Subgroups — C₁₃×#61420 #15747759

Order 3328.

1908 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3400	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3392	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	4	yes	—
24	C₁₃×#557	C₂²	1	2	yes	complemented
25	C₁₃×#557	C₂²	1	2	yes	complemented
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#556	C₂²	1	2	yes	complemented
28	C₁₃×#556	C₂²	1	2	yes	complemented
29	C₁₃×#555	—	2	1	no	—
30	C₁₃×#553	—	2	2	no	—
31	C₁₃×#552	—	2	2	no	—
32	C₁₃×#552	—	2	2	no	—
33	C₁₃×#550	C₂²	1	2	yes	—
34	C₁₃×#547	—	2	1	no	—
35	C₁₃×#541	—	2	2	no	—
36	C₁₃×#538	—	2	2	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#533	—	2	1	no	—
40	C₁₃×#533	—	2	1	no	—
41	C₁₃×#533	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#525	—	2	2	no	—
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#519	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#497	C₂²	1	4	yes	—
50	C₁₃×#497	C₂²	1	4	yes	complemented
51	C₁₃×#496	C₂²	1	4	yes	—
52	C₁₃×#495	C₂²	1	4	yes	—
53	C₁₃×#494	C₂²	1	2	yes	complemented
54	C₁₃×#492	C₂²	1	4	yes	—
55	C₁₃×#492	C₂²	1	2	yes	complemented
56	C₁₃×#464	C₂²	1	4	yes	—
57	C₁₃×#464	C₂²	1	4	yes	—
58	C₁₃×#464	C₂²	1	2	yes	complemented
59	C₁₃×#464	C₂²	1	4	yes	complemented
60	C₁₃×#463	C₂²	1	2	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#462	C₂²	1	4	yes	complemented
64	C₁₃×#461	C₂²	1	2	yes	—
65	C₁₃×#461	C₂²	1	2	yes	—
66	C₁₃×#461	C₂²	1	4	yes	—
67	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#461	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	4	yes	—
70	C₁₃×#460	C₂²	1	4	yes	—
71	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#446	C₂²	1	2	yes	complemented
74	C₁₃×#446	C₂²	1	4	yes	complemented
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
76	C₁₃×#442	C₂²	1	2	yes	—
77	C₁₃×#441	C₂²	1	4	yes	complemented
78	C₁₃×#440	C₂²	1	2	yes	—
79	C₁₃×#440	C₂²	1	4	yes	complemented
80	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	2	yes	—
84	C₁₃×#428	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#418	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	—	2	1	no	—
99	C₁₃×#137	—	2	8	no	—
100	C₁₃×#137	—	4	4	no	—
101	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
102	C₁₃×#135	—	4	4	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	—	4	4	no	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₁₃×D₈	C₂³	1	2	yes	—
115	C₂×C₁₃×D₈	C₂³	1	2	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	—	2	1	no	—
120	C₁₃×C₄⋊Q₈	—	2	1	no	—
121	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₃×#127	C₂³	1	1	yes	characteristic
128	C₁₃×#127	C₂³	1	4	yes	—
129	C₁₃×#126	—	2	4	no	—
130	C₁₃×#126	—	2	4	no	—
131	C₁₃×#126	—	2	4	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	4	no	—
135	C₁₃×#125	—	2	4	no	—
136	C₁₃×#125	D₄	1	2	yes	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	C₂³	1	4	yes	—
139	C₁₃×#124	C₂³	1	2	yes	—
140	C₁₃×#124	C₂³	1	4	yes	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	4	no	—
157	C₁₃×#120	—	2	4	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	4	no	—
172	C₄×D₄×C₁₃	—	2	4	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	4	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	2	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	4	no	—
187	C₁₃×#117	—	2	1	no	—
188	C₁₃×#117	C₂³	1	1	yes	characteristic
189	C₁₃×#117	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₄²×C₁₃	—	2	1	no	—
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	2	yes	—
198	C₁₃×#106	C₂³	1	2	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	2	yes	—
208	C₁₃×#103	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×#102	C₂³	1	2	yes	—
212	C₁₃×#102	C₂³	1	2	yes	—
213	C₁₃×#102	C₂³	1	2	yes	—
214	C₁₃×#97	C₂³	1	2	yes	—
215	C₁₃×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₁₃	C₂³	1	2	yes	—
217	C₄×C₈×C₁₃	C₂³	1	4	yes	—
218	#61420	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂⁴×C₁₃	—	2	1	no	—
220	C₁₃×#41	—	2	2	no	—
221	C₁₃×#41	—	2	4	no	—
222	C₁₃×#41	—	2	2	no	—
223	C₁₃×#41	—	2	4	no	—
224	C₁₃×#41	—	8	4	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	2	4	no	—
227	C₂×Q₈×C₁₃	—	2	4	no	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	—	2	2	no	—
254	C₂²×C₄×C₁₃	—	8	2	no	—
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₁₃×Q₁₆	—	2	8	no	—
259	C₁₃×Q₁₆	—	4	2	no	—
260	C₁₃×Q₁₆	—	4	4	no	—
261	C₁₃×SD₁₆	—	2	4	no	—
262	C₁₃×SD₁₆	—	2	8	no	—
263	C₁₃×SD₁₆	—	4	4	no	—
264	C₁₃×SD₁₆	—	4	4	no	—
265	C₁₃×SD₁₆	—	4	2	no	—
266	C₁₃×SD₁₆	—	4	2	no	—
267	C₁₃×SD₁₆	—	4	4	no	—
268	C₁₃×D₈	—	2	4	no	—
269	C₁₃×D₈	—	4	2	no	—
270	C₁₃×M₁₆	—	2	2	no	—
271	C₁₃×M₁₆	#41	1	4	yes	complemented
272	C₂×C₈×C₁₃	—	2	4	no	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	4	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
293	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
294	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₁₃×C₂²⋊C₄	—	2	2	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	4	no	—
304	C₁₃×C₂²⋊C₄	—	2	1	no	—
305	C₁₃×C₂²⋊C₄	—	2	1	no	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
313	C₄²×C₁₃	—	2	1	no	—
314	C₄²×C₁₃	—	2	1	no	—
315	C₄²×C₁₃	—	2	1	no	—
316	C₄²×C₁₃	—	2	4	no	—
317	C₄²×C₁₃	—	2	4	no	—
318	C₄²×C₁₃	—	2	4	no	—
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₄²×C₁₃	C₂⁴	1	4	yes	—
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3401	C₂×C₁₃	1	4	yes	complemented
327	#3400	C₂×C₁₃	1	4	yes	complemented
328	#3398	C₂×C₁₃	1	2	yes	complemented
329	#3397	C₂×C₁₃	1	2	yes	complemented
330	#3393	C₂×C₁₃	1	2	yes	complemented
331	#3392	C₂×C₁₃	1	2	yes	complemented
332	#3154	C₂×C₁₃	1	2	yes	complemented
333	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#3046	C₂×C₁₃	1	2	yes	complemented
335	#3043	C₂×C₁₃	1	2	yes	complemented
336	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#2947	C₂×C₁₃	1	2	yes	complemented
340	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂³×C₁₃	—	2	1	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	4	2	no	—
345	C₂³×C₁₃	—	8	1	no	—
346	C₂³×C₁₃	—	8	1	no	—
347	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₁₃	—	2	4	no	—
349	Q₈×C₁₃	—	2	1	no	—
350	Q₈×C₁₃	—	2	4	no	—
351	Q₈×C₁₃	—	2	2	no	—
352	Q₈×C₁₃	—	2	4	no	—
353	Q₈×C₁₃	—	2	1	no	—
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	4	2	no	—
356	Q₈×C₁₃	—	4	4	no	—
357	D₄×C₁₃	—	2	1	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	2	1	no	—
361	D₄×C₁₃	—	2	2	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	4	4	no	—
364	D₄×C₁₃	—	4	2	no	—
365	D₄×C₁₃	—	4	2	no	—
366	D₄×C₁₃	—	4	2	no	—
367	D₄×C₁₃	—	8	1	no	—
368	D₄×C₁₃	—	8	4	no	—
369	D₄×C₁₃	—	8	4	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	2	1	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	2	no	—
379	C₂×C₄×C₁₃	—	4	4	no	—
380	C₂×C₄×C₁₃	—	4	2	no	—
381	C₂×C₄×C₁₃	—	4	4	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	4	4	no	—
384	C₂×C₄×C₁₃	—	8	2	no	—
385	C₂×C₄×C₁₃	—	8	4	no	—
386	C₂×C₄×C₁₃	—	8	1	no	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
395	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
397	C₈×C₁₃	—	2	2	no	—
398	C₈×C₁₃	—	2	2	no	—
399	C₈×C₁₃	—	2	2	no	—
400	C₈×C₁₃	C₂×#41	1	4	yes	—
401	C₂×#137	C₂²×C₁₃	1	2	yes	—
402	C₂×#137	C₂²×C₁₃	1	2	yes	—
403	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#135	C₂²×C₁₃	1	2	yes	—
405	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
406	#559	C₂²×C₁₃	1	4	yes	—
407	#557	C₂²×C₁₃	1	2	yes	complemented
408	#557	C₂²×C₁₃	1	2	yes	complemented
409	#556	C₂²×C₁₃	1	2	yes	—
410	#556	C₂²×C₁₃	1	2	yes	complemented
411	#556	C₂²×C₁₃	1	2	yes	complemented
412	#555	—	2	1	no	—
413	#553	—	2	2	no	—
414	#552	—	2	2	no	—
415	#552	—	2	2	no	—
416	#550	C₂²×C₁₃	1	2	yes	—
417	#547	—	2	1	no	—
418	#541	—	2	2	no	—
419	#538	—	2	2	no	—
420	#536	C₂²×C₁₃	1	2	yes	—
421	#535	C₂²×C₁₃	1	2	yes	—
422	#533	—	2	1	no	—
423	#533	—	2	1	no	—
424	#533	C₂²×C₁₃	1	1	yes	characteristic
425	#532	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
427	#525	—	2	2	no	—
428	#520	C₂²×C₁₃	1	2	yes	—
429	#519	C₂²×C₁₃	1	2	yes	—
430	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
432	#497	C₂²×C₁₃	1	4	yes	—
433	#497	C₂²×C₁₃	1	4	yes	complemented
434	#496	C₂²×C₁₃	1	4	yes	—
435	#495	C₂²×C₁₃	1	4	yes	—
436	#494	C₂²×C₁₃	1	2	yes	complemented
437	#492	C₂²×C₁₃	1	4	yes	—
438	#492	C₂²×C₁₃	1	2	yes	complemented
439	#464	C₂²×C₁₃	1	4	yes	—
440	#464	C₂²×C₁₃	1	4	yes	—
441	#464	C₂²×C₁₃	1	4	yes	complemented
442	#464	C₂²×C₁₃	1	2	yes	complemented
443	#463	C₂²×C₁₃	1	4	yes	complemented
444	#463	C₂²×C₁₃	1	2	yes	complemented
445	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#462	C₂²×C₁₃	1	4	yes	complemented
447	#461	C₂²×C₁₃	1	2	yes	—
448	#461	C₂²×C₁₃	1	2	yes	—
449	#461	C₂²×C₁₃	1	4	yes	—
450	#461	C₂²×C₁₃	1	4	yes	complemented
451	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#460	C₂²×C₁₃	1	4	yes	—
453	#460	C₂²×C₁₃	1	4	yes	—
454	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#446	C₂²×C₁₃	1	2	yes	complemented
457	#446	C₂²×C₁₃	1	4	yes	complemented
458	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
459	#442	C₂²×C₁₃	1	2	yes	—
460	#441	C₂²×C₁₃	1	4	yes	complemented
461	#440	C₂²×C₁₃	1	2	yes	—
462	#440	C₂²×C₁₃	1	4	yes	complemented
463	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
464	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
465	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
466	C₄×D₈	C₂²×C₁₃	1	2	yes	—
467	#428	C₂²×C₁₃	1	1	yes	characteristic
468	#424	C₂²×C₁₃	1	2	yes	—
469	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
470	#418	C₂²×C₁₃	1	1	yes	characteristic
471	#417	C₂²×C₁₃	1	1	yes	characteristic
472	#416	C₂²×C₁₃	1	2	yes	—
473	C₂×#103	C₂²×C₁₃	1	2	yes	—
474	#405	C₂²×C₁₃	1	2	yes	—
475	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	4	1	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	1	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	8	4	no	—
488	C₂²×C₁₃	#550	1	2	yes	—
489	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₁₃	—	2	1	no	—
491	C₄×C₁₃	—	2	1	no	—
492	C₄×C₁₃	—	2	4	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	4	no	—
495	C₄×C₁₃	—	4	1	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	1	no	—
498	C₄×C₁₃	—	4	4	no	—
499	C₄×C₁₃	—	4	1	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	#550	1	2	yes	—
502	C₄×C₁₃	#577	1	2	yes	—
503	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
504	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂×#41	—	2	2	no	—
506	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
507	C₂×#41	C₂³×C₁₃	1	2	yes	—
508	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
509	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	#137	—	2	8	no	—
512	#137	—	4	4	no	—
513	AGL(1,ℤ/8)	—	2	4	no	—
514	#135	—	4	4	no	—
515	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
516	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
517	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
518	C₂×SD₁₆	—	4	4	no	—
519	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
520	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
521	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
525	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×D₈	C₂³×C₁₃	1	2	yes	—
527	C₂×D₈	C₂³×C₁₃	1	2	yes	—
528	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
534	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
539	#127	C₂³×C₁₃	1	1	yes	characteristic
540	#127	C₂³×C₁₃	1	4	yes	—
541	#126	—	2	4	no	—
542	#126	—	2	4	no	—
543	#126	—	2	4	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	4	no	—
547	#125	—	2	4	no	—
548	#125	D₄×C₁₃	1	2	yes	—
549	#124	—	2	4	no	—
550	#124	C₂³×C₁₃	1	2	yes	—
551	#124	C₂³×C₁₃	1	4	yes	—
552	#124	C₂³×C₁₃	1	4	yes	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	#123	—	2	4	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
562	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
563	#121	—	2	1	no	—
564	#121	—	2	1	no	—
565	#121	—	2	2	no	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	—	2	4	no	—
569	#120	—	2	4	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
579	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
580	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	4	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	C₂³×C₁₃	1	2	yes	—
590	C₄×D₄	C₂³×C₁₃	1	2	yes	—
591	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₁₃	1	4	yes	—
594	#117	—	2	2	no	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	—	2	4	no	—
599	#117	—	2	1	no	—
600	#117	C₂³×C₁₃	1	1	yes	characteristic
601	#117	C₂³×C₁₃	1	2	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	2	no	—
605	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
609	#107	C₂³×C₁₃	1	2	yes	—
610	#106	C₂³×C₁₃	1	2	yes	—
611	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
614	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
615	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
616	#103	C₂³×C₁₃	1	4	yes	—
617	#103	C₂³×C₁₃	1	4	yes	—
618	#103	C₂³×C₁₃	1	2	yes	—
619	#103	C₂³×C₁₃	1	2	yes	—
620	#103	C₂³×C₁₃	1	2	yes	—
621	#102	C₂³×C₁₃	1	2	yes	—
622	#102	C₂³×C₁₃	1	2	yes	—
623	#102	C₂³×C₁₃	1	2	yes	—
624	#102	C₂³×C₁₃	1	2	yes	—
625	#102	C₂³×C₁₃	1	2	yes	—
626	#97	C₂³×C₁₃	1	2	yes	—
627	#97	C₂³×C₁₃	1	4	yes	—
628	C₄×C₈	C₂³×C₁₃	1	2	yes	—
629	C₄×C₈	C₂³×C₁₃	1	4	yes	—
630	C₂×C₁₃	—	2	2	no	—
631	C₂×C₁₃	—	8	1	no	—
632	C₂×C₁₃	—	8	2	no	—
633	C₂×C₁₃	—	8	2	no	—
634	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
635	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
636	C₂×C₁₃	#3586	1	1	yes	characteristic
637	C₂⁴	—	2	1	no	—
638	#41	—	2	2	no	—
639	#41	—	2	4	no	—
640	#41	—	2	2	no	—
641	#41	—	2	4	no	—
642	#41	—	8	4	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
647	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
649	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
650	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
661	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
676	Q₁₆	—	2	8	no	—
677	Q₁₆	—	4	2	no	—
678	Q₁₆	—	4	4	no	—
679	SD₁₆	—	2	4	no	—
680	SD₁₆	—	2	8	no	—
681	SD₁₆	—	4	4	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	2	no	—
684	SD₁₆	—	4	2	no	—
685	SD₁₆	—	4	4	no	—
686	D₈	—	2	4	no	—
687	D₈	—	4	2	no	—
688	M₁₆	—	2	2	no	—
689	M₁₆	C₁₃×#41	1	4	yes	complemented
690	C₂×C₈	—	2	4	no	—
691	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
692	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
693	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
694	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
710	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
714	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
717	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₄²	C₂⁴×C₁₃	1	4	yes	—
741	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₁₃	#61420	1	1	yes	characteristic, direct product factor, Sylow
743	C₂³	—	2	1	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	8	1	no	—
748	C₂³	—	8	1	no	—
749	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
750	Q₈	—	2	4	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	4	no	—
755	Q₈	—	2	1	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	D₄	—	2	1	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	4	no	—
771	D₄	—	8	4	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	8	2	no	—
787	C₂×C₄	—	8	4	no	—
788	C₂×C₄	—	8	1	no	—
789	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
792	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
797	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
798	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
799	C₈	—	2	2	no	—
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	C₂×C₁₃×#41	1	4	yes	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	8	4	no	—
815	C₂²	C₁₃×#550	1	2	yes	—
816	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
817	C₄	—	2	1	no	—
818	C₄	—	2	4	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	4	no	—
828	C₄	C₁₃×#550	1	2	yes	—
829	C₄	C₁₃×#577	1	2	yes	—
830	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
831	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
832	C₂	—	2	2	no	—
833	C₂	—	8	2	no	—
834	C₂	—	8	1	no	—
835	C₂	—	8	2	no	—
836	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
837	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
838	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3400	C₂	semidirect
5. C₁₃×#3398	C₂	semidirect
6. C₁₃×#3397	C₂	semidirect
7. C₁₃×#3393	C₂	semidirect
8. C₁₃×#3392	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3152	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3043	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#461	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2947	C₂	semidirect
17. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
24. C₁₃×#557	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
53. C₁₃×#494	C₂²	semidirect
55. C₁₃×#492	C₂²	semidirect
58. C₁₃×#464	C₂²	semidirect
59. C₁₃×#464	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#462	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#446	C₂²	semidirect
74. C₁₃×#446	C₂²	semidirect
75. C₈×Q₈×C₁₃	C₂²	semidirect
77. C₁₃×#441	C₂²	semidirect
79. C₁₃×#440	C₂²	semidirect
80. C₄×C₁₃×Q₁₆	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
218. #61420	C₁₃	direct (N × H)
271. C₁₃×M₁₆	#41	semidirect
324. #3509	C₂×C₁₃	semidirect
325. #3506	C₂×C₁₃	semidirect
326. #3401	C₂×C₁₃	semidirect
327. #3400	C₂×C₁₃	semidirect
328. #3398	C₂×C₁₃	semidirect
329. #3397	C₂×C₁₃	semidirect
330. #3393	C₂×C₁₃	semidirect
331. #3392	C₂×C₁₃	semidirect
332. #3154	C₂×C₁₃	semidirect
333. #3152	C₂×C₁₃	semidirect
334. #3046	C₂×C₁₃	semidirect
335. #3043	C₂×C₁₃	semidirect
336. #3035	C₂×C₁₃	semidirect
337. C₂×#461	C₂×C₁₃	semidirect
338. #2962	C₂×C₁₃	semidirect
339. #2947	C₂×C₁₃	semidirect
340. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
407. #557	C₂²×C₁₃	semidirect
408. #557	C₂²×C₁₃	semidirect
410. #556	C₂²×C₁₃	semidirect
411. #556	C₂²×C₁₃	semidirect
433. #497	C₂²×C₁₃	semidirect
436. #494	C₂²×C₁₃	semidirect
438. #492	C₂²×C₁₃	semidirect
441. #464	C₂²×C₁₃	semidirect
442. #464	C₂²×C₁₃	semidirect
443. #463	C₂²×C₁₃	semidirect
444. #463	C₂²×C₁₃	semidirect
445. #462	C₂²×C₁₃	semidirect
446. #462	C₂²×C₁₃	semidirect
450. #461	C₂²×C₁₃	semidirect
451. #461	C₂²×C₁₃	semidirect
454. #460	C₂²×C₁₃	semidirect
455. #459	C₂²×C₁₃	semidirect
456. #446	C₂²×C₁₃	semidirect
457. #446	C₂²×C₁₃	semidirect
458. C₈×Q₈	C₂²×C₁₃	semidirect
460. #441	C₂²×C₁₃	semidirect
462. #440	C₂²×C₁₃	semidirect
463. C₄×Q₁₆	C₂²×C₁₃	semidirect
465. C₄×SD₁₆	C₂²×C₁₃	semidirect
689. M₁₆	C₁₃×#41	semidirect
742. C₁₃	#61420	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×#3509	2
C₁₃×#3506	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3397	2
C₁₃×#3393	2
C₁₃×#3392	2
C₁₃×#3154	2
C₁₃×#3152	2
C₁₃×#3046	2
C₁₃×#3043	2
C₁₃×#3035	2
C₂×C₁₃×#461	2
C₁₃×#2962	2
C₁₃×#2947	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61420	13

Subgroups — C13×#61420 #15747759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61420 #15747759