Subgroups — C₁₃×#61582 #15747921

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3325	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3324	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3274	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3272	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3194	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3003	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₁₃	—	2	1	no	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
17	C₁₃×#559	—	2	2	no	—
18	C₁₃×#556	C₂²	1	2	yes	complemented
19	C₁₃×#555	C₂²	1	2	yes	complemented
20	C₁₃×#553	—	2	2	no	—
21	C₁₃×#550	C₂²	1	2	yes	complemented
22	C₁₃×#547	C₂²	1	2	yes	complemented
23	D₄²×C₁₃	—	2	2	no	—
24	D₄²×C₁₃	—	2	2	no	—
25	D₄²×C₁₃	C₂²	1	4	yes	—
26	D₄²×C₁₃	C₂²	1	4	yes	—
27	C₁₃×#538	—	2	2	no	—
28	C₁₃×#535	—	2	1	no	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#525	C₂²	1	4	yes	complemented
33	C₂×C₁₃×#121	—	2	1	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₁₃×#120	—	2	2	no	—
36	C₁₃×#520	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#493	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#486	C₂²	1	2	yes	complemented
43	C₁₃×#483	C₂²	1	2	yes	complemented
44	C₁₃×#482	C₂²	1	8	yes	complemented
45	C₁₃×#480	C₂²	1	2	yes	complemented
46	C₁₃×#476	C₂²	1	2	yes	complemented
47	C₁₃×#474	C₂²	1	2	yes	complemented
48	C₁₃×#469	C₂²	1	8	yes	complemented
49	C₁₃×#468	C₂²	1	8	yes	complemented
50	C₁₃×#461	C₂²	1	2	yes	complemented
51	C₁₃×#460	C₂²	1	4	yes	complemented
52	C₁₃×#459	C₂²	1	2	yes	complemented
53	C₁₃×#459	C₂²	1	4	yes	complemented
54	C₁₃×#450	C₂²	1	2	yes	—
55	C₁₃×#450	C₂²	1	4	yes	complemented
56	C₁₃×#450	C₂²	1	8	yes	complemented
57	C₁₃×#449	C₂²	1	8	yes	complemented
58	C₁₃×#447	C₂²	1	2	yes	—
59	C₁₃×#447	C₂²	1	4	yes	complemented
60	C₁₃×#447	C₂²	1	8	yes	complemented
61	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
62	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
63	C₁₃×#436	C₂²	1	4	yes	complemented
64	C₁₃×#436	C₂²	1	4	yes	complemented
65	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#418	C₂²	1	8	yes	complemented
68	C₁₃×#407	C₂²	1	4	yes	complemented
69	C₂⁵×C₁₃	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	1	no	—
71	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	4	no	—
74	C₂²×D₄×C₁₃	—	2	4	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	4	8	no	—
80	C₂²×D₄×C₁₃	—	4	8	no	—
81	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
88	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
90	C₂×C₁₃×D₈	C₂³	1	4	yes	—
91	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
92	C₂×C₁₃×M₁₆	C₂³	1	8	yes	complemented
93	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
94	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
95	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
96	C₁₃×#127	—	2	2	no	—
97	C₁₃×#127	—	2	1	no	—
98	C₁₃×#127	—	2	1	no	—
99	C₁₃×#127	C₂³	1	2	yes	—
100	C₁₃×#127	C₂³	1	2	yes	—
101	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
102	C₁₃×#126	—	2	4	no	—
103	C₁₃×#125	—	2	1	no	—
104	C₁₃×#124	—	2	2	no	—
105	C₁₃×#124	—	2	4	no	—
106	C₁₃×#124	—	2	1	no	—
107	C₁₃×#123	—	2	4	no	—
108	C₁₃×#123	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	4	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	—	2	4	no	—
117	C₁₃×#121	—	2	4	no	—
118	C₁₃×#121	—	2	4	no	—
119	C₁₃×#121	C₂³	1	2	yes	—
120	C₁₃×#121	C₂³	1	8	yes	—
121	C₁₃×#121	C₂³	1	4	yes	complemented
122	C₁₃×#120	—	2	4	no	—
123	C₁₃×#120	—	2	8	no	—
124	C₁₃×#120	—	2	8	no	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	—	2	1	no	—
127	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	4	no	—
130	C₄×D₄×C₁₃	—	2	2	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	D₄	1	2	yes	—
135	C₄×D₄×C₁₃	D₄	1	2	yes	—
136	C₄×D₄×C₁₃	C₂³	1	2	yes	—
137	C₄×D₄×C₁₃	C₂³	1	2	yes	—
138	C₄×D₄×C₁₃	C₂³	1	2	yes	—
139	C₄×D₄×C₁₃	C₂³	1	2	yes	—
140	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
141	C₁₃×#117	—	2	1	no	—
142	C₁₃×#117	—	2	2	no	—
143	C₁₃×#117	C₂³	1	4	yes	complemented
144	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₁₃×#107	C₂³	1	4	yes	complemented
152	C₁₃×#106	C₂³	1	4	yes	complemented
153	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
154	C₁₃×C₄⋊C₈	C₂³	1	2	yes	complemented
155	C₁₃×#103	C₂³	1	4	yes	complemented
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×#102	C₂³	1	8	yes	complemented
159	C₁₃×#102	C₂³	1	8	yes	complemented
160	C₁₃×#102	C₂³	1	4	yes	complemented
161	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
163	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
164	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
165	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
166	#61582	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	1	no	—
168	C₂⁴×C₁₃	—	2	2	no	—
169	C₂⁴×C₁₃	—	2	8	no	—
170	C₂⁴×C₁₃	—	4	8	no	—
171	C₂⁴×C₁₃	—	4	8	no	—
172	C₂⁴×C₁₃	—	8	4	no	—
173	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
174	C₁₃×#41	—	4	8	no	—
175	C₁₃×#41	—	4	4	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	16	no	—
181	C₂×D₄×C₁₃	—	2	2	no	—
182	C₂×D₄×C₁₃	—	2	8	no	—
183	C₂×D₄×C₁₃	—	2	4	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	8	no	—
189	C₂×D₄×C₁₃	—	2	2	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	2	no	—
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	2	no	—
195	C₂×D₄×C₁₃	—	4	8	no	—
196	C₂×D₄×C₁₃	—	4	4	no	—
197	C₂×D₄×C₁₃	—	4	16	no	—
198	C₂×D₄×C₁₃	—	4	16	no	—
199	C₂×D₄×C₁₃	—	4	16	no	—
200	C₂×D₄×C₁₃	—	4	8	no	—
201	C₂×D₄×C₁₃	—	4	8	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	8	2	no	—
204	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
207	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	4	4	no	—
215	C₂²×C₄×C₁₃	—	4	4	no	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
222	C₁₃×SD₁₆	—	2	8	no	—
223	C₁₃×SD₁₆	—	4	8	no	—
224	C₁₃×D₈	—	2	8	no	—
225	C₁₃×D₈	—	4	8	no	—
226	C₁₃×M₁₆	—	4	8	no	—
227	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
228	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₃×C₂²⋊C₄	—	2	2	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	2	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₁₃×C₂²⋊C₄	—	2	8	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
252	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
253	C₄²×C₁₃	—	2	4	no	—
254	C₄²×C₁₃	—	2	2	no	—
255	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
259	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#3325	C₂×C₁₃	1	4	yes	complemented
262	#3324	C₂×C₁₃	1	4	yes	complemented
263	#3274	C₂×C₁₃	1	4	yes	complemented
264	#3272	C₂×C₁₃	1	4	yes	complemented
265	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#3194	C₂×C₁₃	1	4	yes	complemented
268	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#3003	C₂×C₁₃	1	4	yes	complemented
271	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂³×C₁₃	—	2	4	no	—
273	C₂³×C₁₃	—	2	4	no	—
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	—	2	2	no	—
276	C₂³×C₁₃	—	2	4	no	—
277	C₂³×C₁₃	—	4	2	no	—
278	C₂³×C₁₃	—	4	2	no	—
279	C₂³×C₁₃	—	4	16	no	—
280	C₂³×C₁₃	—	4	2	no	—
281	C₂³×C₁₃	—	4	4	no	—
282	C₂³×C₁₃	—	4	16	no	—
283	C₂³×C₁₃	—	4	4	no	—
284	C₂³×C₁₃	—	4	2	no	—
285	C₂³×C₁₃	—	4	4	no	—
286	C₂³×C₁₃	—	8	8	no	—
287	C₂³×C₁₃	—	8	32	no	—
288	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
289	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₁₃	—	2	4	no	—
291	Q₈×C₁₃	—	4	2	no	—
292	Q₈×C₁₃	—	8	1	no	—
293	D₄×C₁₃	—	2	4	no	—
294	D₄×C₁₃	—	2	4	no	—
295	D₄×C₁₃	—	2	4	no	—
296	D₄×C₁₃	—	2	2	no	—
297	D₄×C₁₃	—	2	4	no	—
298	D₄×C₁₃	—	2	8	no	—
299	D₄×C₁₃	—	4	16	no	—
300	D₄×C₁₃	—	4	4	no	—
301	D₄×C₁₃	—	4	16	no	—
302	D₄×C₁₃	—	4	4	no	—
303	D₄×C₁₃	—	4	4	no	—
304	D₄×C₁₃	—	4	4	no	—
305	D₄×C₁₃	—	4	2	no	—
306	D₄×C₁₃	—	8	1	no	—
307	D₄×C₁₃	—	8	2	no	—
308	D₄×C₁₃	—	8	2	no	—
309	D₄×C₁₃	—	8	4	no	—
310	D₄×C₁₃	—	8	4	no	—
311	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	2	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	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	2	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	2	no	—
322	C₂×C₄×C₁₃	—	4	4	no	—
323	C₂×C₄×C₁₃	—	4	4	no	—
324	C₂×C₄×C₁₃	—	4	4	no	—
325	C₂×C₄×C₁₃	—	8	4	no	—
326	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
327	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
334	C₈×C₁₃	—	2	4	no	—
335	C₈×C₁₃	—	2	4	no	—
336	C₂³×D₄	—	2	1	no	—
337	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
338	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
339	#559	—	2	2	no	—
340	#556	C₂²×C₁₃	1	2	yes	complemented
341	#555	C₂²×C₁₃	1	2	yes	complemented
342	#553	—	2	2	no	—
343	#550	C₂²×C₁₃	1	2	yes	complemented
344	#547	C₂²×C₁₃	1	2	yes	complemented
345	D₄²	—	2	2	no	—
346	D₄²	—	2	2	no	—
347	D₄²	C₂²×C₁₃	1	4	yes	—
348	D₄²	C₂²×C₁₃	1	4	yes	—
349	#538	—	2	2	no	—
350	#535	—	2	1	no	—
351	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
352	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
354	#525	C₂²×C₁₃	1	4	yes	complemented
355	C₂×#121	—	2	1	no	—
356	C₂×#121	C₂²×C₁₃	1	2	yes	—
357	C₂×#120	—	2	2	no	—
358	#520	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
361	#493	C₂²×C₁₃	1	2	yes	complemented
362	#492	C₂²×C₁₃	1	2	yes	complemented
363	#486	C₂²×C₁₃	1	2	yes	complemented
364	#486	C₂²×C₁₃	1	2	yes	complemented
365	#483	C₂²×C₁₃	1	2	yes	complemented
366	#482	C₂²×C₁₃	1	8	yes	complemented
367	#480	C₂²×C₁₃	1	2	yes	complemented
368	#476	C₂²×C₁₃	1	2	yes	complemented
369	#474	C₂²×C₁₃	1	2	yes	complemented
370	#469	C₂²×C₁₃	1	8	yes	complemented
371	#468	C₂²×C₁₃	1	8	yes	complemented
372	#461	C₂²×C₁₃	1	2	yes	complemented
373	#460	C₂²×C₁₃	1	4	yes	complemented
374	#459	C₂²×C₁₃	1	2	yes	complemented
375	#459	C₂²×C₁₃	1	4	yes	complemented
376	#450	C₂²×C₁₃	1	2	yes	—
377	#450	C₂²×C₁₃	1	4	yes	complemented
378	#450	C₂²×C₁₃	1	8	yes	complemented
379	#449	C₂²×C₁₃	1	8	yes	complemented
380	#447	C₂²×C₁₃	1	2	yes	—
381	#447	C₂²×C₁₃	1	4	yes	complemented
382	#447	C₂²×C₁₃	1	8	yes	complemented
383	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
384	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
385	#436	C₂²×C₁₃	1	4	yes	complemented
386	#436	C₂²×C₁₃	1	4	yes	complemented
387	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#418	C₂²×C₁₃	1	8	yes	complemented
390	#407	C₂²×C₁₃	1	4	yes	complemented
391	C₂²×C₁₃	—	2	1	no	—
392	C₂²×C₁₃	—	2	1	no	—
393	C₂²×C₁₃	—	2	4	no	—
394	C₂²×C₁₃	—	2	4	no	—
395	C₂²×C₁₃	—	2	4	no	—
396	C₂²×C₁₃	—	2	4	no	—
397	C₂²×C₁₃	—	4	8	no	—
398	C₂²×C₁₃	—	4	8	no	—
399	C₂²×C₁₃	—	4	2	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	4	2	no	—
402	C₂²×C₁₃	—	4	4	no	—
403	C₂²×C₁₃	—	4	2	no	—
404	C₂²×C₁₃	—	4	4	no	—
405	C₂²×C₁₃	—	4	2	no	—
406	C₂²×C₁₃	—	4	4	no	—
407	C₂²×C₁₃	—	8	8	no	—
408	C₂²×C₁₃	—	8	32	no	—
409	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
410	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₁₃	—	2	1	no	—
412	C₄×C₁₃	—	2	1	no	—
413	C₄×C₁₃	—	2	1	no	—
414	C₄×C₁₃	—	2	4	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	2	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
420	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
421	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
422	C₂⁵	—	2	2	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
425	C₂²×D₄	—	2	2	no	—
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	—	2	4	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	—	4	8	no	—
433	C₂²×D₄	—	4	8	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	8	yes	—
437	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
440	AGL(1,ℤ/8)	—	4	16	no	—
441	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
442	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
443	C₂×D₈	C₂³×C₁₃	1	4	yes	—
444	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
445	C₂×M₁₆	C₂³×C₁₃	1	8	yes	complemented
446	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
447	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
448	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
449	#127	—	2	2	no	—
450	#127	—	2	1	no	—
451	#127	—	2	1	no	—
452	#127	C₂³×C₁₃	1	2	yes	—
453	#127	C₂³×C₁₃	1	2	yes	—
454	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
455	#126	—	2	4	no	—
456	#125	—	2	1	no	—
457	#124	—	2	2	no	—
458	#124	—	2	4	no	—
459	#124	—	2	1	no	—
460	#123	—	2	4	no	—
461	#123	—	2	4	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
464	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	—	2	4	no	—
468	#121	—	2	1	no	—
469	#121	—	2	4	no	—
470	#121	—	2	4	no	—
471	#121	—	2	4	no	—
472	#121	C₂³×C₁₃	1	8	yes	—
473	#121	C₂³×C₁₃	1	2	yes	—
474	#121	C₂³×C₁₃	1	4	yes	complemented
475	#120	—	2	4	no	—
476	#120	—	2	8	no	—
477	#120	—	2	8	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	2	1	no	—
480	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	D₄×C₁₃	1	2	yes	—
488	C₄×D₄	D₄×C₁₃	1	2	yes	—
489	C₄×D₄	C₂³×C₁₃	1	2	yes	—
490	C₄×D₄	C₂³×C₁₃	1	2	yes	—
491	C₄×D₄	C₂³×C₁₃	1	2	yes	—
492	C₄×D₄	C₂³×C₁₃	1	2	yes	—
493	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
494	#117	—	2	1	no	—
495	#117	—	2	2	no	—
496	#117	C₂³×C₁₃	1	4	yes	complemented
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	2	no	—
502	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
503	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
504	#107	C₂³×C₁₃	1	4	yes	complemented
505	#106	C₂³×C₁₃	1	4	yes	complemented
506	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
507	C₄⋊C₈	C₂³×C₁₃	1	2	yes	complemented
508	#103	C₂³×C₁₃	1	4	yes	complemented
509	#102	C₂³×C₁₃	1	4	yes	—
510	#102	C₂³×C₁₃	1	4	yes	—
511	#102	C₂³×C₁₃	1	8	yes	complemented
512	#102	C₂³×C₁₃	1	8	yes	complemented
513	#102	C₂³×C₁₃	1	4	yes	complemented
514	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
515	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
516	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
517	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
518	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
519	C₂×C₁₃	—	2	2	no	—
520	C₂×C₁₃	—	4	4	no	—
521	C₂×C₁₃	—	4	4	no	—
522	C₂×C₁₃	—	8	2	no	—
523	C₂×C₁₃	—	8	4	no	—
524	C₂×C₁₃	#3484	1	1	yes	characteristic
525	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
526	C₂×C₁₃	#3585	1	1	yes	characteristic
527	C₂⁴	—	2	1	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	8	no	—
530	C₂⁴	—	4	8	no	—
531	C₂⁴	—	4	8	no	—
532	C₂⁴	—	8	4	no	—
533	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
534	#41	—	4	8	no	—
535	#41	—	4	4	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	16	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	8	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	16	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	—	4	16	no	—
560	C₂×D₄	—	4	8	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	8	2	no	—
564	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
565	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
566	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
567	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
579	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
582	SD₁₆	—	2	8	no	—
583	SD₁₆	—	4	8	no	—
584	D₈	—	2	8	no	—
585	D₈	—	4	8	no	—
586	M₁₆	—	4	8	no	—
587	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
588	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
599	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
612	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	2	no	—
615	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₁₃	#61582	1	1	yes	characteristic, direct product factor, Sylow
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	4	16	no	—
631	C₂³	—	4	4	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	8	8	no	—
635	C₂³	—	8	32	no	—
636	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
637	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
638	Q₈	—	2	4	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	8	1	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	4	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	8	no	—
647	D₄	—	4	16	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	16	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	1	no	—
657	D₄	—	8	4	no	—
658	D₄	—	8	4	no	—
659	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
675	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
682	C₈	—	2	4	no	—
683	C₈	—	2	4	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	4	8	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	8	8	no	—
701	C₂²	—	8	32	no	—
702	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
703	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
713	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
714	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
715	C₂	—	2	2	no	—
716	C₂	—	4	4	no	—
717	C₂	—	4	4	no	—
718	C₂	—	8	4	no	—
719	C₂	—	8	2	no	—
720	C₂	C₁₃×#3484	1	1	yes	characteristic
721	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
722	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×#3506	C₂	semidirect
2. C₂×D₄²×C₁₃	C₂	semidirect
3. C₁₃×#3325	C₂	semidirect
4. C₁₃×#3324	C₂	semidirect
5. C₁₃×#3274	C₂	semidirect
6. C₁₃×#3272	C₂	semidirect
7. C₁₃×#3208	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3194	C₂	semidirect
10. C₁₃×#3101	C₂	semidirect
11. C₁₃×#3100	C₂	semidirect
12. C₁₃×#3003	C₂	semidirect
13. C₁₃×#2975	C₂	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₁₃×#556	C₂²	semidirect
19. C₁₃×#555	C₂²	semidirect
21. C₁₃×#550	C₂²	semidirect
22. C₁₃×#547	C₂²	semidirect
29. C₁₃×#533	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
32. C₁₃×#525	C₂²	semidirect
39. C₁₃×#493	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
43. C₁₃×#483	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#480	C₂²	semidirect
46. C₁₃×#476	C₂²	semidirect
47. C₁₃×#474	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#468	C₂²	semidirect
50. C₁₃×#461	C₂²	semidirect
51. C₁₃×#460	C₂²	semidirect
52. C₁₃×#459	C₂²	semidirect
53. C₁₃×#459	C₂²	semidirect
55. C₁₃×#450	C₂²	semidirect
56. C₁₃×#450	C₂²	semidirect
57. C₁₃×#449	C₂²	semidirect
59. C₁₃×#447	C₂²	semidirect
60. C₁₃×#447	C₂²	semidirect
61. C₄×C₁₃×SD₁₆	C₂²	semidirect
62. C₄×C₁₃×D₈	C₂²	semidirect
63. C₁₃×#436	C₂²	semidirect
64. C₁₃×#436	C₂²	semidirect
65. C₁₃×#431	C₂²	semidirect
66. C₁₃×#431	C₂²	semidirect
67. C₁₃×#418	C₂²	semidirect
68. C₁₃×#407	C₂²	semidirect
71. C₂×C₁₃×#41	C₂³	semidirect
89. C₂×C₁₃×SD₁₆	C₂³	semidirect
91. C₂×C₁₃×D₈	C₂³	semidirect
92. C₂×C₁₃×M₁₆	C₂³	semidirect
93. C₁₃×C₄⋊Q₈	C₂³	semidirect
94. C₁₃×C₄⋊Q₈	C₂³	semidirect
95. C₁₃×C₄⋊Q₈	C₂³	semidirect
101. C₁₃×#127	C₂³	semidirect
111. C₁₃×C₂²⋊Q₈	C₂³	semidirect
121. C₁₃×#121	C₂³	semidirect
127. C₄×Q₈×C₁₃	C₂³	semidirect
140. C₄×D₄×C₁₃	C₂³	semidirect
143. C₁₃×#117	C₂³	semidirect
151. C₁₃×#107	C₂³	semidirect
152. C₁₃×#106	C₂³	semidirect
153. C₁₃×C₄⋊C₈	C₂³	semidirect
154. C₁₃×C₄⋊C₈	C₂³	semidirect
155. C₁₃×#103	C₂³	semidirect
158. C₁₃×#102	C₂³	semidirect
159. C₁₃×#102	C₂³	semidirect
160. C₁₃×#102	C₂³	semidirect
163. C₁₃×C₂²⋊C₈	C₂³	semidirect
164. C₄×C₈×C₁₃	C₂³	semidirect
165. C₄×C₈×C₁₃	C₂³	semidirect
166. #61582	C₁₃	direct (N × H)
259. #3506	C₂×C₁₃	semidirect
260. C₂×D₄²	C₂×C₁₃	semidirect
261. #3325	C₂×C₁₃	semidirect
262. #3324	C₂×C₁₃	semidirect
263. #3274	C₂×C₁₃	semidirect
264. #3272	C₂×C₁₃	semidirect
265. #3208	C₂×C₁₃	semidirect
266. #3205	C₂×C₁₃	semidirect
267. #3194	C₂×C₁₃	semidirect
268. #3101	C₂×C₁₃	semidirect
269. #3100	C₂×C₁₃	semidirect
270. #3003	C₂×C₁₃	semidirect
271. #2975	C₂×C₁₃	semidirect
326. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
338. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
340. #556	C₂²×C₁₃	semidirect
341. #555	C₂²×C₁₃	semidirect
343. #550	C₂²×C₁₃	semidirect
344. #547	C₂²×C₁₃	semidirect
351. #533	C₂²×C₁₃	semidirect
352. #532	C₂²×C₁₃	semidirect
354. #525	C₂²×C₁₃	semidirect
361. #493	C₂²×C₁₃	semidirect
362. #492	C₂²×C₁₃	semidirect
363. #486	C₂²×C₁₃	semidirect
364. #486	C₂²×C₁₃	semidirect
365. #483	C₂²×C₁₃	semidirect
366. #482	C₂²×C₁₃	semidirect
367. #480	C₂²×C₁₃	semidirect
368. #476	C₂²×C₁₃	semidirect
369. #474	C₂²×C₁₃	semidirect
370. #469	C₂²×C₁₃	semidirect
371. #468	C₂²×C₁₃	semidirect
372. #461	C₂²×C₁₃	semidirect
373. #460	C₂²×C₁₃	semidirect
374. #459	C₂²×C₁₃	semidirect
375. #459	C₂²×C₁₃	semidirect
377. #450	C₂²×C₁₃	semidirect
378. #450	C₂²×C₁₃	semidirect
379. #449	C₂²×C₁₃	semidirect
381. #447	C₂²×C₁₃	semidirect
382. #447	C₂²×C₁₃	semidirect
383. C₄×SD₁₆	C₂²×C₁₃	semidirect
384. C₄×D₈	C₂²×C₁₃	semidirect
385. #436	C₂²×C₁₃	semidirect
386. #436	C₂²×C₁₃	semidirect
387. #431	C₂²×C₁₃	semidirect
388. #431	C₂²×C₁₃	semidirect
389. #418	C₂²×C₁₃	semidirect
390. #407	C₂²×C₁₃	semidirect
424. C₂×#41	C₂³×C₁₃	semidirect
442. C₂×SD₁₆	C₂³×C₁₃	semidirect
444. C₂×D₈	C₂³×C₁₃	semidirect
445. C₂×M₁₆	C₂³×C₁₃	semidirect
446. C₄⋊Q₈	C₂³×C₁₃	semidirect
447. C₄⋊Q₈	C₂³×C₁₃	semidirect
448. C₄⋊Q₈	C₂³×C₁₃	semidirect
454. #127	C₂³×C₁₃	semidirect
464. C₂²⋊Q₈	C₂³×C₁₃	semidirect
474. #121	C₂³×C₁₃	semidirect
480. C₄×Q₈	C₂³×C₁₃	semidirect
493. C₄×D₄	C₂³×C₁₃	semidirect
496. #117	C₂³×C₁₃	semidirect
504. #107	C₂³×C₁₃	semidirect
505. #106	C₂³×C₁₃	semidirect
506. C₄⋊C₈	C₂³×C₁₃	semidirect
507. C₄⋊C₈	C₂³×C₁₃	semidirect
508. #103	C₂³×C₁₃	semidirect
511. #102	C₂³×C₁₃	semidirect
512. #102	C₂³×C₁₃	semidirect
513. #102	C₂³×C₁₃	semidirect
516. C₂²⋊C₈	C₂³×C₁₃	semidirect
517. C₄×C₈	C₂³×C₁₃	semidirect
518. C₄×C₈	C₂³×C₁₃	semidirect
619. C₁₃	#61582	direct (N × H)
674. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3506	2
C₂×D₄²×C₁₃	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3208	2
C₁₃×#3205	2
C₁₃×#3194	2
C₁₃×#3101	2
C₁₃×#3100	2
C₁₃×#3003	2
C₁₃×#2975	2
#61582	13

Subgroups — C13×#61582 #15747921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61582 #15747921