Subgroups — C₁₃×#61264 #15747603

Order 3328.

1764 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	2	yes	maximal
2	C₁₃×#3349	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3336	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×#3097	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3095	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×Q₁₆	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	C₂²	1	4	yes	—
22	C₁₃×#554	C₂²	1	4	yes	—
23	C₁₃×#552	—	2	4	no	—
24	C₁₃×#552	C₂²	1	4	yes	—
25	C₁₃×#552	C₂²	1	4	yes	—
26	C₁₃×#551	—	2	4	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#542	—	2	2	no	—
29	C₁₃×#541	—	2	2	no	—
30	C₁₃×#536	C₂²	1	2	yes	—
31	C₁₃×#533	—	2	2	no	—
32	C₁₃×#529	—	2	2	no	—
33	C₁₃×#525	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₁₃×#519	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×#485	C₂²	1	4	yes	complemented
45	C₁₃×#484	C₂²	1	4	yes	—
46	C₁₃×#484	C₂²	1	4	yes	complemented
47	C₁₃×#483	C₂²	1	4	yes	—
48	C₁₃×#483	C₂²	1	4	yes	complemented
49	C₁₃×#479	C₂²	1	4	yes	complemented
50	C₁₃×#479	C₂²	1	4	yes	complemented
51	C₁₃×#477	C₂²	1	4	yes	complemented
52	C₁₃×#475	C₂²	1	4	yes	complemented
53	C₁₃×#470	C₂²	1	4	yes	complemented
54	C₁₃×#467	C₂²	1	2	yes	—
55	C₁₃×#467	C₂²	1	2	yes	—
56	C₁₃×#467	C₂²	1	2	yes	—
57	C₁₃×#467	C₂²	1	2	yes	—
58	C₁₃×#467	C₂²	1	2	yes	complemented
59	C₁₃×#467	C₂²	1	2	yes	complemented
60	C₁₃×#441	C₂²	1	4	yes	complemented
61	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
62	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
63	C₁₃×#435	C₂²	1	2	yes	—
64	C₁₃×#435	C₂²	1	2	yes	—
65	C₈×D₄×C₁₃	C₂²	1	2	yes	—
66	C₈×D₄×C₁₃	C₂²	1	2	yes	—
67	C₁₃×#428	C₂²	1	2	yes	—
68	C₁₃×#428	C₂²	1	2	yes	—
69	C₁₃×#428	C₂²	1	4	yes	complemented
70	C₁₃×#427	C₂²	1	1	yes	characteristic
71	C₁₃×#427	C₂²	1	1	yes	characteristic
72	C₁₃×#427	C₂²	1	2	yes	—
73	C₁₃×#427	C₂²	1	1	yes	characteristic
74	C₁₃×#427	C₂²	1	2	yes	—
75	C₁₃×#427	C₂²	1	1	yes	characteristic
76	C₁₃×#427	C₂²	1	2	yes	complemented
77	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	—
84	C₁₃×#419	C₂²	1	2	yes	—
85	C₂×C₁₃×#103	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	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×Q₁₆	—	2	4	no	—
93	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
94	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
95	C₁₃×#131	—	2	4	no	—
96	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
99	C₂²×C₈×C₁₃	—	2	4	no	—
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
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	C₁₃×C₄⋊Q₈	—	2	2	no	—
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	2	no	—
115	C₁₃×#125	—	2	4	no	—
116	C₁₃×#125	—	2	4	no	—
117	C₁₃×#125	—	2	4	no	—
118	C₁₃×#125	C₂³	1	4	yes	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×#123	D₄	1	2	yes	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	4	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
132	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×#121	D₄	1	1	yes	characteristic
137	C₁₃×#121	D₄	1	1	yes	characteristic
138	C₁₃×#120	D₄	1	2	yes	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	4	no	—
143	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
144	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	4	no	—
147	C₄×D₄×C₁₃	—	2	4	no	—
148	C₄×D₄×C₁₃	C₂³	1	2	yes	—
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₁₃×#117	—	2	2	no	—
151	C₁₃×#117	—	2	2	no	—
152	C₁₃×#117	—	2	4	no	—
153	C₁₃×#117	—	2	4	no	—
154	C₁₃×#117	—	2	4	no	—
155	C₁₃×#117	C₂³	1	2	yes	—
156	C₁₃×#117	C₂³	1	2	yes	—
157	C₁₃×#117	C₂³	1	2	yes	—
158	C₁₃×#117	C₂³	1	2	yes	—
159	C₁₃×#117	C₂³	1	4	yes	—
160	C₁₃×#117	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₄²×C₁₃	—	2	2	no	—
169	C₁₃×#107	C₂³	1	1	yes	characteristic
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	1	yes	characteristic
172	C₁₃×#107	C₂³	1	1	yes	characteristic
173	C₁₃×#107	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	2	yes	—
175	C₁₃×#107	C₂³	1	2	yes	—
176	C₁₃×#107	C₂³	1	2	yes	—
177	C₁₃×#107	C₂³	1	4	yes	—
178	C₁₃×#107	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×#106	C₂³	1	2	yes	—
182	C₁₃×#106	C₂³	1	2	yes	—
183	C₁₃×#106	C₂³	1	4	yes	—
184	C₁₃×#106	C₂³	1	4	yes	—
185	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
186	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#103	C₂³	1	4	yes	—
190	C₁₃×#103	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#103	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	#61264	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	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	—	2	4	no	—
205	C₂×Q₈×C₁₃	—	2	4	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	2	no	—
217	C₂²×C₄×C₁₃	—	2	2	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₁₃×Q₁₆	—	2	4	no	—
228	C₁₃×Q₁₆	—	2	4	no	—
229	C₁₃×M₁₆	—	2	2	no	—
230	C₁₃×M₁₆	—	2	2	no	—
231	C₁₃×M₁₆	—	2	4	no	—
232	C₂×C₈×C₁₃	—	2	2	no	—
233	C₂×C₈×C₁₃	—	2	2	no	—
234	C₂×C₈×C₁₃	—	2	2	no	—
235	C₂×C₈×C₁₃	—	2	2	no	—
236	C₂×C₈×C₁₃	—	2	2	no	—
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	#41	1	4	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	4	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	—	2	2	no	—
283	C₄²×C₁₃	—	2	2	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	4	no	—
286	C₄²×C₁₃	—	2	4	no	—
287	C₄²×C₁₃	—	2	4	no	—
288	C₄²×C₁₃	C₂⁴	1	2	yes	—
289	#3495	C₂×C₁₃	1	2	yes	—
290	#3349	C₂×C₁₃	1	4	yes	complemented
291	#3344	C₂×C₁₃	1	4	yes	complemented
292	#3342	C₂×C₁₃	1	2	yes	complemented
293	#3338	C₂×C₁₃	1	2	yes	complemented
294	#3336	C₂×C₁₃	1	2	yes	complemented
295	#3336	C₂×C₁₃	1	2	yes	complemented
296	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#3097	C₂×C₁₃	1	2	yes	complemented
298	#3095	C₂×C₁₃	1	2	yes	complemented
299	#3082	C₂×C₁₃	1	2	yes	complemented
300	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
301	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2929	C₂×C₁₃	1	1	yes	characteristic
304	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
310	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	4	no	—
315	Q₈×C₁₃	—	2	4	no	—
316	Q₈×C₁₃	—	4	4	no	—
317	Q₈×C₁₃	—	8	4	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	4	no	—
320	D₄×C₁₃	—	2	2	no	—
321	D₄×C₁₃	—	4	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	8	4	no	—
340	C₂×C₄×C₁₃	—	8	2	no	—
341	C₂×C₄×C₁₃	—	8	2	no	—
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
349	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
351	C₈×C₁₃	—	2	1	no	—
352	C₈×C₁₃	—	2	1	no	—
353	C₈×C₁₃	—	2	2	no	—
354	C₈×C₁₃	—	2	2	no	—
355	C₈×C₁₃	C₂×#41	1	2	yes	—
356	C₈×C₁₃	C₂×#41	1	2	yes	—
357	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
359	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
360	#556	C₂²×C₁₃	1	4	yes	—
361	#554	C₂²×C₁₃	1	4	yes	—
362	#552	—	2	4	no	—
363	#552	C₂²×C₁₃	1	4	yes	—
364	#552	C₂²×C₁₃	1	4	yes	—
365	#551	—	2	4	no	—
366	#544	C₂²×C₁₃	1	2	yes	—
367	#542	—	2	2	no	—
368	#541	—	2	2	no	—
369	#536	C₂²×C₁₃	1	2	yes	—
370	#533	—	2	2	no	—
371	#529	—	2	2	no	—
372	#525	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
374	#520	C₂²×C₁₃	1	2	yes	—
375	#519	C₂²×C₁₃	1	2	yes	—
376	C₂×#117	C₂²×C₁₃	1	2	yes	—
377	#501	C₂²×C₁₃	1	4	yes	complemented
378	#500	C₂²×C₁₃	1	2	yes	complemented
379	#499	C₂²×C₁₃	1	2	yes	complemented
380	#485	C₂²×C₁₃	1	4	yes	—
381	#485	C₂²×C₁₃	1	4	yes	—
382	#485	C₂²×C₁₃	1	4	yes	complemented
383	#485	C₂²×C₁₃	1	4	yes	complemented
384	#484	C₂²×C₁₃	1	4	yes	—
385	#484	C₂²×C₁₃	1	4	yes	complemented
386	#483	C₂²×C₁₃	1	4	yes	—
387	#483	C₂²×C₁₃	1	4	yes	complemented
388	#479	C₂²×C₁₃	1	4	yes	complemented
389	#479	C₂²×C₁₃	1	4	yes	complemented
390	#477	C₂²×C₁₃	1	4	yes	complemented
391	#475	C₂²×C₁₃	1	4	yes	complemented
392	#470	C₂²×C₁₃	1	4	yes	complemented
393	#467	C₂²×C₁₃	1	2	yes	—
394	#467	C₂²×C₁₃	1	2	yes	—
395	#467	C₂²×C₁₃	1	2	yes	—
396	#467	C₂²×C₁₃	1	2	yes	—
397	#467	C₂²×C₁₃	1	2	yes	complemented
398	#467	C₂²×C₁₃	1	2	yes	complemented
399	#441	C₂²×C₁₃	1	4	yes	complemented
400	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
401	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
402	#435	C₂²×C₁₃	1	2	yes	—
403	#435	C₂²×C₁₃	1	2	yes	—
404	C₈×D₄	C₂²×C₁₃	1	2	yes	—
405	C₈×D₄	C₂²×C₁₃	1	2	yes	—
406	#428	C₂²×C₁₃	1	2	yes	—
407	#428	C₂²×C₁₃	1	2	yes	—
408	#428	C₂²×C₁₃	1	4	yes	complemented
409	#427	C₂²×C₁₃	1	1	yes	characteristic
410	#427	C₂²×C₁₃	1	2	yes	—
411	#427	C₂²×C₁₃	1	1	yes	characteristic
412	#427	C₂²×C₁₃	1	2	yes	—
413	#427	C₂²×C₁₃	1	1	yes	characteristic
414	#427	C₂²×C₁₃	1	1	yes	characteristic
415	#427	C₂²×C₁₃	1	2	yes	complemented
416	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
420	C₂×#106	C₂²×C₁₃	1	2	yes	—
421	#424	C₂²×C₁₃	1	1	yes	characteristic
422	#419	C₂²×C₁₃	1	2	yes	—
423	#419	C₂²×C₁₃	1	2	yes	—
424	C₂×#103	C₂²×C₁₃	1	2	yes	—
425	#408	C₂²×C₁₃	1	1	yes	characteristic
426	#407	C₂²×C₁₃	1	1	yes	characteristic
427	#405	C₂²×C₁₃	1	1	yes	characteristic
428	C₂²×C₁₃	—	2	1	no	—
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	2	1	no	—
431	C₂²×C₁₃	—	2	1	no	—
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	1	no	—
434	C₂²×C₁₃	—	2	1	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	2	1	no	—
438	C₂²×C₁₃	—	4	4	no	—
439	C₂²×C₁₃	#547	1	2	yes	—
440	C₂²×C₁₃	#578	1	2	yes	—
441	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	2	1	no	—
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	4	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	4	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	#547	1	2	yes	—
454	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
455	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×Q₁₆	—	2	4	no	—
460	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
461	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
462	#131	—	2	4	no	—
463	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
465	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×C₈	—	2	4	no	—
467	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
473	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₄⋊Q₈	—	2	2	no	—
475	C₄⋊Q₈	—	2	2	no	—
476	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
477	#126	—	2	4	no	—
478	#126	—	2	4	no	—
479	#126	—	2	4	no	—
480	#126	—	2	4	no	—
481	#125	—	2	2	no	—
482	#125	—	2	4	no	—
483	#125	—	2	4	no	—
484	#125	—	2	4	no	—
485	#125	C₂³×C₁₃	1	4	yes	—
486	#124	—	2	2	no	—
487	#124	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	D₄×C₁₃	1	2	yes	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
498	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
499	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
501	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
502	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
503	#121	D₄×C₁₃	1	1	yes	characteristic
504	#121	D₄×C₁₃	1	1	yes	characteristic
505	#120	D₄×C₁₃	1	2	yes	—
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	C₂³×C₁₃	1	4	yes	—
511	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	C₂³×C₁₃	1	2	yes	—
516	C₄×D₄	C₂³×C₁₃	1	2	yes	—
517	#117	—	2	2	no	—
518	#117	—	2	2	no	—
519	#117	—	2	4	no	—
520	#117	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	C₂³×C₁₃	1	2	yes	—
523	#117	C₂³×C₁₃	1	2	yes	—
524	#117	C₂³×C₁₃	1	2	yes	—
525	#117	C₂³×C₁₃	1	2	yes	—
526	#117	C₂³×C₁₃	1	4	yes	—
527	#117	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	C₂×C₄²	—	2	2	no	—
536	#107	C₂³×C₁₃	1	1	yes	characteristic
537	#107	C₂³×C₁₃	1	2	yes	—
538	#107	C₂³×C₁₃	1	1	yes	characteristic
539	#107	C₂³×C₁₃	1	1	yes	characteristic
540	#107	C₂³×C₁₃	1	1	yes	characteristic
541	#107	C₂³×C₁₃	1	2	yes	—
542	#107	C₂³×C₁₃	1	2	yes	—
543	#107	C₂³×C₁₃	1	2	yes	—
544	#107	C₂³×C₁₃	1	4	yes	—
545	#107	C₂³×C₁₃	1	4	yes	—
546	#106	C₂³×C₁₃	1	2	yes	—
547	#106	C₂³×C₁₃	1	2	yes	—
548	#106	C₂³×C₁₃	1	2	yes	—
549	#106	C₂³×C₁₃	1	2	yes	—
550	#106	C₂³×C₁₃	1	4	yes	—
551	#106	C₂³×C₁₃	1	4	yes	—
552	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
554	#103	C₂³×C₁₃	1	4	yes	—
555	#103	C₂³×C₁₃	1	4	yes	—
556	#103	C₂³×C₁₃	1	4	yes	—
557	#103	C₂³×C₁₃	1	4	yes	—
558	#103	C₂³×C₁₃	1	4	yes	—
559	#103	C₂³×C₁₃	1	4	yes	—
560	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
561	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
562	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
563	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
564	#97	C₂³×C₁₃	1	2	yes	—
565	C₄×C₈	C₂³×C₁₃	1	2	yes	—
566	C₂×C₁₃	—	2	2	no	—
567	C₂×C₁₃	—	2	2	no	—
568	C₂×C₁₃	—	4	2	no	—
569	C₂×C₁₃	—	4	1	no	—
570	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
571	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
572	C₂×C₁₃	#3584	1	1	yes	characteristic
573	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	4	no	—
580	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
582	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
583	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
584	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	Q₁₆	—	2	4	no	—
601	Q₁₆	—	2	4	no	—
602	M₁₆	—	2	2	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	4	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	2	2	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	C₁₃×#41	1	4	yes	—
612	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
613	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
615	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
639	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
650	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₄²	—	2	2	no	—
655	C₄²	—	2	2	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	4	no	—
661	C₄²	C₂⁴×C₁₃	1	2	yes	—
662	C₁₃	#61264	1	1	yes	characteristic, direct product factor, Sylow
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
667	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	Q₈	—	2	2	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	4	4	no	—
674	Q₈	—	8	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
706	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
707	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	C₂×C₁₃×#41	1	2	yes	—
713	C₈	C₂×C₁₃×#41	1	2	yes	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	C₁₃×#547	1	2	yes	—
726	C₂²	C₁₃×#578	1	2	yes	—
727	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	4	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	4	no	—
739	C₄	C₁₃×#547	1	2	yes	—
740	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
741	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
747	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
748	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#525	C₂²
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
2. C₁₃×#3349	C₂	semidirect
3. C₁₃×#3344	C₂	semidirect
4. C₁₃×#3342	C₂	semidirect
5. C₁₃×#3338	C₂	semidirect
6. C₁₃×#3336	C₂	semidirect
7. C₁₃×#3336	C₂	semidirect
8. C₁₃×#3164	C₂	semidirect
9. C₁₃×#3097	C₂	semidirect
10. C₁₃×#3095	C₂	semidirect
11. C₁₃×#3082	C₂	semidirect
12. C₁₃×#3059	C₂	semidirect
13. C₂×C₁₃×#467	C₂	semidirect
14. C₁₃×#2950	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×#485	C₂²	semidirect
46. C₁₃×#484	C₂²	semidirect
48. C₁₃×#483	C₂²	semidirect
49. C₁₃×#479	C₂²	semidirect
50. C₁₃×#479	C₂²	semidirect
51. C₁₃×#477	C₂²	semidirect
52. C₁₃×#475	C₂²	semidirect
53. C₁₃×#470	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#467	C₂²	semidirect
60. C₁₃×#441	C₂²	semidirect
61. C₄×C₁₃×Q₁₆	C₂²	semidirect
62. C₄×C₁₃×Q₁₆	C₂²	semidirect
69. C₁₃×#428	C₂²	semidirect
76. C₁₃×#427	C₂²	semidirect
80. C₂×C₁₃×#107	C₂²	semidirect
199. #61264	C₁₃	direct (N × H)
290. #3349	C₂×C₁₃	semidirect
291. #3344	C₂×C₁₃	semidirect
292. #3342	C₂×C₁₃	semidirect
293. #3338	C₂×C₁₃	semidirect
294. #3336	C₂×C₁₃	semidirect
295. #3336	C₂×C₁₃	semidirect
296. #3164	C₂×C₁₃	semidirect
297. #3097	C₂×C₁₃	semidirect
298. #3095	C₂×C₁₃	semidirect
299. #3082	C₂×C₁₃	semidirect
300. #3059	C₂×C₁₃	semidirect
301. C₂×#467	C₂×C₁₃	semidirect
302. #2950	C₂×C₁₃	semidirect
304. #2913	C₂×C₁₃	semidirect
305. C₂×#427	C₂×C₁₃	semidirect
377. #501	C₂²×C₁₃	semidirect
378. #500	C₂²×C₁₃	semidirect
379. #499	C₂²×C₁₃	semidirect
382. #485	C₂²×C₁₃	semidirect
383. #485	C₂²×C₁₃	semidirect
385. #484	C₂²×C₁₃	semidirect
387. #483	C₂²×C₁₃	semidirect
388. #479	C₂²×C₁₃	semidirect
389. #479	C₂²×C₁₃	semidirect
390. #477	C₂²×C₁₃	semidirect
391. #475	C₂²×C₁₃	semidirect
392. #470	C₂²×C₁₃	semidirect
397. #467	C₂²×C₁₃	semidirect
398. #467	C₂²×C₁₃	semidirect
399. #441	C₂²×C₁₃	semidirect
400. C₄×Q₁₆	C₂²×C₁₃	semidirect
401. C₄×Q₁₆	C₂²×C₁₃	semidirect
408. #428	C₂²×C₁₃	semidirect
415. #427	C₂²×C₁₃	semidirect
419. C₂×#107	C₂²×C₁₃	semidirect
662. C₁₃	#61264	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×#3495	2
C₁₃×#3349	2
C₁₃×#3344	2
C₁₃×#3342	2
C₁₃×#3338	2
C₁₃×#3336	2
C₁₃×#3164	2
C₁₃×#3097	2
C₁₃×#3095	2
C₁₃×#3082	2
C₁₃×#3059	2
C₂×C₁₃×#467	2
C₁₃×#2950	2
C₁₃×#2929	2
C₁₃×#2913	2
C₂×C₁₃×#427	2
#61264	13

Subgroups — C13×#61264 #15747603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61264 #15747603