Subgroups — C₁₃×#25144 #15711483

Order 3328.

1114 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	C₂×C₁₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3003	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
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×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₃×#471	—	2	4	no	—
28	C₁₃×#470	—	2	1	no	—
29	C₁₃×#468	—	2	1	no	—
30	C₁₃×#467	—	2	1	no	—
31	C₁₃×#465	—	2	1	no	—
32	C₁₃×#450	—	2	1	no	—
33	C₁₃×#450	—	2	1	no	—
34	C₁₃×#450	—	2	1	no	—
35	C₁₃×#450	—	2	1	no	—
36	C₁₃×#450	—	2	1	no	—
37	C₁₃×#450	—	2	1	no	—
38	C₁₃×#447	—	2	1	no	—
39	C₁₃×#447	—	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, complemented
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#100	—	2	4	no	—
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, complemented
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, complemented
65	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₁₃	—	2	1	no	—
70	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	4	1	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#137	—	2	2	no	—
85	C₁₃×#137	—	4	1	no	—
86	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₂×C₁₃×Q₁₆	—	2	1	no	—
91	C₂×C₁₃×SD₁₆	—	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	2	no	—
96	C₂×C₁₃×SD₁₆	—	2	1	no	—
97	C₂×C₁₃×SD₁₆	—	2	1	no	—
98	C₂×C₁₃×SD₁₆	—	2	1	no	—
99	C₂×C₁₃×SD₁₆	—	2	1	no	—
100	C₂×C₁₃×SD₁₆	—	4	1	no	—
101	C₂×C₁₃×SD₁₆	—	4	1	no	—
102	C₂×C₁₃×D₈	—	2	1	no	—
103	C₂×C₁₃×D₈	—	2	1	no	—
104	C₁₃×#131	—	2	2	no	—
105	C₁₃×#131	—	4	1	no	—
106	C₂×C₁₃×M₁₆	—	2	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	—	2	1	no	—
109	C₂×C₁₃×M₁₆	—	2	2	no	—
110	C₂×C₁₃×M₁₆	—	2	2	no	—
111	C₂×C₁₃×M₁₆	—	4	1	no	—
112	C₂×C₁₃×M₁₆	—	4	1	no	—
113	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₃	—	2	1	no	—
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₂²×C₈×C₁₃	—	2	1	no	—
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#123	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₁₃×#121	D₄	1	1	yes	characteristic
132	C₁₃×#121	D₄	1	1	yes	characteristic
133	C₁₃×#120	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₁₃×#117	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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×#102	—	2	1	no	—
150	C₁₃×#102	—	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	—	4	1	no	—
160	C₁₃×#100	—	2	2	no	—
161	C₁₃×#100	—	2	2	no	—
162	C₁₃×#100	—	2	2	no	—
163	C₁₃×#100	D₄	1	4	yes	complemented
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	#25144	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	—	2	4	no	—
176	C₂⁴×C₁₃	—	2	1	no	—
177	C₂⁴×C₁₃	—	2	1	no	—
178	C₂⁴×C₁₃	—	4	2	no	—
179	C₂⁴×C₁₃	—	4	1	no	—
180	C₂⁴×C₁₃	—	4	1	no	—
181	C₂⁴×C₁₃	—	8	2	no	—
182	C₂⁴×C₁₃	—	8	2	no	—
183	C₂⁴×C₁₃	#41	1	1	yes	characteristic
184	C₁₃×#41	—	2	1	no	—
185	C₁₃×#41	—	2	1	no	—
186	C₁₃×#41	—	2	1	no	—
187	C₁₃×#41	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	1	no	—
197	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
210	C₂×D₄×C₁₃	—	4	2	no	—
211	C₂×D₄×C₁₃	—	4	2	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	4	2	no	—
218	C₂×D₄×C₁₃	—	4	1	no	—
219	C₂×D₄×C₁₃	—	4	1	no	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	1	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	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×Q₁₆	—	4	2	no	—
237	C₁₃×SD₁₆	—	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×SD₁₆	—	4	2	no	—
244	C₁₃×D₈	—	4	2	no	—
245	C₁₃×D₈	—	4	2	no	—
246	C₁₃×M₁₆	—	2	1	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	—	4	2	no	—
257	C₁₃×M₁₆	—	4	2	no	—
258	C₁₃×M₁₆	—	4	2	no	—
259	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
260	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₁₃	—	2	1	no	—
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	—	4	2	no	—
272	C₂×C₈×C₁₃	—	4	2	no	—
273	C₂×C₈×C₁₃	—	4	2	no	—
274	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
283	C₁₃×C₄⋊C₄	—	4	1	no	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	4	1	no	—
292	C₁₃×C₂²⋊C₄	—	4	1	no	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₂×#471	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3056	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3003	C₂×C₁₃	1	1	yes	characteristic
297	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2933	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂²×#100	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1907	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂³×C₁₃	—	2	1	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	2	2	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	—	4	4	no	—
317	C₂³×C₁₃	—	4	4	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	8	2	no	—
323	C₂³×C₁₃	—	8	2	no	—
324	C₂³×C₁₃	—	8	2	no	—
325	C₂³×C₁₃	—	8	1	no	—
326	C₂³×C₁₃	—	8	1	no	—
327	C₂³×C₁₃	—	8	1	no	—
328	C₂³×C₁₃	—	8	1	no	—
329	C₂³×C₁₃	—	8	8	no	—
330	C₂³×C₁₃	—	8	8	no	—
331	C₂³×C₁₃	—	8	2	no	—
332	C₂³×C₁₃	#121	1	1	yes	characteristic
333	C₂³×C₁₃	#121	1	1	yes	characteristic
334	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
335	Q₈×C₁₃	—	2	1	no	—
336	Q₈×C₁₃	—	2	1	no	—
337	Q₈×C₁₃	—	4	1	no	—
338	Q₈×C₁₃	—	4	1	no	—
339	Q₈×C₁₃	—	4	1	no	—
340	Q₈×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	2	1	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	2	no	—
344	D₄×C₁₃	—	2	1	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	4	4	no	—
348	D₄×C₁₃	—	4	4	no	—
349	D₄×C₁₃	—	4	1	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	4	2	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	1	no	—
354	D₄×C₁₃	—	4	1	no	—
355	D₄×C₁₃	—	4	1	no	—
356	D₄×C₁₃	—	8	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	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	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	1	no	—
376	C₂×C₄×C₁₃	—	8	1	no	—
377	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
378	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
383	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
385	C₈×C₁₃	—	2	1	no	—
386	C₈×C₁₃	—	2	1	no	—
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	2	2	no	—
389	C₈×C₁₃	—	2	1	no	—
390	C₈×C₁₃	—	2	1	no	—
391	C₈×C₁₃	—	4	1	no	—
392	C₈×C₁₃	—	4	1	no	—
393	C₈×C₁₃	—	4	1	no	—
394	C₈×C₁₃	—	4	1	no	—
395	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
399	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
400	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
402	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
404	#525	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
406	#471	—	2	4	no	—
407	#470	—	2	1	no	—
408	#468	—	2	1	no	—
409	#467	—	2	1	no	—
410	#465	—	2	1	no	—
411	#450	—	2	1	no	—
412	#450	—	2	1	no	—
413	#450	—	2	1	no	—
414	#450	—	2	1	no	—
415	#450	—	2	1	no	—
416	#450	—	2	1	no	—
417	#447	—	2	1	no	—
418	#447	—	2	1	no	—
419	#436	—	2	1	no	—
420	#435	—	2	1	no	—
421	#435	—	2	1	no	—
422	C₈×D₄	—	2	1	no	—
423	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#418	C₂²×C₁₃	1	1	yes	characteristic
429	#418	C₂²×C₁₃	1	1	yes	characteristic
430	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	C₂×#100	—	2	4	no	—
436	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
440	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#407	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
443	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#341	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	2	1	no	—
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	4	2	no	—
456	C₂²×C₁₃	—	4	2	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	1	no	—
462	C₂²×C₁₃	—	8	2	no	—
463	C₂²×C₁₃	—	8	2	no	—
464	C₂²×C₁₃	—	8	8	no	—
465	C₂²×C₁₃	—	8	2	no	—
466	C₂²×C₁₃	—	8	2	no	—
467	C₂²×C₁₃	—	8	8	no	—
468	C₂²×C₁₃	—	8	1	no	—
469	C₂²×C₁₃	—	8	1	no	—
470	C₂²×C₁₃	—	8	1	no	—
471	C₂²×C₁₃	—	8	1	no	—
472	C₂²×C₁₃	#471	1	2	yes	complemented
473	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
474	C₂²×C₁₃	#525	1	1	yes	characteristic
475	C₂²×C₁₃	#538	1	1	yes	characteristic
476	C₄×C₁₃	—	2	1	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	8	1	no	—
482	C₄×C₁₃	—	8	1	no	—
483	C₄×C₁₃	D₄²	1	1	yes	characteristic
484	C₄×C₁₃	D₄²	1	1	yes	characteristic
485	C₄×C₁₃	#546	1	1	yes	characteristic
486	C₄×C₁₃	#546	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×D₄	—	2	2	no	—
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
502	#137	—	2	2	no	—
503	#137	—	4	1	no	—
504	AGL(1,ℤ/8)	—	2	2	no	—
505	AGL(1,ℤ/8)	—	2	2	no	—
506	AGL(1,ℤ/8)	—	4	1	no	—
507	AGL(1,ℤ/8)	—	4	1	no	—
508	C₂×Q₁₆	—	2	1	no	—
509	C₂×SD₁₆	—	2	1	no	—
510	C₂×SD₁₆	—	2	1	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	2	no	—
514	C₂×SD₁₆	—	2	1	no	—
515	C₂×SD₁₆	—	2	1	no	—
516	C₂×SD₁₆	—	2	1	no	—
517	C₂×SD₁₆	—	2	1	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂×D₈	—	2	1	no	—
521	C₂×D₈	—	2	1	no	—
522	#131	—	2	2	no	—
523	#131	—	4	1	no	—
524	C₂×M₁₆	—	2	1	no	—
525	C₂×M₁₆	—	2	1	no	—
526	C₂×M₁₆	—	2	1	no	—
527	C₂×M₁₆	—	2	2	no	—
528	C₂×M₁₆	—	2	2	no	—
529	C₂×M₁₆	—	4	1	no	—
530	C₂×M₁₆	—	4	1	no	—
531	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
536	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×C₈	—	2	1	no	—
538	C₂²×C₈	—	2	1	no	—
539	C₂²×C₈	—	2	1	no	—
540	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
542	#123	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
548	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
549	#121	D₄×C₁₃	1	1	yes	characteristic
550	#121	D₄×C₁₃	1	1	yes	characteristic
551	#120	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	#117	C₂³×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	#108	—	2	2	no	—
559	#108	—	4	1	no	—
560	#107	—	2	1	no	—
561	#106	—	2	1	no	—
562	C₄⋊C₈	—	2	1	no	—
563	C₄⋊C₈	—	2	1	no	—
564	#103	—	2	1	no	—
565	#103	—	2	1	no	—
566	#103	—	2	1	no	—
567	#102	—	2	1	no	—
568	#102	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	#102	—	2	1	no	—
573	#102	—	2	1	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#101	—	2	2	no	—
577	#101	—	4	1	no	—
578	#100	—	2	2	no	—
579	#100	—	2	2	no	—
580	#100	—	2	2	no	—
581	#100	D₄×C₁₃	1	4	yes	complemented
582	C₂²⋊C₈	—	2	1	no	—
583	C₂²⋊C₈	—	2	1	no	—
584	C₂²⋊C₈	—	2	1	no	—
585	C₂²⋊C₈	—	2	1	no	—
586	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
587	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
588	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
589	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
590	#97	—	2	1	no	—
591	C₄×C₈	—	2	1	no	—
592	C₂×C₁₃	—	2	1	no	—
593	C₂×C₁₃	—	2	1	no	—
594	C₂×C₁₃	—	2	2	no	—
595	C₂×C₁₃	—	4	1	no	—
596	C₂×C₁₃	—	8	1	no	—
597	C₂×C₁₃	—	8	2	no	—
598	C₂×C₁₃	—	8	2	no	—
599	C₂×C₁₃	#2424	1	1	yes	characteristic
600	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
601	C₂×C₁₃	#3068	1	1	yes	characteristic
602	C₂⁴	—	2	4	no	—
603	C₂⁴	—	2	1	no	—
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	4	2	no	—
606	C₂⁴	—	4	1	no	—
607	C₂⁴	—	4	1	no	—
608	C₂⁴	—	8	2	no	—
609	C₂⁴	—	8	2	no	—
610	C₂⁴	C₁₃×#41	1	1	yes	characteristic
611	#41	—	2	1	no	—
612	#41	—	2	1	no	—
613	#41	—	2	1	no	—
614	#41	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂×D₄	—	2	4	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	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂×D₄	—	4	2	no	—
645	C₂×D₄	—	4	1	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
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	1	no	—
652	C₂²×C₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
663	Q₁₆	—	4	2	no	—
664	SD₁₆	—	4	2	no	—
665	SD₁₆	—	4	2	no	—
666	SD₁₆	—	4	2	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	2	no	—
669	SD₁₆	—	4	2	no	—
670	SD₁₆	—	4	2	no	—
671	D₈	—	4	2	no	—
672	D₈	—	4	2	no	—
673	M₁₆	—	2	1	no	—
674	M₁₆	—	2	1	no	—
675	M₁₆	—	2	1	no	—
676	M₁₆	—	2	1	no	—
677	M₁₆	—	2	1	no	—
678	M₁₆	—	2	1	no	—
679	M₁₆	—	2	1	no	—
680	M₁₆	—	2	1	no	—
681	M₁₆	—	2	1	no	—
682	M₁₆	—	2	1	no	—
683	M₁₆	—	4	2	no	—
684	M₁₆	—	4	2	no	—
685	M₁₆	—	4	2	no	—
686	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
687	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
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	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	4	2	no	—
699	C₂×C₈	—	4	2	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	4	1	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₄²	—	2	1	no	—
721	C₁₃	#25144	1	1	yes	characteristic, direct product factor, Sylow
722	C₂³	—	2	2	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	4	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	1	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	1	no	—
738	C₂³	—	8	1	no	—
739	C₂³	—	8	2	no	—
740	C₂³	—	8	2	no	—
741	C₂³	—	8	2	no	—
742	C₂³	—	8	8	no	—
743	C₂³	—	8	8	no	—
744	C₂³	—	8	2	no	—
745	C₂³	C₁₃×#121	1	1	yes	characteristic
746	C₂³	C₁₃×#121	1	1	yes	characteristic
747	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	4	1	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	4	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	1	no	—
764	D₄	—	4	1	no	—
765	D₄	—	4	1	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	8	1	no	—
770	C₂×C₄	—	2	1	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	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	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	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
791	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
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	C₂×C₁₃×#41	1	1	yes	characteristic
796	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
798	C₈	—	2	1	no	—
799	C₈	—	2	1	no	—
800	C₈	—	2	2	no	—
801	C₈	—	2	2	no	—
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	4	1	no	—
805	C₈	—	4	1	no	—
806	C₈	—	4	1	no	—
807	C₈	—	4	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	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	8	no	—
825	C₂²	—	8	2	no	—
826	C₂²	—	8	2	no	—
827	C₂²	—	8	8	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	1	no	—
832	C₂²	C₁₃×#471	1	2	yes	complemented
833	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
834	C₂²	C₁₃×#525	1	1	yes	characteristic
835	C₂²	C₁₃×#538	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	—	8	1	no	—
842	C₄	—	8	1	no	—
843	C₄	D₄²×C₁₃	1	1	yes	characteristic
844	C₄	D₄²×C₁₃	1	1	yes	characteristic
845	C₄	C₁₃×#546	1	1	yes	characteristic
846	C₄	C₁₃×#546	1	1	yes	characteristic
847	C₂	—	2	2	no	—
848	C₂	—	2	1	no	—
849	C₂	—	2	1	no	—
850	C₂	—	4	1	no	—
851	C₂	—	8	1	no	—
852	C₂	—	8	2	no	—
853	C₂	—	8	2	no	—
854	C₂	C₁₃×#2424	1	1	yes	characteristic
855	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
856	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3003	C₂
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×#3056	C₂	semidirect
4. C₂×C₁₃×#450	C₂	semidirect
5. C₁₃×#2933	C₂	semidirect
6. C₂²×C₁₃×#100	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2051	C₂	semidirect
9. C₁₃×#2046	C₂	semidirect
10. C₁₃×#2019	C₂	semidirect
11. C₁₃×#1977	C₂	semidirect
12. C₁₃×#1931	C₂	semidirect
13. C₁₃×#1907	C₂	semidirect
14. C₁₃×#1901	C₂	semidirect
15. C₁₃×#1855	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×#131	C₂²	semidirect
44. C₂×C₁₃×#108	C₂²	semidirect
45. C₂×C₁₃×#108	C₂²	semidirect
46. C₁₃×#428	C₂²	semidirect
47. C₁₃×#424	C₂²	semidirect
48. C₁₃×#419	C₂²	semidirect
51. C₁₃×#417	C₂²	semidirect
54. C₂×C₁₃×#101	C₂²	semidirect
55. C₂×C₁₃×#101	C₂²	semidirect
61. C₁₃×#408	C₂²	semidirect
64. C₁₃×#405	C₂²	semidirect
65. C₁₃×#343	C₂²	semidirect
66. C₁₃×#343	C₂²	semidirect
67. C₁₃×#341	C₂²	semidirect
68. C₁₃×#341	C₂²	semidirect
163. C₁₃×#100	D₄	semidirect
174. #25144	C₁₃	direct (N × H)
294. C₂×#471	C₂×C₁₃	semidirect
295. #3056	C₂×C₁₃	semidirect
297. C₂×#450	C₂×C₁₃	semidirect
298. #2933	C₂×C₁₃	semidirect
299. C₂²×#100	C₂×C₁₃	semidirect
300. #2063	C₂×C₁₃	semidirect
301. #2051	C₂×C₁₃	semidirect
302. #2046	C₂×C₁₃	semidirect
303. #2019	C₂×C₁₃	semidirect
304. #1977	C₂×C₁₃	semidirect
305. #1931	C₂×C₁₃	semidirect
306. #1907	C₂×C₁₃	semidirect
307. #1901	C₂×C₁₃	semidirect
308. #1855	C₂×C₁₃	semidirect
396. C₂×#137	C₂²×C₁₃	semidirect
401. C₂×#131	C₂²×C₁₃	semidirect
423. C₂×#108	C₂²×C₁₃	semidirect
424. C₂×#108	C₂²×C₁₃	semidirect
425. #428	C₂²×C₁₃	semidirect
426. #424	C₂²×C₁₃	semidirect
427. #419	C₂²×C₁₃	semidirect
430. #417	C₂²×C₁₃	semidirect
433. C₂×#101	C₂²×C₁₃	semidirect
434. C₂×#101	C₂²×C₁₃	semidirect
440. #408	C₂²×C₁₃	semidirect
443. #405	C₂²×C₁₃	semidirect
444. #343	C₂²×C₁₃	semidirect
445. #343	C₂²×C₁₃	semidirect
446. #341	C₂²×C₁₃	semidirect
447. #341	C₂²×C₁₃	semidirect
472. C₂²×C₁₃	#471	semidirect
581. #100	D₄×C₁₃	semidirect
721. C₁₃	#25144	direct (N × H)
832. C₂²	C₁₃×#471	semidirect

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×#3056	2
C₁₃×#3003	2
C₂×C₁₃×#450	2
C₁₃×#2933	2
C₂²×C₁₃×#100	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#2046	2
C₁₃×#2019	2
C₁₃×#1977	2
C₁₃×#1931	2
C₁₃×#1907	2
C₁₃×#1901	2
C₁₃×#1855	2
#25144	13

Subgroups — C13×#25144 #15711483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25144 #15711483