Subgroups — C₁₃×#25146 #15711485

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 830 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
3	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	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×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1908	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	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	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
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×#451	—	2	1	no	—
33	C₁₃×#451	—	2	1	no	—
34	C₁₃×#448	—	2	1	no	—
35	C₁₃×#448	—	2	1	no	—
36	C₁₃×#448	—	2	1	no	—
37	C₁₃×#448	—	2	1	no	—
38	C₁₃×#448	—	2	1	no	—
39	C₁₃×#448	—	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×#419	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×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	—	2	4	no	—
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	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	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	—	2	2	no	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂²×Q₈×C₁₃	—	2	1	no	—
74	C₂²×Q₈×C₁₃	—	2	1	no	—
75	C₂²×Q₈×C₁₃	—	2	1	no	—
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	—	4	1	no	—
78	C₂²×Q₈×C₁₃	—	4	1	no	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃	—	2	1	no	—
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	—	2	2	no	—
87	C₁₃×#137	—	4	1	no	—
88	C₁₃×#137	—	4	1	no	—
89	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
90	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×C₁₃×Q₁₆	—	2	1	no	—
92	C₂×C₁₃×Q₁₆	—	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	—	2	1	no	—
101	C₂×C₁₃×SD₁₆	—	2	1	no	—
102	C₂×C₁₃×SD₁₆	—	4	1	no	—
103	C₂×C₁₃×SD₁₆	—	4	1	no	—
104	C₂×C₁₃×D₈	—	2	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×#103	—	2	1	no	—
152	C₁₃×#103	—	2	1	no	—
153	C₁₃×#103	—	2	1	no	—
154	C₁₃×#103	—	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	—	2	2	no	—
160	C₁₃×#101	—	2	2	no	—
161	C₁₃×#101	D₄	1	4	yes	complemented
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	#25146	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	—	2	1	no	—
176	C₂⁴×C₁₃	#41	1	1	yes	characteristic
177	C₁₃×#41	—	2	1	no	—
178	C₁₃×#41	—	2	1	no	—
179	C₁₃×#41	—	2	1	no	—
180	C₁₃×#41	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	4	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	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	—	4	2	no	—
193	C₂×Q₈×C₁₃	—	4	2	no	—
194	C₂×Q₈×C₁₃	—	4	2	no	—
195	C₂×Q₈×C₁₃	—	4	2	no	—
196	C₂×Q₈×C₁₃	—	4	2	no	—
197	C₂×Q₈×C₁₃	—	4	2	no	—
198	C₂×Q₈×C₁₃	—	4	2	no	—
199	C₂×Q₈×C₁₃	—	4	2	no	—
200	C₂×Q₈×C₁₃	—	4	2	no	—
201	C₂×Q₈×C₁₃	—	4	1	no	—
202	C₂×Q₈×C₁₃	—	4	1	no	—
203	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	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	C₂²×C₄×C₁₃	—	2	1	no	—
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	4	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	—	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×Q₁₆	—	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×SD₁₆	—	4	2	no	—
245	C₁₃×SD₁₆	—	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
295	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
296	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2933	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂²×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2064	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	#2019	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1908	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	2	no	—
311	C₂³×C₁₃	—	2	1	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	—	8	1	no	—
317	C₂³×C₁₃	—	8	1	no	—
318	C₂³×C₁₃	#121	1	1	yes	characteristic
319	C₂³×C₁₃	#121	1	1	yes	characteristic
320	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
321	Q₈×C₁₃	—	2	1	no	—
322	Q₈×C₁₃	—	2	2	no	—
323	Q₈×C₁₃	—	2	2	no	—
324	Q₈×C₁₃	—	2	2	no	—
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	2	1	no	—
327	Q₈×C₁₃	—	4	4	no	—
328	Q₈×C₁₃	—	4	4	no	—
329	Q₈×C₁₃	—	4	1	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	Q₈×C₁₃	—	4	1	no	—
332	Q₈×C₁₃	—	4	1	no	—
333	D₄×C₁₃	—	2	1	no	—
334	D₄×C₁₃	—	2	1	no	—
335	D₄×C₁₃	—	4	1	no	—
336	D₄×C₁₃	—	4	1	no	—
337	D₄×C₁₃	—	4	2	no	—
338	D₄×C₁₃	—	4	1	no	—
339	D₄×C₁₃	—	4	1	no	—
340	D₄×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	4	1	no	—
342	D₄×C₁₃	—	8	1	no	—
343	D₄×C₁₃	—	8	2	no	—
344	D₄×C₁₃	—	8	2	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	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	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	4	4	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	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	—	8	1	no	—
370	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
371	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
376	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
378	C₈×C₁₃	—	2	1	no	—
379	C₈×C₁₃	—	2	1	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	—	2	2	no	—
382	C₈×C₁₃	—	2	1	no	—
383	C₈×C₁₃	—	2	1	no	—
384	C₈×C₁₃	—	4	1	no	—
385	C₈×C₁₃	—	4	1	no	—
386	C₈×C₁₃	—	4	1	no	—
387	C₈×C₁₃	—	4	1	no	—
388	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
392	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
395	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
397	#525	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
399	#471	—	2	4	no	—
400	#469	—	2	1	no	—
401	#468	—	2	1	no	—
402	#466	—	2	1	no	—
403	#465	—	2	1	no	—
404	#451	—	2	1	no	—
405	#451	—	2	1	no	—
406	#448	—	2	1	no	—
407	#448	—	2	1	no	—
408	#448	—	2	1	no	—
409	#448	—	2	1	no	—
410	#448	—	2	1	no	—
411	#448	—	2	1	no	—
412	#436	—	2	1	no	—
413	#435	—	2	1	no	—
414	#435	—	2	1	no	—
415	C₈×D₄	—	2	1	no	—
416	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
418	#428	C₂²×C₁₃	1	1	yes	characteristic
419	#424	C₂²×C₁₃	1	1	yes	characteristic
420	#419	C₂²×C₁₃	1	1	yes	characteristic
421	#419	C₂²×C₁₃	1	1	yes	characteristic
422	#418	C₂²×C₁₃	1	1	yes	characteristic
423	#417	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#101	—	2	4	no	—
427	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
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	#408	C₂²×C₁₃	1	1	yes	characteristic
434	#407	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
436	#405	C₂²×C₁₃	1	1	yes	characteristic
437	#343	C₂²×C₁₃	1	1	yes	characteristic
438	#343	C₂²×C₁₃	1	1	yes	characteristic
439	#341	C₂²×C₁₃	1	1	yes	characteristic
440	#341	C₂²×C₁₃	1	1	yes	characteristic
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
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	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	8	1	no	—
454	C₂²×C₁₃	—	8	1	no	—
455	C₂²×C₁₃	—	8	1	no	—
456	C₂²×C₁₃	—	16	1	no	—
457	C₂²×C₁₃	—	16	1	no	—
458	C₂²×C₁₃	#471	1	2	yes	complemented
459	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
460	C₂²×C₁₃	#525	1	1	yes	characteristic
461	C₂²×C₁₃	#538	1	1	yes	characteristic
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	2	1	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	1	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	8	1	no	—
470	C₄×C₁₃	D₄²	1	1	yes	characteristic
471	C₄×C₁₃	D₄²	1	1	yes	characteristic
472	C₄×C₁₃	#546	1	1	yes	characteristic
473	C₄×C₁₃	#546	1	1	yes	characteristic
474	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×Q₈	—	2	2	no	—
476	C₂²×Q₈	—	2	2	no	—
477	C₂²×Q₈	—	2	1	no	—
478	C₂²×Q₈	—	2	1	no	—
479	C₂²×Q₈	—	2	1	no	—
480	C₂²×Q₈	—	2	1	no	—
481	C₂²×Q₈	—	2	1	no	—
482	C₂²×Q₈	—	4	1	no	—
483	C₂²×Q₈	—	4	1	no	—
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
490	#137	—	2	2	no	—
491	#137	—	2	2	no	—
492	#137	—	4	1	no	—
493	#137	—	4	1	no	—
494	AGL(1,ℤ/8)	—	2	2	no	—
495	AGL(1,ℤ/8)	—	4	1	no	—
496	C₂×Q₁₆	—	2	1	no	—
497	C₂×Q₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×SD₁₆	—	2	1	no	—
500	C₂×SD₁₆	—	2	2	no	—
501	C₂×SD₁₆	—	2	1	no	—
502	C₂×SD₁₆	—	2	1	no	—
503	C₂×SD₁₆	—	2	1	no	—
504	C₂×SD₁₆	—	2	1	no	—
505	C₂×SD₁₆	—	2	1	no	—
506	C₂×SD₁₆	—	2	1	no	—
507	C₂×SD₁₆	—	4	1	no	—
508	C₂×SD₁₆	—	4	1	no	—
509	C₂×D₈	—	2	1	no	—
510	#131	—	2	2	no	—
511	#131	—	4	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	2	no	—
516	C₂×M₁₆	—	2	2	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
521	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×C₈	—	2	1	no	—
526	C₂²×C₈	—	2	1	no	—
527	C₂²×C₈	—	2	1	no	—
528	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
530	#123	—	2	1	no	—
531	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
532	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	D₄×C₁₃	1	1	yes	characteristic
538	#121	D₄×C₁₃	1	1	yes	characteristic
539	#120	—	2	1	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	#117	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	#108	—	2	2	no	—
546	#108	—	4	1	no	—
547	#107	—	2	1	no	—
548	#106	—	2	1	no	—
549	C₄⋊C₈	—	2	1	no	—
550	C₄⋊C₈	—	2	1	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#103	—	2	1	no	—
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	—	2	1	no	—
557	#103	—	2	1	no	—
558	#103	—	2	1	no	—
559	#103	—	2	1	no	—
560	#102	—	2	1	no	—
561	#102	—	2	1	no	—
562	#102	—	2	1	no	—
563	#101	—	2	2	no	—
564	#101	—	2	2	no	—
565	#101	—	2	2	no	—
566	#101	D₄×C₁₃	1	4	yes	complemented
567	#100	—	2	2	no	—
568	#100	—	4	1	no	—
569	C₂²⋊C₈	—	2	1	no	—
570	C₂²⋊C₈	—	2	1	no	—
571	C₂²⋊C₈	—	2	1	no	—
572	C₂²⋊C₈	—	2	1	no	—
573	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
574	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
575	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
576	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
577	#97	—	2	1	no	—
578	C₄×C₈	—	2	1	no	—
579	C₂×C₁₃	—	2	1	no	—
580	C₂×C₁₃	—	2	1	no	—
581	C₂×C₁₃	—	2	2	no	—
582	C₂×C₁₃	—	4	1	no	—
583	C₂×C₁₃	—	8	1	no	—
584	C₂×C₁₃	—	16	1	no	—
585	C₂×C₁₃	#2424	1	1	yes	characteristic
586	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
587	C₂×C₁₃	#3069	1	1	yes	characteristic
588	C₂⁴	—	2	1	no	—
589	C₂⁴	C₁₃×#41	1	1	yes	characteristic
590	#41	—	2	1	no	—
591	#41	—	2	1	no	—
592	#41	—	2	1	no	—
593	#41	—	2	1	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	4	2	no	—
606	C₂×Q₈	—	4	2	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	1	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
617	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂×Q₈	C₁₃×#41	1	2	yes	—
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	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	8	2	no	—
631	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	4	2	no	—
642	C₂²×C₄	—	4	1	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
650	Q₁₆	—	4	2	no	—
651	Q₁₆	—	4	2	no	—
652	SD₁₆	—	4	2	no	—
653	SD₁₆	—	4	2	no	—
654	SD₁₆	—	4	2	no	—
655	SD₁₆	—	4	2	no	—
656	SD₁₆	—	4	2	no	—
657	SD₁₆	—	4	2	no	—
658	SD₁₆	—	4	2	no	—
659	D₈	—	4	2	no	—
660	M₁₆	—	2	1	no	—
661	M₁₆	—	2	1	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	4	2	no	—
671	M₁₆	—	4	2	no	—
672	M₁₆	—	4	2	no	—
673	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
674	M₁₆	C₂×D₄×C₁₃	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	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	4	2	no	—
686	C₂×C₈	—	4	2	no	—
687	C₂×C₈	—	4	2	no	—
688	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	4	1	no	—
704	C₂²⋊C₄	—	4	1	no	—
705	C₄²	—	2	1	no	—
706	C₁₃	#25146	1	1	yes	characteristic, direct product factor, Sylow
707	C₂³	—	2	2	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	C₁₃×#121	1	1	yes	characteristic
718	C₂³	C₁₃×#121	1	1	yes	characteristic
719	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
720	Q₈	—	2	1	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	4	4	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	1	no	—
729	Q₈	—	4	1	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	D₄	—	2	1	no	—
733	D₄	—	2	1	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	8	1	no	—
742	D₄	—	8	2	no	—
743	D₄	—	8	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
770	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
775	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
777	C₈	—	2	1	no	—
778	C₈	—	2	1	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	16	1	no	—
803	C₂²	—	16	1	no	—
804	C₂²	C₁₃×#471	1	2	yes	complemented
805	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
806	C₂²	C₁₃×#525	1	1	yes	characteristic
807	C₂²	C₁₃×#538	1	1	yes	characteristic
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	2	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	1	no	—
815	C₄	—	8	1	no	—
816	C₄	D₄²×C₁₃	1	1	yes	characteristic
817	C₄	D₄²×C₁₃	1	1	yes	characteristic
818	C₄	C₁₃×#546	1	1	yes	characteristic
819	C₄	C₁₃×#546	1	1	yes	characteristic
820	C₂	—	2	1	no	—
821	C₂	—	2	1	no	—
822	C₂	—	2	2	no	—
823	C₂	—	4	1	no	—
824	C₂	—	8	1	no	—
825	C₂	—	16	1	no	—
826	C₂	C₁₃×#2424	1	1	yes	characteristic
827	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
828	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3055	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
3. C₁₃×#3004	C₂	semidirect
4. C₂×C₁₃×#448	C₂	semidirect
5. C₁₃×#2933	C₂	semidirect
6. C₂²×C₁₃×#101	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2052	C₂	semidirect
9. C₁₃×#2046	C₂	semidirect
10. C₁₃×#2019	C₂	semidirect
11. C₁₃×#1977	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1908	C₂	semidirect
14. C₁₃×#1900	C₂	semidirect
15. C₁₃×#1855	C₂	semidirect
161. C₁₃×#101	D₄	semidirect
174. #25146	C₁₃	direct (N × H)
293. C₂×#471	C₂×C₁₃	semidirect
295. #3004	C₂×C₁₃	semidirect
296. C₂×#448	C₂×C₁₃	semidirect
297. #2933	C₂×C₁₃	semidirect
298. C₂²×#101	C₂×C₁₃	semidirect
299. #2064	C₂×C₁₃	semidirect
300. #2052	C₂×C₁₃	semidirect
301. #2046	C₂×C₁₃	semidirect
302. #2019	C₂×C₁₃	semidirect
303. #1977	C₂×C₁₃	semidirect
304. #1930	C₂×C₁₃	semidirect
305. #1908	C₂×C₁₃	semidirect
306. #1900	C₂×C₁₃	semidirect
307. #1855	C₂×C₁₃	semidirect
458. C₂²×C₁₃	#471	semidirect
566. #101	D₄×C₁₃	semidirect
706. C₁₃	#25146	direct (N × H)
804. 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×#3055	2
C₁₃×#3004	2
C₂×C₁₃×#448	2
C₁₃×#2933	2
C₂²×C₁₃×#101	2
C₁₃×#2064	2
C₁₃×#2052	2
C₁₃×#2046	2
C₁₃×#2019	2
C₁₃×#1977	2
C₁₃×#1930	2
C₁₃×#1908	2
C₁₃×#1900	2
C₁₃×#1855	2
#25146	13

Subgroups — C13×#25146 #15711485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25146 #15711485