Subgroups — C₁₃×#61334 #15747673

Order 3328.

1794 conjugacy classes of subgroups.

The subgroup lattice has 752 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
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3375	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3368	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	4	yes	—
19	Q₈²×C₁₃	—	2	1	no	—
20	Q₈²×C₁₃	C₂²	1	2	yes	complemented
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	2	no	—
23	C₁₃×#557	C₂²	1	4	yes	complemented
24	C₁₃×#557	C₂²	1	2	yes	complemented
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#555	—	2	1	no	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#550	C₂²	1	2	yes	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#544	—	2	2	no	—
31	C₁₃×#544	C₂²	1	2	yes	—
32	C₁₃×#538	—	2	2	no	—
33	C₁₃×#535	C₂²	1	2	yes	—
34	C₁₃×#533	—	2	2	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#525	—	2	2	no	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#519	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#491	C₂²	1	2	yes	complemented
44	C₁₃×#490	C₂²	1	4	yes	—
45	C₁₃×#490	C₂²	1	2	yes	complemented
46	C₁₃×#489	C₂²	1	4	yes	—
47	C₁₃×#489	C₂²	1	2	yes	complemented
48	C₁₃×#489	C₂²	1	2	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#486	C₂²	1	4	yes	—
51	C₁₃×#479	C₂²	1	4	yes	complemented
52	C₁₃×#478	C₂²	1	4	yes	—
53	C₁₃×#478	C₂²	1	4	yes	complemented
54	C₁₃×#477	C₂²	1	4	yes	complemented
55	C₁₃×#476	C₂²	1	2	yes	—
56	C₁₃×#474	C₂²	1	2	yes	—
57	C₁₃×#474	C₂²	1	4	yes	complemented
58	C₁₃×#464	C₂²	1	4	yes	—
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#462	C₂²	1	2	yes	complemented
62	C₁₃×#460	C₂²	1	4	yes	—
63	C₁₃×#460	C₂²	1	4	yes	—
64	C₁₃×#460	C₂²	1	2	yes	complemented
65	C₁₃×#446	C₂²	1	4	yes	complemented
66	C₁₃×#446	C₂²	1	4	yes	complemented
67	C₁₃×#441	C₂²	1	4	yes	complemented
68	C₁₃×#440	C₂²	1	4	yes	—
69	C₁₃×#440	C₂²	1	4	yes	—
70	C₁₃×#440	C₂²	1	4	yes	complemented
71	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
72	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
73	C₁₃×#428	C₂²	1	2	yes	—
74	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
75	C₁₃×#424	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	1	yes	characteristic
77	C₁₃×#418	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₁₃×#416	C₂²	1	2	yes	—
81	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	—
84	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	C₂³	1	2	yes	—
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	—	2	1	no	—
90	C₁₃×#137	—	2	8	no	—
91	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	—	2	4	no	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
96	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	—	2	4	no	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	—	2	4	no	—
102	C₁₃×C₄⋊Q₈	—	2	2	no	—
103	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₁₃×#127	C₂³	1	4	yes	—
110	C₁₃×#127	C₂³	1	1	yes	characteristic
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#125	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	—	2	2	no	—
116	C₁₃×#125	D₄	1	2	yes	—
117	C₁₃×#125	C₂³	1	2	yes	—
118	C₁₃×#125	C₂³	1	4	yes	—
119	C₁₃×#124	—	2	4	no	—
120	C₁₃×#124	C₂³	1	4	yes	—
121	C₁₃×#124	C₂³	1	2	yes	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	—	2	2	no	—
135	C₁₃×#121	—	2	4	no	—
136	C₁₃×#120	—	2	4	no	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	4	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	1	no	—
143	C₄×Q₈×C₁₃	—	2	1	no	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	—	2	4	no	—
154	C₄×D₄×C₁₃	—	2	4	no	—
155	C₄×D₄×C₁₃	—	2	1	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	C₂³	1	4	yes	—
160	C₄×D₄×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	C₂³	1	2	yes	—
162	C₁₃×#117	—	2	2	no	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	—	2	4	no	—
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₁₃×#117	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₂×C₄²×C₁₃	—	2	1	no	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	4	yes	—
175	C₁₃×#107	C₂³	1	4	yes	—
176	C₁₃×#106	C₂³	1	4	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	2	yes	—
189	C₁₃×#102	C₂³	1	2	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#97	C₂³	1	2	yes	—
196	C₁₃×#97	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₁₃	C₂³	1	4	yes	—
199	#61334	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	—	2	1	no	—
201	C₁₃×#41	—	2	4	no	—
202	C₁₃×#41	—	2	4	no	—
203	C₁₃×#41	—	8	4	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	—	2	4	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
212	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
213	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	2	no	—
222	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	2	no	—
231	C₂²×C₄×C₁₃	—	8	2	no	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×Q₁₆	—	2	8	no	—
236	C₁₃×SD₁₆	—	2	8	no	—
237	C₁₃×SD₁₆	—	2	8	no	—
238	C₁₃×M₁₆	—	2	4	no	—
239	C₂×C₈×C₁₃	—	2	2	no	—
240	C₂×C₈×C₁₃	—	2	2	no	—
241	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
265	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	4	no	—
283	C₄²×C₁₃	—	2	4	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₁₃	C₂⁴	1	4	yes	—
288	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
290	#3506	C₂×C₁₃	1	1	yes	characteristic
291	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3377	C₂×C₁₃	1	4	yes	complemented
293	#3375	C₂×C₁₃	1	4	yes	complemented
294	#3371	C₂×C₁₃	1	4	yes	complemented
295	#3368	C₂×C₁₃	1	4	yes	complemented
296	#3136	C₂×C₁₃	1	2	yes	complemented
297	#3135	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3083	C₂×C₁₃	1	2	yes	complemented
299	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3043	C₂×C₁₃	1	2	yes	complemented
301	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2947	C₂×C₁₃	1	2	yes	complemented
304	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	4	2	no	—
308	C₂³×C₁₃	—	8	1	no	—
309	C₂³×C₁₃	—	8	1	no	—
310	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₁₃	—	2	4	no	—
312	Q₈×C₁₃	—	2	2	no	—
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	4	2	no	—
316	Q₈×C₁₃	—	4	2	no	—
317	Q₈×C₁₃	—	4	2	no	—
318	Q₈×C₁₃	—	8	1	no	—
319	Q₈×C₁₃	—	8	4	no	—
320	Q₈×C₁₃	C₂×#41	1	4	yes	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	4	2	no	—
326	D₄×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	4	2	no	—
328	D₄×C₁₃	—	8	1	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	8	2	no	—
343	C₂×C₄×C₁₃	—	8	4	no	—
344	C₂×C₄×C₁₃	—	8	1	no	—
345	C₂×C₄×C₁₃	—	8	1	no	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
354	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
355	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
356	C₈×C₁₃	—	2	2	no	—
357	C₈×C₁₃	—	2	4	no	—
358	C₈×C₁₃	—	2	2	no	—
359	C₂×#137	C₂²×C₁₃	1	2	yes	—
360	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
361	#559	C₂²×C₁₃	1	4	yes	—
362	Q₈²	—	2	1	no	—
363	Q₈²	C₂²×C₁₃	1	2	yes	complemented
364	#557	—	2	1	no	—
365	#557	—	2	2	no	—
366	#557	C₂²×C₁₃	1	4	yes	complemented
367	#557	C₂²×C₁₃	1	2	yes	complemented
368	#556	C₂²×C₁₃	1	2	yes	—
369	#555	—	2	1	no	—
370	#553	—	2	2	no	—
371	#550	C₂²×C₁₃	1	2	yes	—
372	#547	—	2	1	no	—
373	#544	—	2	2	no	—
374	#544	C₂²×C₁₃	1	2	yes	—
375	#538	—	2	2	no	—
376	#535	C₂²×C₁₃	1	2	yes	—
377	#533	—	2	2	no	—
378	#533	C₂²×C₁₃	1	1	yes	characteristic
379	#533	C₂²×C₁₃	1	1	yes	characteristic
380	#532	C₂²×C₁₃	1	1	yes	characteristic
381	#525	—	2	2	no	—
382	#520	C₂²×C₁₃	1	2	yes	—
383	#519	C₂²×C₁₃	1	2	yes	—
384	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
386	#491	C₂²×C₁₃	1	2	yes	complemented
387	#490	C₂²×C₁₃	1	4	yes	—
388	#490	C₂²×C₁₃	1	2	yes	complemented
389	#489	C₂²×C₁₃	1	4	yes	—
390	#489	C₂²×C₁₃	1	2	yes	complemented
391	#489	C₂²×C₁₃	1	2	yes	complemented
392	#488	C₂²×C₁₃	1	4	yes	—
393	#486	C₂²×C₁₃	1	4	yes	—
394	#479	C₂²×C₁₃	1	4	yes	complemented
395	#478	C₂²×C₁₃	1	4	yes	—
396	#478	C₂²×C₁₃	1	4	yes	complemented
397	#477	C₂²×C₁₃	1	4	yes	complemented
398	#476	C₂²×C₁₃	1	2	yes	—
399	#474	C₂²×C₁₃	1	2	yes	—
400	#474	C₂²×C₁₃	1	4	yes	complemented
401	#464	C₂²×C₁₃	1	4	yes	—
402	#464	C₂²×C₁₃	1	4	yes	—
403	#464	C₂²×C₁₃	1	4	yes	complemented
404	#462	C₂²×C₁₃	1	2	yes	complemented
405	#460	C₂²×C₁₃	1	4	yes	—
406	#460	C₂²×C₁₃	1	4	yes	—
407	#460	C₂²×C₁₃	1	2	yes	complemented
408	#446	C₂²×C₁₃	1	4	yes	complemented
409	#446	C₂²×C₁₃	1	4	yes	complemented
410	#441	C₂²×C₁₃	1	4	yes	complemented
411	#440	C₂²×C₁₃	1	4	yes	—
412	#440	C₂²×C₁₃	1	4	yes	—
413	#440	C₂²×C₁₃	1	4	yes	complemented
414	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
415	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
416	#428	C₂²×C₁₃	1	2	yes	—
417	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
418	#424	C₂²×C₁₃	1	2	yes	—
419	#423	C₂²×C₁₃	1	1	yes	characteristic
420	#418	C₂²×C₁₃	1	2	yes	—
421	#417	C₂²×C₁₃	1	2	yes	—
422	#416	C₂²×C₁₃	1	2	yes	—
423	#416	C₂²×C₁₃	1	2	yes	—
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
426	#405	C₂²×C₁₃	1	2	yes	—
427	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	8	4	no	—
437	C₂²×C₁₃	#548	1	2	yes	—
438	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	1	no	—
441	C₄×C₁₃	—	2	4	no	—
442	C₄×C₁₃	—	2	1	no	—
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	2	4	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	#548	1	2	yes	—
452	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
453	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×#41	—	2	2	no	—
455	C₂×#41	C₂³×C₁₃	1	2	yes	—
456	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂³×C₄	—	2	1	no	—
459	#137	—	2	8	no	—
460	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
461	C₂×SD₁₆	—	2	4	no	—
462	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
463	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
464	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
465	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	2	4	no	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	—	2	4	no	—
471	C₄⋊Q₈	—	2	2	no	—
472	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
473	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
478	#127	C₂³×C₁₃	1	1	yes	characteristic
479	#127	C₂³×C₁₃	1	4	yes	—
480	#126	—	2	4	no	—
481	#125	—	2	4	no	—
482	#125	—	2	4	no	—
483	#125	—	2	4	no	—
484	#125	—	2	2	no	—
485	#125	D₄×C₁₃	1	2	yes	—
486	#125	C₂³×C₁₃	1	2	yes	—
487	#125	C₂³×C₁₃	1	4	yes	—
488	#124	—	2	4	no	—
489	#124	C₂³×C₁₃	1	2	yes	—
490	#124	C₂³×C₁₃	1	4	yes	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	1	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
498	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#120	—	2	4	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	4	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	—	2	1	no	—
512	C₄×Q₈	—	2	1	no	—
513	C₄×Q₈	—	2	1	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
516	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
517	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
518	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
519	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
521	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	C₂³×C₁₃	1	2	yes	—
529	C₄×D₄	C₂³×C₁₃	1	2	yes	—
530	C₄×D₄	C₂³×C₁₃	1	4	yes	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	—	2	4	no	—
534	#117	C₂³×C₁₃	1	2	yes	—
535	#117	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
543	#107	C₂³×C₁₃	1	4	yes	—
544	#107	C₂³×C₁₃	1	4	yes	—
545	#106	C₂³×C₁₃	1	4	yes	—
546	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
549	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
550	#103	C₂³×C₁₃	1	4	yes	—
551	#103	C₂³×C₁₃	1	2	yes	—
552	#103	C₂³×C₁₃	1	2	yes	—
553	#103	C₂³×C₁₃	1	2	yes	—
554	#103	C₂³×C₁₃	1	2	yes	—
555	#103	C₂³×C₁₃	1	4	yes	—
556	#102	C₂³×C₁₃	1	4	yes	—
557	#102	C₂³×C₁₃	1	2	yes	—
558	#102	C₂³×C₁₃	1	2	yes	—
559	#102	C₂³×C₁₃	1	2	yes	—
560	#102	C₂³×C₁₃	1	2	yes	—
561	#102	C₂³×C₁₃	1	4	yes	—
562	#102	C₂³×C₁₃	1	4	yes	—
563	#102	C₂³×C₁₃	1	4	yes	—
564	#97	C₂³×C₁₃	1	2	yes	—
565	#97	C₂³×C₁₃	1	2	yes	—
566	#97	C₂³×C₁₃	1	4	yes	—
567	C₄×C₈	C₂³×C₁₃	1	4	yes	—
568	C₂×C₁₃	—	2	2	no	—
569	C₂×C₁₃	—	8	2	no	—
570	C₂×C₁₃	—	8	2	no	—
571	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
572	C₂×C₁₃	#3585	1	1	yes	characteristic
573	C₂×C₁₃	#3586	1	1	yes	characteristic
574	C₂⁴	—	2	1	no	—
575	#41	—	2	4	no	—
576	#41	—	2	4	no	—
577	#41	—	8	4	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	4	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
584	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
585	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
586	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	8	2	no	—
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
609	Q₁₆	—	2	8	no	—
610	SD₁₆	—	2	8	no	—
611	SD₁₆	—	2	8	no	—
612	M₁₆	—	2	4	no	—
613	C₂×C₈	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
617	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
638	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
639	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₄²	C₂⁴×C₁₃	1	4	yes	—
662	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
663	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
664	C₁₃	#61334	1	1	yes	characteristic, direct product factor, Sylow
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	8	1	no	—
669	C₂³	—	8	1	no	—
670	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	Q₈	—	2	4	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	2	2	no	—
675	Q₈	—	4	2	no	—
676	Q₈	—	4	2	no	—
677	Q₈	—	4	2	no	—
678	Q₈	—	8	1	no	—
679	Q₈	—	8	4	no	—
680	Q₈	C₂×C₁₃×#41	1	4	yes	—
681	D₄	—	2	2	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	2	no	—
688	D₄	—	8	1	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	8	2	no	—
703	C₂×C₄	—	8	4	no	—
704	C₂×C₄	—	8	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
714	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
715	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
716	C₈	—	2	2	no	—
717	C₈	—	2	4	no	—
718	C₈	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	4	no	—
728	C₂²	C₁₃×#548	1	2	yes	—
729	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	4	no	—
736	C₄	—	2	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₁₃×#548	1	2	yes	—
743	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
744	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
749	C₂	C₁₃×#3585	1	1	yes	characteristic
750	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3375	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3368	C₂	semidirect
7. C₁₃×#3136	C₂	semidirect
8. C₁₃×#3135	C₂	semidirect
9. C₁₃×#3083	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#3043	C₂	semidirect
12. C₁₃×#3037	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2947	C₂	semidirect
15. C₂×C₁₃×#440	C₂	semidirect
20. Q₈²×C₁₃	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
24. C₁₃×#557	C₂²	semidirect
43. C₁₃×#491	C₂²	semidirect
45. C₁₃×#490	C₂²	semidirect
47. C₁₃×#489	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
53. C₁₃×#478	C₂²	semidirect
54. C₁₃×#477	C₂²	semidirect
57. C₁₃×#474	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#446	C₂²	semidirect
66. C₁₃×#446	C₂²	semidirect
67. C₁₃×#441	C₂²	semidirect
70. C₁₃×#440	C₂²	semidirect
71. C₄×C₁₃×Q₁₆	C₂²	semidirect
72. C₄×C₁₃×SD₁₆	C₂²	semidirect
199. #61334	C₁₃	direct (N × H)
211. C₂×Q₈×C₁₃	#41	semidirect
291. #3502	C₂×C₁₃	semidirect
292. #3377	C₂×C₁₃	semidirect
293. #3375	C₂×C₁₃	semidirect
294. #3371	C₂×C₁₃	semidirect
295. #3368	C₂×C₁₃	semidirect
296. #3136	C₂×C₁₃	semidirect
297. #3135	C₂×C₁₃	semidirect
298. #3083	C₂×C₁₃	semidirect
299. #3077	C₂×C₁₃	semidirect
300. #3043	C₂×C₁₃	semidirect
301. #3037	C₂×C₁₃	semidirect
302. #2961	C₂×C₁₃	semidirect
303. #2947	C₂×C₁₃	semidirect
304. C₂×#440	C₂×C₁₃	semidirect
363. Q₈²	C₂²×C₁₃	semidirect
366. #557	C₂²×C₁₃	semidirect
367. #557	C₂²×C₁₃	semidirect
386. #491	C₂²×C₁₃	semidirect
388. #490	C₂²×C₁₃	semidirect
390. #489	C₂²×C₁₃	semidirect
391. #489	C₂²×C₁₃	semidirect
394. #479	C₂²×C₁₃	semidirect
396. #478	C₂²×C₁₃	semidirect
397. #477	C₂²×C₁₃	semidirect
400. #474	C₂²×C₁₃	semidirect
403. #464	C₂²×C₁₃	semidirect
404. #462	C₂²×C₁₃	semidirect
407. #460	C₂²×C₁₃	semidirect
408. #446	C₂²×C₁₃	semidirect
409. #446	C₂²×C₁₃	semidirect
410. #441	C₂²×C₁₃	semidirect
413. #440	C₂²×C₁₃	semidirect
414. C₄×Q₁₆	C₂²×C₁₃	semidirect
415. C₄×SD₁₆	C₂²×C₁₃	semidirect
585. C₂×Q₈	C₁₃×#41	semidirect
664. C₁₃	#61334	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×#3506	2
C₁₃×#3502	2
C₁₃×#3377	2
C₁₃×#3375	2
C₁₃×#3371	2
C₁₃×#3368	2
C₁₃×#3136	2
C₁₃×#3135	2
C₁₃×#3083	2
C₁₃×#3077	2
C₁₃×#3043	2
C₁₃×#3037	2
C₁₃×#2961	2
C₁₃×#2947	2
C₂×C₁₃×#440	2
#61334	13

Subgroups — C13×#61334 #15747673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61334 #15747673