yes	—
502	#95	C₂³×C₁₃	1	2	yes	—
503	#95	C₂³×C₁₃	1	2	yes	—
504	#95	C₂³×C₁₃	1	4	yes	—
505	#95	C₂³×C₁₃	1	4	yes	—
506	#95	C₂³×C₁₃	1	2	yes	—
507	#95	C₂³×C₁₃	1	2	yes	—
508	#95	C₂³×C₁₃	1	2	yes	—
509	#95	C₂³×C₁₃	1	4	yes	—
510	#95	C₂³×C₁₃	1	4	yes	—
511	#95	C₂³×C₁₃	1	4	yes	—
512	#95	C₂³×C₁₃	1	4	yes	—
513	C₂×C₁₃	—	4	4	no	—
514	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
515	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
516	C₂×C₁₃	#3461	1	1	yes	characteristic
517	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
518	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
519	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
520	C₂×C₁₃	#3482	1	1	yes	characteristic
521	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
522	C₂×Q₈	—	2	8	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	8	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	4	4	no	—
530	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
543	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₄⋊C₄	—	2	8	no	—
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	8	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
577	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
579	C₄⋊C₄	C₁₃×#41	1	4	yes	—
580	C₄⋊C₄	C₁₃×#41	1	4	yes	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	4	4	no	—
587	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
588	C₄²	—	2	4	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	8	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	4	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	4	no	—
599	C₄²	—	4	1	no	—
600	C₄²	—	4	2	no	—
601	C₄²	C₂×D₄×C₁₃	1	4	yes	—
602	C₄²	C₂×D₄×C₁₃	1	8	yes	—
603	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
604	C₄²	C₁₃×#41	1	4	yes	—
605	C₁₃	#34929	1	1	yes	characteristic, direct product factor, Sylow
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
613	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
614	Q₈	—	2	8	no	—
615	Q₈	—	4	16	no	—
616	Q₈	—	4	8	no	—
617	D₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	16	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
654	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
658	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
659	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
660	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
661	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
662	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
663	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
664	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
665	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
666	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
667	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
668	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
677	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
678	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
679	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
680	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
681	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
682	C₂²	C₁₃×#585	1	1	yes	characteristic
683	C₄	—	2	4	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	1	no	—
696	C₄	C₁₃×#532	1	4	yes	—
697	C₄	C₁₃×#533	1	4	yes	complemented
698	C₄	D₄×Q₈×C₁₃	1	4	yes	—
699	C₂	—	4	4	no	—
700	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
701	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
702	C₂	C₁₃×#3461	1	1	yes	characteristic
703	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
704	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
705	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
706	C₂	C₁₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
2. C₁₃×#2556	C₂	semidirect
3. C₁₃×#2551	C₂	semidirect
4. C₁₃×#2546	C₂	semidirect
7. C₁₃×#2506	C₂	semidirect
8. C₁₃×#2492	C₂	semidirect
10. C₁₃×#2429	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
16. C₄²×Q₈×C₁₃	C₂	semidirect
104. C₄×Q₈×C₁₃	D₄	semidirect
107. C₄×D₄×C₁₃	Q₈	semidirect
168. #34929	C₁₃	direct (N × H)
253. C₂×#533	C₂×C₁₃	semidirect
254. #2556	C₂×C₁₃	semidirect
255. #2551	C₂×C₁₃	semidirect
256. #2546	C₂×C₁₃	semidirect
259. #2506	C₂×C₁₃	semidirect
260. #2492	C₂×C₁₃	semidirect
262. #2429	C₂×C₁₃	semidirect
263. #2396	C₂×C₁₃	semidirect
264. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
265. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
266. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
268. C₄²×Q₈	C₂×C₁₃	semidirect
427. C₄×C₁₃	#533	semidirect
449. C₄×Q₈	D₄×C₁₃	semidirect
452. C₄×D₄	Q₈×C₁₃	semidirect
605. C₁₃	#34929	direct (N × H)
697. C₄	C₁₃×#533	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₁₃×#2556	2
C₁₃×#2551	2
C₁₃×#2546	2
C₁₃×#2542	2
C₁₃×#2538	2
C₁₃×#2506	2
C₁₃×#2492	2
C₁₃×#2452	2
C₁₃×#2429	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
C₄²×D₄×C₁₃	2
#34929	13

Subgroups — C13×#34929 #15721268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34929 #15721268