Subgroups — C₁₃×#61569 #15747908

Order 3328.

2514 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	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3306	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3264	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3192	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#447	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
16	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
17	C₁₃×#547	C₂²	1	4	yes	complemented
18	C₁₃×#546	—	2	4	no	—
19	C₁₃×#546	—	2	4	no	—
20	C₁₃×#546	C₂²	1	8	yes	complemented
21	D₄²×C₁₃	C₂²	1	4	yes	complemented
22	C₁₃×#537	—	2	1	no	—
23	C₁₃×#534	—	2	1	no	—
24	C₁₃×#534	—	2	1	no	—
25	C₁₃×#532	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×#123	—	2	1	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	—	2	1	no	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#120	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#496	C₂²	1	4	yes	complemented
38	C₁₃×#489	C₂²	1	4	yes	complemented
39	C₁₃×#483	C₂²	1	4	yes	complemented
40	C₁₃×#481	C₂²	1	4	yes	complemented
41	C₁₃×#481	C₂²	1	4	yes	complemented
42	C₁₃×#476	C₂²	1	4	yes	complemented
43	C₁₃×#469	C₂²	1	8	yes	complemented
44	C₁₃×#465	C₂²	1	8	yes	complemented
45	C₁₃×#463	C₂²	1	8	yes	complemented
46	C₁₃×#459	C₂²	1	4	yes	complemented
47	C₁₃×#450	C₂²	1	4	yes	complemented
48	C₁₃×#449	C₂²	1	8	yes	complemented
49	C₁₃×#448	C₂²	1	4	yes	complemented
50	C₁₃×#447	C₂²	1	4	yes	complemented
51	C₁₃×#447	C₂²	1	8	yes	complemented
52	C₁₃×#447	C₂²	1	4	yes	complemented
53	C₁₃×#447	C₂²	1	4	yes	complemented
54	C₁₃×#442	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#432	C₂²	1	2	yes	complemented
57	C₁₃×#417	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	complemented
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
61	C₂⁵×C₁₃	—	2	1	no	—
62	C₁₃×H(5,𝔽₂)	—	4	8	no	—
63	C₂×C₁₃×#41	—	2	4	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	4	4	no	—
67	C₂×C₁₃×#41	C₂³	1	4	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	2	no	—
71	C₂²×D₄×C₁₃	—	2	2	no	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	4	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	4	4	no	—
77	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	—	2	1	no	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
88	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
89	C₂×C₁₃×D₈	—	4	8	no	—
90	C₂×C₁₃×D₈	C₂³	1	8	yes	—
91	C₂×C₁₃×D₈	C₂³	1	8	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	4	yes	complemented
93	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
95	C₁₃×#127	C₂³	1	2	yes	complemented
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	C₂³	1	4	yes	—
99	C₁₃×#123	—	2	8	no	—
100	C₁₃×#123	—	2	4	no	—
101	C₁₃×#123	—	2	4	no	—
102	C₁₃×C₂²⋊Q₈	—	2	2	no	—
103	C₁₃×C₂²⋊Q₈	—	2	4	no	—
104	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	—	2	2	no	—
107	C₁₃×#121	—	2	2	no	—
108	C₁₃×#121	—	2	2	no	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	4	no	—
112	C₁₃×#121	—	2	8	no	—
113	C₁₃×#121	C₂³	1	4	yes	—
114	C₁₃×#121	C₂³	1	4	yes	—
115	C₁₃×#121	C₂³	1	4	yes	—
116	C₁₃×#121	C₂³	1	4	yes	complemented
117	C₁₃×#120	—	2	8	no	—
118	C₁₃×#120	—	2	4	no	—
119	C₁₃×#120	—	2	4	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	D₄	1	4	yes	—
123	C₄×D₄×C₁₃	C₂³	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
131	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
139	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×#106	C₂³	1	8	yes	complemented
143	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
144	C₁₃×#103	C₂³	1	8	yes	complemented
145	C₁₃×#102	C₂³	1	8	yes	—
146	C₁₃×#102	C₂³	1	8	yes	—
147	C₁₃×#102	C₂³	1	8	yes	complemented
148	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
151	C₁₃×#97	C₂³	1	4	yes	complemented
152	#61569	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	—	2	4	no	—
156	C₂⁴×C₁₃	—	2	2	no	—
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	—	4	4	no	—
159	C₂⁴×C₁₃	—	4	4	no	—
160	C₂⁴×C₁₃	—	8	2	no	—
161	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₁₃×#41	—	2	8	no	—
164	C₁₃×#41	—	4	4	no	—
165	C₁₃×#41	—	4	8	no	—
166	C₁₃×#41	—	4	8	no	—
167	C₁₃×#41	—	4	16	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	2	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	2	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	2	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	—	4	4	no	—
191	C₂×D₄×C₁₃	—	4	8	no	—
192	C₂×D₄×C₁₃	—	4	16	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	4	8	no	—
196	C₂×D₄×C₁₃	—	4	8	no	—
197	C₂×D₄×C₁₃	—	8	2	no	—
198	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
199	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
201	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	4	no	—
209	C₂²×C₄×C₁₃	—	4	2	no	—
210	C₂²×C₄×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	—	4	4	no	—
212	C₂²×C₄×C₁₃	—	8	2	no	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₁₃×SD₁₆	—	4	8	no	—
223	C₁₃×D₈	—	2	16	no	—
224	C₁₃×D₈	—	4	8	no	—
225	C₁₃×M₁₆	—	4	4	no	—
226	C₂×C₈×C₁₃	—	4	4	no	—
227	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
235	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
246	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
247	C₄²×C₁₃	C₂×D₄	1	2	yes	—
248	C₄²×C₁₃	C₂⁴	1	2	yes	—
249	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3306	C₂×C₁₃	1	8	yes	complemented
252	#3264	C₂×C₁₃	1	8	yes	complemented
253	#3213	C₂×C₁₃	1	2	yes	complemented
254	#3192	C₂×C₁₃	1	2	yes	complemented
255	#3187	C₂×C₁₃	1	2	yes	complemented
256	#3109	C₂×C₁₃	1	2	yes	complemented
257	#3006	C₂×C₁₃	1	2	yes	complemented
258	C₂×#447	C₂×C₁₃	1	2	yes	complemented
259	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂³×C₁₃	—	2	4	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	4	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	8	no	—
270	C₂³×C₁₃	—	4	2	no	—
271	C₂³×C₁₃	—	4	2	no	—
272	C₂³×C₁₃	—	4	2	no	—
273	C₂³×C₁₃	—	4	4	no	—
274	C₂³×C₁₃	—	4	2	no	—
275	C₂³×C₁₃	—	4	8	no	—
276	C₂³×C₁₃	—	4	2	no	—
277	C₂³×C₁₃	—	4	4	no	—
278	C₂³×C₁₃	—	8	4	no	—
279	C₂³×C₁₃	—	8	2	no	—
280	C₂³×C₁₃	—	8	2	no	—
281	C₂³×C₁₃	—	8	2	no	—
282	C₂³×C₁₃	—	8	2	no	—
283	C₂³×C₁₃	—	8	16	no	—
284	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
285	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₁₃	—	2	4	no	—
289	Q₈×C₁₃	—	4	2	no	—
290	Q₈×C₁₃	—	4	4	no	—
291	D₄×C₁₃	—	2	4	no	—
292	D₄×C₁₃	—	2	8	no	—
293	D₄×C₁₃	—	2	2	no	—
294	D₄×C₁₃	—	2	8	no	—
295	D₄×C₁₃	—	2	4	no	—
296	D₄×C₁₃	—	4	8	no	—
297	D₄×C₁₃	—	4	2	no	—
298	D₄×C₁₃	—	4	4	no	—
299	D₄×C₁₃	—	4	8	no	—
300	D₄×C₁₃	—	4	8	no	—
301	D₄×C₁₃	—	4	8	no	—
302	D₄×C₁₃	—	4	8	no	—
303	D₄×C₁₃	—	8	2	no	—
304	D₄×C₁₃	—	8	2	no	—
305	D₄×C₁₃	—	8	2	no	—
306	D₄×C₁₃	—	8	4	no	—
307	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	2	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	2	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	8	no	—
321	C₂×C₄×C₁₃	—	4	8	no	—
322	C₂×C₄×C₁₃	—	4	2	no	—
323	C₂×C₄×C₁₃	—	4	2	no	—
324	C₂×C₄×C₁₃	—	4	4	no	—
325	C₂×C₄×C₁₃	—	4	4	no	—
326	C₂×C₄×C₁₃	—	8	4	no	—
327	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₁₃	—	2	8	no	—
334	C₂×H(5,𝔽₂)	—	2	1	no	—
335	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
338	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
339	#547	C₂²×C₁₃	1	4	yes	complemented
340	#546	—	2	4	no	—
341	#546	—	2	4	no	—
342	#546	C₂²×C₁₃	1	8	yes	complemented
343	D₄²	C₂²×C₁₃	1	4	yes	complemented
344	#537	—	2	1	no	—
345	#534	—	2	1	no	—
346	#534	—	2	1	no	—
347	#532	C₂²×C₁₃	1	2	yes	complemented
348	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
349	C₂×#123	—	2	1	no	—
350	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
351	C₂×#121	—	2	1	no	—
352	C₂×#121	C₂²×C₁₃	1	2	yes	—
353	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
354	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
355	C₂×#120	—	2	1	no	—
356	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
358	C₂²×C₂²⋊C₄	—	2	1	no	—
359	#496	C₂²×C₁₃	1	4	yes	complemented
360	#489	C₂²×C₁₃	1	4	yes	complemented
361	#483	C₂²×C₁₃	1	4	yes	complemented
362	#481	C₂²×C₁₃	1	4	yes	complemented
363	#481	C₂²×C₁₃	1	4	yes	complemented
364	#476	C₂²×C₁₃	1	4	yes	complemented
365	#469	C₂²×C₁₃	1	8	yes	complemented
366	#465	C₂²×C₁₃	1	8	yes	complemented
367	#463	C₂²×C₁₃	1	8	yes	complemented
368	#459	C₂²×C₁₃	1	4	yes	complemented
369	#450	C₂²×C₁₃	1	4	yes	complemented
370	#449	C₂²×C₁₃	1	8	yes	complemented
371	#448	C₂²×C₁₃	1	4	yes	complemented
372	#447	C₂²×C₁₃	1	4	yes	complemented
373	#447	C₂²×C₁₃	1	4	yes	complemented
374	#447	C₂²×C₁₃	1	8	yes	complemented
375	#447	C₂²×C₁₃	1	4	yes	complemented
376	#442	C₂²×C₁₃	1	8	yes	complemented
377	#435	C₂²×C₁₃	1	8	yes	complemented
378	#432	C₂²×C₁₃	1	2	yes	complemented
379	#417	C₂²×C₁₃	1	4	yes	complemented
380	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
381	#407	C₂²×C₁₃	1	2	yes	complemented
382	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	2	no	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	4	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	4	4	no	—
392	C₂²×C₁₃	—	4	8	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	4	no	—
397	C₂²×C₁₃	—	4	2	no	—
398	C₂²×C₁₃	—	4	4	no	—
399	C₂²×C₁₃	—	4	4	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	8	2	no	—
402	C₂²×C₁₃	—	8	16	no	—
403	C₂²×C₁₃	—	8	4	no	—
404	C₂²×C₁₃	—	16	4	no	—
405	C₂²×C₁₃	—	16	4	no	—
406	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
407	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
408	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
409	C₄×C₁₃	—	2	2	no	—
410	C₄×C₁₃	—	2	2	no	—
411	C₄×C₁₃	—	2	1	no	—
412	C₄×C₁₃	—	2	2	no	—
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	4	no	—
417	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂⁵	—	2	1	no	—
419	H(5,𝔽₂)	—	4	8	no	—
420	C₂×#41	—	2	4	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	2	no	—
423	C₂×#41	—	4	4	no	—
424	C₂×#41	C₂³×C₁₃	1	4	yes	—
425	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	—	2	2	no	—
428	C₂²×D₄	—	2	2	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	4	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	4	4	no	—
434	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
435	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
437	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
438	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
439	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
440	C₂³×C₄	—	2	1	no	—
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	AGL(1,ℤ/8)	—	4	8	no	—
445	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
446	C₂×D₈	—	4	8	no	—
447	C₂×D₈	C₂³×C₁₃	1	8	yes	—
448	C₂×D₈	C₂³×C₁₃	1	8	yes	—
449	C₂×M₁₆	C₂³×C₁₃	1	4	yes	complemented
450	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
451	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
452	#127	C₂³×C₁₃	1	2	yes	complemented
453	#124	—	2	2	no	—
454	#124	—	2	2	no	—
455	#124	C₂³×C₁₃	1	4	yes	—
456	#123	—	2	8	no	—
457	#123	—	2	4	no	—
458	#123	—	2	4	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	4	no	—
461	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
462	#121	—	2	2	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	—	2	2	no	—
468	#121	—	2	4	no	—
469	#121	—	2	8	no	—
470	#121	C₂³×C₁₃	1	4	yes	—
471	#121	C₂³×C₁₃	1	4	yes	—
472	#121	C₂³×C₁₃	1	4	yes	—
473	#121	C₂³×C₁₃	1	4	yes	complemented
474	#120	—	2	8	no	—
475	#120	—	2	4	no	—
476	#120	—	2	4	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	D₄×C₁₃	1	4	yes	—
480	C₄×D₄	C₂³×C₁₃	1	4	yes	—
481	C₄×D₄	C₂³×C₁₃	1	4	yes	—
482	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	complemented
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	2	no	—
495	C₂×C₂²⋊C₄	—	2	8	no	—
496	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
499	#106	C₂³×C₁₃	1	8	yes	complemented
500	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
501	#103	C₂³×C₁₃	1	8	yes	complemented
502	#102	C₂³×C₁₃	1	8	yes	—
503	#102	C₂³×C₁₃	1	8	yes	—
504	#102	C₂³×C₁₃	1	8	yes	complemented
505	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
506	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
507	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
508	#97	C₂³×C₁₃	1	4	yes	complemented
509	C₂×C₁₃	—	2	2	no	—
510	C₂×C₁₃	—	2	4	no	—
511	C₂×C₁₃	—	4	2	no	—
512	C₂×C₁₃	—	4	4	no	—
513	C₂×C₁₃	—	8	2	no	—
514	C₂×C₁₃	—	8	4	no	—
515	C₂×C₁₃	#3484	1	1	yes	characteristic
516	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₂×C₁₃	#3585	1	1	yes	characteristic
518	C₂⁴	—	2	1	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	4	no	—
521	C₂⁴	—	2	2	no	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	4	4	no	—
524	C₂⁴	—	4	4	no	—
525	C₂⁴	—	8	2	no	—
526	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
528	#41	—	2	8	no	—
529	#41	—	4	4	no	—
530	#41	—	4	8	no	—
531	#41	—	4	8	no	—
532	#41	—	4	16	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	4	2	no	—
536	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	—	4	16	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	8	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	8	2	no	—
563	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
564	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
565	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
566	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	8	2	no	—
578	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
587	SD₁₆	—	4	8	no	—
588	D₈	—	2	16	no	—
589	D₈	—	4	8	no	—
590	M₁₆	—	4	4	no	—
591	C₂×C₈	—	4	4	no	—
592	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
599	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
600	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
611	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
612	C₄²	C₂×D₄×C₁₃	1	2	yes	—
613	C₄²	C₂⁴×C₁₃	1	2	yes	—
614	C₁₃	#61569	1	1	yes	characteristic, direct product factor, Sylow
615	C₂³	—	2	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	8	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	2	no	—
628	C₂³	—	4	4	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	2	no	—
632	C₂³	—	4	4	no	—
633	C₂³	—	8	4	no	—
634	C₂³	—	8	2	no	—
635	C₂³	—	8	2	no	—
636	C₂³	—	8	2	no	—
637	C₂³	—	8	2	no	—
638	C₂³	—	8	16	no	—
639	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
640	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
641	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
642	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
643	Q₈	—	2	4	no	—
644	Q₈	—	4	2	no	—
645	Q₈	—	4	4	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	8	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	8	no	—
650	D₄	—	2	4	no	—
651	D₄	—	4	8	no	—
652	D₄	—	4	2	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	8	no	—
655	D₄	—	4	8	no	—
656	D₄	—	4	8	no	—
657	D₄	—	4	8	no	—
658	D₄	—	8	2	no	—
659	D₄	—	8	2	no	—
660	D₄	—	8	2	no	—
661	D₄	—	8	4	no	—
662	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	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	—	4	1	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	4	2	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
687	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
688	C₈	—	2	8	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	8	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	16	no	—
709	C₂²	—	8	4	no	—
710	C₂²	—	16	4	no	—
711	C₂²	—	16	4	no	—
712	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
713	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
714	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	2	4	no	—
726	C₂	—	4	2	no	—
727	C₂	—	4	4	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	4	no	—
730	C₂	C₁₃×#3484	1	1	yes	characteristic
731	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
732	C₂	C₁₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3306	C₂	semidirect
4. C₁₃×#3264	C₂	semidirect
5. C₁₃×#3213	C₂	semidirect
6. C₁₃×#3192	C₂	semidirect
7. C₁₃×#3187	C₂	semidirect
8. C₁₃×#3109	C₂	semidirect
9. C₁₃×#3006	C₂	semidirect
10. C₂×C₁₃×#447	C₂	semidirect
11. C₁₃×#2973	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂²×C₁₃×D₈	C₂²	semidirect
17. C₁₃×#547	C₂²	semidirect
20. C₁₃×#546	C₂²	semidirect
21. D₄²×C₁₃	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
32. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
39. C₁₃×#483	C₂²	semidirect
40. C₁₃×#481	C₂²	semidirect
41. C₁₃×#481	C₂²	semidirect
42. C₁₃×#476	C₂²	semidirect
43. C₁₃×#469	C₂²	semidirect
44. C₁₃×#465	C₂²	semidirect
45. C₁₃×#463	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
47. C₁₃×#450	C₂²	semidirect
48. C₁₃×#449	C₂²	semidirect
49. C₁₃×#448	C₂²	semidirect
50. C₁₃×#447	C₂²	semidirect
51. C₁₃×#447	C₂²	semidirect
52. C₁₃×#447	C₂²	semidirect
53. C₁₃×#447	C₂²	semidirect
54. C₁₃×#442	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#432	C₂²	semidirect
57. C₁₃×#417	C₂²	semidirect
58. C₂×C₁₃×#102	C₂²	semidirect
59. C₁₃×#407	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
82. C₂²×D₄×C₁₃	C₂³	semidirect
88. C₂×C₁₃×SD₁₆	C₂³	semidirect
92. C₂×C₁₃×M₁₆	C₂³	semidirect
94. C₁₃×C₄⋊Q₈	C₂³	semidirect
95. C₁₃×#127	C₂³	semidirect
116. C₁₃×#121	C₂³	semidirect
125. C₄×D₄×C₁₃	C₂³	semidirect
130. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
142. C₁₃×#106	C₂³	semidirect
143. C₁₃×C₄⋊C₈	C₂³	semidirect
144. C₁₃×#103	C₂³	semidirect
147. C₁₃×#102	C₂³	semidirect
150. C₁₃×C₂²⋊C₈	C₂³	semidirect
151. C₁₃×#97	C₂³	semidirect
152. #61569	C₁₃	direct (N × H)
249. #3496	C₂×C₁₃	semidirect
250. C₂×#546	C₂×C₁₃	semidirect
251. #3306	C₂×C₁₃	semidirect
252. #3264	C₂×C₁₃	semidirect
253. #3213	C₂×C₁₃	semidirect
254. #3192	C₂×C₁₃	semidirect
255. #3187	C₂×C₁₃	semidirect
256. #3109	C₂×C₁₃	semidirect
257. #3006	C₂×C₁₃	semidirect
258. C₂×#447	C₂×C₁₃	semidirect
259. #2973	C₂×C₁₃	semidirect
284. C₂³×C₁₃	AGL(1,ℤ/8)	semidirect
307. D₄×C₁₃	H(5,𝔽₂)	semidirect
335. C₂²×#41	C₂²×C₁₃	semidirect
336. C₂³×D₄	C₂²×C₁₃	semidirect
337. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
338. C₂²×D₈	C₂²×C₁₃	semidirect
339. #547	C₂²×C₁₃	semidirect
342. #546	C₂²×C₁₃	semidirect
343. D₄²	C₂²×C₁₃	semidirect
347. #532	C₂²×C₁₃	semidirect
348. C₂×#124	C₂²×C₁₃	semidirect
350. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
353. C₂×#121	C₂²×C₁₃	semidirect
354. C₂×#121	C₂²×C₁₃	semidirect
357. C₂×C₄×D₄	C₂²×C₁₃	semidirect
359. #496	C₂²×C₁₃	semidirect
360. #489	C₂²×C₁₃	semidirect
361. #483	C₂²×C₁₃	semidirect
362. #481	C₂²×C₁₃	semidirect
363. #481	C₂²×C₁₃	semidirect
364. #476	C₂²×C₁₃	semidirect
365. #469	C₂²×C₁₃	semidirect
366. #465	C₂²×C₁₃	semidirect
367. #463	C₂²×C₁₃	semidirect
368. #459	C₂²×C₁₃	semidirect
369. #450	C₂²×C₁₃	semidirect
370. #449	C₂²×C₁₃	semidirect
371. #448	C₂²×C₁₃	semidirect
372. #447	C₂²×C₁₃	semidirect
373. #447	C₂²×C₁₃	semidirect
374. #447	C₂²×C₁₃	semidirect
375. #447	C₂²×C₁₃	semidirect
376. #442	C₂²×C₁₃	semidirect
377. #435	C₂²×C₁₃	semidirect
378. #432	C₂²×C₁₃	semidirect
379. #417	C₂²×C₁₃	semidirect
380. C₂×#102	C₂²×C₁₃	semidirect
381. #407	C₂²×C₁₃	semidirect
382. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
439. C₂²×D₄	C₂³×C₁₃	semidirect
445. C₂×SD₁₆	C₂³×C₁₃	semidirect
449. C₂×M₁₆	C₂³×C₁₃	semidirect
451. C₄⋊Q₈	C₂³×C₁₃	semidirect
452. #127	C₂³×C₁₃	semidirect
473. #121	C₂³×C₁₃	semidirect
482. C₄×D₄	C₂³×C₁₃	semidirect
487. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
499. #106	C₂³×C₁₃	semidirect
500. C₄⋊C₈	C₂³×C₁₃	semidirect
501. #103	C₂³×C₁₃	semidirect
504. #102	C₂³×C₁₃	semidirect
507. C₂²⋊C₈	C₂³×C₁₃	semidirect
508. #97	C₂³×C₁₃	semidirect
614. C₁₃	#61569	direct (N × H)
639. C₂³	C₁₃×AGL(1,ℤ/8)	semidirect
662. D₄	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3496	2
C₂×C₁₃×#546	2
C₁₃×#3306	2
C₁₃×#3264	2
C₁₃×#3213	2
C₁₃×#3192	2
C₁₃×#3187	2
C₁₃×#3109	2
C₁₃×#3006	2
C₂×C₁₃×#447	2
C₁₃×#2973	2
#61569	13

Subgroups — C13×#61569 #15747908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61569 #15747908