Subgroups — C₁₃×#61261 #15747600

Order 3328.

1782 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3350	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3348	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3341	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3093	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#556	—	2	2	no	—
22	C₁₃×#556	C₂²	1	4	yes	—
23	C₁₃×#555	—	2	2	no	—
24	C₁₃×#555	C₂²	1	4	yes	—
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#553	C₂²	1	4	yes	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	4	yes	—
29	C₁₃×#544	C₂²	1	2	yes	—
30	C₁₃×#538	—	2	4	no	—
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#529	—	2	4	no	—
33	C₁₃×#525	C₂²	1	2	yes	—
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#520	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₁₃×#501	C₂²	1	4	yes	complemented
39	C₁₃×#500	C₂²	1	2	yes	complemented
40	C₁₃×#499	C₂²	1	2	yes	complemented
41	C₁₃×#485	C₂²	1	4	yes	—
42	C₁₃×#485	C₂²	1	4	yes	—
43	C₁₃×#485	C₂²	1	4	yes	complemented
44	C₁₃×#483	C₂²	1	4	yes	complemented
45	C₁₃×#482	C₂²	1	4	yes	—
46	C₁₃×#482	C₂²	1	4	yes	—
47	C₁₃×#482	C₂²	1	4	yes	complemented
48	C₁₃×#481	C₂²	1	4	yes	complemented
49	C₁₃×#479	C₂²	1	4	yes	complemented
50	C₁₃×#478	C₂²	1	4	yes	complemented
51	C₁₃×#476	C₂²	1	4	yes	complemented
52	C₁₃×#475	C₂²	1	4	yes	complemented
53	C₁₃×#468	C₂²	1	4	yes	complemented
54	C₁₃×#467	C₂²	1	1	yes	characteristic
55	C₁₃×#467	C₂²	1	1	yes	characteristic
56	C₁₃×#467	C₂²	1	2	yes	complemented
57	C₁₃×#466	C₂²	1	1	yes	characteristic
58	C₁₃×#466	C₂²	1	1	yes	characteristic
59	C₁₃×#466	C₂²	1	2	yes	complemented
60	C₁₃×#465	C₂²	1	2	yes	—
61	C₁₃×#465	C₂²	1	2	yes	—
62	C₁₃×#440	C₂²	1	4	yes	complemented
63	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
64	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
65	C₁₃×#435	C₂²	1	2	yes	—
66	C₁₃×#435	C₂²	1	2	yes	—
67	C₈×D₄×C₁₃	C₂²	1	2	yes	—
68	C₈×D₄×C₁₃	C₂²	1	2	yes	—
69	C₁₃×#428	C₂²	1	2	yes	—
70	C₁₃×#428	C₂²	1	2	yes	—
71	C₁₃×#428	C₂²	1	4	yes	complemented
72	C₁₃×#427	C₂²	1	1	yes	characteristic
73	C₁₃×#427	C₂²	1	2	yes	—
74	C₁₃×#427	C₂²	1	2	yes	—
75	C₁₃×#427	C₂²	1	2	yes	—
76	C₁₃×#427	C₂²	1	2	yes	—
77	C₁₃×#427	C₂²	1	2	yes	complemented
78	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
79	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
80	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
81	C₂×C₁₃×#106	C₂²	1	2	yes	—
82	C₁₃×#424	C₂²	1	1	yes	characteristic
83	C₁₃×#417	C₂²	1	2	yes	—
84	C₁₃×#417	C₂²	1	2	yes	—
85	C₁₃×#416	C₂²	1	2	yes	—
86	C₁₃×#408	C₂²	1	1	yes	characteristic
87	C₁₃×#407	C₂²	1	1	yes	characteristic
88	C₁₃×#405	C₂²	1	1	yes	characteristic
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#135	—	2	4	no	—
93	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
95	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
96	C₁₃×#131	—	2	4	no	—
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₃	—	2	4	no	—
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#126	—	2	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	—	2	2	no	—
116	C₁₃×#125	C₂³	1	4	yes	—
117	C₁₃×#124	—	2	4	no	—
118	C₁₃×#124	—	2	4	no	—
119	C₁₃×#124	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	2	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	D₄	1	2	yes	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₃×#121	—	2	4	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	4	no	—
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	D₄	1	1	yes	characteristic
136	C₁₃×#121	D₄	1	1	yes	characteristic
137	C₁₃×#121	C₂³	1	2	yes	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₁₃×#121	C₂³	1	4	yes	—
140	C₁₃×#120	—	2	2	no	—
141	C₁₃×#120	D₄	1	2	yes	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	4	no	—
144	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	2	no	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	—	2	4	no	—
150	C₄×D₄×C₁₃	—	2	4	no	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₄×D₄×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	C₂³	1	2	yes	—
154	C₁₃×#117	—	2	2	no	—
155	C₁₃×#117	—	2	2	no	—
156	C₁₃×#117	—	2	2	no	—
157	C₁₃×#117	—	2	4	no	—
158	C₁₃×#117	—	2	4	no	—
159	C₁₃×#117	C₂³	1	2	yes	—
160	C₁₃×#117	C₂³	1	4	yes	—
161	C₁₃×#117	C₂³	1	4	yes	—
162	C₁₃×#117	C₂³	1	4	yes	—
163	C₁₃×#117	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₄²×C₁₃	—	2	2	no	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#107	C₂³	1	2	yes	—
173	C₁₃×#107	C₂³	1	2	yes	—
174	C₁₃×#107	C₂³	1	1	yes	characteristic
175	C₁₃×#107	C₂³	1	4	yes	—
176	C₁₃×#107	C₂³	1	1	yes	characteristic
177	C₁₃×#107	C₂³	1	4	yes	—
178	C₁₃×#106	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	4	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×#106	C₂³	1	4	yes	—
182	C₁₃×#106	C₂³	1	4	yes	—
183	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	2	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	2	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₁₃	C₂³	1	2	yes	—
199	#61261	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₁₃×#41	—	2	2	no	—
202	C₁₃×#41	—	2	2	no	—
203	C₁₃×#41	—	2	4	no	—
204	C₁₃×#41	—	2	4	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
216	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	2	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	4	no	—
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₁₃×Q₁₆	—	2	2	no	—
232	C₁₃×SD₁₆	—	2	4	no	—
233	C₁₃×D₈	—	2	2	no	—
234	C₁₃×M₁₆	—	2	2	no	—
235	C₁₃×M₁₆	—	2	2	no	—
236	C₁₃×M₁₆	—	2	4	no	—
237	C₂×C₈×C₁₃	—	2	2	no	—
238	C₂×C₈×C₁₃	—	2	2	no	—
239	C₂×C₈×C₁₃	—	2	2	no	—
240	C₂×C₈×C₁₃	—	2	2	no	—
241	C₂×C₈×C₁₃	—	2	2	no	—
242	C₂×C₈×C₁₃	—	2	4	no	—
243	C₂×C₈×C₁₃	#41	1	4	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	C₂⁴	1	2	yes	—
290	#3493	C₂×C₁₃	1	2	yes	complemented
291	#3350	C₂×C₁₃	1	4	yes	complemented
292	#3348	C₂×C₁₃	1	4	yes	complemented
293	#3342	C₂×C₁₃	1	2	yes	complemented
294	#3341	C₂×C₁₃	1	2	yes	complemented
295	#3339	C₂×C₁₃	1	2	yes	complemented
296	#3336	C₂×C₁₃	1	2	yes	complemented
297	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3099	C₂×C₁₃	1	2	yes	complemented
299	#3093	C₂×C₁₃	1	2	yes	complemented
300	#3084	C₂×C₁₃	1	2	yes	complemented
301	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2929	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
314	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	2	2	no	—
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	8	4	no	—
319	D₄×C₁₃	—	2	4	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	4	2	no	—
324	D₄×C₁₃	—	4	2	no	—
325	D₄×C₁₃	—	4	4	no	—
326	D₄×C₁₃	—	8	2	no	—
327	D₄×C₁₃	—	8	4	no	—
328	D₄×C₁₃	—	8	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	2	1	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	1	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	4	4	no	—
344	C₂×C₄×C₁₃	—	8	4	no	—
345	C₂×C₄×C₁₃	—	8	2	no	—
346	C₂×C₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	—	8	2	no	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
355	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
356	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
357	C₈×C₁₃	—	2	1	no	—
358	C₈×C₁₃	—	2	1	no	—
359	C₈×C₁₃	—	2	2	no	—
360	C₈×C₁₃	—	2	2	no	—
361	C₈×C₁₃	C₂×#41	1	2	yes	—
362	C₈×C₁₃	C₂×#41	1	2	yes	—
363	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
365	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
366	#556	—	2	2	no	—
367	#556	C₂²×C₁₃	1	4	yes	—
368	#555	—	2	2	no	—
369	#555	C₂²×C₁₃	1	4	yes	—
370	#553	—	2	2	no	—
371	#553	C₂²×C₁₃	1	4	yes	—
372	#552	—	2	2	no	—
373	#552	C₂²×C₁₃	1	4	yes	—
374	#544	C₂²×C₁₃	1	2	yes	—
375	#538	—	2	4	no	—
376	#537	C₂²×C₁₃	1	2	yes	—
377	#529	—	2	4	no	—
378	#525	C₂²×C₁₃	1	2	yes	—
379	#525	C₂²×C₁₃	1	1	yes	characteristic
380	#520	C₂²×C₁₃	1	2	yes	—
381	#520	C₂²×C₁₃	1	2	yes	—
382	C₂×#117	C₂²×C₁₃	1	2	yes	—
383	#501	C₂²×C₁₃	1	4	yes	complemented
384	#500	C₂²×C₁₃	1	2	yes	complemented
385	#499	C₂²×C₁₃	1	2	yes	complemented
386	#485	C₂²×C₁₃	1	4	yes	—
387	#485	C₂²×C₁₃	1	4	yes	—
388	#485	C₂²×C₁₃	1	4	yes	complemented
389	#483	C₂²×C₁₃	1	4	yes	complemented
390	#482	C₂²×C₁₃	1	4	yes	—
391	#482	C₂²×C₁₃	1	4	yes	—
392	#482	C₂²×C₁₃	1	4	yes	complemented
393	#481	C₂²×C₁₃	1	4	yes	complemented
394	#479	C₂²×C₁₃	1	4	yes	complemented
395	#478	C₂²×C₁₃	1	4	yes	complemented
396	#476	C₂²×C₁₃	1	4	yes	complemented
397	#475	C₂²×C₁₃	1	4	yes	complemented
398	#468	C₂²×C₁₃	1	4	yes	complemented
399	#467	C₂²×C₁₃	1	1	yes	characteristic
400	#467	C₂²×C₁₃	1	1	yes	characteristic
401	#467	C₂²×C₁₃	1	2	yes	complemented
402	#466	C₂²×C₁₃	1	1	yes	characteristic
403	#466	C₂²×C₁₃	1	1	yes	characteristic
404	#466	C₂²×C₁₃	1	2	yes	complemented
405	#465	C₂²×C₁₃	1	2	yes	—
406	#465	C₂²×C₁₃	1	2	yes	—
407	#440	C₂²×C₁₃	1	4	yes	complemented
408	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
409	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
410	#435	C₂²×C₁₃	1	2	yes	—
411	#435	C₂²×C₁₃	1	2	yes	—
412	C₈×D₄	C₂²×C₁₃	1	2	yes	—
413	C₈×D₄	C₂²×C₁₃	1	2	yes	—
414	#428	C₂²×C₁₃	1	2	yes	—
415	#428	C₂²×C₁₃	1	2	yes	—
416	#428	C₂²×C₁₃	1	4	yes	complemented
417	#427	C₂²×C₁₃	1	2	yes	—
418	#427	C₂²×C₁₃	1	2	yes	—
419	#427	C₂²×C₁₃	1	2	yes	—
420	#427	C₂²×C₁₃	1	2	yes	—
421	#427	C₂²×C₁₃	1	1	yes	characteristic
422	#427	C₂²×C₁₃	1	2	yes	complemented
423	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
426	C₂×#106	C₂²×C₁₃	1	2	yes	—
427	#424	C₂²×C₁₃	1	1	yes	characteristic
428	#417	C₂²×C₁₃	1	2	yes	—
429	#417	C₂²×C₁₃	1	2	yes	—
430	#416	C₂²×C₁₃	1	2	yes	—
431	#408	C₂²×C₁₃	1	1	yes	characteristic
432	#407	C₂²×C₁₃	1	1	yes	characteristic
433	#405	C₂²×C₁₃	1	1	yes	characteristic
434	C₂²×C₁₃	—	2	1	no	—
435	C₂²×C₁₃	—	2	1	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	2	1	no	—
438	C₂²×C₁₃	—	2	1	no	—
439	C₂²×C₁₃	—	2	2	no	—
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	4	4	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	#547	1	2	yes	—
450	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	2	2	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	2	1	no	—
455	C₄×C₁₃	—	2	2	no	—
456	C₄×C₁₃	—	4	4	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	4	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	#547	1	2	yes	—
462	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
463	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
464	C₂×#41	C₂³×C₁₃	1	2	yes	—
465	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	#135	—	2	4	no	—
468	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
470	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
471	#131	—	2	4	no	—
472	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
474	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×C₈	—	2	4	no	—
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
482	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#126	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	2	no	—
491	#125	C₂³×C₁₃	1	4	yes	—
492	#124	—	2	4	no	—
493	#124	—	2	4	no	—
494	#124	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	2	no	—
497	#123	—	2	4	no	—
498	#123	D₄×C₁₃	1	2	yes	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
502	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
503	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
504	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
506	#121	—	2	4	no	—
507	#121	—	2	2	no	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	D₄×C₁₃	1	1	yes	characteristic
511	#121	D₄×C₁₃	1	1	yes	characteristic
512	#121	C₂³×C₁₃	1	2	yes	—
513	#121	C₂³×C₁₃	1	2	yes	—
514	#121	C₂³×C₁₃	1	4	yes	—
515	#120	—	2	2	no	—
516	#120	D₄×C₁₃	1	2	yes	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	4	no	—
519	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	C₂³×C₁₃	1	4	yes	—
527	C₄×D₄	C₂³×C₁₃	1	2	yes	—
528	C₄×D₄	C₂³×C₁₃	1	2	yes	—
529	#117	—	2	2	no	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	#117	—	2	4	no	—
533	#117	—	2	4	no	—
534	#117	C₂³×C₁₃	1	4	yes	—
535	#117	C₂³×C₁₃	1	4	yes	—
536	#117	C₂³×C₁₃	1	2	yes	—
537	#117	C₂³×C₁₃	1	4	yes	—
538	#117	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	—	2	2	no	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
543	C₂×C₂²⋊C₄	—	2	2	no	—
544	C₂×C₄²	—	2	2	no	—
545	#107	C₂³×C₁₃	1	2	yes	—
546	#107	C₂³×C₁₃	1	2	yes	—
547	#107	C₂³×C₁₃	1	2	yes	—
548	#107	C₂³×C₁₃	1	2	yes	—
549	#107	C₂³×C₁₃	1	1	yes	characteristic
550	#107	C₂³×C₁₃	1	4	yes	—
551	#107	C₂³×C₁₃	1	1	yes	characteristic
552	#107	C₂³×C₁₃	1	4	yes	—
553	#106	C₂³×C₁₃	1	4	yes	—
554	#106	C₂³×C₁₃	1	4	yes	—
555	#106	C₂³×C₁₃	1	2	yes	—
556	#106	C₂³×C₁₃	1	4	yes	—
557	#106	C₂³×C₁₃	1	4	yes	—
558	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
560	#103	C₂³×C₁₃	1	2	yes	—
561	#103	C₂³×C₁₃	1	2	yes	—
562	#103	C₂³×C₁₃	1	4	yes	—
563	#103	C₂³×C₁₃	1	4	yes	—
564	#102	C₂³×C₁₃	1	2	yes	—
565	#102	C₂³×C₁₃	1	2	yes	—
566	#102	C₂³×C₁₃	1	4	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
571	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
572	#97	C₂³×C₁₃	1	2	yes	—
573	C₄×C₈	C₂³×C₁₃	1	2	yes	—
574	C₂×C₁₃	—	2	2	no	—
575	C₂×C₁₃	—	4	2	no	—
576	C₂×C₁₃	—	4	1	no	—
577	C₂×C₁₃	—	4	1	no	—
578	C₂×C₁₃	—	8	2	no	—
579	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
580	C₂×C₁₃	#3584	1	1	yes	characteristic
581	C₂×C₁₃	#3584	1	1	yes	characteristic
582	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
583	#41	—	2	2	no	—
584	#41	—	2	2	no	—
585	#41	—	2	4	no	—
586	#41	—	2	4	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
595	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
597	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	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	—	2	4	no	—
606	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
613	Q₁₆	—	2	2	no	—
614	SD₁₆	—	2	4	no	—
615	D₈	—	2	2	no	—
616	M₁₆	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	4	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	4	no	—
625	C₂×C₈	C₁₃×#41	1	4	yes	—
626	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
627	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
630	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
645	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
647	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
648	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
649	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
663	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
664	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
665	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	C₂⁴×C₁₃	1	2	yes	—
672	C₁₃	#61261	1	1	yes	characteristic, direct product factor, Sylow
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
678	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
680	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	8	4	no	—
685	D₄	—	2	4	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	4	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	4	no	—
694	D₄	—	8	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	—	8	2	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
720	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
721	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
722	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
723	C₈	—	2	1	no	—
724	C₈	—	2	1	no	—
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×C₁₃×#41	1	2	yes	—
728	C₈	C₂×C₁₃×#41	1	2	yes	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	C₁₃×#547	1	2	yes	—
745	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	C₁₃×#547	1	2	yes	—
757	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
758	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	2	no	—
764	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
765	C₂	C₁₃×#3584	1	1	yes	characteristic
766	C₂	C₁₃×#3584	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 ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3493	C₂	semidirect
2. C₁₃×#3350	C₂	semidirect
3. C₁₃×#3348	C₂	semidirect
4. C₁₃×#3342	C₂	semidirect
5. C₁₃×#3341	C₂	semidirect
6. C₁₃×#3339	C₂	semidirect
7. C₁₃×#3336	C₂	semidirect
8. C₁₃×#3164	C₂	semidirect
9. C₁₃×#3099	C₂	semidirect
10. C₁₃×#3093	C₂	semidirect
11. C₁₃×#3084	C₂	semidirect
12. C₁₃×#3061	C₂	semidirect
13. C₁₃×#3050	C₂	semidirect
14. C₁₃×#2951	C₂	semidirect
15. C₁₃×#2929	C₂	semidirect
16. C₁₃×#2913	C₂	semidirect
17. C₂×C₁₃×#427	C₂	semidirect
38. C₁₃×#501	C₂²	semidirect
39. C₁₃×#500	C₂²	semidirect
40. C₁₃×#499	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
44. C₁₃×#483	C₂²	semidirect
47. C₁₃×#482	C₂²	semidirect
48. C₁₃×#481	C₂²	semidirect
49. C₁₃×#479	C₂²	semidirect
50. C₁₃×#478	C₂²	semidirect
51. C₁₃×#476	C₂²	semidirect
52. C₁₃×#475	C₂²	semidirect
53. C₁₃×#468	C₂²	semidirect
56. C₁₃×#467	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
62. C₁₃×#440	C₂²	semidirect
63. C₄×C₁₃×Q₁₆	C₂²	semidirect
64. C₄×C₁₃×D₈	C₂²	semidirect
71. C₁₃×#428	C₂²	semidirect
77. C₁₃×#427	C₂²	semidirect
80. C₂×C₁₃×#107	C₂²	semidirect
199. #61261	C₁₃	direct (N × H)
290. #3493	C₂×C₁₃	semidirect
291. #3350	C₂×C₁₃	semidirect
292. #3348	C₂×C₁₃	semidirect
293. #3342	C₂×C₁₃	semidirect
294. #3341	C₂×C₁₃	semidirect
295. #3339	C₂×C₁₃	semidirect
296. #3336	C₂×C₁₃	semidirect
297. #3164	C₂×C₁₃	semidirect
298. #3099	C₂×C₁₃	semidirect
299. #3093	C₂×C₁₃	semidirect
300. #3084	C₂×C₁₃	semidirect
301. #3061	C₂×C₁₃	semidirect
302. #3050	C₂×C₁₃	semidirect
303. #2951	C₂×C₁₃	semidirect
304. #2929	C₂×C₁₃	semidirect
305. #2913	C₂×C₁₃	semidirect
306. C₂×#427	C₂×C₁₃	semidirect
383. #501	C₂²×C₁₃	semidirect
384. #500	C₂²×C₁₃	semidirect
385. #499	C₂²×C₁₃	semidirect
388. #485	C₂²×C₁₃	semidirect
389. #483	C₂²×C₁₃	semidirect
392. #482	C₂²×C₁₃	semidirect
393. #481	C₂²×C₁₃	semidirect
394. #479	C₂²×C₁₃	semidirect
395. #478	C₂²×C₁₃	semidirect
396. #476	C₂²×C₁₃	semidirect
397. #475	C₂²×C₁₃	semidirect
398. #468	C₂²×C₁₃	semidirect
401. #467	C₂²×C₁₃	semidirect
404. #466	C₂²×C₁₃	semidirect
407. #440	C₂²×C₁₃	semidirect
408. C₄×Q₁₆	C₂²×C₁₃	semidirect
409. C₄×D₈	C₂²×C₁₃	semidirect
416. #428	C₂²×C₁₃	semidirect
422. #427	C₂²×C₁₃	semidirect
425. C₂×#107	C₂²×C₁₃	semidirect
672. C₁₃	#61261	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×#3493	2
C₁₃×#3350	2
C₁₃×#3348	2
C₁₃×#3342	2
C₁₃×#3341	2
C₁₃×#3339	2
C₁₃×#3336	2
C₁₃×#3164	2
C₁₃×#3099	2
C₁₃×#3093	2
C₁₃×#3084	2
C₁₃×#3061	2
C₁₃×#3050	2
C₁₃×#2951	2
C₁₃×#2929	2
C₁₃×#2913	2
C₂×C₁₃×#427	2
#61261	13

Subgroups — C13×#61261 #15747600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61261 #15747600