Subgroups — C₁₃×#24148 #15710487

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2003	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2002	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1888	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1887	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₃×#559	—	2	1	no	—
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#551	—	2	2	no	—
22	C₁₃×#551	—	2	2	no	—
23	C₁₃×#542	—	2	1	no	—
24	C₁₃×#542	—	2	1	no	—
25	C₁₃×#536	C₂²	1	1	yes	characteristic
26	C₁₃×#535	C₂²	1	1	yes	characteristic
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₁₃×#519	C₂²	1	1	yes	characteristic
34	C₁₃×#518	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#478	—	2	1	no	—
38	C₁₃×#478	—	2	1	no	—
39	C₁₃×#476	—	2	1	no	—
40	C₁₃×#474	—	2	1	no	—
41	C₁₃×#442	—	2	1	no	—
42	C₁₃×#440	—	2	1	no	—
43	C₄×C₁₃×SD₁₆	—	2	1	no	—
44	C₄×C₁₃×D₈	—	2	1	no	—
45	C₁₃×#428	C₂²	1	1	yes	characteristic
46	C₁₃×#428	C₂²	1	1	yes	characteristic
47	C₁₃×#428	C₂²	1	1	yes	characteristic
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₁₃×#418	C₂²	1	1	yes	characteristic
52	C₁₃×#418	C₂²	1	1	yes	characteristic
53	C₁₃×#418	C₂²	1	1	yes	characteristic
54	C₁₃×#417	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
60	C₁₃×#394	—	2	2	no	—
61	C₁₃×#391	C₂²	1	1	yes	characteristic
62	C₁₃×#390	C₂²	1	1	yes	characteristic
63	C₁₃×#386	—	2	2	no	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₁₃×#339	C₂²	1	1	yes	characteristic
68	C₁₃×#339	C₂²	1	1	yes	characteristic
69	C₁₃×#339	C₂²	1	1	yes	characteristic
70	C₁₃×#339	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	1	no	—
80	C₂×C₁₃×D₈	—	2	1	no	—
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
87	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
88	C₁₃×#127	—	2	1	no	—
89	C₁₃×#127	—	2	2	no	—
90	C₁₃×#127	—	4	1	no	—
91	C₁₃×#126	—	2	2	no	—
92	C₁₃×#126	—	2	2	no	—
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	2	no	—
95	C₁₃×#125	D₄	1	1	yes	characteristic, complemented
96	C₁₃×#125	D₄	1	1	yes	characteristic, complemented
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	—	2	2	no	—
99	C₁₃×#124	—	2	1	no	—
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	2	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₁₃×#124	—	2	1	no	—
105	C₁₃×#124	—	2	1	no	—
106	C₁₃×#124	—	4	1	no	—
107	C₁₃×#123	—	2	2	no	—
108	C₁₃×#123	—	2	2	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×#123	—	2	2	no	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#120	—	2	2	no	—
121	C₄×Q₈×C₁₃	—	2	1	no	—
122	C₄×Q₈×C₁₃	—	2	1	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	—	2	1	no	—
127	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic, complemented
128	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic, complemented
129	C₄×D₄×C₁₃	—	2	2	no	—
130	C₄×D₄×C₁₃	—	2	2	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic, complemented
142	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic, complemented
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	2	no	—
145	C₁₃×#117	—	2	2	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₁₃×#117	C₂³	1	1	yes	characteristic
149	C₁₃×#117	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
156	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
157	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
158	C₂×C₄²×C₁₃	—	2	1	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×#107	—	2	1	no	—
163	C₁₃×#107	—	2	1	no	—
164	C₁₃×#107	—	2	1	no	—
165	C₁₃×#106	—	2	1	no	—
166	C₁₃×#106	—	2	1	no	—
167	C₁₃×#106	—	2	1	no	—
168	C₁₃×C₄⋊C₈	—	2	1	no	—
169	C₁₃×C₄⋊C₈	—	2	1	no	—
170	C₁₃×#104	—	4	1	no	—
171	C₁₃×#104	—	4	1	no	—
172	C₁₃×#103	—	2	1	no	—
173	C₁₃×#102	—	2	1	no	—
174	C₁₃×#102	—	2	1	no	—
175	C₁₃×#102	—	2	1	no	—
176	C₁₃×#102	—	2	1	no	—
177	C₁₃×#102	—	2	1	no	—
178	C₁₃×#102	—	2	1	no	—
179	C₁₃×#102	—	2	1	no	—
180	C₁₃×#101	—	2	2	no	—
181	C₁₃×#101	—	4	1	no	—
182	C₁₃×#100	—	2	2	no	—
183	C₁₃×#100	—	4	1	no	—
184	C₁₃×#97	—	2	1	no	—
185	C₄×C₈×C₁₃	—	2	1	no	—
186	C₁₃×#95	—	2	1	no	—
187	C₁₃×#95	—	2	2	no	—
188	#24148	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂⁴×C₁₃	—	2	1	no	—
190	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
191	C₁₃×#41	—	2	1	no	—
192	C₁₃×#41	—	2	1	no	—
193	C₁₃×#41	—	2	1	no	—
194	C₁₃×#41	—	2	1	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	1	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	2	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	4	4	no	—
219	C₂×D₄×C₁₃	—	4	4	no	—
220	C₂×D₄×C₁₃	—	8	2	no	—
221	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₁₃	#41	1	2	yes	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	—	4	1	no	—
232	C₂²×C₄×C₁₃	—	4	1	no	—
233	C₂²×C₄×C₁₃	—	8	2	no	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₁₃×SD₁₆	—	2	4	no	—
239	C₁₃×D₈	—	2	4	no	—
240	C₁₃×M₁₆	—	2	1	no	—
241	C₁₃×M₁₆	—	2	1	no	—
242	C₁₃×M₁₆	—	2	1	no	—
243	C₁₃×M₁₆	—	2	1	no	—
244	C₁₃×M₁₆	—	2	1	no	—
245	C₁₃×M₁₆	—	2	1	no	—
246	C₁₃×M₁₆	—	2	1	no	—
247	C₁₃×M₁₆	#41	1	2	yes	—
248	C₂×C₈×C₁₃	—	2	1	no	—
249	C₂×C₈×C₁₃	—	2	1	no	—
250	C₂×C₈×C₁₃	—	2	1	no	—
251	C₂×C₈×C₁₃	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	4	2	no	—
267	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
270	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
272	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	2	no	—
278	C₁₃×C₂²⋊C₄	—	2	2	no	—
279	C₁₃×C₂²⋊C₄	—	2	1	no	—
280	C₁₃×C₂²⋊C₄	—	2	1	no	—
281	C₁₃×C₂²⋊C₄	—	2	1	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	4	4	no	—
289	C₁₃×C₂²⋊C₄	—	4	1	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₁₃×C₂²⋊C₄	—	8	2	no	—
292	C₄²×C₁₃	—	2	2	no	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	—	2	1	no	—
300	C₄²×C₁₃	—	2	1	no	—
301	C₄²×C₁₃	—	2	1	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2544	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2003	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#2002	C₂×C₁₃	1	1	yes	characteristic
315	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#1888	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#1887	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	—	4	2	no	—
328	C₂³×C₁₃	—	4	2	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	4	2	no	—
331	C₂³×C₁₃	—	4	1	no	—
332	C₂³×C₁₃	—	4	1	no	—
333	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₁₃	—	2	1	no	—
335	Q₈×C₁₃	—	2	1	no	—
336	Q₈×C₁₃	—	4	1	no	—
337	Q₈×C₁₃	—	4	1	no	—
338	Q₈×C₁₃	—	4	1	no	—
339	Q₈×C₁₃	—	4	1	no	—
340	Q₈×C₁₃	—	8	1	no	—
341	Q₈×C₁₃	—	8	1	no	—
342	D₄×C₁₃	—	2	1	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	1	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	—	4	1	no	—
349	D₄×C₁₃	—	4	1	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	8	2	no	—
355	D₄×C₁₃	—	8	2	no	—
356	D₄×C₁₃	—	8	8	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	—	8	2	no	—
382	C₂×C₄×C₁₃	—	8	2	no	—
383	C₂×C₄×C₁₃	—	8	2	no	—
384	C₂×C₄×C₁₃	—	8	2	no	—
385	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
386	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
387	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
388	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
393	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
394	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
395	C₈×C₁₃	—	2	2	no	—
396	C₈×C₁₃	—	4	1	no	—
397	C₈×C₁₃	—	4	1	no	—
398	C₈×C₁₃	—	4	1	no	—
399	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
400	#559	—	2	1	no	—
401	#559	—	2	1	no	—
402	#556	—	2	1	no	—
403	#556	—	2	1	no	—
404	#551	—	2	2	no	—
405	#551	—	2	2	no	—
406	#542	—	2	1	no	—
407	#542	—	2	1	no	—
408	#536	C₂²×C₁₃	1	1	yes	characteristic
409	#535	C₂²×C₁₃	1	1	yes	characteristic
410	#533	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
412	#529	—	2	1	no	—
413	#529	—	2	1	no	—
414	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
416	#519	C₂²×C₁₃	1	1	yes	characteristic
417	#518	C₂²×C₁₃	1	1	yes	characteristic
418	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
420	#478	—	2	1	no	—
421	#478	—	2	1	no	—
422	#476	—	2	1	no	—
423	#474	—	2	1	no	—
424	#442	—	2	1	no	—
425	#440	—	2	1	no	—
426	C₄×SD₁₆	—	2	1	no	—
427	C₄×D₈	—	2	1	no	—
428	#428	C₂²×C₁₃	1	1	yes	characteristic
429	#428	C₂²×C₁₃	1	1	yes	characteristic
430	#428	C₂²×C₁₃	1	1	yes	characteristic
431	#423	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
434	#418	C₂²×C₁₃	1	1	yes	characteristic
435	#418	C₂²×C₁₃	1	1	yes	characteristic
436	#418	C₂²×C₁₃	1	1	yes	characteristic
437	#417	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
442	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
443	#394	—	2	2	no	—
444	#391	C₂²×C₁₃	1	1	yes	characteristic
445	#390	C₂²×C₁₃	1	1	yes	characteristic
446	#386	—	2	2	no	—
447	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
448	#339	C₂²×C₁₃	1	1	yes	characteristic
449	#339	C₂²×C₁₃	1	1	yes	characteristic
450	#339	C₂²×C₁₃	1	1	yes	characteristic
451	#339	C₂²×C₁₃	1	1	yes	characteristic
452	#339	C₂²×C₁₃	1	1	yes	characteristic
453	#339	C₂²×C₁₃	1	1	yes	characteristic
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	4	4	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	8	2	no	—
465	C₂²×C₁₃	—	8	2	no	—
466	C₂²×C₁₃	—	8	2	no	—
467	C₂²×C₁₃	—	8	1	no	—
468	C₂²×C₁₃	—	8	1	no	—
469	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
470	C₂²×C₁₃	#546	1	1	yes	characteristic
471	C₂²×C₁₃	#547	1	1	yes	characteristic
472	C₄×C₁₃	—	2	1	no	—
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	1	no	—
482	C₄×C₁₃	—	4	1	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	8	1	no	—
486	C₄×C₁₃	—	8	1	no	—
487	C₄×C₁₃	#525	1	1	yes	characteristic
488	C₄×C₁₃	#537	1	1	yes	characteristic
489	C₄×C₁₃	#548	1	1	yes	characteristic
490	C₄×C₁₃	#550	1	1	yes	characteristic
491	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	—	2	1	no	—
497	AGL(1,ℤ/8)	—	2	2	no	—
498	AGL(1,ℤ/8)	—	2	2	no	—
499	C₂×SD₁₆	—	2	1	no	—
500	C₂×D₈	—	2	1	no	—
501	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
507	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
508	#127	—	2	1	no	—
509	#127	—	2	2	no	—
510	#127	—	4	1	no	—
511	#126	—	2	2	no	—
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#126	—	2	2	no	—
515	#125	D₄×C₁₃	1	1	yes	characteristic, complemented
516	#125	D₄×C₁₃	1	1	yes	characteristic, complemented
517	#124	—	2	2	no	—
518	#124	—	2	2	no	—
519	#124	—	2	1	no	—
520	#124	—	2	1	no	—
521	#124	—	2	2	no	—
522	#124	—	2	1	no	—
523	#124	—	2	1	no	—
524	#124	—	2	1	no	—
525	#124	—	2	1	no	—
526	#124	—	4	1	no	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	#121	—	2	1	no	—
539	#121	—	2	1	no	—
540	#120	—	2	2	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
548	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic, complemented
562	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic, complemented
563	#117	—	2	2	no	—
564	#117	—	2	2	no	—
565	#117	—	2	2	no	—
566	#117	—	2	1	no	—
567	#117	C₂³×C₁₃	1	1	yes	characteristic
568	#117	C₂³×C₁₃	1	1	yes	characteristic
569	#117	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	—	2	2	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	2	no	—
575	C₂×C₂²⋊C₄	—	2	2	no	—
576	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
577	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
582	#107	—	2	1	no	—
583	#107	—	2	1	no	—
584	#107	—	2	1	no	—
585	#106	—	2	1	no	—
586	#106	—	2	1	no	—
587	#106	—	2	1	no	—
588	C₄⋊C₈	—	2	1	no	—
589	C₄⋊C₈	—	2	1	no	—
590	#104	—	4	1	no	—
591	#104	—	4	1	no	—
592	#103	—	2	1	no	—
593	#102	—	2	1	no	—
594	#102	—	2	1	no	—
595	#102	—	2	1	no	—
596	#102	—	2	1	no	—
597	#102	—	2	1	no	—
598	#102	—	2	1	no	—
599	#102	—	2	1	no	—
600	#101	—	2	2	no	—
601	#101	—	4	1	no	—
602	#100	—	2	2	no	—
603	#100	—	4	1	no	—
604	#97	—	2	1	no	—
605	C₄×C₈	—	2	1	no	—
606	#95	—	2	1	no	—
607	#95	—	2	2	no	—
608	C₂×C₁₃	—	2	1	no	—
609	C₂×C₁₃	—	2	1	no	—
610	C₂×C₁₃	—	8	1	no	—
611	C₂×C₁₃	—	8	2	no	—
612	C₂×C₁₃	—	8	2	no	—
613	C₂×C₁₃	#2407	1	1	yes	characteristic
614	C₂×C₁₃	#3018	1	1	yes	characteristic
615	C₂×C₁₃	#3021	1	1	yes	characteristic
616	C₂⁴	—	2	1	no	—
617	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
618	#41	—	2	1	no	—
619	#41	—	2	1	no	—
620	#41	—	2	1	no	—
621	#41	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	4	no	—
647	C₂×D₄	—	8	2	no	—
648	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂×D₄	C₁₃×#41	1	2	yes	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	8	2	no	—
661	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
665	SD₁₆	—	2	4	no	—
666	D₈	—	2	4	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	2	1	no	—
671	M₁₆	—	2	1	no	—
672	M₁₆	—	2	1	no	—
673	M₁₆	—	2	1	no	—
674	M₁₆	C₁₃×#41	1	2	yes	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	4	4	no	—
716	C₂²⋊C₄	—	4	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	8	2	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	—	2	1	no	—
729	C₄²	—	2	1	no	—
730	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
734	C₁₃	#24148	1	1	yes	characteristic, direct product factor, Sylow
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	Q₈	—	2	1	no	—
748	Q₈	—	2	1	no	—
749	Q₈	—	4	1	no	—
750	Q₈	—	4	1	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	8	1	no	—
754	Q₈	—	8	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	2	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	8	2	no	—
768	D₄	—	8	2	no	—
769	D₄	—	8	8	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	—	8	1	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	—	8	2	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
799	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
800	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
801	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
805	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
806	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
807	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
808	C₈	—	2	2	no	—
809	C₈	—	4	1	no	—
810	C₈	—	4	1	no	—
811	C₈	—	4	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	4	4	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	8	2	no	—
823	C₂²	—	8	2	no	—
824	C₂²	—	8	2	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
828	C₂²	C₁₃×#546	1	1	yes	characteristic
829	C₂²	C₁₃×#547	1	1	yes	characteristic
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	8	1	no	—
844	C₄	—	8	1	no	—
845	C₄	C₁₃×#525	1	1	yes	characteristic
846	C₄	C₁₃×#537	1	1	yes	characteristic
847	C₄	C₁₃×#548	1	1	yes	characteristic
848	C₄	C₁₃×#550	1	1	yes	characteristic
849	C₂	—	2	1	no	—
850	C₂	—	2	1	no	—
851	C₂	—	8	2	no	—
852	C₂	—	8	2	no	—
853	C₂	—	8	1	no	—
854	C₂	C₁₃×#2407	1	1	yes	characteristic
855	C₂	C₁₃×#3018	1	1	yes	characteristic
856	C₂	C₁₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2002	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
3. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₁₃×#2544	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
6. C₁₃×#2037	C₂	semidirect
7. C₁₃×#2003	C₂	semidirect
9. C₁₃×#1986	C₂	semidirect
10. C₁₃×#1967	C₂	semidirect
11. C₁₃×#1888	C₂	semidirect
12. C₁₃×#1887	C₂	semidirect
13. C₁₃×#1857	C₂	semidirect
14. C₁₃×#1856	C₂	semidirect
15. C₁₃×#1806	C₂	semidirect
86. C₁₃×C₄⋊Q₈	D₄	semidirect
87. C₁₃×C₄⋊Q₈	D₄	semidirect
95. C₁₃×#125	D₄	semidirect
96. C₁₃×#125	D₄	semidirect
127. C₄×Q₈×C₁₃	D₄	semidirect
128. C₄×Q₈×C₁₃	D₄	semidirect
141. C₄×D₄×C₁₃	D₄	semidirect
142. C₄×D₄×C₁₃	D₄	semidirect
188. #24148	C₁₃	direct (N × H)
307. #3510	C₂×C₁₃	semidirect
308. #3077	C₂×C₁₃	semidirect
309. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
310. #2544	C₂×C₁₃	semidirect
311. #2038	C₂×C₁₃	semidirect
312. #2037	C₂×C₁₃	semidirect
313. #2003	C₂×C₁₃	semidirect
315. #1986	C₂×C₁₃	semidirect
316. #1967	C₂×C₁₃	semidirect
317. #1888	C₂×C₁₃	semidirect
318. #1887	C₂×C₁₃	semidirect
319. #1857	C₂×C₁₃	semidirect
320. #1856	C₂×C₁₃	semidirect
321. #1806	C₂×C₁₃	semidirect
506. C₄⋊Q₈	D₄×C₁₃	semidirect
507. C₄⋊Q₈	D₄×C₁₃	semidirect
515. #125	D₄×C₁₃	semidirect
516. #125	D₄×C₁₃	semidirect
547. C₄×Q₈	D₄×C₁₃	semidirect
548. C₄×Q₈	D₄×C₁₃	semidirect
561. C₄×D₄	D₄×C₁₃	semidirect
562. C₄×D₄	D₄×C₁₃	semidirect
734. C₁₃	#24148	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×#3510	2
C₁₃×#3077	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2544	2
C₁₃×#2038	2
C₁₃×#2037	2
C₁₃×#2003	2
C₁₃×#2002	2
C₁₃×#1986	2
C₁₃×#1967	2
C₁₃×#1888	2
C₁₃×#1887	2
C₁₃×#1857	2
C₁₃×#1856	2
C₁₃×#1806	2
#24148	13

Subgroups — C13×#24148 #15710487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24148 #15710487