Subgroups — C₁₃×#61674 #15748013

Order 3328.

2032 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3313	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3270	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3202	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3200	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3116	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#559	—	2	1	no	—
23	Q₈²×C₁₃	—	2	1	no	—
24	C₁₃×#556	C₂²	1	4	yes	complemented
25	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
26	C₁₃×#548	C₂²	1	4	yes	—
27	C₁₃×#546	—	2	4	no	—
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#542	—	2	4	no	—
30	C₁₃×#536	—	2	1	no	—
31	C₁₃×#536	C₂²	1	2	yes	—
32	C₁₃×#536	C₂²	1	1	yes	characteristic
33	C₁₃×#536	C₂²	1	2	yes	complemented
34	C₁₃×#535	—	2	1	no	—
35	C₁₃×#535	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	2	yes	complemented
37	C₁₃×#532	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#124	—	2	1	no	—
40	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
42	C₁₃×#497	C₂²	1	4	yes	complemented
43	C₁₃×#489	C₂²	1	4	yes	complemented
44	C₁₃×#485	C₂²	1	4	yes	complemented
45	C₁₃×#485	C₂²	1	4	yes	complemented
46	C₁₃×#482	C₂²	1	4	yes	complemented
47	C₁₃×#477	C₂²	1	2	yes	complemented
48	C₁₃×#476	C₂²	1	2	yes	complemented
49	C₁₃×#470	C₂²	1	4	yes	complemented
50	C₁₃×#468	C₂²	1	4	yes	complemented
51	C₁₃×#467	C₂²	1	4	yes	complemented
52	C₁₃×#465	C₂²	1	4	yes	complemented
53	C₁₃×#464	C₂²	1	4	yes	complemented
54	C₁₃×#464	C₂²	1	4	yes	complemented
55	C₁₃×#462	C₂²	1	2	yes	complemented
56	C₁₃×#461	C₂²	1	2	yes	complemented
57	C₁₃×#452	C₂²	1	4	yes	—
58	C₁₃×#452	C₂²	1	4	yes	—
59	C₁₃×#452	C₂²	1	4	yes	complemented
60	C₁₃×#451	C₂²	1	4	yes	complemented
61	C₁₃×#451	C₂²	1	4	yes	complemented
62	C₁₃×#451	C₂²	1	4	yes	complemented
63	C₁₃×#450	C₂²	1	4	yes	—
64	C₁₃×#450	C₂²	1	4	yes	—
65	C₁₃×#448	C₂²	1	4	yes	complemented
66	C₁₃×#441	C₂²	1	4	yes	complemented
67	C₁₃×#440	C₂²	1	4	yes	complemented
68	C₁₃×#435	C₂²	1	4	yes	complemented
69	C₁₃×#435	C₂²	1	4	yes	complemented
70	C₁₃×#432	C₂²	1	2	yes	complemented
71	C₁₃×#419	C₂²	1	2	yes	complemented
72	C₁₃×#418	C₂²	1	2	yes	—
73	C₁₃×#416	C₂²	1	2	yes	—
74	C₁₃×#416	C₂²	1	2	yes	complemented
75	C₁₃×#408	C₂²	1	2	yes	—
76	C₁₃×#408	C₂²	1	2	yes	complemented
77	C₁₃×2₋¹⁺⁴	—	4	2	no	—
78	C₁₃×2₋¹⁺⁴	—	4	2	no	—
79	C₁₃×H(5,𝔽₂)	—	4	2	no	—
80	C₁₃×H(5,𝔽₂)	—	4	2	no	—
81	C₂×C₁₃×#41	—	2	1	no	—
82	C₂×C₁₃×#41	—	2	1	no	—
83	C₂×C₁₃×#41	—	2	2	no	—
84	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	—	2	1	no	—
90	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	—	2	1	no	—
95	C₂²×D₄×C₁₃	—	2	2	no	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#137	—	4	4	no	—
99	C₁₃×#137	—	4	4	no	—
100	C₂×C₁₃×Q₁₆	—	4	4	no	—
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	—	4	4	no	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	—	2	4	no	—
116	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×#127	—	2	1	no	—
120	C₁₃×#127	D₄	1	1	yes	characteristic
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#124	—	2	1	no	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	4	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	D₄	1	1	yes	characteristic
133	C₁₃×#124	D₄	1	1	yes	characteristic
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₁₃×#121	—	2	4	no	—
150	C₁₃×#121	—	2	4	no	—
151	C₁₃×#121	D₄	1	4	yes	—
152	C₁₃×#121	C₂³	1	4	yes	—
153	C₁₃×#120	—	2	4	no	—
154	C₁₃×#120	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	4	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	4	no	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	4	yes	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	1	no	—
166	C₁₃×#117	C₂³	1	2	yes	—
167	C₁₃×#117	C₂³	1	2	yes	—
168	C₁₃×#117	C₂³	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₁₃×#107	C₂³	1	4	yes	—
174	C₁₃×#106	C₂³	1	4	yes	—
175	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×#103	C₂³	1	4	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#103	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₃×#97	C₂³	1	4	yes	—
189	#61674	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂⁴×C₁₃	—	2	2	no	—
191	C₂⁴×C₁₃	—	2	1	no	—
192	C₁₃×#41	—	2	2	no	—
193	C₁₃×#41	—	2	2	no	—
194	C₁₃×#41	—	2	4	no	—
195	C₁₃×#41	—	2	4	no	—
196	C₁₃×#41	—	4	1	no	—
197	C₁₃×#41	—	4	1	no	—
198	C₁₃×#41	—	4	1	no	—
199	C₁₃×#41	—	4	1	no	—
200	C₁₃×#41	—	4	2	no	—
201	C₁₃×#41	—	4	2	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	8	no	—
205	C₂×Q₈×C₁₃	—	2	2	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	1	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	2	2	no	—
210	C₂×Q₈×C₁₃	—	2	4	no	—
211	C₂×Q₈×C₁₃	—	4	2	no	—
212	C₂×Q₈×C₁₃	—	4	1	no	—
213	C₂×Q₈×C₁₃	—	4	1	no	—
214	C₂×Q₈×C₁₃	—	4	4	no	—
215	C₂×Q₈×C₁₃	—	4	2	no	—
216	C₂×Q₈×C₁₃	—	4	2	no	—
217	C₂×Q₈×C₁₃	—	4	2	no	—
218	C₂×Q₈×C₁₃	—	4	2	no	—
219	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
223	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	4	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	—	4	1	no	—
233	C₂×D₄×C₁₃	—	4	1	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	4	8	no	—
236	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₁₃×Q₁₆	—	2	8	no	—
256	C₁₃×Q₁₆	—	4	4	no	—
257	C₁₃×Q₁₆	—	4	4	no	—
258	C₁₃×SD₁₆	—	2	8	no	—
259	C₁₃×SD₁₆	—	4	4	no	—
260	C₁₃×SD₁₆	—	4	4	no	—
261	C₁₃×M₁₆	—	4	2	no	—
262	C₁₃×M₁₆	—	4	2	no	—
263	C₂×C₈×C₁₃	—	4	2	no	—
264	C₂×C₈×C₁₃	—	4	2	no	—
265	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₂²⋊C₄	—	2	4	no	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	1	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₄²×C₁₃	—	2	1	no	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	4	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂⁴	1	2	yes	—
300	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#3500	C₂×C₁₃	1	1	yes	characteristic
302	#3313	C₂×C₁₃	1	4	yes	complemented
303	#3311	C₂×C₁₃	1	4	yes	complemented
304	#3270	C₂×C₁₃	1	4	yes	complemented
305	#3266	C₂×C₁₃	1	4	yes	complemented
306	#3215	C₂×C₁₃	1	2	yes	complemented
307	#3202	C₂×C₁₃	1	2	yes	complemented
308	#3200	C₂×C₁₃	1	2	yes	complemented
309	#3116	C₂×C₁₃	1	2	yes	complemented
310	#3011	C₂×C₁₃	1	2	yes	complemented
311	#3009	C₂×C₁₃	1	2	yes	complemented
312	#2980	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	4	no	—
316	C₂³×C₁₃	—	4	2	no	—
317	C₂³×C₁₃	—	8	2	no	—
318	C₂³×C₁₃	—	8	4	no	—
319	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
322	Q₈×C₁₃	—	2	1	no	—
323	Q₈×C₁₃	—	2	4	no	—
324	Q₈×C₁₃	—	2	4	no	—
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	4	1	no	—
328	Q₈×C₁₃	—	4	1	no	—
329	Q₈×C₁₃	—	4	4	no	—
330	Q₈×C₁₃	—	4	4	no	—
331	Q₈×C₁₃	—	4	2	no	—
332	Q₈×C₁₃	—	8	2	no	—
333	Q₈×C₁₃	—	8	2	no	—
334	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
335	D₄×C₁₃	—	2	4	no	—
336	D₄×C₁₃	—	2	1	no	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	4	2	no	—
341	D₄×C₁₃	—	4	4	no	—
342	D₄×C₁₃	—	4	1	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	4	4	no	—
345	D₄×C₁₃	—	4	4	no	—
346	D₄×C₁₃	—	4	2	no	—
347	D₄×C₁₃	—	4	4	no	—
348	D₄×C₁₃	—	8	4	no	—
349	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	4	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	4	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	4	no	—
364	C₂×C₄×C₁₃	—	4	4	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	8	2	no	—
368	C₂×C₄×C₁₃	—	8	2	no	—
369	C₂×C₄×C₁₃	—	8	2	no	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
376	C₈×C₁₃	—	2	4	no	—
377	C₈×C₁₃	—	2	4	no	—
378	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
379	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#137	C₂²×C₁₃	1	2	yes	—
381	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
382	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
383	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
384	#563	—	2	1	no	—
385	#563	—	2	1	no	—
386	#559	—	2	1	no	—
387	Q₈²	—	2	1	no	—
388	#556	C₂²×C₁₃	1	4	yes	complemented
389	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
390	#548	C₂²×C₁₃	1	4	yes	—
391	#546	—	2	4	no	—
392	#546	C₂²×C₁₃	1	4	yes	—
393	#542	—	2	4	no	—
394	#536	—	2	1	no	—
395	#536	C₂²×C₁₃	1	1	yes	characteristic
396	#536	C₂²×C₁₃	1	2	yes	—
397	#536	C₂²×C₁₃	1	2	yes	complemented
398	#535	—	2	1	no	—
399	#535	C₂²×C₁₃	1	1	yes	characteristic
400	#533	C₂²×C₁₃	1	2	yes	complemented
401	#532	—	2	1	no	—
402	#532	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#124	—	2	1	no	—
404	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
406	#497	C₂²×C₁₃	1	4	yes	complemented
407	#489	C₂²×C₁₃	1	4	yes	complemented
408	#485	C₂²×C₁₃	1	4	yes	complemented
409	#485	C₂²×C₁₃	1	4	yes	complemented
410	#482	C₂²×C₁₃	1	4	yes	complemented
411	#477	C₂²×C₁₃	1	2	yes	complemented
412	#476	C₂²×C₁₃	1	2	yes	complemented
413	#470	C₂²×C₁₃	1	4	yes	complemented
414	#468	C₂²×C₁₃	1	4	yes	complemented
415	#467	C₂²×C₁₃	1	4	yes	complemented
416	#465	C₂²×C₁₃	1	4	yes	complemented
417	#464	C₂²×C₁₃	1	4	yes	complemented
418	#464	C₂²×C₁₃	1	4	yes	complemented
419	#462	C₂²×C₁₃	1	2	yes	complemented
420	#461	C₂²×C₁₃	1	2	yes	complemented
421	#452	C₂²×C₁₃	1	4	yes	—
422	#452	C₂²×C₁₃	1	4	yes	—
423	#452	C₂²×C₁₃	1	4	yes	complemented
424	#451	C₂²×C₁₃	1	4	yes	complemented
425	#451	C₂²×C₁₃	1	4	yes	complemented
426	#451	C₂²×C₁₃	1	4	yes	complemented
427	#450	C₂²×C₁₃	1	4	yes	—
428	#450	C₂²×C₁₃	1	4	yes	—
429	#448	C₂²×C₁₃	1	4	yes	complemented
430	#441	C₂²×C₁₃	1	4	yes	complemented
431	#440	C₂²×C₁₃	1	4	yes	complemented
432	#435	C₂²×C₁₃	1	4	yes	complemented
433	#435	C₂²×C₁₃	1	4	yes	complemented
434	#432	C₂²×C₁₃	1	2	yes	complemented
435	#419	C₂²×C₁₃	1	2	yes	complemented
436	#418	C₂²×C₁₃	1	2	yes	—
437	#416	C₂²×C₁₃	1	2	yes	—
438	#416	C₂²×C₁₃	1	2	yes	complemented
439	#408	C₂²×C₁₃	1	2	yes	—
440	#408	C₂²×C₁₃	1	2	yes	complemented
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	4	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	4	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	16	4	no	—
452	C₂²×C₁₃	—	16	2	no	—
453	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₁₃	—	2	2	no	—
455	C₄×C₁₃	—	2	2	no	—
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	2	2	no	—
459	C₄×C₁₃	—	2	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	4	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	4	no	—
464	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
466	2₋¹⁺⁴	—	4	2	no	—
467	2₋¹⁺⁴	—	4	2	no	—
468	H(5,𝔽₂)	—	4	2	no	—
469	H(5,𝔽₂)	—	4	2	no	—
470	C₂×#41	—	2	1	no	—
471	C₂×#41	—	2	1	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×#41	C₂³×C₁₃	1	2	yes	—
475	C₂×#41	C₂³×C₁₃	1	2	yes	—
476	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
480	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
482	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	2	no	—
485	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	#137	—	4	4	no	—
488	#137	—	4	4	no	—
489	C₂×Q₁₆	—	4	4	no	—
490	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
491	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂×SD₁₆	—	4	4	no	—
494	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
497	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
498	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
499	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
500	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	4	no	—
505	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
507	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
508	#127	—	2	1	no	—
509	#127	D₄×C₁₃	1	1	yes	characteristic
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#125	—	2	2	no	—
513	#124	—	2	1	no	—
514	#124	—	2	1	no	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	—	2	4	no	—
518	#124	—	2	4	no	—
519	#124	—	2	1	no	—
520	#124	—	2	1	no	—
521	#124	D₄×C₁₃	1	1	yes	characteristic
522	#124	D₄×C₁₃	1	1	yes	characteristic
523	#124	C₂³×C₁₃	1	4	yes	—
524	#123	—	2	2	no	—
525	#123	—	2	2	no	—
526	#123	—	2	2	no	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	4	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
538	#121	—	2	4	no	—
539	#121	—	2	4	no	—
540	#121	D₄×C₁₃	1	4	yes	—
541	#121	C₂³×C₁₃	1	4	yes	—
542	#120	—	2	4	no	—
543	#120	—	2	2	no	—
544	C₄×Q₈	—	2	4	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	C₂³×C₁₃	1	2	yes	—
552	C₄×D₄	C₂³×C₁₃	1	4	yes	—
553	#117	—	2	2	no	—
554	#117	—	2	1	no	—
555	#117	C₂³×C₁₃	1	1	yes	characteristic
556	#117	C₂³×C₁₃	1	2	yes	—
557	#117	C₂³×C₁₃	1	2	yes	—
558	C₂×C₂²⋊C₄	—	2	2	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₄²	—	2	1	no	—
561	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	#107	C₂³×C₁₃	1	4	yes	—
563	#106	C₂³×C₁₃	1	4	yes	—
564	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
565	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
566	#103	C₂³×C₁₃	1	4	yes	—
567	#103	C₂³×C₁₃	1	4	yes	—
568	#103	C₂³×C₁₃	1	4	yes	—
569	#103	C₂³×C₁₃	1	4	yes	—
570	#103	C₂³×C₁₃	1	4	yes	—
571	#102	C₂³×C₁₃	1	4	yes	—
572	#102	C₂³×C₁₃	1	4	yes	—
573	#102	C₂³×C₁₃	1	4	yes	—
574	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
577	#97	C₂³×C₁₃	1	4	yes	—
578	C₂×C₁₃	—	4	2	no	—
579	C₂×C₁₃	—	4	1	no	—
580	C₂×C₁₃	—	4	2	no	—
581	C₂×C₁₃	—	4	2	no	—
582	C₂×C₁₃	—	8	2	no	—
583	C₂×C₁₃	#3484	1	1	yes	characteristic
584	C₂×C₁₃	#3586	1	2	yes	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	1	no	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	2	4	no	—
590	#41	—	2	4	no	—
591	#41	—	4	1	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	4	2	no	—
596	#41	—	4	2	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	8	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	4	2	no	—
607	C₂×Q₈	—	4	1	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	—	4	4	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
615	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
616	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
618	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	8	no	—
631	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
632	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
635	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
650	Q₁₆	—	2	8	no	—
651	Q₁₆	—	4	4	no	—
652	Q₁₆	—	4	4	no	—
653	SD₁₆	—	2	8	no	—
654	SD₁₆	—	4	4	no	—
655	SD₁₆	—	4	4	no	—
656	M₁₆	—	4	2	no	—
657	M₁₆	—	4	2	no	—
658	C₂×C₈	—	4	2	no	—
659	C₂×C₈	—	4	2	no	—
660	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
661	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
686	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	2	no	—
692	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₄²	C₂⁴×C₁₃	1	2	yes	—
695	C₁₃	#61674	1	1	yes	characteristic, direct product factor, Sylow
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	4	no	—
702	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
703	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	4	4	no	—
715	Q₈	—	8	2	no	—
716	Q₈	—	8	2	no	—
717	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	4	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	4	no	—
731	D₄	—	8	4	no	—
732	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
758	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
759	C₈	—	2	4	no	—
760	C₈	—	2	4	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	16	4	no	—
772	C₂²	—	16	2	no	—
773	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	4	no	—
784	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
785	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂	—	4	1	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	2	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₁₃×#3484	1	1	yes	characteristic
792	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
3. C₁₃×#3313	C₂	semidirect
4. C₁₃×#3311	C₂	semidirect
5. C₁₃×#3270	C₂	semidirect
6. C₁₃×#3266	C₂	semidirect
7. C₁₃×#3215	C₂	semidirect
8. C₁₃×#3202	C₂	semidirect
9. C₁₃×#3200	C₂	semidirect
10. C₁₃×#3116	C₂	semidirect
11. C₁₃×#3011	C₂	semidirect
12. C₁₃×#3009	C₂	semidirect
13. C₁₃×#2980	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂²×C₁₃×Q₁₆	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
42. C₁₃×#497	C₂²	semidirect
43. C₁₃×#489	C₂²	semidirect
44. C₁₃×#485	C₂²	semidirect
45. C₁₃×#485	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
47. C₁₃×#477	C₂²	semidirect
48. C₁₃×#476	C₂²	semidirect
49. C₁₃×#470	C₂²	semidirect
50. C₁₃×#468	C₂²	semidirect
51. C₁₃×#467	C₂²	semidirect
52. C₁₃×#465	C₂²	semidirect
53. C₁₃×#464	C₂²	semidirect
54. C₁₃×#464	C₂²	semidirect
55. C₁₃×#462	C₂²	semidirect
56. C₁₃×#461	C₂²	semidirect
59. C₁₃×#452	C₂²	semidirect
60. C₁₃×#451	C₂²	semidirect
61. C₁₃×#451	C₂²	semidirect
62. C₁₃×#451	C₂²	semidirect
65. C₁₃×#448	C₂²	semidirect
66. C₁₃×#441	C₂²	semidirect
67. C₁₃×#440	C₂²	semidirect
68. C₁₃×#435	C₂²	semidirect
69. C₁₃×#435	C₂²	semidirect
70. C₁₃×#432	C₂²	semidirect
71. C₁₃×#419	C₂²	semidirect
74. C₁₃×#416	C₂²	semidirect
76. C₁₃×#408	C₂²	semidirect
189. #61674	C₁₃	direct (N × H)
300. #3550	C₂×C₁₃	semidirect
302. #3313	C₂×C₁₃	semidirect
303. #3311	C₂×C₁₃	semidirect
304. #3270	C₂×C₁₃	semidirect
305. #3266	C₂×C₁₃	semidirect
306. #3215	C₂×C₁₃	semidirect
307. #3202	C₂×C₁₃	semidirect
308. #3200	C₂×C₁₃	semidirect
309. #3116	C₂×C₁₃	semidirect
310. #3011	C₂×C₁₃	semidirect
311. #3009	C₂×C₁₃	semidirect
312. #2980	C₂×C₁₃	semidirect
381. C₂×#137	C₂²×C₁₃	semidirect
382. C₂²×Q₁₆	C₂²×C₁₃	semidirect
388. #556	C₂²×C₁₃	semidirect
389. D₄×Q₈	C₂²×C₁₃	semidirect
397. #536	C₂²×C₁₃	semidirect
400. #533	C₂²×C₁₃	semidirect
406. #497	C₂²×C₁₃	semidirect
407. #489	C₂²×C₁₃	semidirect
408. #485	C₂²×C₁₃	semidirect
409. #485	C₂²×C₁₃	semidirect
410. #482	C₂²×C₁₃	semidirect
411. #477	C₂²×C₁₃	semidirect
412. #476	C₂²×C₁₃	semidirect
413. #470	C₂²×C₁₃	semidirect
414. #468	C₂²×C₁₃	semidirect
415. #467	C₂²×C₁₃	semidirect
416. #465	C₂²×C₁₃	semidirect
417. #464	C₂²×C₁₃	semidirect
418. #464	C₂²×C₁₃	semidirect
419. #462	C₂²×C₁₃	semidirect
420. #461	C₂²×C₁₃	semidirect
423. #452	C₂²×C₁₃	semidirect
424. #451	C₂²×C₁₃	semidirect
425. #451	C₂²×C₁₃	semidirect
426. #451	C₂²×C₁₃	semidirect
429. #448	C₂²×C₁₃	semidirect
430. #441	C₂²×C₁₃	semidirect
431. #440	C₂²×C₁₃	semidirect
432. #435	C₂²×C₁₃	semidirect
433. #435	C₂²×C₁₃	semidirect
434. #432	C₂²×C₁₃	semidirect
435. #419	C₂²×C₁₃	semidirect
438. #416	C₂²×C₁₃	semidirect
440. #408	C₂²×C₁₃	semidirect
695. C₁₃	#61674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3550	2
C₁₃×#3500	2
C₁₃×#3313	2
C₁₃×#3311	2
C₁₃×#3270	2
C₁₃×#3266	2
C₁₃×#3215	2
C₁₃×#3202	2
C₁₃×#3200	2
C₁₃×#3116	2
C₁₃×#3011	2
C₁₃×#3009	2
C₁₃×#2980	2
#61674	13

Subgroups — C13×#61674 #15748013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61674 #15748013