Subgroups — C₁₃×#62608 #15748947

Order 3328.

1774 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3543	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3323	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3174	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	C₁₃×#560	—	2	2	no	—
26	C₁₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	—	2	1	no	—
29	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#556	C₂²	1	2	yes	complemented
33	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#552	C₂²	1	2	yes	complemented
35	C₁₃×#550	C₂²	1	1	yes	characteristic
36	C₁₃×#550	C₂²	1	1	yes	characteristic
37	C₁₃×#546	—	2	1	no	—
38	C₁₃×#546	C₂²	1	2	yes	—
39	D₄²×C₁₃	—	2	1	no	—
40	D₄²×C₁₃	C₂²	1	1	yes	characteristic
41	D₄²×C₁₃	C₂²	1	2	yes	—
42	C₁₃×#544	C₂²	1	2	yes	complemented
43	C₁₃×#542	—	2	1	no	—
44	C₁₃×#541	—	2	2	no	—
45	C₁₃×#541	—	2	1	no	—
46	C₁₃×#541	C₂²	1	2	yes	complemented
47	C₁₃×#540	—	2	1	no	—
48	C₁₃×#540	C₂²	1	2	yes	—
49	C₁₃×#535	—	2	1	no	—
50	C₁₃×#535	C₂²	1	2	yes	—
51	C₁₃×#534	—	2	2	no	—
52	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
55	C₁₃×#529	C₂²	1	1	yes	characteristic
56	C₁₃×#529	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#499	C₂²	1	2	yes	complemented
59	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#492	C₂²	1	2	yes	complemented
61	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#490	C₂²	1	2	yes	complemented
63	C₁₃×#490	C₂²	1	2	yes	complemented
64	C₁₃×#490	C₂²	1	2	yes	complemented
65	C₁₃×#489	C₂²	1	2	yes	complemented
66	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#488	C₂²	1	2	yes	complemented
68	C₁₃×#488	C₂²	1	2	yes	complemented
69	C₁₃×#486	C₂²	1	1	yes	characteristic
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#486	C₂²	1	2	yes	complemented
73	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#486	C₂²	1	2	yes	complemented
75	C₁₃×#485	C₂²	1	2	yes	complemented
76	C₁₃×#482	C₂²	1	2	yes	—
77	C₁₃×#482	C₂²	1	2	yes	complemented
78	C₁₃×#482	C₂²	1	2	yes	complemented
79	C₁₃×#481	C₂²	1	2	yes	complemented
80	C₁₃×#480	C₂²	1	2	yes	complemented
81	C₁₃×#478	C₂²	1	2	yes	complemented
82	C₁₃×#478	C₂²	1	2	yes	complemented
83	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#476	C₂²	1	2	yes	complemented
86	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#474	C₂²	1	2	yes	complemented
89	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#468	C₂²	1	1	yes	characteristic
92	C₁₃×#468	C₂²	1	1	yes	characteristic
93	C₁₃×#468	C₂²	1	2	yes	complemented
94	C₁₃×#468	C₂²	1	2	yes	complemented
95	C₁₃×#465	C₂²	1	2	yes	complemented
96	C₁₃×#465	C₂²	1	2	yes	complemented
97	C₁₃×#464	C₂²	1	2	yes	complemented
98	C₁₃×#464	C₂²	1	2	yes	complemented
99	C₁₃×#460	C₂²	1	1	yes	characteristic
100	C₁₃×#460	C₂²	1	1	yes	characteristic
101	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#460	C₂²	1	2	yes	complemented
103	C₁₃×#460	C₂²	1	2	yes	complemented
104	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#452	C₂²	1	2	yes	complemented
107	C₁₃×#450	C₂²	1	2	yes	complemented
108	C₁₃×#450	C₂²	1	2	yes	complemented
109	C₁₃×#450	C₂²	1	2	yes	complemented
110	C₁₃×#450	C₂²	1	2	yes	complemented
111	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#440	C₂²	1	2	yes	complemented
114	C₁₃×#440	C₂²	1	2	yes	complemented
115	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
121	C₁₃×#436	C₂²	1	2	yes	complemented
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#418	C₂²	1	2	yes	complemented
128	C₁₃×#418	C₂²	1	2	yes	complemented
129	C₁₃×#418	C₂²	1	2	yes	complemented
130	C₁₃×#417	C₂²	1	2	yes	complemented
131	C₁₃×#416	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	—	2	2	no	—
138	C₂²×D₄×C₁₃	—	2	1	no	—
139	C₂²×D₄×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
154	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
155	C₁₃×C₄⋊Q₈	—	2	1	no	—
156	C₁₃×C₄⋊Q₈	—	2	2	no	—
157	C₁₃×C₄⋊Q₈	—	2	1	no	—
158	C₁₃×C₄⋊Q₈	—	2	2	no	—
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#127	—	2	1	no	—
165	C₁₃×#127	—	2	1	no	—
166	C₁₃×#127	—	2	1	no	—
167	C₁₃×#127	C₂³	1	1	yes	characteristic
168	C₁₃×#127	C₂³	1	1	yes	characteristic
169	C₁₃×#127	C₂³	1	2	yes	—
170	C₁₃×#127	C₂³	1	2	yes	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	—	2	2	no	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#126	—	2	2	no	—
177	C₁₃×#126	—	2	1	no	—
178	C₁₃×#126	D₄	1	2	yes	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	1	no	—
183	C₁₃×#125	—	2	2	no	—
184	C₁₃×#125	—	2	2	no	—
185	C₁₃×#125	—	2	1	no	—
186	C₁₃×#125	D₄	1	1	yes	characteristic
187	C₁₃×#125	C₂³	1	2	yes	—
188	C₁₃×#125	C₂³	1	2	yes	—
189	C₁₃×#125	C₂³	1	1	yes	characteristic
190	C₁₃×#124	—	2	1	no	—
191	C₁₃×#124	—	2	1	no	—
192	C₁₃×#124	—	2	2	no	—
193	C₁₃×#124	D₄	1	1	yes	characteristic
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#124	C₂³	1	1	yes	characteristic
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	1	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	D₄	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	—	2	1	no	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₁₃×#121	—	2	2	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	—	2	2	no	—
222	C₁₃×#121	—	2	2	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	D₄	1	1	yes	characteristic
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	2	yes	—
228	C₁₃×#121	C₂³	1	1	yes	characteristic
229	C₁₃×#120	—	2	2	no	—
230	C₁₃×#120	—	2	2	no	—
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₁₃×#120	—	2	2	no	—
234	C₁₃×#120	—	2	2	no	—
235	C₄×Q₈×C₁₃	—	2	1	no	—
236	C₄×Q₈×C₁₃	—	2	2	no	—
237	C₄×Q₈×C₁₃	—	2	1	no	—
238	C₄×Q₈×C₁₃	—	2	1	no	—
239	C₄×Q₈×C₁₃	—	2	1	no	—
240	C₄×Q₈×C₁₃	—	2	1	no	—
241	C₄×Q₈×C₁₃	—	2	1	no	—
242	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	1	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	2	no	—
259	C₁₃×#117	—	2	1	no	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₁₃×#117	C₂³	1	2	yes	—
262	C₁₃×#117	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	1	yes	characteristic
267	C₁₃×#107	C₂³	1	1	yes	characteristic
268	C₁₃×#107	C₂³	1	2	yes	—
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×#103	C₂³	1	1	yes	characteristic
279	C₁₃×#103	C₂³	1	2	yes	—
280	C₁₃×#103	C₂³	1	1	yes	characteristic
281	C₁₃×#103	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	1	yes	characteristic
283	C₁₃×#103	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#102	C₂³	1	1	yes	characteristic
287	C₁₃×#102	C₂³	1	2	yes	—
288	C₁₃×#102	C₂³	1	2	yes	—
289	C₁₃×#102	C₂³	1	2	yes	—
290	C₁₃×#102	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×#97	C₂³	1	1	yes	characteristic
306	C₁₃×#97	C₂³	1	1	yes	characteristic
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#62608	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂⁴×C₁₃	—	2	2	no	—
314	C₂⁴×C₁₃	—	2	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	2	no	—
317	C₁₃×#41	—	8	2	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₁₃	—	2	1	no	—
327	C₂×D₄×C₁₃	—	2	2	no	—
328	C₂×D₄×C₁₃	—	2	2	no	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	1	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	4	2	no	—
341	C₂×D₄×C₁₃	—	4	2	no	—
342	C₂×D₄×C₁₃	—	4	2	no	—
343	C₂×D₄×C₁₃	—	4	2	no	—
344	C₂×D₄×C₁₃	—	8	2	no	—
345	C₂×D₄×C₁₃	—	8	2	no	—
346	C₂×D₄×C₁₃	—	8	2	no	—
347	C₂×D₄×C₁₃	—	8	4	no	—
348	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
352	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	2	no	—
356	C₂²×C₄×C₁₃	—	2	2	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
362	C₁₃×Q₁₆	—	4	1	no	—
363	C₁₃×Q₁₆	—	4	1	no	—
364	C₁₃×SD₁₆	—	4	2	no	—
365	C₁₃×SD₁₆	—	4	2	no	—
366	C₁₃×SD₁₆	—	4	2	no	—
367	C₁₃×SD₁₆	—	4	2	no	—
368	C₁₃×SD₁₆	—	4	1	no	—
369	C₁₃×SD₁₆	—	4	1	no	—
370	C₁₃×M₁₆	—	4	1	no	—
371	C₁₃×M₁₆	—	4	2	no	—
372	C₁₃×M₁₆	—	4	1	no	—
373	C₂×C₈×C₁₃	—	4	2	no	—
374	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
376	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
380	C₁₃×C₄⋊C₄	—	2	2	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	1	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	1	no	—
417	C₁₃×C₂²⋊C₄	—	2	1	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	1	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	1	no	—
439	C₄²×C₁₃	—	2	1	no	—
440	C₄²×C₁₃	—	2	1	no	—
441	C₄²×C₁₃	—	2	2	no	—
442	C₄²×C₁₃	—	2	2	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
448	C₄²×C₁₃	C₂⁴	1	2	yes	—
449	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3543	C₂×C₁₃	1	1	yes	characteristic
451	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3365	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3324	C₂×C₁₃	1	2	yes	complemented
458	#3323	C₂×C₁₃	1	2	yes	complemented
459	#3311	C₂×C₁₃	1	2	yes	complemented
460	#3310	C₂×C₁₃	1	2	yes	complemented
461	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3241	C₂×C₁₃	1	2	yes	complemented
464	#3233	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3222	C₂×C₁₃	1	2	yes	complemented
466	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3174	C₂×C₁₃	1	2	yes	complemented
468	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3136	C₂×C₁₃	1	2	yes	complemented
471	#2969	C₂×C₁₃	1	1	yes	characteristic, complemented
472	C₂³×C₁₃	—	2	2	no	—
473	C₂³×C₁₃	—	2	1	no	—
474	C₂³×C₁₃	—	2	2	no	—
475	C₂³×C₁₃	—	4	4	no	—
476	C₂³×C₁₃	—	8	2	no	—
477	C₂³×C₁₃	—	8	2	no	—
478	C₂³×C₁₃	—	8	2	no	—
479	C₂³×C₁₃	—	8	2	no	—
480	C₂³×C₁₃	—	8	2	no	—
481	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
483	Q₈×C₁₃	—	2	2	no	—
484	Q₈×C₁₃	—	2	1	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	1	no	—
487	Q₈×C₁₃	—	2	1	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	2	1	no	—
490	Q₈×C₁₃	—	4	2	no	—
491	Q₈×C₁₃	—	8	1	no	—
492	Q₈×C₁₃	—	8	1	no	—
493	Q₈×C₁₃	—	8	2	no	—
494	D₄×C₁₃	—	2	2	no	—
495	D₄×C₁₃	—	2	2	no	—
496	D₄×C₁₃	—	2	1	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	1	no	—
499	D₄×C₁₃	—	2	2	no	—
500	D₄×C₁₃	—	2	2	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	4	2	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	4	2	no	—
505	D₄×C₁₃	—	8	2	no	—
506	D₄×C₁₃	—	8	2	no	—
507	D₄×C₁₃	—	8	1	no	—
508	D₄×C₁₃	—	8	2	no	—
509	D₄×C₁₃	—	8	1	no	—
510	D₄×C₁₃	—	8	2	no	—
511	D₄×C₁₃	—	8	2	no	—
512	D₄×C₁₃	—	8	2	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	—	8	2	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	2	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	4	1	no	—
531	C₂×C₄×C₁₃	—	4	2	no	—
532	C₂×C₄×C₁₃	—	8	2	no	—
533	C₂×C₄×C₁₃	—	8	2	no	—
534	C₂×C₄×C₁₃	—	8	2	no	—
535	C₂×C₄×C₁₃	—	8	2	no	—
536	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
545	C₈×C₁₃	—	2	1	no	—
546	C₈×C₁₃	—	2	2	no	—
547	C₈×C₁₃	—	2	1	no	—
548	C₈×C₁₃	—	2	2	no	—
549	C₈×C₁₃	—	2	1	no	—
550	C₈×C₁₃	—	2	1	no	—
551	#563	—	2	2	no	—
552	#560	—	2	2	no	—
553	#559	C₂²×C₁₃	1	1	yes	characteristic
554	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
555	#557	—	2	1	no	—
556	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
557	#556	—	2	1	no	—
558	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#556	C₂²×C₁₃	1	2	yes	complemented
560	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	#552	C₂²×C₁₃	1	2	yes	complemented
562	#550	C₂²×C₁₃	1	1	yes	characteristic
563	#550	C₂²×C₁₃	1	1	yes	characteristic
564	#546	—	2	1	no	—
565	#546	C₂²×C₁₃	1	2	yes	—
566	D₄²	—	2	1	no	—
567	D₄²	C₂²×C₁₃	1	1	yes	characteristic
568	D₄²	C₂²×C₁₃	1	2	yes	—
569	#544	C₂²×C₁₃	1	2	yes	complemented
570	#542	—	2	1	no	—
571	#541	—	2	2	no	—
572	#541	—	2	1	no	—
573	#541	C₂²×C₁₃	1	2	yes	complemented
574	#540	—	2	1	no	—
575	#540	C₂²×C₁₃	1	2	yes	—
576	#535	—	2	1	no	—
577	#535	C₂²×C₁₃	1	2	yes	—
578	#534	—	2	2	no	—
579	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
581	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
582	#529	C₂²×C₁₃	1	1	yes	characteristic
583	#529	C₂²×C₁₃	1	1	yes	characteristic
584	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
585	#499	C₂²×C₁₃	1	2	yes	complemented
586	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	#492	C₂²×C₁₃	1	2	yes	complemented
588	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#490	C₂²×C₁₃	1	2	yes	complemented
590	#490	C₂²×C₁₃	1	2	yes	complemented
591	#490	C₂²×C₁₃	1	2	yes	complemented
592	#489	C₂²×C₁₃	1	2	yes	complemented
593	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#488	C₂²×C₁₃	1	2	yes	complemented
595	#488	C₂²×C₁₃	1	2	yes	complemented
596	#486	C₂²×C₁₃	1	1	yes	characteristic
597	#486	C₂²×C₁₃	1	1	yes	characteristic
598	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
599	#486	C₂²×C₁₃	1	2	yes	complemented
600	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#486	C₂²×C₁₃	1	2	yes	complemented
602	#485	C₂²×C₁₃	1	2	yes	complemented
603	#482	C₂²×C₁₃	1	2	yes	—
604	#482	C₂²×C₁₃	1	2	yes	complemented
605	#482	C₂²×C₁₃	1	2	yes	complemented
606	#481	C₂²×C₁₃	1	2	yes	complemented
607	#480	C₂²×C₁₃	1	2	yes	complemented
608	#478	C₂²×C₁₃	1	2	yes	complemented
609	#478	C₂²×C₁₃	1	2	yes	complemented
610	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#476	C₂²×C₁₃	1	2	yes	complemented
613	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#474	C₂²×C₁₃	1	2	yes	complemented
616	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
618	#468	C₂²×C₁₃	1	1	yes	characteristic
619	#468	C₂²×C₁₃	1	1	yes	characteristic
620	#468	C₂²×C₁₃	1	2	yes	complemented
621	#468	C₂²×C₁₃	1	2	yes	complemented
622	#465	C₂²×C₁₃	1	2	yes	complemented
623	#465	C₂²×C₁₃	1	2	yes	complemented
624	#464	C₂²×C₁₃	1	2	yes	complemented
625	#464	C₂²×C₁₃	1	2	yes	complemented
626	#460	C₂²×C₁₃	1	1	yes	characteristic
627	#460	C₂²×C₁₃	1	1	yes	characteristic
628	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#460	C₂²×C₁₃	1	2	yes	complemented
631	#460	C₂²×C₁₃	1	2	yes	complemented
632	#452	C₂²×C₁₃	1	2	yes	complemented
633	#452	C₂²×C₁₃	1	2	yes	complemented
634	#450	C₂²×C₁₃	1	2	yes	complemented
635	#450	C₂²×C₁₃	1	2	yes	complemented
636	#450	C₂²×C₁₃	1	2	yes	complemented
637	#450	C₂²×C₁₃	1	2	yes	complemented
638	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#440	C₂²×C₁₃	1	2	yes	complemented
641	#440	C₂²×C₁₃	1	2	yes	complemented
642	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
645	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
646	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
647	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	#436	C₂²×C₁₃	1	2	yes	complemented
650	#435	C₂²×C₁₃	1	2	yes	complemented
651	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#433	C₂²×C₁₃	1	2	yes	complemented
653	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#418	C₂²×C₁₃	1	2	yes	complemented
655	#418	C₂²×C₁₃	1	2	yes	complemented
656	#418	C₂²×C₁₃	1	2	yes	complemented
657	#417	C₂²×C₁₃	1	2	yes	complemented
658	#416	C₂²×C₁₃	1	2	yes	complemented
659	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
660	#405	C₂²×C₁₃	1	2	yes	complemented
661	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	C₂²×C₁₃	—	2	1	no	—
663	C₂²×C₁₃	—	2	2	no	—
664	C₂²×C₁₃	—	2	2	no	—
665	C₂²×C₁₃	—	2	1	no	—
666	C₂²×C₁₃	—	2	1	no	—
667	C₂²×C₁₃	—	2	2	no	—
668	C₂²×C₁₃	—	4	2	no	—
669	C₂²×C₁₃	—	4	1	no	—
670	C₂²×C₁₃	—	4	2	no	—
671	C₂²×C₁₃	—	4	2	no	—
672	C₂²×C₁₃	—	4	2	no	—
673	C₂²×C₁₃	—	4	1	no	—
674	C₂²×C₁₃	—	4	1	no	—
675	C₂²×C₁₃	—	4	2	no	—
676	C₂²×C₁₃	—	4	2	no	—
677	C₂²×C₁₃	—	16	4	no	—
678	C₂²×C₁₃	—	16	4	no	—
679	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
680	C₄×C₁₃	—	2	1	no	—
681	C₄×C₁₃	—	2	1	no	—
682	C₄×C₁₃	—	2	2	no	—
683	C₄×C₁₃	—	2	2	no	—
684	C₄×C₁₃	—	2	1	no	—
685	C₄×C₁₃	—	2	1	no	—
686	C₄×C₁₃	—	2	2	no	—
687	C₄×C₁₃	—	4	1	no	—
688	C₄×C₁₃	—	4	1	no	—
689	C₄×C₁₃	—	4	2	no	—
690	C₄×C₁₃	—	4	1	no	—
691	C₄×C₁₃	—	4	1	no	—
692	C₄×C₁₃	—	4	1	no	—
693	C₄×C₁₃	—	4	1	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	2	no	—
696	C₄×C₁₃	#577	1	2	yes	—
697	C₄×C₁₃	#585	1	1	yes	characteristic
698	C₄×C₁₃	#585	1	1	yes	characteristic
699	C₂×#41	—	2	1	no	—
700	C₂×#41	C₂³×C₁₃	1	2	yes	—
701	C₂²×D₄	—	2	2	no	—
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
706	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
707	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
715	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
719	C₄⋊Q₈	—	2	1	no	—
720	C₄⋊Q₈	—	2	2	no	—
721	C₄⋊Q₈	—	2	1	no	—
722	C₄⋊Q₈	—	2	2	no	—
723	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
728	#127	—	2	1	no	—
729	#127	—	2	1	no	—
730	#127	—	2	1	no	—
731	#127	C₂³×C₁₃	1	2	yes	—
732	#127	C₂³×C₁₃	1	1	yes	characteristic
733	#127	C₂³×C₁₃	1	1	yes	characteristic
734	#127	C₂³×C₁₃	1	2	yes	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	1	no	—
742	#126	D₄×C₁₃	1	2	yes	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	D₄×C₁₃	1	1	yes	characteristic
751	#125	C₂³×C₁₃	1	1	yes	characteristic
752	#125	C₂³×C₁₃	1	2	yes	—
753	#125	C₂³×C₁₃	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	D₄×C₁₃	1	1	yes	characteristic
758	#124	C₂³×C₁₃	1	1	yes	characteristic
759	#124	C₂³×C₁₃	1	2	yes	—
760	#123	—	2	2	no	—
761	#123	—	2	1	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₁₃	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
774	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	D₄×C₁₃	1	1	yes	characteristic
790	#121	C₂³×C₁₃	1	1	yes	characteristic
791	#121	C₂³×C₁₃	1	2	yes	—
792	#121	C₂³×C₁₃	1	2	yes	—
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	#120	—	2	2	no	—
796	#120	—	2	2	no	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
810	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
811	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₁₃	1	2	yes	—
818	C₄×D₄	C₂³×C₁₃	1	2	yes	—
819	C₄×D₄	C₂³×C₁₃	1	2	yes	—
820	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	C₂³×C₁₃	1	2	yes	—
825	#117	C₂³×C₁₃	1	2	yes	—
826	#117	C₂³×C₁₃	1	2	yes	—
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
830	#107	C₂³×C₁₃	1	1	yes	characteristic
831	#107	C₂³×C₁₃	1	1	yes	characteristic
832	#107	C₂³×C₁₃	1	2	yes	—
833	#107	C₂³×C₁₃	1	2	yes	—
834	#106	C₂³×C₁₃	1	2	yes	—
835	#106	C₂³×C₁₃	1	2	yes	—
836	#106	C₂³×C₁₃	1	1	yes	characteristic
837	#106	C₂³×C₁₃	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
841	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
842	#103	C₂³×C₁₃	1	1	yes	characteristic
843	#103	C₂³×C₁₃	1	2	yes	—
844	#103	C₂³×C₁₃	1	1	yes	characteristic
845	#103	C₂³×C₁₃	1	2	yes	—
846	#103	C₂³×C₁₃	1	1	yes	characteristic
847	#103	C₂³×C₁₃	1	1	yes	characteristic
848	#103	C₂³×C₁₃	1	1	yes	characteristic
849	#103	C₂³×C₁₃	1	1	yes	characteristic
850	#102	C₂³×C₁₃	1	1	yes	characteristic
851	#102	C₂³×C₁₃	1	2	yes	—
852	#102	C₂³×C₁₃	1	2	yes	—
853	#102	C₂³×C₁₃	1	2	yes	—
854	#102	C₂³×C₁₃	1	2	yes	—
855	#102	C₂³×C₁₃	1	2	yes	—
856	#102	C₂³×C₁₃	1	2	yes	—
857	#102	C₂³×C₁₃	1	2	yes	—
858	#102	C₂³×C₁₃	1	1	yes	characteristic
859	#102	C₂³×C₁₃	1	2	yes	—
860	#102	C₂³×C₁₃	1	2	yes	—
861	#102	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	2	yes	—
863	#102	C₂³×C₁₃	1	2	yes	—
864	#102	C₂³×C₁₃	1	2	yes	—
865	#102	C₂³×C₁₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
869	#97	C₂³×C₁₃	1	1	yes	characteristic
870	#97	C₂³×C₁₃	1	1	yes	characteristic
871	#97	C₂³×C₁₃	1	2	yes	—
872	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₁₃	1	2	yes	—
875	C₄×C₈	C₂³×C₁₃	1	2	yes	—
876	C₂×C₁₃	—	4	2	no	—
877	C₂×C₁₃	—	4	1	no	—
878	C₂×C₁₃	—	8	2	no	—
879	C₂×C₁₃	—	8	2	no	—
880	C₂×C₁₃	—	8	1	no	—
881	C₂×C₁₃	#3500	1	1	yes	characteristic
882	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
883	C₂×C₁₃	#3585	1	1	yes	characteristic
884	C₂⁴	—	2	2	no	—
885	C₂⁴	—	2	2	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	8	2	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	8	2	no	—
916	C₂×D₄	—	8	2	no	—
917	C₂×D₄	—	8	2	no	—
918	C₂×D₄	—	8	4	no	—
919	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
920	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
921	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
923	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
933	Q₁₆	—	4	1	no	—
934	Q₁₆	—	4	1	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	1	no	—
940	SD₁₆	—	4	1	no	—
941	M₁₆	—	4	1	no	—
942	M₁₆	—	4	2	no	—
943	M₁₆	—	4	1	no	—
944	C₂×C₈	—	4	2	no	—
945	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
947	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1016	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₁₃	1	2	yes	—
1020	C₁₃	#62608	1	1	yes	characteristic, direct product factor, Sylow
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	4	4	no	—
1025	C₂³	—	8	2	no	—
1026	C₂³	—	8	2	no	—
1027	C₂³	—	8	2	no	—
1028	C₂³	—	8	2	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	1	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	1	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	16	4	no	—
1116	C₂²	—	16	4	no	—
1117	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	C₁₃×#577	1	2	yes	—
1135	C₄	C₁₃×#585	1	1	yes	characteristic
1136	C₄	C₁₃×#585	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	—	8	2	no	—
1141	C₂	—	8	2	no	—
1142	C₂	C₁₃×#3500	1	1	yes	characteristic
1143	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1144	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3543	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3555	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3368	C₂	semidirect
5. C₁₃×#3365	C₂	semidirect
6. C₁₃×#3362	C₂	semidirect
7. C₁₃×#3333	C₂	semidirect
8. C₁₃×#3324	C₂	semidirect
9. C₁₃×#3324	C₂	semidirect
10. C₁₃×#3323	C₂	semidirect
11. C₁₃×#3311	C₂	semidirect
12. C₁₃×#3310	C₂	semidirect
13. C₁₃×#3304	C₂	semidirect
14. C₁₃×#3295	C₂	semidirect
15. C₁₃×#3241	C₂	semidirect
16. C₁₃×#3233	C₂	semidirect
17. C₁₃×#3222	C₂	semidirect
18. C₁₃×#3208	C₂	semidirect
19. C₁₃×#3174	C₂	semidirect
20. C₁₃×#3172	C₂	semidirect
21. C₁₃×#3138	C₂	semidirect
22. C₁₃×#3136	C₂	semidirect
23. C₁₃×#2969	C₂	semidirect
27. Q₈²×C₁₃	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
33. C₁₃×#554	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
42. C₁₃×#544	C₂²	semidirect
46. C₁₃×#541	C₂²	semidirect
52. C₁₃×#533	C₂²	semidirect
53. C₁₃×#533	C₂²	semidirect
57. C₁₃×#501	C₂²	semidirect
58. C₁₃×#499	C₂²	semidirect
59. C₁₃×#497	C₂²	semidirect
60. C₁₃×#492	C₂²	semidirect
61. C₁₃×#491	C₂²	semidirect
62. C₁₃×#490	C₂²	semidirect
63. C₁₃×#490	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#489	C₂²	semidirect
66. C₁₃×#489	C₂²	semidirect
67. C₁₃×#488	C₂²	semidirect
68. C₁₃×#488	C₂²	semidirect
71. C₁₃×#486	C₂²	semidirect
72. C₁₃×#486	C₂²	semidirect
73. C₁₃×#486	C₂²	semidirect
74. C₁₃×#486	C₂²	semidirect
75. C₁₃×#485	C₂²	semidirect
77. C₁₃×#482	C₂²	semidirect
78. C₁₃×#482	C₂²	semidirect
79. C₁₃×#481	C₂²	semidirect
80. C₁₃×#480	C₂²	semidirect
81. C₁₃×#478	C₂²	semidirect
82. C₁₃×#478	C₂²	semidirect
83. C₁₃×#477	C₂²	semidirect
84. C₁₃×#476	C₂²	semidirect
85. C₁₃×#476	C₂²	semidirect
86. C₁₃×#475	C₂²	semidirect
87. C₁₃×#474	C₂²	semidirect
88. C₁₃×#474	C₂²	semidirect
89. C₁₃×#470	C₂²	semidirect
90. C₁₃×#470	C₂²	semidirect
93. C₁₃×#468	C₂²	semidirect
94. C₁₃×#468	C₂²	semidirect
95. C₁₃×#465	C₂²	semidirect
96. C₁₃×#465	C₂²	semidirect
97. C₁₃×#464	C₂²	semidirect
98. C₁₃×#464	C₂²	semidirect
101. C₁₃×#460	C₂²	semidirect
102. C₁₃×#460	C₂²	semidirect
103. C₁₃×#460	C₂²	semidirect
104. C₁₃×#460	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#452	C₂²	semidirect
107. C₁₃×#450	C₂²	semidirect
108. C₁₃×#450	C₂²	semidirect
109. C₁₃×#450	C₂²	semidirect
110. C₁₃×#450	C₂²	semidirect
111. C₁₃×#446	C₂²	semidirect
112. C₈×Q₈×C₁₃	C₂²	semidirect
113. C₁₃×#440	C₂²	semidirect
114. C₁₃×#440	C₂²	semidirect
115. C₄×C₁₃×Q₁₆	C₂²	semidirect
116. C₄×C₁₃×Q₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×SD₁₆	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#418	C₂²	semidirect
128. C₁₃×#418	C₂²	semidirect
129. C₁₃×#418	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
131. C₁₃×#416	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₄×C₁₃×M₁₆	C₂²	semidirect
312. #62608	C₁₃	direct (N × H)
449. #3555	C₂×C₁₃	semidirect
451. #3375	C₂×C₁₃	semidirect
452. #3368	C₂×C₁₃	semidirect
453. #3365	C₂×C₁₃	semidirect
454. #3362	C₂×C₁₃	semidirect
455. #3333	C₂×C₁₃	semidirect
456. #3324	C₂×C₁₃	semidirect
457. #3324	C₂×C₁₃	semidirect
458. #3323	C₂×C₁₃	semidirect
459. #3311	C₂×C₁₃	semidirect
460. #3310	C₂×C₁₃	semidirect
461. #3304	C₂×C₁₃	semidirect
462. #3295	C₂×C₁₃	semidirect
463. #3241	C₂×C₁₃	semidirect
464. #3233	C₂×C₁₃	semidirect
465. #3222	C₂×C₁₃	semidirect
466. #3208	C₂×C₁₃	semidirect
467. #3174	C₂×C₁₃	semidirect
468. #3172	C₂×C₁₃	semidirect
469. #3138	C₂×C₁₃	semidirect
470. #3136	C₂×C₁₃	semidirect
471. #2969	C₂×C₁₃	semidirect
554. Q₈²	C₂²×C₁₃	semidirect
556. #557	C₂²×C₁₃	semidirect
558. #556	C₂²×C₁₃	semidirect
559. #556	C₂²×C₁₃	semidirect
560. #554	C₂²×C₁₃	semidirect
561. #552	C₂²×C₁₃	semidirect
569. #544	C₂²×C₁₃	semidirect
573. #541	C₂²×C₁₃	semidirect
579. #533	C₂²×C₁₃	semidirect
580. #533	C₂²×C₁₃	semidirect
584. #501	C₂²×C₁₃	semidirect
585. #499	C₂²×C₁₃	semidirect
586. #497	C₂²×C₁₃	semidirect
587. #492	C₂²×C₁₃	semidirect
588. #491	C₂²×C₁₃	semidirect
589. #490	C₂²×C₁₃	semidirect
590. #490	C₂²×C₁₃	semidirect
591. #490	C₂²×C₁₃	semidirect
592. #489	C₂²×C₁₃	semidirect
593. #489	C₂²×C₁₃	semidirect
594. #488	C₂²×C₁₃	semidirect
595. #488	C₂²×C₁₃	semidirect
598. #486	C₂²×C₁₃	semidirect
599. #486	C₂²×C₁₃	semidirect
600. #486	C₂²×C₁₃	semidirect
601. #486	C₂²×C₁₃	semidirect
602. #485	C₂²×C₁₃	semidirect
604. #482	C₂²×C₁₃	semidirect
605. #482	C₂²×C₁₃	semidirect
606. #481	C₂²×C₁₃	semidirect
607. #480	C₂²×C₁₃	semidirect
608. #478	C₂²×C₁₃	semidirect
609. #478	C₂²×C₁₃	semidirect
610. #477	C₂²×C₁₃	semidirect
611. #476	C₂²×C₁₃	semidirect
612. #476	C₂²×C₁₃	semidirect
613. #475	C₂²×C₁₃	semidirect
614. #474	C₂²×C₁₃	semidirect
615. #474	C₂²×C₁₃	semidirect
616. #470	C₂²×C₁₃	semidirect
617. #470	C₂²×C₁₃	semidirect
620. #468	C₂²×C₁₃	semidirect
621. #468	C₂²×C₁₃	semidirect
622. #465	C₂²×C₁₃	semidirect
623. #465	C₂²×C₁₃	semidirect
624. #464	C₂²×C₁₃	semidirect
625. #464	C₂²×C₁₃	semidirect
628. #460	C₂²×C₁₃	semidirect
629. #460	C₂²×C₁₃	semidirect
630. #460	C₂²×C₁₃	semidirect
631. #460	C₂²×C₁₃	semidirect
632. #452	C₂²×C₁₃	semidirect
633. #452	C₂²×C₁₃	semidirect
634. #450	C₂²×C₁₃	semidirect
635. #450	C₂²×C₁₃	semidirect
636. #450	C₂²×C₁₃	semidirect
637. #450	C₂²×C₁₃	semidirect
638. #446	C₂²×C₁₃	semidirect
639. C₈×Q₈	C₂²×C₁₃	semidirect
640. #440	C₂²×C₁₃	semidirect
641. #440	C₂²×C₁₃	semidirect
642. C₄×Q₁₆	C₂²×C₁₃	semidirect
643. C₄×Q₁₆	C₂²×C₁₃	semidirect
644. C₄×SD₁₆	C₂²×C₁₃	semidirect
645. C₄×SD₁₆	C₂²×C₁₃	semidirect
646. C₄×SD₁₆	C₂²×C₁₃	semidirect
647. C₄×SD₁₆	C₂²×C₁₃	semidirect
648. #436	C₂²×C₁₃	semidirect
649. #436	C₂²×C₁₃	semidirect
650. #435	C₂²×C₁₃	semidirect
651. C₈×D₄	C₂²×C₁₃	semidirect
652. #433	C₂²×C₁₃	semidirect
653. #431	C₂²×C₁₃	semidirect
654. #418	C₂²×C₁₃	semidirect
655. #418	C₂²×C₁₃	semidirect
656. #418	C₂²×C₁₃	semidirect
657. #417	C₂²×C₁₃	semidirect
658. #416	C₂²×C₁₃	semidirect
659. C₂×#102	C₂²×C₁₃	semidirect
660. #405	C₂²×C₁₃	semidirect
661. C₄×M₁₆	C₂²×C₁₃	semidirect
1020. C₁₃	#62608	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×#3555	2
C₁₃×#3543	2
C₁₃×#3375	2
C₁₃×#3368	2
C₁₃×#3365	2
C₁₃×#3362	2
C₁₃×#3333	2
C₁₃×#3324	2
C₁₃×#3323	2
C₁₃×#3311	2
C₁₃×#3310	2
C₁₃×#3304	2
C₁₃×#3295	2
C₁₃×#3241	2
C₁₃×#3233	2
C₁₃×#3222	2
C₁₃×#3208	2
C₁₃×#3174	2
C₁₃×#3172	2
C₁₃×#3138	2
C₁₃×#3136	2
C₁₃×#2969	2
#62608	13

Subgroups — C13×#62608 #15748947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62608 #15748947