Subgroups — C₁₃×#25147 #15711486

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#413	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×#525	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₁₃×#471	—	2	4	no	—
28	C₁₃×#469	—	2	1	no	—
29	C₁₃×#468	—	2	1	no	—
30	C₁₃×#466	—	2	1	no	—
31	C₁₃×#465	—	2	1	no	—
32	C₁₃×#452	—	2	1	no	—
33	C₁₃×#452	—	2	1	no	—
34	C₁₃×#449	—	2	1	no	—
35	C₁₃×#449	—	2	1	no	—
36	C₁₃×#449	—	2	1	no	—
37	C₁₃×#449	—	2	1	no	—
38	C₁₃×#449	—	2	1	no	—
39	C₁₃×#449	—	2	1	no	—
40	C₁₃×#436	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₁₃×#435	—	2	1	no	—
43	C₈×D₄×C₁₃	—	2	1	no	—
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
46	C₁₃×#428	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₁₃×#413	—	2	4	no	—
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	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
61	C₁₃×#408	C₂²	1	1	yes	characteristic
62	C₁₃×#407	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×#405	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#341	C₂²	1	1	yes	characteristic
68	C₁₃×#341	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	2	1	no	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	4	1	no	—
76	C₂×C₁₃×#41	—	4	1	no	—
77	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#137	—	2	2	no	—
86	C₁₃×#137	—	4	1	no	—
87	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×C₁₃×Q₁₆	—	2	1	no	—
92	C₂×C₁₃×SD₁₆	—	2	1	no	—
93	C₂×C₁₃×SD₁₆	—	2	1	no	—
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	1	no	—
96	C₂×C₁₃×SD₁₆	—	2	1	no	—
97	C₂×C₁₃×SD₁₆	—	2	1	no	—
98	C₂×C₁₃×SD₁₆	—	4	1	no	—
99	C₂×C₁₃×D₈	—	2	1	no	—
100	C₂×C₁₃×D₈	—	2	1	no	—
101	C₂×C₁₃×D₈	—	2	2	no	—
102	C₂×C₁₃×D₈	—	2	1	no	—
103	C₂×C₁₃×D₈	—	2	1	no	—
104	C₂×C₁₃×D₈	—	4	1	no	—
105	C₁₃×#131	—	2	2	no	—
106	C₁₃×#131	—	4	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	—	2	1	no	—
109	C₂×C₁₃×M₁₆	—	2	1	no	—
110	C₂×C₁₃×M₁₆	—	2	2	no	—
111	C₂×C₁₃×M₁₆	—	2	2	no	—
112	C₂×C₁₃×M₁₆	—	4	1	no	—
113	C₂×C₁₃×M₁₆	—	4	1	no	—
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₂²×C₈×C₁₃	—	2	1	no	—
122	C₂²×C₈×C₁₃	—	2	1	no	—
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#123	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₁₃×#121	—	2	1	no	—
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	D₄	1	1	yes	characteristic
133	C₁₃×#121	D₄	1	1	yes	characteristic
134	C₁₃×#120	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₁₃×#117	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×#108	—	2	2	no	—
141	C₁₃×#108	—	4	1	no	—
142	C₁₃×#107	—	2	1	no	—
143	C₁₃×#106	—	2	1	no	—
144	C₁₃×C₄⋊C₈	—	2	1	no	—
145	C₁₃×C₄⋊C₈	—	2	1	no	—
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#103	—	2	1	no	—
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#102	—	2	1	no	—
152	C₁₃×#102	—	2	1	no	—
153	C₁₃×#102	—	2	1	no	—
154	C₁₃×#102	—	2	1	no	—
155	C₁₃×#102	—	2	1	no	—
156	C₁₃×#102	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#101	—	2	2	no	—
159	C₁₃×#101	D₄	1	4	yes	complemented
160	C₁₃×#100	—	2	2	no	—
161	C₁₃×#100	—	2	2	no	—
162	C₁₃×#100	—	2	2	no	—
163	C₁₃×#100	—	4	1	no	—
164	C₁₃×C₂²⋊C₈	—	2	1	no	—
165	C₁₃×C₂²⋊C₈	—	2	1	no	—
166	C₁₃×C₂²⋊C₈	—	2	1	no	—
167	C₁₃×C₂²⋊C₈	—	2	1	no	—
168	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	#25147	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	—	2	1	no	—
176	C₂⁴×C₁₃	—	2	1	no	—
177	C₂⁴×C₁₃	#41	1	1	yes	characteristic
178	C₁₃×#41	—	2	1	no	—
179	C₁₃×#41	—	2	1	no	—
180	C₁₃×#41	—	2	1	no	—
181	C₁₃×#41	—	2	1	no	—
182	C₁₃×#41	—	4	2	no	—
183	C₁₃×#41	—	4	2	no	—
184	C₁₃×#41	—	4	2	no	—
185	C₁₃×#41	—	4	2	no	—
186	C₁₃×#41	—	4	2	no	—
187	C₁₃×#41	—	4	2	no	—
188	C₁₃×#41	—	4	2	no	—
189	C₁₃×#41	—	4	2	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
196	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	1	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	1	no	—
214	C₂×D₄×C₁₃	—	4	1	no	—
215	C₂×D₄×C₁₃	—	4	1	no	—
216	C₂×D₄×C₁₃	—	4	1	no	—
217	C₂×D₄×C₁₃	—	8	2	no	—
218	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₁₃	#41	1	2	yes	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	4	2	no	—
229	C₂²×C₄×C₁₃	—	4	1	no	—
230	C₂²×C₄×C₁₃	—	4	1	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₁₃×Q₁₆	—	4	2	no	—
238	C₁₃×SD₁₆	—	4	2	no	—
239	C₁₃×SD₁₆	—	4	2	no	—
240	C₁₃×SD₁₆	—	4	2	no	—
241	C₁₃×SD₁₆	—	4	2	no	—
242	C₁₃×SD₁₆	—	4	2	no	—
243	C₁₃×D₈	—	4	2	no	—
244	C₁₃×D₈	—	4	2	no	—
245	C₁₃×D₈	—	4	2	no	—
246	C₁₃×D₈	—	4	2	no	—
247	C₁₃×M₁₆	—	2	1	no	—
248	C₁₃×M₁₆	—	2	1	no	—
249	C₁₃×M₁₆	—	2	1	no	—
250	C₁₃×M₁₆	—	2	1	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	—	2	1	no	—
253	C₁₃×M₁₆	—	2	1	no	—
254	C₁₃×M₁₆	—	2	1	no	—
255	C₁₃×M₁₆	—	2	1	no	—
256	C₁₃×M₁₆	—	2	1	no	—
257	C₁₃×M₁₆	—	4	2	no	—
258	C₁₃×M₁₆	—	4	2	no	—
259	C₁₃×M₁₆	—	4	2	no	—
260	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
261	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	2	1	no	—
269	C₂×C₈×C₁₃	—	2	1	no	—
270	C₂×C₈×C₁₃	—	2	1	no	—
271	C₂×C₈×C₁₃	—	2	1	no	—
272	C₂×C₈×C₁₃	—	4	2	no	—
273	C₂×C₈×C₁₃	—	4	2	no	—
274	C₂×C₈×C₁₃	—	4	2	no	—
275	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
284	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₁₃×C₂²⋊C₄	—	4	1	no	—
292	C₄²×C₁₃	—	2	1	no	—
293	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#3055	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3005	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2933	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#413	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2018	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	4	1	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	1	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	8	1	no	—
320	C₂³×C₁₃	—	8	1	no	—
321	C₂³×C₁₃	—	8	1	no	—
322	C₂³×C₁₃	—	8	1	no	—
323	C₂³×C₁₃	#121	1	1	yes	characteristic
324	C₂³×C₁₃	#121	1	1	yes	characteristic
325	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
326	Q₈×C₁₃	—	2	1	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	1	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	Q₈×C₁₃	—	4	1	no	—
332	D₄×C₁₃	—	2	1	no	—
333	D₄×C₁₃	—	2	2	no	—
334	D₄×C₁₃	—	2	1	no	—
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	4	2	no	—
337	D₄×C₁₃	—	4	4	no	—
338	D₄×C₁₃	—	4	4	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	4	1	no	—
342	D₄×C₁₃	—	4	1	no	—
343	D₄×C₁₃	—	4	1	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	8	1	no	—
348	D₄×C₁₃	—	8	2	no	—
349	D₄×C₁₃	—	8	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	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	1	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	4	4	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	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	—	8	1	no	—
372	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
373	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
380	C₈×C₁₃	—	2	1	no	—
381	C₈×C₁₃	—	2	1	no	—
382	C₈×C₁₃	—	2	2	no	—
383	C₈×C₁₃	—	2	2	no	—
384	C₈×C₁₃	—	2	1	no	—
385	C₈×C₁₃	—	2	1	no	—
386	C₈×C₁₃	—	4	1	no	—
387	C₈×C₁₃	—	4	1	no	—
388	C₈×C₁₃	—	4	1	no	—
389	C₈×C₁₃	—	4	1	no	—
390	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
394	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
397	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
398	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
399	#525	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
401	#471	—	2	4	no	—
402	#469	—	2	1	no	—
403	#468	—	2	1	no	—
404	#466	—	2	1	no	—
405	#465	—	2	1	no	—
406	#452	—	2	1	no	—
407	#452	—	2	1	no	—
408	#449	—	2	1	no	—
409	#449	—	2	1	no	—
410	#449	—	2	1	no	—
411	#449	—	2	1	no	—
412	#449	—	2	1	no	—
413	#449	—	2	1	no	—
414	#436	—	2	1	no	—
415	#435	—	2	1	no	—
416	#435	—	2	1	no	—
417	C₈×D₄	—	2	1	no	—
418	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
420	#428	C₂²×C₁₃	1	1	yes	characteristic
421	#424	C₂²×C₁₃	1	1	yes	characteristic
422	#419	C₂²×C₁₃	1	1	yes	characteristic
423	#418	C₂²×C₁₃	1	1	yes	characteristic
424	#418	C₂²×C₁₃	1	1	yes	characteristic
425	#417	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
428	#413	—	2	4	no	—
429	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
435	#408	C₂²×C₁₃	1	1	yes	characteristic
436	#407	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
438	#405	C₂²×C₁₃	1	1	yes	characteristic
439	#343	C₂²×C₁₃	1	1	yes	characteristic
440	#343	C₂²×C₁₃	1	1	yes	characteristic
441	#341	C₂²×C₁₃	1	1	yes	characteristic
442	#341	C₂²×C₁₃	1	1	yes	characteristic
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	1	no	—
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	4	1	no	—
455	C₂²×C₁₃	—	8	1	no	—
456	C₂²×C₁₃	—	8	1	no	—
457	C₂²×C₁₃	—	8	2	no	—
458	C₂²×C₁₃	—	8	2	no	—
459	C₂²×C₁₃	—	8	1	no	—
460	C₂²×C₁₃	—	8	1	no	—
461	C₂²×C₁₃	—	8	1	no	—
462	C₂²×C₁₃	—	8	1	no	—
463	C₂²×C₁₃	—	8	1	no	—
464	C₂²×C₁₃	—	16	1	no	—
465	C₂²×C₁₃	—	16	1	no	—
466	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
467	C₂²×C₁₃	#525	1	1	yes	characteristic
468	C₂²×C₁₃	#538	1	1	yes	characteristic
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	1	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	—	4	1	no	—
475	C₄×C₁₃	—	8	1	no	—
476	C₄×C₁₃	D₄²	1	1	yes	characteristic
477	C₄×C₁₃	D₄²	1	1	yes	characteristic
478	C₄×C₁₃	#546	1	1	yes	characteristic
479	C₄×C₁₃	#546	1	1	yes	characteristic
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	2	1	no	—
483	C₂×#41	—	2	1	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	—	4	1	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂³×C₄	—	2	1	no	—
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	#137	—	2	2	no	—
497	#137	—	4	1	no	—
498	AGL(1,ℤ/8)	—	2	2	no	—
499	AGL(1,ℤ/8)	—	2	2	no	—
500	AGL(1,ℤ/8)	—	4	1	no	—
501	AGL(1,ℤ/8)	—	4	1	no	—
502	C₂×Q₁₆	—	2	1	no	—
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	1	no	—
505	C₂×SD₁₆	—	2	1	no	—
506	C₂×SD₁₆	—	2	1	no	—
507	C₂×SD₁₆	—	2	1	no	—
508	C₂×SD₁₆	—	2	1	no	—
509	C₂×SD₁₆	—	4	1	no	—
510	C₂×D₈	—	2	1	no	—
511	C₂×D₈	—	2	1	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	2	1	no	—
514	C₂×D₈	—	2	1	no	—
515	C₂×D₈	—	4	1	no	—
516	#131	—	2	2	no	—
517	#131	—	4	1	no	—
518	C₂×M₁₆	—	2	1	no	—
519	C₂×M₁₆	—	2	1	no	—
520	C₂×M₁₆	—	2	1	no	—
521	C₂×M₁₆	—	2	2	no	—
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	4	1	no	—
524	C₂×M₁₆	—	4	1	no	—
525	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
527	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
530	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×C₈	—	2	1	no	—
532	C₂²×C₈	—	2	1	no	—
533	C₂²×C₈	—	2	1	no	—
534	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
536	#123	—	2	1	no	—
537	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
538	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	D₄×C₁₃	1	1	yes	characteristic
544	#121	D₄×C₁₃	1	1	yes	characteristic
545	#120	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	#117	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	#108	—	2	2	no	—
552	#108	—	4	1	no	—
553	#107	—	2	1	no	—
554	#106	—	2	1	no	—
555	C₄⋊C₈	—	2	1	no	—
556	C₄⋊C₈	—	2	1	no	—
557	#103	—	2	1	no	—
558	#103	—	2	1	no	—
559	#103	—	2	1	no	—
560	#103	—	2	1	no	—
561	#103	—	2	1	no	—
562	#102	—	2	1	no	—
563	#102	—	2	1	no	—
564	#102	—	2	1	no	—
565	#102	—	2	1	no	—
566	#102	—	2	1	no	—
567	#102	—	2	1	no	—
568	#102	—	2	1	no	—
569	#101	—	2	2	no	—
570	#101	D₄×C₁₃	1	4	yes	complemented
571	#100	—	2	2	no	—
572	#100	—	2	2	no	—
573	#100	—	2	2	no	—
574	#100	—	4	1	no	—
575	C₂²⋊C₈	—	2	1	no	—
576	C₂²⋊C₈	—	2	1	no	—
577	C₂²⋊C₈	—	2	1	no	—
578	C₂²⋊C₈	—	2	1	no	—
579	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
580	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
581	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
582	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
583	#97	—	2	1	no	—
584	C₄×C₈	—	2	1	no	—
585	C₂×C₁₃	—	2	1	no	—
586	C₂×C₁₃	—	2	1	no	—
587	C₂×C₁₃	—	4	1	no	—
588	C₂×C₁₃	—	4	1	no	—
589	C₂×C₁₃	—	8	1	no	—
590	C₂×C₁₃	—	8	2	no	—
591	C₂×C₁₃	—	16	1	no	—
592	C₂×C₁₃	#2424	1	1	yes	characteristic
593	C₂×C₁₃	#3067	1	1	yes	characteristic
594	C₂×C₁₃	#3068	1	1	yes	characteristic
595	C₂⁴	—	2	1	no	—
596	C₂⁴	—	2	1	no	—
597	C₂⁴	C₁₃×#41	1	1	yes	characteristic
598	#41	—	2	1	no	—
599	#41	—	2	1	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	4	2	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	2	no	—
606	#41	—	4	2	no	—
607	#41	—	4	2	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
616	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	8	2	no	—
638	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂×D₄	C₁₃×#41	1	2	yes	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	Q₁₆	—	4	2	no	—
658	SD₁₆	—	4	2	no	—
659	SD₁₆	—	4	2	no	—
660	SD₁₆	—	4	2	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	2	no	—
663	D₈	—	4	2	no	—
664	D₈	—	4	2	no	—
665	D₈	—	4	2	no	—
666	D₈	—	4	2	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	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	4	2	no	—
678	M₁₆	—	4	2	no	—
679	M₁₆	—	4	2	no	—
680	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
681	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	4	2	no	—
693	C₂×C₈	—	4	2	no	—
694	C₂×C₈	—	4	2	no	—
695	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	4	1	no	—
711	C₂²⋊C₄	—	4	1	no	—
712	C₄²	—	2	1	no	—
713	C₁₃	#25147	1	1	yes	characteristic, direct product factor, Sylow
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	C₁₃×#121	1	1	yes	characteristic
730	C₂³	C₁₃×#121	1	1	yes	characteristic
731	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
732	Q₈	—	2	1	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	2	2	no	—
735	Q₈	—	2	1	no	—
736	Q₈	—	4	1	no	—
737	Q₈	—	4	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	1	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	1	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	8	1	no	—
754	D₄	—	8	2	no	—
755	D₄	—	8	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	8	1	no	—
778	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
779	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
784	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
785	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
786	C₈	—	2	1	no	—
787	C₈	—	2	1	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₈	—	2	1	no	—
791	C₈	—	2	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	2	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	1	no	—
813	C₂²	—	8	1	no	—
814	C₂²	—	8	1	no	—
815	C₂²	—	8	1	no	—
816	C₂²	—	8	1	no	—
817	C₂²	—	16	1	no	—
818	C₂²	—	16	1	no	—
819	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
820	C₂²	C₁₃×#525	1	1	yes	characteristic
821	C₂²	C₁₃×#538	1	1	yes	characteristic
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	8	1	no	—
829	C₄	D₄²×C₁₃	1	1	yes	characteristic
830	C₄	D₄²×C₁₃	1	1	yes	characteristic
831	C₄	C₁₃×#546	1	1	yes	characteristic
832	C₄	C₁₃×#546	1	1	yes	characteristic
833	C₂	—	2	1	no	—
834	C₂	—	2	1	no	—
835	C₂	—	4	1	no	—
836	C₂	—	4	1	no	—
837	C₂	—	8	1	no	—
838	C₂	—	8	2	no	—
839	C₂	—	16	1	no	—
840	C₂	C₁₃×#2424	1	1	yes	characteristic
841	C₂	C₁₃×#3067	1	1	yes	characteristic
842	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#471	C₂	semidirect
2. C₁₃×#3055	C₂	semidirect
3. C₁₃×#3005	C₂	semidirect
4. C₂×C₁₃×#449	C₂	semidirect
5. C₁₃×#2933	C₂	semidirect
6. C₂×C₁₃×#413	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2052	C₂	semidirect
9. C₁₃×#2046	C₂	semidirect
10. C₁₃×#2018	C₂	semidirect
11. C₁₃×#1978	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1907	C₂	semidirect
14. C₁₃×#1900	C₂	semidirect
15. C₁₃×#1855	C₂	semidirect
159. C₁₃×#101	D₄	semidirect
174. #25147	C₁₃	direct (N × H)
293. C₂×#471	C₂×C₁₃	semidirect
294. #3055	C₂×C₁₃	semidirect
295. #3005	C₂×C₁₃	semidirect
296. C₂×#449	C₂×C₁₃	semidirect
297. #2933	C₂×C₁₃	semidirect
298. C₂×#413	C₂×C₁₃	semidirect
299. #2063	C₂×C₁₃	semidirect
300. #2052	C₂×C₁₃	semidirect
301. #2046	C₂×C₁₃	semidirect
302. #2018	C₂×C₁₃	semidirect
303. #1978	C₂×C₁₃	semidirect
304. #1930	C₂×C₁₃	semidirect
305. #1907	C₂×C₁₃	semidirect
306. #1900	C₂×C₁₃	semidirect
307. #1855	C₂×C₁₃	semidirect
570. #101	D₄×C₁₃	semidirect
713. C₁₃	#25147	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#471	2
C₁₃×#3055	2
C₁₃×#3005	2
C₂×C₁₃×#449	2
C₁₃×#2933	2
C₂×C₁₃×#413	2
C₁₃×#2063	2
C₁₃×#2052	2
C₁₃×#2046	2
C₁₃×#2018	2
C₁₃×#1978	2
C₁₃×#1930	2
C₁₃×#1907	2
C₁₃×#1900	2
C₁₃×#1855	2
#25147	13

Subgroups — C13×#25147 #15711486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25147 #15711486