Subgroups — C₁₃×#24474 #15710813

Order 3328.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3586	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3069	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#456	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2050	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2009	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1902	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1902	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1861	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1796	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#585	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₁₃×#578	—	2	2	no	—
19	C₁₃×#578	—	2	2	no	—
20	C₁₃×#577	—	2	2	no	—
21	C₁₃×#577	—	2	2	no	—
22	C₁₃×#575	—	2	2	no	—
23	C₁₃×#575	C₂²	1	1	yes	characteristic
24	C₁₃×#575	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#137	—	2	2	no	—
26	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#568	C₂²	1	1	yes	characteristic
32	C₁₃×#568	C₂²	1	1	yes	characteristic
33	C₁₃×#536	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₁₃×#473	—	2	2	no	—
37	C₁₃×#471	—	2	2	no	—
38	C₁₃×#462	—	2	2	no	—
39	C₁₃×#461	—	2	2	no	—
40	C₁₃×#456	—	2	2	no	—
41	C₁₃×#456	—	2	2	no	—
42	C₁₃×#456	—	2	2	no	—
43	C₁₃×#455	—	2	2	no	—
44	C₁₃×#430	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#421	—	2	2	no	—
47	C₁₃×#421	C₂²	1	1	yes	characteristic
48	C₁₃×#421	C₂²	1	1	yes	characteristic
49	C₁₃×#421	C₂²	1	1	yes	characteristic
50	C₁₃×#421	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#104	—	2	2	no	—
52	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#413	C₂²	1	1	yes	characteristic
59	C₁₃×#413	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#410	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#344	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#344	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#338	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×2₋¹⁺⁴	—	2	2	no	—
68	C₁₃×2₋¹⁺⁴	—	2	2	no	—
69	C₁₃×2₋¹⁺⁴	—	2	1	no	—
70	C₁₃×2₋¹⁺⁴	—	2	1	no	—
71	C₁₃×2₋¹⁺⁴	—	2	2	no	—
72	C₁₃×2₋¹⁺⁴	—	4	1	no	—
73	C₁₃×2₋¹⁺⁴	D₄	1	2	yes	—
74	C₁₃×H(5,𝔽₂)	—	2	1	no	—
75	C₁₃×H(5,𝔽₂)	—	2	1	no	—
76	C₁₃×H(5,𝔽₂)	—	4	1	no	—
77	C₁₃×H(5,𝔽₂)	D₄	1	2	yes	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	1	no	—
81	C₂×C₁₃×#41	—	2	1	no	—
82	C₂×C₁₃×#41	—	4	1	no	—
83	C₂×C₁₃×#41	—	4	1	no	—
84	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	—	2	1	no	—
89	C₂²×Q₈×C₁₃	—	2	1	no	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#137	—	2	4	no	—
93	C₁₃×#137	—	2	4	no	—
94	C₁₃×#137	—	2	4	no	—
95	C₁₃×#137	—	2	2	no	—
96	C₁₃×#137	—	2	2	no	—
97	C₁₃×#137	—	2	1	no	—
98	C₁₃×#137	—	2	2	no	—
99	C₁₃×#137	—	2	1	no	—
100	C₁₃×#137	—	2	1	no	—
101	C₁₃×#137	—	2	2	no	—
102	C₁₃×#137	—	2	2	no	—
103	C₁₃×#137	—	2	2	no	—
104	C₁₃×#137	—	2	2	no	—
105	C₁₃×#137	—	2	2	no	—
106	C₁₃×#137	—	2	2	no	—
107	C₁₃×#137	—	4	1	no	—
108	C₁₃×#137	D₄	1	2	yes	—
109	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
112	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
113	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
114	C₁₃×#135	—	2	4	no	—
115	C₁₃×#135	—	2	4	no	—
116	C₁₃×#135	—	2	2	no	—
117	C₁₃×#135	—	2	2	no	—
118	C₂×C₁₃×Q₁₆	—	2	4	no	—
119	C₂×C₁₃×Q₁₆	—	2	1	no	—
120	C₂×C₁₃×Q₁₆	—	2	1	no	—
121	C₂×C₁₃×Q₁₆	—	2	1	no	—
122	C₂×C₁₃×Q₁₆	—	2	1	no	—
123	C₂×C₁₃×Q₁₆	D₄	1	2	yes	—
124	C₂×C₁₃×SD₁₆	—	2	4	no	—
125	C₂×C₁₃×SD₁₆	—	2	1	no	—
126	C₂×C₁₃×SD₁₆	—	2	1	no	—
127	C₂×C₁₃×SD₁₆	—	2	1	no	—
128	C₂×C₁₃×SD₁₆	—	2	1	no	—
129	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
130	C₁₃×#131	—	2	2	no	—
131	C₁₃×#131	—	2	2	no	—
132	C₁₃×#131	—	2	2	no	—
133	C₁₃×#131	—	4	1	no	—
134	C₂×C₁₃×M₁₆	—	2	2	no	—
135	C₂×C₁₃×M₁₆	—	2	2	no	—
136	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	—	2	1	no	—
143	C₁₃×C₄⋊Q₈	—	2	2	no	—
144	C₁₃×C₄⋊Q₈	—	2	1	no	—
145	C₁₃×C₄⋊Q₈	—	2	1	no	—
146	C₁₃×#124	—	2	1	no	—
147	C₁₃×#123	—	4	1	no	—
148	C₁₃×C₂²⋊Q₈	—	4	1	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	4	1	no	—
152	C₁₃×#117	—	2	1	no	—
153	C₁₃×#117	C₂³	1	1	yes	characteristic
154	C₁₃×#117	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
156	C₂×C₄²×C₁₃	—	2	1	no	—
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#108	—	2	2	no	—
159	C₁₃×C₄⋊C₈	—	2	2	no	—
160	C₁₃×#104	—	2	2	no	—
161	C₁₃×#104	—	2	2	no	—
162	C₁₃×#104	—	2	2	no	—
163	C₁₃×#104	—	2	2	no	—
164	C₁₃×#104	—	2	1	no	—
165	C₁₃×#104	—	2	1	no	—
166	C₁₃×#104	—	2	1	no	—
167	C₁₃×#104	—	2	1	no	—
168	C₁₃×#104	D₄	1	2	yes	—
169	C₁₃×#104	D₄	1	2	yes	—
170	C₁₃×#103	—	2	2	no	—
171	C₁₃×#103	—	2	2	no	—
172	C₁₃×#103	—	4	1	no	—
173	C₁₃×#101	—	2	1	no	—
174	C₁₃×#101	—	2	1	no	—
175	C₁₃×#101	—	2	2	no	—
176	C₁₃×#101	—	2	2	no	—
177	C₁₃×#100	—	2	1	no	—
178	C₁₃×#100	—	2	1	no	—
179	C₁₃×#99	—	4	1	no	—
180	#24474	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₁₃×#41	—	2	1	no	—
182	C₁₃×#41	—	2	1	no	—
183	C₁₃×#41	—	2	1	no	—
184	C₁₃×#41	—	2	1	no	—
185	C₁₃×#41	—	2	4	no	—
186	C₁₃×#41	—	2	2	no	—
187	C₁₃×#41	—	2	2	no	—
188	C₁₃×#41	—	2	2	no	—
189	C₁₃×#41	—	2	2	no	—
190	C₁₃×#41	—	2	1	no	—
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	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	4	2	no	—
199	C₁₃×#41	—	4	2	no	—
200	C₁₃×#41	—	4	2	no	—
201	C₁₃×#41	—	4	2	no	—
202	C₁₃×#41	—	4	2	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	2	no	—
205	C₁₃×#41	—	4	1	no	—
206	C₁₃×#41	—	4	1	no	—
207	C₁₃×#41	—	4	4	no	—
208	C₁₃×#41	—	4	2	no	—
209	C₁₃×#41	C₂×D₄	1	2	yes	—
210	C₁₃×#41	C₂×D₄	1	2	yes	—
211	C₁₃×#41	C₂×D₄	1	2	yes	—
212	C₁₃×#41	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	4	no	—
215	C₂×Q₈×C₁₃	—	2	2	no	—
216	C₂×Q₈×C₁₃	—	2	2	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	4	1	no	—
228	C₂×Q₈×C₁₃	—	4	2	no	—
229	C₂×Q₈×C₁₃	—	4	2	no	—
230	C₂×Q₈×C₁₃	—	4	1	no	—
231	C₂×Q₈×C₁₃	—	4	2	no	—
232	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
237	C₂×D₄×C₁₃	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	1	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	4	2	no	—
244	C₂×D₄×C₁₃	—	4	1	no	—
245	C₂×D₄×C₁₃	—	4	2	no	—
246	C₂×D₄×C₁₃	—	4	2	no	—
247	C₂×D₄×C₁₃	—	4	1	no	—
248	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	4	2	no	—
260	C₂²×C₄×C₁₃	—	4	1	no	—
261	C₂²×C₄×C₁₃	—	4	1	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₁₃×Q₁₆	—	2	4	no	—
265	C₁₃×Q₁₆	—	2	2	no	—
266	C₁₃×Q₁₆	—	2	2	no	—
267	C₁₃×Q₁₆	—	2	4	no	—
268	C₁₃×Q₁₆	—	4	2	no	—
269	C₁₃×Q₁₆	—	4	2	no	—
270	C₁₃×Q₁₆	—	4	2	no	—
271	C₁₃×SD₁₆	—	2	4	no	—
272	C₁₃×SD₁₆	—	2	2	no	—
273	C₁₃×SD₁₆	—	2	2	no	—
274	C₁₃×SD₁₆	—	2	2	no	—
275	C₁₃×SD₁₆	—	2	2	no	—
276	C₁₃×SD₁₆	—	2	4	no	—
277	C₁₃×SD₁₆	—	4	2	no	—
278	C₁₃×SD₁₆	—	4	2	no	—
279	C₁₃×SD₁₆	—	4	2	no	—
280	C₁₃×D₈	—	2	2	no	—
281	C₁₃×D₈	—	2	2	no	—
282	C₁₃×M₁₆	—	2	4	no	—
283	C₁₃×M₁₆	—	2	1	no	—
284	C₁₃×M₁₆	—	2	1	no	—
285	C₁₃×M₁₆	—	2	1	no	—
286	C₁₃×M₁₆	—	2	1	no	—
287	C₁₃×M₁₆	—	2	1	no	—
288	C₁₃×M₁₆	—	2	1	no	—
289	C₁₃×M₁₆	—	2	1	no	—
290	C₁₃×M₁₆	—	2	1	no	—
291	C₁₃×M₁₆	—	2	1	no	—
292	C₁₃×M₁₆	—	2	1	no	—
293	C₁₃×M₁₆	—	4	2	no	—
294	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
295	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
296	C₂×C₈×C₁₃	—	2	4	no	—
297	C₂×C₈×C₁₃	—	2	1	no	—
298	C₂×C₈×C₁₃	—	2	1	no	—
299	C₂×C₈×C₁₃	—	2	1	no	—
300	C₂×C₈×C₁₃	—	2	1	no	—
301	C₂×C₈×C₁₃	—	2	1	no	—
302	C₂×C₈×C₁₃	—	4	2	no	—
303	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	4	2	no	—
307	C₁₃×C₄⋊C₄	—	4	2	no	—
308	C₁₃×C₄⋊C₄	—	4	1	no	—
309	C₁₃×C₄⋊C₄	—	4	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	4	1	no	—
313	C₁₃×C₂²⋊C₄	—	4	2	no	—
314	C₄²×C₁₃	—	2	1	no	—
315	C₄²×C₁₃	—	2	1	no	—
316	C₄²×C₁₃	—	2	1	no	—
317	C₄²×C₁₃	—	4	1	no	—
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	#3586	C₂×C₁₃	1	1	yes	characteristic
321	#3069	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3022	C₂×C₁₃	1	1	yes	characteristic, complemented
324	C₂×#456	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#2901	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#2050	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#2049	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2009	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2005	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#1906	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#1902	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#1902	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#1861	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#1796	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂³×C₁₃	—	2	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	—	2	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	—	4	2	no	—
340	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
341	Q₈×C₁₃	—	2	1	no	—
342	Q₈×C₁₃	—	2	1	no	—
343	Q₈×C₁₃	—	2	1	no	—
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	2	1	no	—
346	Q₈×C₁₃	—	2	1	no	—
347	Q₈×C₁₃	—	2	1	no	—
348	Q₈×C₁₃	—	2	2	no	—
349	Q₈×C₁₃	—	4	2	no	—
350	Q₈×C₁₃	—	4	4	no	—
351	Q₈×C₁₃	—	4	1	no	—
352	Q₈×C₁₃	—	4	1	no	—
353	Q₈×C₁₃	—	4	1	no	—
354	Q₈×C₁₃	—	4	1	no	—
355	Q₈×C₁₃	—	4	1	no	—
356	Q₈×C₁₃	—	4	1	no	—
357	Q₈×C₁₃	#120	1	2	yes	—
358	Q₈×C₁₃	#121	1	2	yes	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	2	2	no	—
361	D₄×C₁₃	—	2	2	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	2	1	no	—
364	D₄×C₁₃	—	2	1	no	—
365	D₄×C₁₃	—	2	1	no	—
366	D₄×C₁₃	—	2	1	no	—
367	D₄×C₁₃	—	2	1	no	—
368	D₄×C₁₃	—	2	1	no	—
369	D₄×C₁₃	—	4	2	no	—
370	D₄×C₁₃	—	4	2	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	1	no	—
374	D₄×C₁₃	—	4	1	no	—
375	D₄×C₁₃	—	4	1	no	—
376	D₄×C₁₃	—	4	1	no	—
377	D₄×C₁₃	#120	1	2	yes	—
378	D₄×C₁₃	#121	1	2	yes	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	4	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	1	no	—
403	C₂×C₄×C₁₃	—	4	1	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	1	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
413	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
414	C₈×C₁₃	—	2	2	no	—
415	C₈×C₁₃	—	2	2	no	—
416	C₈×C₁₃	—	2	2	no	—
417	C₈×C₁₃	—	4	1	no	—
418	C₈×C₁₃	—	4	1	no	—
419	C₈×C₁₃	—	4	1	no	—
420	#585	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
422	#578	—	2	2	no	—
423	#578	—	2	2	no	—
424	#577	—	2	2	no	—
425	#577	—	2	2	no	—
426	#575	—	2	2	no	—
427	#575	C₂²×C₁₃	1	1	yes	characteristic
428	#575	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#137	—	2	2	no	—
430	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#568	C₂²×C₁₃	1	1	yes	characteristic
436	#568	C₂²×C₁₃	1	1	yes	characteristic
437	#536	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
440	#473	—	2	2	no	—
441	#471	—	2	2	no	—
442	#462	—	2	2	no	—
443	#461	—	2	2	no	—
444	#456	—	2	2	no	—
445	#456	—	2	2	no	—
446	#456	—	2	2	no	—
447	#455	—	2	2	no	—
448	#430	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#421	—	2	2	no	—
451	#421	C₂²×C₁₃	1	1	yes	characteristic
452	#421	C₂²×C₁₃	1	1	yes	characteristic
453	#421	C₂²×C₁₃	1	1	yes	characteristic
454	#421	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#104	—	2	2	no	—
456	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#413	C₂²×C₁₃	1	1	yes	characteristic
463	#413	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#410	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#344	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#344	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#338	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	2	no	—
473	C₂²×C₁₃	—	4	1	no	—
474	C₂²×C₁₃	—	4	1	no	—
475	C₂²×C₁₃	—	4	1	no	—
476	C₂²×C₁₃	—	8	1	no	—
477	C₂²×C₁₃	—	8	1	no	—
478	C₂²×C₁₃	—	8	1	no	—
479	C₂²×C₁₃	—	8	1	no	—
480	C₂²×C₁₃	—	16	2	no	—
481	C₂²×C₁₃	#534	1	1	yes	characteristic
482	C₂²×C₁₃	D₄²	1	1	yes	characteristic
483	C₂²×C₁₃	#546	1	1	yes	characteristic
484	C₄×C₁₃	—	2	2	no	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	—	8	1	no	—
492	C₄×C₁₃	—	8	1	no	—
493	C₄×C₁₃	—	8	1	no	—
494	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
495	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
496	C₄×C₁₃	D₄²	1	1	yes	characteristic
497	C₄×C₁₃	#546	1	1	yes	characteristic
498	2₋¹⁺⁴	—	2	2	no	—
499	2₋¹⁺⁴	—	2	2	no	—
500	2₋¹⁺⁴	—	2	1	no	—
501	2₋¹⁺⁴	—	2	1	no	—
502	2₋¹⁺⁴	—	2	2	no	—
503	2₋¹⁺⁴	—	4	1	no	—
504	2₋¹⁺⁴	D₄×C₁₃	1	2	yes	—
505	H(5,𝔽₂)	—	2	1	no	—
506	H(5,𝔽₂)	—	2	1	no	—
507	H(5,𝔽₂)	—	4	1	no	—
508	H(5,𝔽₂)	D₄×C₁₃	1	2	yes	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	1	no	—
512	C₂×#41	—	2	1	no	—
513	C₂×#41	—	4	1	no	—
514	C₂×#41	—	4	1	no	—
515	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×Q₈	—	2	1	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
523	#137	—	2	4	no	—
524	#137	—	2	4	no	—
525	#137	—	2	4	no	—
526	#137	—	2	2	no	—
527	#137	—	2	2	no	—
528	#137	—	2	1	no	—
529	#137	—	2	2	no	—
530	#137	—	2	1	no	—
531	#137	—	2	1	no	—
532	#137	—	2	2	no	—
533	#137	—	2	2	no	—
534	#137	—	2	2	no	—
535	#137	—	2	2	no	—
536	#137	—	2	2	no	—
537	#137	—	2	2	no	—
538	#137	—	4	1	no	—
539	#137	D₄×C₁₃	1	2	yes	—
540	AGL(1,ℤ/8)	—	2	4	no	—
541	AGL(1,ℤ/8)	—	2	1	no	—
542	AGL(1,ℤ/8)	—	2	1	no	—
543	AGL(1,ℤ/8)	—	2	1	no	—
544	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	—
545	#135	—	2	4	no	—
546	#135	—	2	4	no	—
547	#135	—	2	2	no	—
548	#135	—	2	2	no	—
549	C₂×Q₁₆	—	2	4	no	—
550	C₂×Q₁₆	—	2	1	no	—
551	C₂×Q₁₆	—	2	1	no	—
552	C₂×Q₁₆	—	2	1	no	—
553	C₂×Q₁₆	—	2	1	no	—
554	C₂×Q₁₆	D₄×C₁₃	1	2	yes	—
555	C₂×SD₁₆	—	2	4	no	—
556	C₂×SD₁₆	—	2	1	no	—
557	C₂×SD₁₆	—	2	1	no	—
558	C₂×SD₁₆	—	2	1	no	—
559	C₂×SD₁₆	—	2	1	no	—
560	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
561	#131	—	2	2	no	—
562	#131	—	2	2	no	—
563	#131	—	2	2	no	—
564	#131	—	4	1	no	—
565	C₂×M₁₆	—	2	2	no	—
566	C₂×M₁₆	—	2	2	no	—
567	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
570	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊Q₈	—	2	2	no	—
574	C₄⋊Q₈	—	2	1	no	—
575	C₄⋊Q₈	—	2	1	no	—
576	C₄⋊Q₈	—	2	1	no	—
577	#124	—	2	1	no	—
578	#123	—	4	1	no	—
579	C₂²⋊Q₈	—	4	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	4	1	no	—
583	#117	—	2	1	no	—
584	#117	C₂³×C₁₃	1	1	yes	characteristic
585	#117	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	—	4	1	no	—
587	C₂×C₄²	—	2	1	no	—
588	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
589	#108	—	2	2	no	—
590	C₄⋊C₈	—	2	2	no	—
591	#104	—	2	2	no	—
592	#104	—	2	2	no	—
593	#104	—	2	2	no	—
594	#104	—	2	2	no	—
595	#104	—	2	1	no	—
596	#104	—	2	1	no	—
597	#104	—	2	1	no	—
598	#104	—	2	1	no	—
599	#104	D₄×C₁₃	1	2	yes	—
600	#104	D₄×C₁₃	1	2	yes	—
601	#103	—	2	2	no	—
602	#103	—	2	2	no	—
603	#103	—	4	1	no	—
604	#101	—	2	1	no	—
605	#101	—	2	1	no	—
606	#101	—	2	2	no	—
607	#101	—	2	2	no	—
608	#100	—	2	1	no	—
609	#100	—	2	1	no	—
610	#99	—	4	1	no	—
611	C₂×C₁₃	—	2	1	no	—
612	C₂×C₁₃	—	2	1	no	—
613	C₂×C₁₃	—	2	1	no	—
614	C₂×C₁₃	—	4	2	no	—
615	C₂×C₁₃	—	4	2	no	—
616	C₂×C₁₃	—	8	1	no	—
617	C₂×C₁₃	—	8	1	no	—
618	C₂×C₁₃	#2410	1	1	yes	characteristic
619	#41	—	2	1	no	—
620	#41	—	2	1	no	—
621	#41	—	2	1	no	—
622	#41	—	2	1	no	—
623	#41	—	2	4	no	—
624	#41	—	2	2	no	—
625	#41	—	2	2	no	—
626	#41	—	2	2	no	—
627	#41	—	2	2	no	—
628	#41	—	2	1	no	—
629	#41	—	2	1	no	—
630	#41	—	2	1	no	—
631	#41	—	2	1	no	—
632	#41	—	2	1	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	4	2	no	—
637	#41	—	4	2	no	—
638	#41	—	4	2	no	—
639	#41	—	4	2	no	—
640	#41	—	4	2	no	—
641	#41	—	4	4	no	—
642	#41	—	4	2	no	—
643	#41	—	4	1	no	—
644	#41	—	4	1	no	—
645	#41	—	4	4	no	—
646	#41	—	4	2	no	—
647	#41	C₂×D₄×C₁₃	1	2	yes	—
648	#41	C₂×D₄×C₁₃	1	2	yes	—
649	#41	C₂×D₄×C₁₃	1	2	yes	—
650	#41	C₂×D₄×C₁₃	1	2	yes	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	4	1	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×Q₈	—	4	2	no	—
670	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
673	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	Q₁₆	—	2	4	no	—
703	Q₁₆	—	2	2	no	—
704	Q₁₆	—	2	2	no	—
705	Q₁₆	—	2	4	no	—
706	Q₁₆	—	4	2	no	—
707	Q₁₆	—	4	2	no	—
708	Q₁₆	—	4	2	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	2	2	no	—
711	SD₁₆	—	2	2	no	—
712	SD₁₆	—	2	2	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	2	4	no	—
715	SD₁₆	—	4	2	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	D₈	—	2	2	no	—
719	D₈	—	2	2	no	—
720	M₁₆	—	2	4	no	—
721	M₁₆	—	2	1	no	—
722	M₁₆	—	2	1	no	—
723	M₁₆	—	2	1	no	—
724	M₁₆	—	2	1	no	—
725	M₁₆	—	2	1	no	—
726	M₁₆	—	2	1	no	—
727	M₁₆	—	2	1	no	—
728	M₁₆	—	2	1	no	—
729	M₁₆	—	2	1	no	—
730	M₁₆	—	2	1	no	—
731	M₁₆	—	4	2	no	—
732	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
733	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
734	C₂×C₈	—	2	4	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	4	2	no	—
741	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₄²	—	2	1	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	1	no	—
755	C₄²	—	4	1	no	—
756	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₁₃	#24474	1	1	yes	characteristic, direct product factor, Sylow
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	4	2	no	—
764	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
765	Q₈	—	2	1	no	—
766	Q₈	—	2	1	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	1	no	—
770	Q₈	—	2	1	no	—
771	Q₈	—	2	1	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	1	no	—
776	Q₈	—	4	1	no	—
777	Q₈	—	4	1	no	—
778	Q₈	—	4	1	no	—
779	Q₈	—	4	1	no	—
780	Q₈	—	4	1	no	—
781	Q₈	C₁₃×#120	1	2	yes	—
782	Q₈	C₁₃×#121	1	2	yes	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	1	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	C₁₃×#120	1	2	yes	—
802	D₄	C₁₃×#121	1	2	yes	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
836	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
837	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	2	no	—
841	C₈	—	4	1	no	—
842	C₈	—	4	1	no	—
843	C₈	—	4	1	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	16	2	no	—
854	C₂²	C₁₃×#534	1	1	yes	characteristic
855	C₂²	D₄²×C₁₃	1	1	yes	characteristic
856	C₂²	C₁₃×#546	1	1	yes	characteristic
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	8	1	no	—
865	C₄	—	8	1	no	—
866	C₄	—	8	1	no	—
867	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
868	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
869	C₄	D₄²×C₁₃	1	1	yes	characteristic
870	C₄	C₁₃×#546	1	1	yes	characteristic
871	C₂	—	2	1	no	—
872	C₂	—	2	1	no	—
873	C₂	—	2	1	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	8	1	no	—
877	C₂	—	8	1	no	—
878	C₂	C₁₃×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3586	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3069	C₂	semidirect
3. C₁₃×#3039	C₂	semidirect
4. C₁₃×#3022	C₂	semidirect
5. C₂×C₁₃×#456	C₂	semidirect
6. C₁₃×#2901	C₂	semidirect
7. C₁₃×#2050	C₂	semidirect
8. C₁₃×#2049	C₂	semidirect
9. C₁₃×#2009	C₂	semidirect
10. C₁₃×#2005	C₂	semidirect
11. C₁₃×#1906	C₂	semidirect
12. C₁₃×#1902	C₂	semidirect
13. C₁₃×#1902	C₂	semidirect
14. C₁₃×#1861	C₂	semidirect
15. C₁₃×#1796	C₂	semidirect
30. C₂×C₁₃×#137	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
44. C₁₃×#430	C₂²	semidirect
45. C₁₃×#423	C₂²	semidirect
54. C₂×C₁₃×#104	C₂²	semidirect
55. C₁₃×#419	C₂²	semidirect
56. C₁₃×#419	C₂²	semidirect
57. C₁₃×#419	C₂²	semidirect
59. C₁₃×#413	C₂²	semidirect
60. C₂×C₁₃×#101	C₂²	semidirect
61. C₂×C₁₃×#101	C₂²	semidirect
62. C₁₃×#410	C₂²	semidirect
63. C₁₃×#344	C₂²	semidirect
64. C₁₃×#344	C₂²	semidirect
65. C₁₃×#339	C₂²	semidirect
66. C₁₃×#338	C₂²	semidirect
180. #24474	C₁₃	direct (N × H)
321. #3069	C₂×C₁₃	semidirect
322. #3039	C₂×C₁₃	semidirect
323. #3022	C₂×C₁₃	semidirect
324. C₂×#456	C₂×C₁₃	semidirect
325. #2901	C₂×C₁₃	semidirect
326. #2050	C₂×C₁₃	semidirect
327. #2049	C₂×C₁₃	semidirect
328. #2009	C₂×C₁₃	semidirect
329. #2005	C₂×C₁₃	semidirect
330. #1906	C₂×C₁₃	semidirect
331. #1902	C₂×C₁₃	semidirect
332. #1902	C₂×C₁₃	semidirect
333. #1861	C₂×C₁₃	semidirect
334. #1796	C₂×C₁₃	semidirect
434. C₂×#137	C₂²×C₁₃	semidirect
438. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
448. #430	C₂²×C₁₃	semidirect
449. #423	C₂²×C₁₃	semidirect
458. C₂×#104	C₂²×C₁₃	semidirect
459. #419	C₂²×C₁₃	semidirect
460. #419	C₂²×C₁₃	semidirect
461. #419	C₂²×C₁₃	semidirect
463. #413	C₂²×C₁₃	semidirect
464. C₂×#101	C₂²×C₁₃	semidirect
465. C₂×#101	C₂²×C₁₃	semidirect
466. #410	C₂²×C₁₃	semidirect
467. #344	C₂²×C₁₃	semidirect
468. #344	C₂²×C₁₃	semidirect
469. #339	C₂²×C₁₃	semidirect
470. #338	C₂²×C₁₃	semidirect
758. C₁₃	#24474	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×#3586	2
C₁₃×#3069	2
C₁₃×#3039	2
C₁₃×#3022	2
C₂×C₁₃×#456	2
C₁₃×#2901	2
C₁₃×#2050	2
C₁₃×#2049	2
C₁₃×#2009	2
C₁₃×#2005	2
C₁₃×#1906	2
C₁₃×#1902	2
C₁₃×#1861	2
C₁₃×#1796	2
#24474	13

Subgroups — C13×#24474 #15710813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24474 #15710813