Subgroups — C₁₃×#61448 #15747787

Order 3328.

1904 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3307	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
26	C₁₃×#559	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#556	C₂²	1	1	yes	characteristic
29	C₁₃×#556	C₂²	1	2	yes	complemented
30	C₁₃×#554	C₂²	1	1	yes	characteristic
31	C₁₃×#554	C₂²	1	1	yes	characteristic
32	C₁₃×#553	—	2	1	no	—
33	C₁₃×#553	C₂²	1	2	yes	—
34	C₁₃×#552	—	2	1	no	—
35	C₁₃×#552	—	2	2	no	—
36	C₁₃×#551	—	2	2	no	—
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#548	—	2	1	no	—
39	C₁₃×#547	C₂²	1	1	yes	characteristic
40	C₁₃×#547	C₂²	1	2	yes	complemented
41	C₁₃×#546	—	2	1	no	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#533	C₂²	1	2	yes	complemented
45	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	—	2	1	no	—
49	C₁₃×#529	—	2	2	no	—
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₁₃×#525	—	2	2	no	—
52	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
57	C₂×C₄×D₄×C₁₃	—	2	1	no	—
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#497	C₂²	1	2	yes	complemented
62	C₁₃×#492	C₂²	1	1	yes	characteristic
63	C₁₃×#491	C₂²	1	2	yes	complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#483	C₂²	1	2	yes	complemented
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#476	C₂²	1	2	yes	—
77	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#476	C₂²	1	2	yes	complemented
79	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic
81	C₁₃×#470	C₂²	1	2	yes	complemented
82	C₁₃×#470	C₂²	1	2	yes	complemented
83	C₁₃×#468	C₂²	1	2	yes	—
84	C₁₃×#468	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	complemented
89	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#461	C₂²	1	2	yes	—
91	C₁₃×#461	C₂²	1	1	yes	characteristic
92	C₁₃×#461	C₂²	1	2	yes	complemented
93	C₁₃×#460	C₂²	1	1	yes	characteristic
94	C₁₃×#459	C₂²	1	1	yes	characteristic
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	—
98	C₁₃×#450	C₂²	1	2	yes	—
99	C₁₃×#449	C₂²	1	2	yes	—
100	C₁₃×#449	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	complemented
107	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
109	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
110	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#435	C₂²	1	2	yes	complemented
124	C₁₃×#435	C₂²	1	2	yes	complemented
125	C₁₃×#431	C₂²	1	2	yes	complemented
126	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	2	yes	complemented
128	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#418	C₂²	1	2	yes	—
130	C₁₃×#417	C₂²	1	2	yes	complemented
131	C₁₃×#416	C₂²	1	1	yes	characteristic
132	C₁₃×#416	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×#41	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	—	2	2	no	—
144	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
145	C₁₃×#135	—	2	4	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×D₈	C₂³	1	2	yes	—
155	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×#127	C₂³	1	1	yes	characteristic
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#125	—	2	1	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	1	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	C₂³	1	2	yes	—
177	C₁₃×#124	—	2	1	no	—
178	C₁₃×#124	—	2	1	no	—
179	C₁₃×#124	—	2	2	no	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	1	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	1	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#120	—	2	2	no	—
209	C₁₃×#120	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₁₃	D₄	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₄×D₄×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	—	2	1	no	—
251	C₁₃×#117	—	2	1	no	—
252	C₁₃×#117	—	2	2	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	D₄	1	2	yes	—
255	C₁₃×#117	D₄	1	1	yes	characteristic
256	C₁₃×#117	C₂³	1	1	yes	characteristic
257	C₁₃×#117	C₂³	1	1	yes	characteristic
258	C₁₃×#117	C₂³	1	2	yes	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	—	2	1	no	—
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	2	2	no	—
268	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61448	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	2	no	—
316	C₁₃×#41	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	2	4	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	1	no	—
321	C₁₃×#41	—	4	1	no	—
322	C₁₃×#41	—	4	2	no	—
323	C₁₃×#41	—	8	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	—	2	1	no	—
327	C₂×Q₈×C₁₃	—	4	4	no	—
328	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₁₃	—	2	4	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	1	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	—	2	1	no	—
341	C₂×D₄×C₁₃	—	4	2	no	—
342	C₂×D₄×C₁₃	—	4	4	no	—
343	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
346	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	—	8	4	no	—
361	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
363	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
366	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₁₃×Q₁₆	—	2	2	no	—
368	C₁₃×Q₁₆	—	4	2	no	—
369	C₁₃×SD₁₆	—	2	2	no	—
370	C₁₃×SD₁₆	—	2	2	no	—
371	C₁₃×SD₁₆	—	2	4	no	—
372	C₁₃×SD₁₆	—	2	4	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×D₈	—	2	4	no	—
376	C₁₃×D₈	#41	1	4	yes	complemented
377	C₁₃×M₁₆	—	2	4	no	—
378	C₁₃×M₁₆	—	4	2	no	—
379	C₂×C₈×C₁₃	—	2	2	no	—
380	C₂×C₈×C₁₃	—	4	1	no	—
381	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	2	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	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	1	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
413	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₄²×C₁₃	—	2	1	no	—
440	C₄²×C₁₃	—	2	1	no	—
441	C₄²×C₁₃	—	2	2	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	1	no	—
446	C₄²×C₁₃	—	2	1	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂×D₄	1	2	yes	—
450	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₁₃	C₂×D₄	1	2	yes	—
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₁₃	C₂⁴	1	2	yes	—
454	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
455	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3481	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3356	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3350	C₂×C₁₃	1	2	yes	complemented
463	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3311	C₂×C₁₃	1	2	yes	complemented
466	#3307	C₂×C₁₃	1	2	yes	complemented
467	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3267	C₂×C₁₃	1	2	yes	complemented
469	#3172	C₂×C₁₃	1	2	yes	complemented
470	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3102	C₂×C₁₃	1	2	yes	complemented
474	#3101	C₂×C₁₃	1	2	yes	complemented
475	#2965	C₂×C₁₃	1	1	yes	characteristic, complemented
476	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
477	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
478	C₂³×C₁₃	—	2	1	no	—
479	C₂³×C₁₃	—	2	1	no	—
480	C₂³×C₁₃	—	2	2	no	—
481	C₂³×C₁₃	—	4	4	no	—
482	C₂³×C₁₃	—	4	4	no	—
483	C₂³×C₁₃	—	8	2	no	—
484	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₁₃	—	2	2	no	—
487	Q₈×C₁₃	—	2	2	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	2	1	no	—
490	Q₈×C₁₃	—	2	1	no	—
491	Q₈×C₁₃	—	2	2	no	—
492	Q₈×C₁₃	—	2	1	no	—
493	Q₈×C₁₃	—	4	4	no	—
494	Q₈×C₁₃	—	4	2	no	—
495	Q₈×C₁₃	—	8	1	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	1	no	—
499	D₄×C₁₃	—	2	1	no	—
500	D₄×C₁₃	—	2	2	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	4	2	no	—
505	D₄×C₁₃	—	4	4	no	—
506	D₄×C₁₃	—	4	4	no	—
507	D₄×C₁₃	—	4	2	no	—
508	D₄×C₁₃	—	8	1	no	—
509	D₄×C₁₃	—	8	2	no	—
510	D₄×C₁₃	C₂×#41	1	2	yes	—
511	D₄×C₁₃	C₂×#41	1	2	yes	—
512	C₂×C₄×C₁₃	—	2	2	no	—
513	C₂×C₄×C₁₃	—	2	4	no	—
514	C₂×C₄×C₁₃	—	2	2	no	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	2	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	2	no	—
523	C₂×C₄×C₁₃	—	2	1	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	2	no	—
528	C₂×C₄×C₁₃	—	4	2	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	4	2	no	—
531	C₂×C₄×C₁₃	—	4	4	no	—
532	C₂×C₄×C₁₃	—	4	4	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	4	4	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
550	C₈×C₁₃	—	2	1	no	—
551	C₈×C₁₃	—	2	2	no	—
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	—	2	1	no	—
554	C₈×C₁₃	—	2	2	no	—
555	C₈×C₁₃	C₂×#41	1	2	yes	—
556	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
557	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
558	#559	C₂²×C₁₃	1	1	yes	characteristic
559	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#556	C₂²×C₁₃	1	1	yes	characteristic
561	#556	C₂²×C₁₃	1	2	yes	complemented
562	#554	C₂²×C₁₃	1	1	yes	characteristic
563	#554	C₂²×C₁₃	1	1	yes	characteristic
564	#553	—	2	1	no	—
565	#553	C₂²×C₁₃	1	2	yes	—
566	#552	—	2	1	no	—
567	#552	—	2	2	no	—
568	#551	—	2	2	no	—
569	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
570	#548	—	2	1	no	—
571	#547	C₂²×C₁₃	1	1	yes	characteristic
572	#547	C₂²×C₁₃	1	2	yes	complemented
573	#546	—	2	1	no	—
574	#546	C₂²×C₁₃	1	2	yes	—
575	D₄²	C₂²×C₁₃	1	1	yes	characteristic
576	#533	C₂²×C₁₃	1	2	yes	complemented
577	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	#532	C₂²×C₁₃	1	1	yes	characteristic
579	#529	—	2	1	no	—
580	#529	—	2	1	no	—
581	#529	—	2	2	no	—
582	#529	C₂²×C₁₃	1	2	yes	—
583	#525	—	2	2	no	—
584	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
585	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
586	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
587	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	C₂×C₄×Q₈	—	2	1	no	—
589	C₂×C₄×D₄	—	2	1	no	—
590	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
591	#501	C₂²×C₁₃	1	2	yes	complemented
592	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	#497	C₂²×C₁₃	1	2	yes	complemented
594	#492	C₂²×C₁₃	1	1	yes	characteristic
595	#491	C₂²×C₁₃	1	2	yes	complemented
596	#489	C₂²×C₁₃	1	2	yes	complemented
597	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#486	C₂²×C₁₃	1	1	yes	characteristic
599	#485	C₂²×C₁₃	1	2	yes	complemented
600	#485	C₂²×C₁₃	1	2	yes	complemented
601	#483	C₂²×C₁₃	1	2	yes	complemented
602	#483	C₂²×C₁₃	1	2	yes	complemented
603	#482	C₂²×C₁₃	1	2	yes	—
604	#482	C₂²×C₁₃	1	2	yes	complemented
605	#479	C₂²×C₁₃	1	2	yes	complemented
606	#478	C₂²×C₁₃	1	2	yes	complemented
607	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#476	C₂²×C₁₃	1	2	yes	—
609	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#476	C₂²×C₁₃	1	2	yes	complemented
611	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#474	C₂²×C₁₃	1	1	yes	characteristic
613	#470	C₂²×C₁₃	1	2	yes	complemented
614	#470	C₂²×C₁₃	1	2	yes	complemented
615	#468	C₂²×C₁₃	1	2	yes	—
616	#468	C₂²×C₁₃	1	2	yes	—
617	#465	C₂²×C₁₃	1	2	yes	complemented
618	#465	C₂²×C₁₃	1	2	yes	complemented
619	#464	C₂²×C₁₃	1	2	yes	complemented
620	#463	C₂²×C₁₃	1	2	yes	complemented
621	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#461	C₂²×C₁₃	1	2	yes	—
623	#461	C₂²×C₁₃	1	1	yes	characteristic
624	#461	C₂²×C₁₃	1	2	yes	complemented
625	#460	C₂²×C₁₃	1	1	yes	characteristic
626	#459	C₂²×C₁₃	1	1	yes	characteristic
627	#452	C₂²×C₁₃	1	2	yes	—
628	#452	C₂²×C₁₃	1	2	yes	complemented
629	#450	C₂²×C₁₃	1	2	yes	—
630	#450	C₂²×C₁₃	1	2	yes	—
631	#449	C₂²×C₁₃	1	2	yes	—
632	#449	C₂²×C₁₃	1	2	yes	complemented
633	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#442	C₂²×C₁₃	1	2	yes	—
636	#442	C₂²×C₁₃	1	2	yes	complemented
637	#440	C₂²×C₁₃	1	2	yes	—
638	#440	C₂²×C₁₃	1	2	yes	complemented
639	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
641	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
642	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
643	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
644	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
645	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
647	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
648	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
650	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
651	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
652	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
653	#436	C₂²×C₁₃	1	1	yes	characteristic
654	#436	C₂²×C₁₃	1	1	yes	characteristic
655	#435	C₂²×C₁₃	1	2	yes	complemented
656	#435	C₂²×C₁₃	1	2	yes	complemented
657	#431	C₂²×C₁₃	1	2	yes	complemented
658	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#428	C₂²×C₁₃	1	2	yes	complemented
660	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#418	C₂²×C₁₃	1	2	yes	—
662	#417	C₂²×C₁₃	1	2	yes	complemented
663	#416	C₂²×C₁₃	1	1	yes	characteristic
664	#416	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
666	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	C₂²×C₁₃	—	2	1	no	—
668	C₂²×C₁₃	—	2	2	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	2	2	no	—
671	C₂²×C₁₃	—	2	1	no	—
672	C₂²×C₁₃	—	2	2	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	1	no	—
675	C₂²×C₁₃	—	4	1	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	2	no	—
681	C₂²×C₁₃	—	4	2	no	—
682	C₂²×C₁₃	—	8	8	no	—
683	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
684	C₄×C₁₃	—	2	1	no	—
685	C₄×C₁₃	—	2	2	no	—
686	C₄×C₁₃	—	2	1	no	—
687	C₄×C₁₃	—	2	2	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	2	1	no	—
690	C₄×C₁₃	—	4	1	no	—
691	C₄×C₁₃	—	4	2	no	—
692	C₄×C₁₃	—	4	1	no	—
693	C₄×C₁₃	—	4	1	no	—
694	C₄×C₁₃	—	4	2	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	1	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	2	no	—
699	C₄×C₁₃	#575	1	2	yes	—
700	C₄×C₁₃	#577	1	2	yes	—
701	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
702	C₄×C₁₃	#585	1	1	yes	characteristic
703	C₂×#41	—	2	1	no	—
704	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
705	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
706	C₂×#41	C₂³×C₁₃	1	2	yes	—
707	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
708	C₂²×Q₈	—	2	1	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
711	C₂³×C₄	—	2	2	no	—
712	AGL(1,ℤ/8)	—	2	8	no	—
713	#135	—	2	4	no	—
714	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×D₈	C₂³×C₁₃	1	2	yes	—
723	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
732	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
733	#127	C₂³×C₁₃	1	1	yes	characteristic
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	1	no	—
742	#125	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	C₂³×C₁₃	1	2	yes	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	C₂³×C₁₃	1	2	yes	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
768	#121	—	2	2	no	—
769	#121	—	2	1	no	—
770	#121	—	2	2	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	C₂³×C₁₃	1	2	yes	—
775	#121	C₂³×C₁₃	1	2	yes	—
776	#120	—	2	2	no	—
777	#120	—	2	2	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
790	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
805	C₄×D₄	D₄×C₁₃	1	2	yes	—
806	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₁₃	1	2	yes	—
808	C₄×D₄	C₂³×C₁₃	1	2	yes	—
809	C₄×D₄	C₂³×C₁₃	1	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₁₃	1	2	yes	—
814	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₁₃	1	2	yes	—
816	#117	—	2	2	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	1	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	D₄×C₁₃	1	2	yes	—
823	#117	D₄×C₁₃	1	1	yes	characteristic
824	#117	C₂³×C₁₃	1	1	yes	characteristic
825	#117	C₂³×C₁₃	1	2	yes	—
826	#117	C₂³×C₁₃	1	1	yes	characteristic
827	C₂×C₄⋊C₄	—	2	1	no	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	2	no	—
830	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	—	2	2	no	—
836	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
837	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
838	#107	C₂³×C₁₃	1	1	yes	characteristic
839	#107	C₂³×C₁₃	1	1	yes	characteristic
840	#107	C₂³×C₁₃	1	2	yes	—
841	#107	C₂³×C₁₃	1	2	yes	—
842	#106	C₂³×C₁₃	1	1	yes	characteristic
843	#106	C₂³×C₁₃	1	1	yes	characteristic
844	#106	C₂³×C₁₃	1	2	yes	—
845	#106	C₂³×C₁₃	1	2	yes	—
846	#106	C₂³×C₁₃	1	2	yes	—
847	#106	C₂³×C₁₃	1	2	yes	—
848	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
850	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
852	#103	C₂³×C₁₃	1	1	yes	characteristic
853	#103	C₂³×C₁₃	1	1	yes	characteristic
854	#103	C₂³×C₁₃	1	1	yes	characteristic
855	#103	C₂³×C₁₃	1	1	yes	characteristic
856	#103	C₂³×C₁₃	1	2	yes	—
857	#103	C₂³×C₁₃	1	2	yes	—
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	2	yes	—
861	#103	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	1	yes	characteristic
863	#102	C₂³×C₁₃	1	1	yes	characteristic
864	#102	C₂³×C₁₃	1	1	yes	characteristic
865	#102	C₂³×C₁₃	1	1	yes	characteristic
866	#102	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	2	yes	—
868	#102	C₂³×C₁₃	1	2	yes	—
869	#102	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	2	yes	—
871	#102	C₂³×C₁₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
875	#97	C₂³×C₁₃	1	2	yes	—
876	#97	C₂³×C₁₃	1	2	yes	—
877	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₁₃	1	2	yes	—
882	C₂×C₁₃	—	4	1	no	—
883	C₂×C₁₃	—	4	2	no	—
884	C₂×C₁₃	—	4	2	no	—
885	C₂×C₁₃	—	4	2	no	—
886	C₂×C₁₃	—	8	2	no	—
887	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
888	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
889	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
890	C₂⁴	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	4	no	—
894	#41	—	4	2	no	—
895	#41	—	4	1	no	—
896	#41	—	4	1	no	—
897	#41	—	4	2	no	—
898	#41	—	8	2	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	4	4	no	—
903	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
904	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
905	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
906	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
907	C₂×D₄	—	2	4	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	4	no	—
918	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
919	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
920	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
921	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	8	4	no	—
936	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
937	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
938	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
942	Q₁₆	—	2	2	no	—
943	Q₁₆	—	4	2	no	—
944	SD₁₆	—	2	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	4	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	D₈	—	2	4	no	—
951	D₈	C₁₃×#41	1	4	yes	complemented
952	M₁₆	—	2	4	no	—
953	M₁₆	—	4	2	no	—
954	C₂×C₈	—	2	2	no	—
955	C₂×C₈	—	4	1	no	—
956	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
960	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
961	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1024	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1025	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1026	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1027	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₁₃	1	2	yes	—
1030	C₁₃	#61448	1	1	yes	characteristic, direct product factor, Sylow
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	4	4	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	4	4	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	8	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	C₂×C₁₃×#41	1	2	yes	—
1064	D₄	C₂×C₁₃×#41	1	2	yes	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	4	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	2	no	—
1108	C₈	C₂×C₁₃×#41	1	2	yes	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	8	8	no	—
1125	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	C₁₃×#575	1	2	yes	—
1142	C₄	C₁₃×#577	1	2	yes	—
1143	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1144	C₄	C₁₃×#585	1	1	yes	characteristic
1145	C₂	—	4	2	no	—
1146	C₂	—	4	1	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1151	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1152	C₂	C₂×C₁₃×#577	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×#3482	C₂	semidirect
2. C₁₃×#3481	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3373	C₂	semidirect
6. C₁₃×#3372	C₂	semidirect
7. C₁₃×#3356	C₂	semidirect
8. C₁₃×#3350	C₂	semidirect
9. C₁₃×#3331	C₂	semidirect
10. C₁₃×#3324	C₂	semidirect
11. C₁₃×#3311	C₂	semidirect
12. C₁₃×#3307	C₂	semidirect
13. C₁₃×#3272	C₂	semidirect
14. C₁₃×#3267	C₂	semidirect
15. C₁₃×#3172	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3107	C₂	semidirect
18. C₁₃×#3106	C₂	semidirect
19. C₁₃×#3102	C₂	semidirect
20. C₁₃×#3101	C₂	semidirect
21. C₁₃×#2965	C₂	semidirect
22. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₄×C₁₃×#135	C₂	semidirect
27. C₁₃×#557	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#547	C₂²	semidirect
44. C₁₃×#533	C₂²	semidirect
45. C₁₃×#533	C₂²	semidirect
54. C₄×C₁₃×#41	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
61. C₁₃×#497	C₂²	semidirect
63. C₁₃×#491	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#483	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#476	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
81. C₁₃×#470	C₂²	semidirect
82. C₁₃×#470	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#463	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
100. C₁₃×#449	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
106. C₁₃×#440	C₂²	semidirect
107. C₄×C₁₃×Q₁₆	C₂²	semidirect
108. C₄×C₁₃×Q₁₆	C₂²	semidirect
109. C₄×C₁₃×Q₁₆	C₂²	semidirect
113. C₄×C₁₃×SD₁₆	C₂²	semidirect
114. C₄×C₁₃×SD₁₆	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
123. C₁₃×#435	C₂²	semidirect
124. C₁₃×#435	C₂²	semidirect
125. C₁₃×#431	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₁₃×#427	C₂²	semidirect
130. C₁₃×#417	C₂²	semidirect
132. C₁₃×#416	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
134. C₂×C₄×C₈×C₁₃	C₂²	semidirect
314. #61448	C₁₃	direct (N × H)
376. C₁₃×D₈	#41	semidirect
455. #3482	C₂×C₁₃	semidirect
456. #3481	C₂×C₁₃	semidirect
457. #3400	C₂×C₁₃	semidirect
458. #3384	C₂×C₁₃	semidirect
459. #3373	C₂×C₁₃	semidirect
460. #3372	C₂×C₁₃	semidirect
461. #3356	C₂×C₁₃	semidirect
462. #3350	C₂×C₁₃	semidirect
463. #3331	C₂×C₁₃	semidirect
464. #3324	C₂×C₁₃	semidirect
465. #3311	C₂×C₁₃	semidirect
466. #3307	C₂×C₁₃	semidirect
467. #3272	C₂×C₁₃	semidirect
468. #3267	C₂×C₁₃	semidirect
469. #3172	C₂×C₁₃	semidirect
470. #3167	C₂×C₁₃	semidirect
471. #3107	C₂×C₁₃	semidirect
472. #3106	C₂×C₁₃	semidirect
473. #3102	C₂×C₁₃	semidirect
474. #3101	C₂×C₁₃	semidirect
475. #2965	C₂×C₁₃	semidirect
476. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
477. C₄×#135	C₂×C₁₃	semidirect
559. #557	C₂²×C₁₃	semidirect
561. #556	C₂²×C₁₃	semidirect
569. D₄×Q₈	C₂²×C₁₃	semidirect
572. #547	C₂²×C₁₃	semidirect
576. #533	C₂²×C₁₃	semidirect
577. #533	C₂²×C₁₃	semidirect
586. C₄×#41	C₂²×C₁₃	semidirect
587. C₄×#41	C₂²×C₁₃	semidirect
591. #501	C₂²×C₁₃	semidirect
592. #498	C₂²×C₁₃	semidirect
593. #497	C₂²×C₁₃	semidirect
595. #491	C₂²×C₁₃	semidirect
596. #489	C₂²×C₁₃	semidirect
597. #487	C₂²×C₁₃	semidirect
599. #485	C₂²×C₁₃	semidirect
600. #485	C₂²×C₁₃	semidirect
601. #483	C₂²×C₁₃	semidirect
602. #483	C₂²×C₁₃	semidirect
604. #482	C₂²×C₁₃	semidirect
605. #479	C₂²×C₁₃	semidirect
606. #478	C₂²×C₁₃	semidirect
607. #477	C₂²×C₁₃	semidirect
609. #476	C₂²×C₁₃	semidirect
610. #476	C₂²×C₁₃	semidirect
611. #475	C₂²×C₁₃	semidirect
613. #470	C₂²×C₁₃	semidirect
614. #470	C₂²×C₁₃	semidirect
617. #465	C₂²×C₁₃	semidirect
618. #465	C₂²×C₁₃	semidirect
619. #464	C₂²×C₁₃	semidirect
620. #463	C₂²×C₁₃	semidirect
621. #462	C₂²×C₁₃	semidirect
624. #461	C₂²×C₁₃	semidirect
628. #452	C₂²×C₁₃	semidirect
632. #449	C₂²×C₁₃	semidirect
633. #446	C₂²×C₁₃	semidirect
634. #446	C₂²×C₁₃	semidirect
636. #442	C₂²×C₁₃	semidirect
638. #440	C₂²×C₁₃	semidirect
639. C₄×Q₁₆	C₂²×C₁₃	semidirect
640. C₄×Q₁₆	C₂²×C₁₃	semidirect
641. C₄×Q₁₆	C₂²×C₁₃	semidirect
645. C₄×SD₁₆	C₂²×C₁₃	semidirect
646. C₄×SD₁₆	C₂²×C₁₃	semidirect
647. C₄×SD₁₆	C₂²×C₁₃	semidirect
648. C₄×SD₁₆	C₂²×C₁₃	semidirect
649. C₄×SD₁₆	C₂²×C₁₃	semidirect
652. C₄×D₈	C₂²×C₁₃	semidirect
655. #435	C₂²×C₁₃	semidirect
656. #435	C₂²×C₁₃	semidirect
657. #431	C₂²×C₁₃	semidirect
658. #431	C₂²×C₁₃	semidirect
659. #428	C₂²×C₁₃	semidirect
660. #427	C₂²×C₁₃	semidirect
662. #417	C₂²×C₁₃	semidirect
664. #416	C₂²×C₁₃	semidirect
665. C₄×M₁₆	C₂²×C₁₃	semidirect
666. C₂×C₄×C₈	C₂²×C₁₃	semidirect
951. D₈	C₁₃×#41	semidirect
1030. C₁₃	#61448	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×#3482	2
C₁₃×#3481	2
C₁₃×#3400	2
C₁₃×#3384	2
C₁₃×#3373	2
C₁₃×#3372	2
C₁₃×#3356	2
C₁₃×#3350	2
C₁₃×#3331	2
C₁₃×#3324	2
C₁₃×#3311	2
C₁₃×#3307	2
C₁₃×#3272	2
C₁₃×#3267	2
C₁₃×#3172	2
C₁₃×#3167	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#3102	2
C₁₃×#3101	2
C₁₃×#2965	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₄×C₁₃×#135	2
#61448	13

Subgroups — C13×#61448 #15747787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61448 #15747787