Subgroups — C₁₃×#61868 #15748207

Order 3328.

1756 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3380	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3241	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3119	C₂	1	4	yes	maximal, complemented
15	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#562	—	2	2	no	—
19	Q₈²×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#557	C₂²	1	2	yes	—
21	C₁₃×#554	—	2	2	no	—
22	C₁₃×#554	C₂²	1	2	yes	—
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	2	yes	—
25	C₁₃×#550	C₂²	1	2	yes	—
26	C₁₃×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	—	2	2	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#547	—	2	1	no	—
30	C₁₃×#547	—	2	1	no	—
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#540	C₂²	1	4	yes	—
34	C₁₃×#537	—	2	2	no	—
35	C₁₃×#537	—	2	2	no	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#501	C₂²	1	4	yes	—
45	C₁₃×#500	C₂²	1	2	yes	—
46	C₁₃×#499	C₂²	1	4	yes	—
47	C₁₃×#498	C₂²	1	2	yes	—
48	C₁₃×#490	C₂²	1	4	yes	—
49	C₁₃×#486	C₂²	1	4	yes	—
50	C₁₃×#486	C₂²	1	2	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#482	C₂²	1	2	yes	—
53	C₁₃×#482	C₂²	1	2	yes	—
54	C₁₃×#481	C₂²	1	4	yes	—
55	C₁₃×#480	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	1	yes	characteristic
61	C₁₃×#477	C₂²	1	1	yes	characteristic
62	C₁₃×#476	C₂²	1	1	yes	characteristic
63	C₁₃×#476	C₂²	1	1	yes	characteristic
64	C₁₃×#476	C₂²	1	2	yes	—
65	C₁₃×#476	C₂²	1	4	yes	—
66	C₁₃×#476	C₂²	1	2	yes	—
67	C₁₃×#474	C₂²	1	2	yes	—
68	C₁₃×#474	C₂²	1	4	yes	—
69	C₁₃×#474	C₂²	1	2	yes	—
70	C₁₃×#460	C₂²	1	1	yes	characteristic
71	C₁₃×#460	C₂²	1	1	yes	characteristic
72	C₁₃×#460	C₂²	1	4	yes	—
73	C₁₃×#459	C₂²	1	1	yes	characteristic
74	C₁₃×#459	C₂²	1	4	yes	—
75	C₁₃×#459	C₂²	1	1	yes	characteristic
76	C₁₃×#449	C₂²	1	2	yes	—
77	C₁₃×#449	C₂²	1	2	yes	—
78	C₁₃×#446	C₂²	1	2	yes	—
79	C₁₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
82	C₁₃×#442	C₂²	1	4	yes	—
83	C₁₃×#440	C₂²	1	4	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
86	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
87	C₄×C₁₃×D₈	C₂²	1	2	yes	—
88	C₄×C₁₃×D₈	C₂²	1	4	yes	—
89	C₄×C₁₃×D₈	C₂²	1	2	yes	—
90	C₁₃×#433	C₂²	1	4	yes	—
91	C₁₃×#431	C₂²	1	1	yes	characteristic
92	C₁₃×#431	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	—	2	2	no	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	1	no	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×D₈	C₂³	1	2	yes	—
103	C₂×C₁₃×D₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#127	C₂³	1	4	yes	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	D₄	1	2	yes	—
123	C₁₃×#125	C₂³	1	4	yes	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#124	—	2	1	no	—
126	C₁₃×#124	—	2	1	no	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
139	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
140	C₁₃×#121	—	2	1	no	—
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	4	no	—
145	C₁₃×#121	—	2	4	no	—
146	C₁₃×#121	—	2	4	no	—
147	C₁₃×#121	—	2	4	no	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	—	2	1	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	4	yes	—
167	C₄×D₄×C₁₃	C₂³	1	4	yes	—
168	C₄×D₄×C₁₃	C₂³	1	4	yes	—
169	C₁₃×#117	—	2	2	no	—
170	C₁₃×#117	—	2	1	no	—
171	C₁₃×#117	C₂³	1	1	yes	characteristic
172	C₁₃×#117	C₂³	1	2	yes	—
173	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₃	—	2	1	no	—
180	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
181	C₁₃×#107	C₂³	1	2	yes	—
182	C₁₃×#107	C₂³	1	4	yes	—
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	4	yes	—
185	C₁₃×#106	C₂³	1	2	yes	—
186	C₁₃×#106	C₂³	1	4	yes	—
187	C₁₃×#106	C₂³	1	2	yes	—
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×#103	C₂³	1	2	yes	—
196	C₁₃×#103	C₂³	1	2	yes	—
197	C₁₃×#102	C₂³	1	2	yes	—
198	C₁₃×#102	C₂³	1	2	yes	—
199	C₁₃×#102	C₂³	1	2	yes	—
200	C₁₃×#102	C₂³	1	4	yes	—
201	C₁₃×#102	C₂³	1	2	yes	—
202	C₁₃×#102	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₁₃	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	2	yes	—
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61868	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃×#41	—	2	2	no	—
215	C₁₃×#41	—	2	2	no	—
216	C₁₃×#41	—	8	2	no	—
217	C₁₃×#41	—	8	2	no	—
218	C₁₃×#41	—	8	4	no	—
219	C₁₃×#41	—	8	4	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	4	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	8	2	no	—
226	C₂×Q₈×C₁₃	—	8	4	no	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	4	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×SD₁₆	—	2	4	no	—
255	C₁₃×SD₁₆	—	2	4	no	—
256	C₁₃×D₈	—	2	4	no	—
257	C₁₃×D₈	—	2	4	no	—
258	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	2	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
283	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	—	2	1	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	4	yes	—
306	#3548	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3385	C₂×C₁₃	1	2	yes	complemented
309	#3384	C₂×C₁₃	1	2	yes	complemented
310	#3381	C₂×C₁₃	1	2	yes	complemented
311	#3380	C₂×C₁₃	1	2	yes	complemented
312	#3368	C₂×C₁₃	1	2	yes	complemented
313	#3366	C₂×C₁₃	1	2	yes	complemented
314	#3362	C₂×C₁₃	1	2	yes	complemented
315	#3358	C₂×C₁₃	1	2	yes	complemented
316	#3241	C₂×C₁₃	1	4	yes	complemented
317	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3119	C₂×C₁₃	1	4	yes	complemented
320	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₁₃	—	2	4	no	—
328	Q₈×C₁₃	—	2	4	no	—
329	Q₈×C₁₃	—	2	1	no	—
330	Q₈×C₁₃	—	4	4	no	—
331	Q₈×C₁₃	—	8	2	no	—
332	Q₈×C₁₃	—	8	4	no	—
333	Q₈×C₁₃	—	8	1	no	—
334	Q₈×C₁₃	—	8	1	no	—
335	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
336	D₄×C₁₃	—	2	4	no	—
337	D₄×C₁₃	—	2	1	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	2	2	no	—
340	D₄×C₁₃	—	2	2	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	4	2	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	8	1	no	—
345	D₄×C₁₃	—	8	4	no	—
346	D₄×C₁₃	—	8	1	no	—
347	D₄×C₁₃	—	8	4	no	—
348	D₄×C₁₃	—	8	2	no	—
349	D₄×C₁₃	—	8	2	no	—
350	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	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	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	4	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	8	4	no	—
367	C₂×C₄×C₁₃	—	8	4	no	—
368	C₂×C₄×C₁₃	—	8	4	no	—
369	C₂×C₄×C₁₃	—	8	2	no	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
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	4	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
378	C₈×C₁₃	—	2	2	no	—
379	C₈×C₁₃	—	2	2	no	—
380	C₈×C₁₃	—	2	2	no	—
381	C₈×C₁₃	—	2	2	no	—
382	#562	—	2	2	no	—
383	Q₈²	C₂²×C₁₃	1	2	yes	—
384	#557	C₂²×C₁₃	1	2	yes	—
385	#554	—	2	2	no	—
386	#554	C₂²×C₁₃	1	2	yes	—
387	#554	C₂²×C₁₃	1	2	yes	—
388	#554	C₂²×C₁₃	1	2	yes	—
389	#550	C₂²×C₁₃	1	2	yes	—
390	#550	C₂²×C₁₃	1	2	yes	—
391	D₄×Q₈	—	2	2	no	—
392	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
393	#547	—	2	1	no	—
394	#547	—	2	1	no	—
395	#544	—	2	2	no	—
396	#544	C₂²×C₁₃	1	2	yes	—
397	#540	C₂²×C₁₃	1	4	yes	—
398	#537	—	2	2	no	—
399	#537	—	2	2	no	—
400	#533	—	2	1	no	—
401	#533	C₂²×C₁₃	1	1	yes	characteristic
402	#532	C₂²×C₁₃	1	1	yes	characteristic
403	#532	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊Q₈	—	2	1	no	—
405	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
406	#520	C₂²×C₁₃	1	2	yes	—
407	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
408	#501	C₂²×C₁₃	1	4	yes	—
409	#500	C₂²×C₁₃	1	2	yes	—
410	#499	C₂²×C₁₃	1	4	yes	—
411	#498	C₂²×C₁₃	1	2	yes	—
412	#490	C₂²×C₁₃	1	4	yes	—
413	#486	C₂²×C₁₃	1	4	yes	—
414	#486	C₂²×C₁₃	1	2	yes	—
415	#486	C₂²×C₁₃	1	2	yes	—
416	#482	C₂²×C₁₃	1	2	yes	—
417	#482	C₂²×C₁₃	1	2	yes	—
418	#481	C₂²×C₁₃	1	4	yes	—
419	#480	C₂²×C₁₃	1	4	yes	—
420	#479	C₂²×C₁₃	1	4	yes	—
421	#478	C₂²×C₁₃	1	4	yes	—
422	#478	C₂²×C₁₃	1	4	yes	—
423	#478	C₂²×C₁₃	1	4	yes	—
424	#477	C₂²×C₁₃	1	1	yes	characteristic
425	#477	C₂²×C₁₃	1	1	yes	characteristic
426	#476	C₂²×C₁₃	1	1	yes	characteristic
427	#476	C₂²×C₁₃	1	1	yes	characteristic
428	#476	C₂²×C₁₃	1	2	yes	—
429	#476	C₂²×C₁₃	1	4	yes	—
430	#476	C₂²×C₁₃	1	2	yes	—
431	#474	C₂²×C₁₃	1	2	yes	—
432	#474	C₂²×C₁₃	1	4	yes	—
433	#474	C₂²×C₁₃	1	2	yes	—
434	#460	C₂²×C₁₃	1	1	yes	characteristic
435	#460	C₂²×C₁₃	1	1	yes	characteristic
436	#460	C₂²×C₁₃	1	4	yes	—
437	#459	C₂²×C₁₃	1	1	yes	characteristic
438	#459	C₂²×C₁₃	1	4	yes	—
439	#459	C₂²×C₁₃	1	1	yes	characteristic
440	#449	C₂²×C₁₃	1	2	yes	—
441	#449	C₂²×C₁₃	1	2	yes	—
442	#446	C₂²×C₁₃	1	2	yes	—
443	#446	C₂²×C₁₃	1	2	yes	—
444	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
445	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
446	#442	C₂²×C₁₃	1	4	yes	—
447	#440	C₂²×C₁₃	1	4	yes	—
448	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
449	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
450	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
451	C₄×D₈	C₂²×C₁₃	1	2	yes	—
452	C₄×D₈	C₂²×C₁₃	1	4	yes	—
453	C₄×D₈	C₂²×C₁₃	1	2	yes	—
454	#433	C₂²×C₁₃	1	4	yes	—
455	#431	C₂²×C₁₃	1	1	yes	characteristic
456	#431	C₂²×C₁₃	1	1	yes	characteristic
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	2	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	2	no	—
472	C₄×C₁₃	—	2	1	no	—
473	C₄×C₁₃	—	2	4	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	4	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	1	no	—
478	C₄×C₁₃	—	4	4	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	#576	1	2	yes	—
482	C₄×C₁₃	#577	1	2	yes	—
483	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
484	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
493	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
494	C₂×D₈	C₂³×C₁₃	1	2	yes	—
495	C₂×D₈	C₂³×C₁₃	1	2	yes	—
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	4	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
506	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
509	#127	C₂³×C₁₃	1	1	yes	characteristic
510	#127	C₂³×C₁₃	1	1	yes	characteristic
511	#127	C₂³×C₁₃	1	4	yes	—
512	#125	—	2	2	no	—
513	#125	—	2	4	no	—
514	#125	D₄×C₁₃	1	2	yes	—
515	#125	C₂³×C₁₃	1	4	yes	—
516	#125	C₂³×C₁₃	1	4	yes	—
517	#124	—	2	1	no	—
518	#124	—	2	1	no	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
531	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	4	no	—
537	#121	—	2	4	no	—
538	#121	—	2	4	no	—
539	#121	—	2	4	no	—
540	#121	C₂³×C₁₃	1	2	yes	—
541	#121	C₂³×C₁₃	1	2	yes	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	4	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₁₃	1	4	yes	—
557	C₄×D₄	C₂³×C₁₃	1	2	yes	—
558	C₄×D₄	C₂³×C₁₃	1	2	yes	—
559	C₄×D₄	C₂³×C₁₃	1	4	yes	—
560	C₄×D₄	C₂³×C₁₃	1	4	yes	—
561	#117	—	2	2	no	—
562	#117	—	2	1	no	—
563	#117	C₂³×C₁₃	1	1	yes	characteristic
564	#117	C₂³×C₁₃	1	2	yes	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	2	no	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	—	2	2	no	—
569	C₂×C₄⋊C₄	—	2	2	no	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
573	#107	C₂³×C₁₃	1	2	yes	—
574	#107	C₂³×C₁₃	1	4	yes	—
575	#107	C₂³×C₁₃	1	2	yes	—
576	#107	C₂³×C₁₃	1	4	yes	—
577	#106	C₂³×C₁₃	1	2	yes	—
578	#106	C₂³×C₁₃	1	4	yes	—
579	#106	C₂³×C₁₃	1	2	yes	—
580	#106	C₂³×C₁₃	1	4	yes	—
581	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
582	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
586	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
587	#103	C₂³×C₁₃	1	2	yes	—
588	#103	C₂³×C₁₃	1	2	yes	—
589	#102	C₂³×C₁₃	1	2	yes	—
590	#102	C₂³×C₁₃	1	2	yes	—
591	#102	C₂³×C₁₃	1	2	yes	—
592	#102	C₂³×C₁₃	1	4	yes	—
593	#102	C₂³×C₁₃	1	2	yes	—
594	#102	C₂³×C₁₃	1	2	yes	—
595	#102	C₂³×C₁₃	1	4	yes	—
596	#102	C₂³×C₁₃	1	2	yes	—
597	#102	C₂³×C₁₃	1	4	yes	—
598	#102	C₂³×C₁₃	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
601	#97	C₂³×C₁₃	1	4	yes	—
602	C₄×C₈	C₂³×C₁₃	1	2	yes	—
603	C₄×C₈	C₂³×C₁₃	1	2	yes	—
604	C₄×C₈	C₂³×C₁₃	1	4	yes	—
605	C₂×C₁₃	—	4	1	no	—
606	C₂×C₁₃	—	4	2	no	—
607	C₂×C₁₃	—	8	2	no	—
608	C₂×C₁₃	—	8	2	no	—
609	C₂×C₁₃	#3486	1	1	yes	characteristic
610	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
611	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
612	#41	—	2	2	no	—
613	#41	—	2	2	no	—
614	#41	—	8	2	no	—
615	#41	—	8	2	no	—
616	#41	—	8	4	no	—
617	#41	—	8	4	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	4	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	8	2	no	—
624	C₂×Q₈	—	8	4	no	—
625	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
626	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
639	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
652	SD₁₆	—	2	4	no	—
653	SD₁₆	—	2	4	no	—
654	D₈	—	2	4	no	—
655	D₈	—	2	4	no	—
656	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
657	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
658	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
659	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
679	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
695	C₄²	—	2	1	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	4	no	—
699	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₁₃	1	4	yes	—
704	C₁₃	#61868	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	1	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
709	Q₈	—	2	4	no	—
710	Q₈	—	2	4	no	—
711	Q₈	—	2	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	8	2	no	—
714	Q₈	—	8	4	no	—
715	Q₈	—	8	1	no	—
716	Q₈	—	8	1	no	—
717	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	2	no	—
726	D₄	—	8	1	no	—
727	D₄	—	8	4	no	—
728	D₄	—	8	1	no	—
729	D₄	—	8	4	no	—
730	D₄	—	8	2	no	—
731	D₄	—	8	2	no	—
732	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
759	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
760	C₈	—	2	2	no	—
761	C₈	—	2	2	no	—
762	C₈	—	2	2	no	—
763	C₈	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	1	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
777	C₄	—	2	1	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	4	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	C₁₃×#576	1	2	yes	—
789	C₄	C₁₃×#577	1	2	yes	—
790	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
791	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
792	C₂	—	4	1	no	—
793	C₂	—	4	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₁₃×#3486	1	1	yes	characteristic
797	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
798	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3548	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3381	C₂	semidirect
6. C₁₃×#3380	C₂	semidirect
7. C₁₃×#3368	C₂	semidirect
8. C₁₃×#3366	C₂	semidirect
9. C₁₃×#3362	C₂	semidirect
10. C₁₃×#3358	C₂	semidirect
11. C₁₃×#3241	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3226	C₂	semidirect
14. C₁₃×#3119	C₂	semidirect
15. C₁₃×#3106	C₂	semidirect
16. C₁₃×#3106	C₂	semidirect
17. C₁₃×#2986	C₂	semidirect
213. #61868	C₁₃	direct (N × H)
306. #3548	C₂×C₁₃	semidirect
307. #3503	C₂×C₁₃	semidirect
308. #3385	C₂×C₁₃	semidirect
309. #3384	C₂×C₁₃	semidirect
310. #3381	C₂×C₁₃	semidirect
311. #3380	C₂×C₁₃	semidirect
312. #3368	C₂×C₁₃	semidirect
313. #3366	C₂×C₁₃	semidirect
314. #3362	C₂×C₁₃	semidirect
315. #3358	C₂×C₁₃	semidirect
316. #3241	C₂×C₁₃	semidirect
317. #3227	C₂×C₁₃	semidirect
318. #3226	C₂×C₁₃	semidirect
319. #3119	C₂×C₁₃	semidirect
320. #3106	C₂×C₁₃	semidirect
321. #3106	C₂×C₁₃	semidirect
322. #2986	C₂×C₁₃	semidirect
704. C₁₃	#61868	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×#3548	2
C₁₃×#3503	2
C₁₃×#3385	2
C₁₃×#3384	2
C₁₃×#3381	2
C₁₃×#3380	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3241	2
C₁₃×#3227	2
C₁₃×#3226	2
C₁₃×#3119	2
C₁₃×#3106	2
C₁₃×#2986	2
#61868	13

Subgroups — C13×#61868 #15748207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61868 #15748207