Subgroups — C₁₃×#61427 #15747766

Order 3328.

1890 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×#3475	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3303	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3296	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3102	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
15	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#135	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#135	C₂²	1	2	yes	—
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₁₃×#556	C₂²	1	2	yes	complemented
21	C₁₃×#555	C₂²	1	2	yes	complemented
22	C₁₃×#554	C₂²	1	2	yes	complemented
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	C₂²	1	4	yes	—
26	C₁₃×#551	—	2	4	no	—
27	C₁₃×#547	C₂²	1	2	yes	complemented
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#533	C₂²	1	2	yes	—
30	C₁₃×#529	—	2	4	no	—
31	C₁₃×#529	C₂²	1	4	yes	complemented
32	C₁₃×#525	—	2	2	no	—
33	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	—	2	2	no	—
37	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#499	C₂²	1	2	yes	complemented
39	C₁₃×#495	C₂²	1	2	yes	—
40	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#488	C₂²	1	4	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#485	C₂²	1	4	yes	complemented
44	C₁₃×#483	C₂²	1	4	yes	—
45	C₁₃×#482	C₂²	1	4	yes	complemented
46	C₁₃×#479	C₂²	1	4	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#476	C₂²	1	2	yes	complemented
49	C₁₃×#476	C₂²	1	2	yes	complemented
50	C₁₃×#467	C₂²	1	2	yes	—
51	C₁₃×#467	C₂²	1	2	yes	—
52	C₁₃×#467	C₂²	1	2	yes	complemented
53	C₁₃×#466	C₂²	1	2	yes	—
54	C₁₃×#465	C₂²	1	4	yes	complemented
55	C₁₃×#464	C₂²	1	4	yes	complemented
56	C₁₃×#463	C₂²	1	4	yes	—
57	C₁₃×#461	C₂²	1	2	yes	complemented
58	C₁₃×#461	C₂²	1	2	yes	complemented
59	C₁₃×#452	C₂²	1	4	yes	complemented
60	C₁₃×#450	C₂²	1	4	yes	—
61	C₁₃×#449	C₂²	1	4	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
65	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
66	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
67	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
68	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
69	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
70	C₄×C₁₃×D₈	C₂²	1	2	yes	—
71	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×D₈	C₂²	1	2	yes	—
73	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×D₈	C₂²	1	2	yes	—
75	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
76	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₁₃	C₂²	1	2	yes	—
78	C₈×D₄×C₁₃	C₂²	1	2	yes	—
79	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#431	C₂²	1	1	yes	characteristic
82	C₁₃×#431	C₂²	1	2	yes	complemented
83	C₁₃×#427	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
85	C₁₃×#416	C₂²	1	4	yes	complemented
86	C₂×C₁₃×#102	C₂²	1	2	yes	—
87	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
89	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	2	2	no	—
93	C₁₃×#135	—	2	8	no	—
94	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
95	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	—	2	4	no	—
99	C₂×C₁₃×D₈	C₂³	1	2	yes	—
100	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×D₈	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	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#125	—	2	4	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#124	—	2	4	no	—
115	C₁₃×#124	C₂³	1	4	yes	—
116	C₁₃×#123	—	2	4	no	—
117	C₁₃×#123	—	2	4	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	2	no	—
123	C₁₃×C₂²⋊Q₈	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	4	no	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₁₃×#120	—	2	4	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
133	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	D₄	1	2	yes	—
142	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
143	C₄×D₄×C₁₃	C₂³	1	2	yes	—
144	C₄×D₄×C₁₃	C₂³	1	2	yes	—
145	C₄×D₄×C₁₃	C₂³	1	2	yes	—
146	C₄×D₄×C₁₃	C₂³	1	2	yes	—
147	C₄×D₄×C₁₃	C₂³	1	4	yes	—
148	C₄×D₄×C₁₃	C₂³	1	2	yes	—
149	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₁₃×#117	—	2	2	no	—
151	C₁₃×#117	—	2	2	no	—
152	C₁₃×#117	—	2	2	no	—
153	C₁₃×#117	—	2	4	no	—
154	C₁₃×#117	—	2	4	no	—
155	C₁₃×#117	—	2	4	no	—
156	C₁₃×#117	D₄	1	1	yes	characteristic
157	C₁₃×#117	D₄	1	2	yes	—
158	C₁₃×#117	C₂³	1	4	yes	—
159	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₂×C₄²×C₁₃	—	2	4	no	—
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	4	yes	—
173	C₁₃×#106	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	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	2	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	2	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	2	yes	—
196	C₄×C₈×C₁₃	C₂³	1	2	yes	—
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#61427	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂⁴×C₁₃	—	2	2	no	—
200	C₁₃×#41	—	2	4	no	—
201	C₁₃×#41	—	2	8	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
206	C₂×D₄×C₁₃	—	2	4	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
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	—	4	8	no	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
229	C₁₃×Q₁₆	—	2	4	no	—
230	C₁₃×Q₁₆	—	4	2	no	—
231	C₁₃×SD₁₆	—	2	8	no	—
232	C₁₃×SD₁₆	—	4	4	no	—
233	C₁₃×D₈	—	2	4	no	—
234	C₁₃×D₈	—	2	2	no	—
235	C₁₃×D₈	#41	1	4	yes	complemented
236	C₂×C₈×C₁₃	—	2	2	no	—
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	—	4	2	no	—
239	C₂×C₈×C₁₃	—	4	1	no	—
240	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
257	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	—	2	4	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₃	C₂×D₄	1	2	yes	—
283	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	2	yes	—
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	#3475	C₂×C₁₃	1	2	yes	complemented
288	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#3380	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#3360	C₂×C₁₃	1	2	yes	complemented
291	#3341	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3336	C₂×C₁₃	1	2	yes	complemented
293	#3303	C₂×C₁₃	1	2	yes	complemented
294	#3296	C₂×C₁₃	1	4	yes	complemented
295	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3280	C₂×C₁₃	1	2	yes	complemented
297	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3168	C₂×C₁₃	1	2	yes	complemented
299	#3102	C₂×C₁₃	1	4	yes	complemented
300	#3101	C₂×C₁₃	1	2	yes	complemented
301	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₄×#135	C₂×C₁₃	1	2	yes	complemented
303	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	2	no	—
306	C₂³×C₁₃	—	4	4	no	—
307	C₂³×C₁₃	—	4	4	no	—
308	C₂³×C₁₃	—	8	2	no	—
309	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
310	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₁₃	—	2	2	no	—
312	Q₈×C₁₃	—	2	4	no	—
313	Q₈×C₁₃	—	2	4	no	—
314	Q₈×C₁₃	—	8	2	no	—
315	D₄×C₁₃	—	2	4	no	—
316	D₄×C₁₃	—	2	2	no	—
317	D₄×C₁₃	—	2	2	no	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	4	4	no	—
321	D₄×C₁₃	—	4	8	no	—
322	D₄×C₁₃	—	8	4	no	—
323	D₄×C₁₃	C₂×#41	1	4	yes	—
324	C₂×C₄×C₁₃	—	2	4	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	8	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	4	no	—
339	C₂×C₄×C₁₃	—	4	4	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	8	4	no	—
342	C₂×C₄×C₁₃	#135	1	4	yes	complemented
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	1	yes	characteristic
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	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
352	C₈×C₁₃	—	2	1	no	—
353	C₈×C₁₃	—	2	2	no	—
354	C₈×C₁₃	—	2	1	no	—
355	C₈×C₁₃	—	2	2	no	—
356	C₈×C₁₃	—	2	1	no	—
357	C₈×C₁₃	C₂×#41	1	2	yes	—
358	C₂×#135	C₂²×C₁₃	1	2	yes	—
359	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
360	#556	C₂²×C₁₃	1	2	yes	complemented
361	#555	C₂²×C₁₃	1	2	yes	complemented
362	#554	C₂²×C₁₃	1	2	yes	complemented
363	#553	—	2	2	no	—
364	#552	—	2	2	no	—
365	#552	C₂²×C₁₃	1	4	yes	—
366	#551	—	2	4	no	—
367	#547	C₂²×C₁₃	1	2	yes	complemented
368	#546	C₂²×C₁₃	1	4	yes	—
369	#533	C₂²×C₁₃	1	2	yes	—
370	#529	—	2	4	no	—
371	#529	C₂²×C₁₃	1	4	yes	complemented
372	#525	—	2	2	no	—
373	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
374	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
375	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
376	C₂×#117	—	2	2	no	—
377	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
378	#499	C₂²×C₁₃	1	2	yes	complemented
379	#495	C₂²×C₁₃	1	2	yes	—
380	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#488	C₂²×C₁₃	1	4	yes	complemented
382	#487	C₂²×C₁₃	1	2	yes	complemented
383	#485	C₂²×C₁₃	1	4	yes	complemented
384	#483	C₂²×C₁₃	1	4	yes	—
385	#482	C₂²×C₁₃	1	4	yes	complemented
386	#479	C₂²×C₁₃	1	4	yes	complemented
387	#478	C₂²×C₁₃	1	4	yes	complemented
388	#476	C₂²×C₁₃	1	2	yes	complemented
389	#476	C₂²×C₁₃	1	2	yes	complemented
390	#467	C₂²×C₁₃	1	2	yes	—
391	#467	C₂²×C₁₃	1	2	yes	—
392	#467	C₂²×C₁₃	1	2	yes	complemented
393	#466	C₂²×C₁₃	1	2	yes	—
394	#465	C₂²×C₁₃	1	4	yes	complemented
395	#464	C₂²×C₁₃	1	4	yes	complemented
396	#463	C₂²×C₁₃	1	4	yes	—
397	#461	C₂²×C₁₃	1	2	yes	complemented
398	#461	C₂²×C₁₃	1	2	yes	complemented
399	#452	C₂²×C₁₃	1	4	yes	complemented
400	#450	C₂²×C₁₃	1	4	yes	—
401	#449	C₂²×C₁₃	1	4	yes	—
402	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
405	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
406	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
407	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
408	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
409	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
410	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
411	C₄×D₈	C₂²×C₁₃	1	2	yes	—
412	C₄×D₈	C₂²×C₁₃	1	2	yes	—
413	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
414	C₄×D₈	C₂²×C₁₃	1	2	yes	—
415	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₈×D₄	C₂²×C₁₃	1	2	yes	—
418	C₈×D₄	C₂²×C₁₃	1	2	yes	—
419	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	#431	C₂²×C₁₃	1	1	yes	characteristic
422	#431	C₂²×C₁₃	1	2	yes	complemented
423	#427	C₂²×C₁₃	1	2	yes	complemented
424	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
425	#416	C₂²×C₁₃	1	4	yes	complemented
426	C₂×#102	C₂²×C₁₃	1	2	yes	—
427	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
429	C₂²×C₁₃	—	2	1	no	—
430	C₂²×C₁₃	—	2	1	no	—
431	C₂²×C₁₃	—	2	2	no	—
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	4	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	4	2	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	—	4	2	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	8	8	no	—
441	C₂²×C₁₃	C₂×#135	1	2	yes	—
442	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	2	2	no	—
445	C₄×C₁₃	—	2	1	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	1	no	—
448	C₄×C₁₃	—	2	2	no	—
449	C₄×C₁₃	—	4	4	no	—
450	C₄×C₁₃	—	4	4	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	2	no	—
453	C₄×C₁₃	C₂×#135	1	2	yes	—
454	C₄×C₁₃	C₂×#135	1	2	yes	—
455	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
456	C₄×C₁₃	#585	1	1	yes	characteristic
457	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
458	C₂×#41	C₂³×C₁₃	1	4	yes	—
459	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
460	C₂³×C₄	—	2	2	no	—
461	#135	—	2	8	no	—
462	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
463	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
464	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
465	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
466	C₂×D₈	—	2	4	no	—
467	C₂×D₈	C₂³×C₁₃	1	2	yes	—
468	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
472	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
475	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#126	—	2	4	no	—
479	#125	—	2	4	no	—
480	#125	—	2	2	no	—
481	#125	C₂³×C₁₃	1	4	yes	—
482	#124	—	2	4	no	—
483	#124	C₂³×C₁₃	1	4	yes	—
484	#123	—	2	4	no	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
493	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	4	no	—
497	#121	C₂³×C₁₃	1	4	yes	—
498	#120	—	2	4	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
501	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
502	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
503	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	4	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	D₄×C₁₃	1	2	yes	—
510	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
511	C₄×D₄	C₂³×C₁₃	1	2	yes	—
512	C₄×D₄	C₂³×C₁₃	1	2	yes	—
513	C₄×D₄	C₂³×C₁₃	1	2	yes	—
514	C₄×D₄	C₂³×C₁₃	1	2	yes	—
515	C₄×D₄	C₂³×C₁₃	1	4	yes	—
516	C₄×D₄	C₂³×C₁₃	1	2	yes	—
517	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
518	#117	—	2	2	no	—
519	#117	—	2	2	no	—
520	#117	—	2	2	no	—
521	#117	—	2	4	no	—
522	#117	—	2	4	no	—
523	#117	—	2	4	no	—
524	#117	D₄×C₁₃	1	1	yes	characteristic
525	#117	D₄×C₁₃	1	2	yes	—
526	#117	C₂³×C₁₃	1	4	yes	—
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₂²⋊C₄	—	2	2	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₄²	—	2	4	no	—
533	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
535	#107	C₂³×C₁₃	1	1	yes	characteristic
536	#107	C₂³×C₁₃	1	1	yes	characteristic
537	#107	C₂³×C₁₃	1	2	yes	—
538	#107	C₂³×C₁₃	1	2	yes	—
539	#107	C₂³×C₁₃	1	2	yes	—
540	#106	C₂³×C₁₃	1	4	yes	—
541	#106	C₂³×C₁₃	1	4	yes	—
542	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
546	#103	C₂³×C₁₃	1	4	yes	—
547	#103	C₂³×C₁₃	1	4	yes	—
548	#103	C₂³×C₁₃	1	4	yes	—
549	#103	C₂³×C₁₃	1	4	yes	—
550	#102	C₂³×C₁₃	1	2	yes	—
551	#102	C₂³×C₁₃	1	2	yes	—
552	#102	C₂³×C₁₃	1	2	yes	—
553	#102	C₂³×C₁₃	1	2	yes	—
554	#102	C₂³×C₁₃	1	4	yes	—
555	#102	C₂³×C₁₃	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
557	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
558	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
559	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
563	C₄×C₈	C₂³×C₁₃	1	2	yes	—
564	C₄×C₈	C₂³×C₁₃	1	2	yes	—
565	C₄×C₈	C₂³×C₁₃	1	2	yes	—
566	C₂×C₁₃	—	2	2	no	—
567	C₂×C₁₃	—	4	2	no	—
568	C₂×C₁₃	—	4	4	no	—
569	C₂×C₁₃	—	8	2	no	—
570	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
571	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
572	C₂×C₁₃	#3584	1	1	yes	characteristic
573	C₂⁴	—	2	2	no	—
574	#41	—	2	4	no	—
575	#41	—	2	8	no	—
576	#41	—	4	4	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
579	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	4	2	no	—
585	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
586	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
587	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
588	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	4	8	no	—
597	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	Q₁₆	—	2	4	no	—
604	Q₁₆	—	4	2	no	—
605	SD₁₆	—	2	8	no	—
606	SD₁₆	—	4	4	no	—
607	D₈	—	2	4	no	—
608	D₈	—	2	2	no	—
609	D₈	C₁₃×#41	1	4	yes	complemented
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	—	4	2	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	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	2	no	—
630	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
649	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
650	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	C₂×D₄×C₁₃	1	2	yes	—
655	C₄²	C₂×D₄×C₁₃	1	2	yes	—
656	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
659	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
660	C₄²	C₂⁴×C₁₃	1	2	yes	—
661	C₁₃	#61427	1	1	yes	characteristic, direct product factor, Sylow
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	8	2	no	—
667	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	8	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	4	no	—
681	D₄	C₂×C₁₃×#41	1	4	yes	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	C₁₃×#135	1	4	yes	complemented
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
709	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	C₂×C₁₃×#41	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	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	8	no	—
728	C₂²	C₂×C₁₃×#135	1	2	yes	—
729	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	4	no	—
739	C₄	—	4	4	no	—
740	C₄	C₂×C₁₃×#135	1	2	yes	—
741	C₄	C₂×C₁₃×#135	1	2	yes	—
742	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
743	C₄	C₁₃×#585	1	1	yes	characteristic
744	C₂	—	2	2	no	—
745	C₂	—	4	2	no	—
746	C₂	—	4	4	no	—
747	C₂	—	8	2	no	—
748	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
749	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
750	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3475	C₂	semidirect
2. C₁₃×#3393	C₂	semidirect
3. C₁₃×#3380	C₂	semidirect
4. C₁₃×#3360	C₂	semidirect
5. C₁₃×#3341	C₂	semidirect
6. C₁₃×#3336	C₂	semidirect
7. C₁₃×#3303	C₂	semidirect
8. C₁₃×#3296	C₂	semidirect
9. C₁₃×#3283	C₂	semidirect
10. C₁₃×#3280	C₂	semidirect
11. C₁₃×#3170	C₂	semidirect
12. C₁₃×#3168	C₂	semidirect
13. C₁₃×#3102	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₈×C₁₃×#41	C₂	semidirect
16. C₄×C₁₃×#135	C₂	semidirect
17. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#555	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
27. C₁₃×#547	C₂²	semidirect
31. C₁₃×#529	C₂²	semidirect
34. C₄×C₁₃×#41	C₂²	semidirect
37. C₁₃×#500	C₂²	semidirect
38. C₁₃×#499	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#479	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#476	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
52. C₁₃×#467	C₂²	semidirect
54. C₁₃×#465	C₂²	semidirect
55. C₁₃×#464	C₂²	semidirect
57. C₁₃×#461	C₂²	semidirect
58. C₁₃×#461	C₂²	semidirect
59. C₁₃×#452	C₂²	semidirect
62. C₈×Q₈×C₁₃	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
64. C₄×C₁₃×Q₁₆	C₂²	semidirect
65. C₄×C₁₃×Q₁₆	C₂²	semidirect
66. C₄×C₁₃×Q₁₆	C₂²	semidirect
67. C₄×C₁₃×SD₁₆	C₂²	semidirect
68. C₄×C₁₃×SD₁₆	C₂²	semidirect
69. C₄×C₁₃×SD₁₆	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₈×D₄×C₁₃	C₂²	semidirect
82. C₁₃×#431	C₂²	semidirect
83. C₁₃×#427	C₂²	semidirect
85. C₁₃×#416	C₂²	semidirect
88. C₂×C₄×C₈×C₁₃	C₂²	semidirect
198. #61427	C₁₃	direct (N × H)
235. C₁₃×D₈	#41	semidirect
287. #3475	C₂×C₁₃	semidirect
288. #3393	C₂×C₁₃	semidirect
289. #3380	C₂×C₁₃	semidirect
290. #3360	C₂×C₁₃	semidirect
291. #3341	C₂×C₁₃	semidirect
292. #3336	C₂×C₁₃	semidirect
293. #3303	C₂×C₁₃	semidirect
294. #3296	C₂×C₁₃	semidirect
295. #3283	C₂×C₁₃	semidirect
296. #3280	C₂×C₁₃	semidirect
297. #3170	C₂×C₁₃	semidirect
298. #3168	C₂×C₁₃	semidirect
299. #3102	C₂×C₁₃	semidirect
300. #3101	C₂×C₁₃	semidirect
301. C₈×#41	C₂×C₁₃	semidirect
302. C₄×#135	C₂×C₁₃	semidirect
303. C₂×C₄×D₈	C₂×C₁₃	semidirect
342. C₂×C₄×C₁₃	#135	semidirect
360. #556	C₂²×C₁₃	semidirect
361. #555	C₂²×C₁₃	semidirect
362. #554	C₂²×C₁₃	semidirect
367. #547	C₂²×C₁₃	semidirect
371. #529	C₂²×C₁₃	semidirect
374. C₄×#41	C₂²×C₁₃	semidirect
377. #500	C₂²×C₁₃	semidirect
378. #499	C₂²×C₁₃	semidirect
380. #494	C₂²×C₁₃	semidirect
381. #488	C₂²×C₁₃	semidirect
382. #487	C₂²×C₁₃	semidirect
383. #485	C₂²×C₁₃	semidirect
385. #482	C₂²×C₁₃	semidirect
386. #479	C₂²×C₁₃	semidirect
387. #478	C₂²×C₁₃	semidirect
388. #476	C₂²×C₁₃	semidirect
389. #476	C₂²×C₁₃	semidirect
392. #467	C₂²×C₁₃	semidirect
394. #465	C₂²×C₁₃	semidirect
395. #464	C₂²×C₁₃	semidirect
397. #461	C₂²×C₁₃	semidirect
398. #461	C₂²×C₁₃	semidirect
399. #452	C₂²×C₁₃	semidirect
402. C₈×Q₈	C₂²×C₁₃	semidirect
403. C₈×Q₈	C₂²×C₁₃	semidirect
404. C₄×Q₁₆	C₂²×C₁₃	semidirect
405. C₄×Q₁₆	C₂²×C₁₃	semidirect
406. C₄×Q₁₆	C₂²×C₁₃	semidirect
407. C₄×SD₁₆	C₂²×C₁₃	semidirect
408. C₄×SD₁₆	C₂²×C₁₃	semidirect
409. C₄×SD₁₆	C₂²×C₁₃	semidirect
419. C₈×D₄	C₂²×C₁₃	semidirect
420. C₈×D₄	C₂²×C₁₃	semidirect
422. #431	C₂²×C₁₃	semidirect
423. #427	C₂²×C₁₃	semidirect
425. #416	C₂²×C₁₃	semidirect
428. C₂×C₄×C₈	C₂²×C₁₃	semidirect
609. D₈	C₁₃×#41	semidirect
661. C₁₃	#61427	direct (N × H)
700. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3475	2
C₁₃×#3393	2
C₁₃×#3380	2
C₁₃×#3360	2
C₁₃×#3341	2
C₁₃×#3336	2
C₁₃×#3303	2
C₁₃×#3296	2
C₁₃×#3283	2
C₁₃×#3280	2
C₁₃×#3170	2
C₁₃×#3168	2
C₁₃×#3102	2
C₁₃×#3101	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×D₈	2
#61427	13

Subgroups — C13×#61427 #15747766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61427 #15747766