Subgroups — C₁₃×#34481 #15720820

Order 3328.

2132 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2383	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2367	C₂	1	2	yes	maximal
4	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
6	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2347	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2334	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2326	C₂	1	2	yes	maximal
12	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2320	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2317	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#556	C₄	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#126	C₂²	1	4	yes	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#391	C₂²	1	1	yes	characteristic
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	4	yes	—
49	C₁₃×#389	C₂²	1	4	yes	—
50	C₁₃×#389	C₂²	1	4	yes	—
51	C₁₃×#388	C₂²	1	2	yes	—
52	C₁₃×#388	C₂²	1	2	yes	—
53	C₁₃×#388	C₂²	1	4	yes	—
54	C₁₃×#388	C₂²	1	4	yes	—
55	C₁₃×#388	C₂²	1	4	yes	—
56	C₁₃×#388	C₂²	1	4	yes	—
57	C₁₃×#387	C₂²	1	2	yes	—
58	C₁₃×#387	C₂²	1	2	yes	—
59	C₁₃×#387	C₂²	1	4	yes	—
60	C₁₃×#387	C₂²	1	4	yes	—
61	C₁₃×#387	C₂²	1	4	yes	—
62	C₁₃×#385	C₂²	1	4	yes	—
63	C₁₃×#385	C₂²	1	4	yes	—
64	C₁₃×#385	C₂²	1	4	yes	—
65	C₁₃×#385	C₂²	1	4	yes	—
66	C₁₃×#384	C₂²	1	1	yes	characteristic
67	C₁₃×#384	C₂²	1	4	yes	—
68	C₁₃×#384	C₂²	1	2	yes	—
69	C₁₃×#383	C₂²	1	4	yes	—
70	C₁₃×#382	C₂²	1	4	yes	—
71	C₁₃×#380	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₁₃×#376	C₂²	1	2	yes	—
83	C₄³×C₁₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
89	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₁₃×#126	C₂×C₄	1	32	yes	complemented
91	C₁₃×#124	C₂×C₄	1	16	yes	—
92	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
93	C₄×Q₈×C₁₃	—	4	4	no	—
94	C₄×Q₈×C₁₃	—	4	4	no	—
95	C₄×Q₈×C₁₃	—	4	4	no	—
96	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
97	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
98	C₄×D₄×C₁₃	—	4	4	no	—
99	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
100	C₁₃×#117	—	4	4	no	—
101	C₁₃×#117	C₂×C₄	1	16	yes	complemented
102	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
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	2	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	#34481	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₁₃	—	2	2	no	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
170	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₁₃	—	2	2	no	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	4	4	no	—
177	C₂²×C₄×C₁₃	—	4	4	no	—
178	C₂²×C₄×C₁₃	—	4	4	no	—
179	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	4	4	no	—
204	C₁₃×C₄⋊C₄	—	4	2	no	—
205	C₁₃×C₄⋊C₄	—	4	2	no	—
206	C₁₃×C₄⋊C₄	—	4	4	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	4	no	—
210	C₁₃×C₄⋊C₄	—	4	4	no	—
211	C₁₃×C₄⋊C₄	—	4	4	no	—
212	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
213	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
214	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
215	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
216	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
217	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	4	no	—
223	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
224	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
225	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
226	C₄²×C₁₃	—	2	2	no	—
227	C₄²×C₁₃	—	2	4	no	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	2	no	—
231	C₄²×C₁₃	—	2	2	no	—
232	C₄²×C₁₃	—	2	2	no	—
233	C₄²×C₁₃	—	4	1	no	—
234	C₄²×C₁₃	—	4	4	no	—
235	C₄²×C₁₃	—	4	4	no	—
236	C₄²×C₁₃	—	4	4	no	—
237	C₄²×C₁₃	C₂²×C₄	1	16	yes	—
238	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
239	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
240	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
241	#2383	C₂×C₁₃	1	4	yes	complemented
242	#2367	C₂×C₁₃	1	2	yes	—
243	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2360	C₂×C₁₃	1	2	yes	complemented
245	Q₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
246	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
247	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
248	#2347	C₂×C₁₃	1	2	yes	complemented
249	#2334	C₂×C₁₃	1	4	yes	complemented
250	#2326	C₂×C₁₃	1	2	yes	—
251	#2323	C₂×C₁₃	1	2	yes	complemented
252	#2320	C₂×C₁₃	1	2	yes	complemented
253	#2317	C₂×C₁₃	1	2	yes	complemented
254	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
255	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2293	C₂×C₁₃	1	1	yes	characteristic
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
264	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₃	—	2	8	no	—
266	Q₈×C₁₃	—	2	16	no	—
267	D₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	16	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	1	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	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	8	8	no	—
306	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
310	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
314	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
315	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
316	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
317	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
318	#556	C₄×C₁₃	1	16	yes	complemented
319	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#126	C₂²×C₁₃	1	4	yes	—
321	C₂×#124	C₂²×C₁₃	1	2	yes	—
322	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
324	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
325	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
326	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#117	C₂²×C₁₃	1	2	yes	—
331	C₂×#117	C₂²×C₁₃	1	2	yes	—
332	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
333	#391	C₂²×C₁₃	1	2	yes	—
334	#391	C₂²×C₁₃	1	2	yes	—
335	#391	C₂²×C₁₃	1	1	yes	characteristic
336	#391	C₂²×C₁₃	1	1	yes	characteristic
337	#390	C₂²×C₁₃	1	1	yes	characteristic
338	#390	C₂²×C₁₃	1	1	yes	characteristic
339	#389	C₂²×C₁₃	1	2	yes	—
340	#389	C₂²×C₁₃	1	2	yes	—
341	#389	C₂²×C₁₃	1	1	yes	characteristic
342	#389	C₂²×C₁₃	1	2	yes	—
343	#389	C₂²×C₁₃	1	2	yes	—
344	#389	C₂²×C₁₃	1	1	yes	characteristic
345	#389	C₂²×C₁₃	1	2	yes	—
346	#389	C₂²×C₁₃	1	4	yes	—
347	#389	C₂²×C₁₃	1	4	yes	—
348	#389	C₂²×C₁₃	1	4	yes	—
349	#389	C₂²×C₁₃	1	1	yes	characteristic
350	#389	C₂²×C₁₃	1	1	yes	characteristic
351	#388	C₂²×C₁₃	1	4	yes	—
352	#388	C₂²×C₁₃	1	4	yes	—
353	#388	C₂²×C₁₃	1	4	yes	—
354	#388	C₂²×C₁₃	1	2	yes	—
355	#388	C₂²×C₁₃	1	4	yes	—
356	#388	C₂²×C₁₃	1	2	yes	—
357	#387	C₂²×C₁₃	1	4	yes	—
358	#387	C₂²×C₁₃	1	4	yes	—
359	#387	C₂²×C₁₃	1	2	yes	—
360	#387	C₂²×C₁₃	1	4	yes	—
361	#387	C₂²×C₁₃	1	2	yes	—
362	#385	C₂²×C₁₃	1	4	yes	—
363	#385	C₂²×C₁₃	1	4	yes	—
364	#385	C₂²×C₁₃	1	4	yes	—
365	#385	C₂²×C₁₃	1	4	yes	—
366	#384	C₂²×C₁₃	1	1	yes	characteristic
367	#384	C₂²×C₁₃	1	4	yes	—
368	#384	C₂²×C₁₃	1	2	yes	—
369	#383	C₂²×C₁₃	1	4	yes	—
370	#382	C₂²×C₁₃	1	4	yes	—
371	#380	C₂²×C₁₃	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
382	#376	C₂²×C₁₃	1	2	yes	—
383	C₄³	C₂²×C₁₃	1	1	yes	characteristic
384	C₂²×C₁₃	—	2	4	no	—
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	4	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	2	no	—
391	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
392	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
395	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
396	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
397	C₂²×C₁₃	#585	1	1	yes	characteristic
398	C₄×C₁₃	—	2	4	no	—
399	C₄×C₁₃	—	2	4	no	—
400	C₄×C₁₃	—	2	8	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	4	no	—
403	C₄×C₁₃	—	2	2	no	—
404	C₄×C₁₃	—	4	1	no	—
405	C₄×C₁₃	—	4	2	no	—
406	C₄×C₁₃	—	4	4	no	—
407	C₄×C₁₃	—	4	2	no	—
408	C₄×C₁₃	—	4	2	no	—
409	C₄×C₁₃	—	4	1	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	—	4	1	no	—
412	C₄×C₁₃	#520	1	4	yes	—
413	C₄×C₁₃	#520	1	4	yes	—
414	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
416	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
418	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
419	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
420	#126	C₂×C₄×C₁₃	1	32	yes	complemented
421	#124	C₂×C₄×C₁₃	1	16	yes	—
422	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
423	C₄×Q₈	—	4	4	no	—
424	C₄×Q₈	—	4	4	no	—
425	C₄×Q₈	—	4	4	no	—
426	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
427	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
428	C₄×D₄	—	4	4	no	—
429	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
430	#117	—	4	4	no	—
431	#117	C₂×C₄×C₁₃	1	16	yes	complemented
432	C₂×C₄⋊C₄	—	4	4	no	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
471	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
472	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
477	#95	C₂³×C₁₃	1	2	yes	—
478	#95	C₂³×C₁₃	1	2	yes	—
479	#95	C₂³×C₁₃	1	2	yes	—
480	#95	C₂³×C₁₃	1	2	yes	—
481	#95	C₂³×C₁₃	1	2	yes	—
482	#95	C₂³×C₁₃	1	2	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	2	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	#95	C₂³×C₁₃	1	4	yes	—
487	#95	C₂³×C₁₃	1	4	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	#95	C₂³×C₁₃	1	2	yes	—
491	#95	C₂³×C₁₃	1	2	yes	—
492	#95	C₂³×C₁₃	1	2	yes	—
493	C₂×C₁₃	—	4	4	no	—
494	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
495	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
496	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
497	C₂×C₁₃	#3546	1	1	yes	characteristic
498	C₂×C₁₃	#3550	1	1	yes	characteristic
499	C₂×C₁₃	#3552	1	1	yes	characteristic
500	C₂×C₁₃	#3555	1	1	yes	characteristic
501	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
507	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	4	4	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
517	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	4	4	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	4	no	—
544	C₄⋊C₄	—	4	4	no	—
545	C₄⋊C₄	—	4	4	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
550	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
551	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
561	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
563	C₄²	—	2	2	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	4	4	no	—
571	C₄²	—	4	4	no	—
572	C₄²	—	4	4	no	—
573	C₄²	—	4	1	no	—
574	C₄²	C₂²×C₄×C₁₃	1	16	yes	—
575	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
576	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
577	C₁₃	#34481	1	1	yes	characteristic, direct product factor, Sylow
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
585	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
586	Q₈	—	2	8	no	—
587	Q₈	—	2	16	no	—
588	D₄	—	2	8	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	16	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	8	8	no	—
627	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
628	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
629	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
630	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
631	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
634	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
635	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
636	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
637	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
638	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
647	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
649	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
650	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
651	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
652	C₂²	C₁₃×#585	1	1	yes	characteristic
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	1	no	—
667	C₄	C₁₃×#520	1	4	yes	—
668	C₄	C₁₃×#520	1	4	yes	—
669	C₂	—	4	4	no	—
670	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
671	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
672	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂	C₁₃×#3546	1	1	yes	characteristic
674	C₂	C₁₃×#3550	1	1	yes	characteristic
675	C₂	C₁₃×#3552	1	1	yes	characteristic
676	C₂	C₁₃×#3555	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2383	C₂	semidirect
4. C₁₃×#2365	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
7. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
9. C₁₃×#2347	C₂	semidirect
10. C₁₃×#2334	C₂	semidirect
12. C₁₃×#2323	C₂	semidirect
13. C₁₃×#2320	C₂	semidirect
14. C₁₃×#2317	C₂	semidirect
15. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₁₃×#2295	C₂	semidirect
18. C₁₃×#556	C₄	semidirect
89. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
90. C₁₃×#126	C₂×C₄	semidirect
92. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
96. C₄×Q₈×C₁₃	C₂×C₄	semidirect
97. C₄×Q₈×C₁₃	C₂×C₄	semidirect
101. C₁₃×#117	C₂×C₄	semidirect
163. #34481	C₁₃	direct (N × H)
241. #2383	C₂×C₁₃	semidirect
243. #2365	C₂×C₁₃	semidirect
244. #2360	C₂×C₁₃	semidirect
245. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
246. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
248. #2347	C₂×C₁₃	semidirect
249. #2334	C₂×C₁₃	semidirect
251. #2323	C₂×C₁₃	semidirect
252. #2320	C₂×C₁₃	semidirect
253. #2317	C₂×C₁₃	semidirect
254. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
255. #2295	C₂×C₁₃	semidirect
318. #556	C₄×C₁₃	semidirect
419. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
420. #126	C₂×C₄×C₁₃	semidirect
422. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
426. C₄×Q₈	C₂×C₄×C₁₃	semidirect
427. C₄×Q₈	C₂×C₄×C₁₃	semidirect
431. #117	C₂×C₄×C₁₃	semidirect
577. C₁₃	#34481	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×#556	2
C₁₃×#2383	2
C₁₃×#2367	2
C₁₃×#2365	2
C₁₃×#2360	2
Q₈×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2347	2
C₁₃×#2334	2
C₁₃×#2326	2
C₁₃×#2323	2
C₁₃×#2320	2
C₁₃×#2317	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2295	2
C₁₃×#2293	2
#34481	13

Subgroups — C13×#34481 #15720820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34481 #15720820