Subgroups — C₁₃×#61501 #15747840

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3521	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3267	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#556	C₂²	1	2	yes	complemented
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#553	—	2	2	no	—
26	C₁₃×#553	C₂²	1	2	yes	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	2	yes	—
29	C₁₃×#551	—	2	2	no	—
30	C₁₃×#551	—	2	2	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#546	C₂²	1	2	yes	—
33	C₁₃×#546	C₂²	1	2	yes	complemented
34	C₁₃×#542	C₂²	1	2	yes	—
35	C₁₃×#541	C₂²	1	2	yes	complemented
36	C₁₃×#539	—	2	2	no	—
37	C₁₃×#538	—	2	2	no	—
38	C₁₃×#529	—	2	2	no	—
39	C₁₃×#529	C₂²	1	1	yes	characteristic
40	C₁₃×#529	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#126	—	2	2	no	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#518	C₂²	1	2	yes	complemented
44	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
45	C₁₃×#501	C₂²	1	2	yes	complemented
46	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#497	C₂²	1	2	yes	complemented
48	C₁₃×#495	C₂²	1	1	yes	characteristic
49	C₁₃×#488	C₂²	1	2	yes	complemented
50	C₁₃×#488	C₂²	1	2	yes	complemented
51	C₁₃×#487	C₂²	1	2	yes	complemented
52	C₁₃×#485	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#484	C₂²	1	2	yes	complemented
55	C₁₃×#483	C₂²	1	2	yes	complemented
56	C₁₃×#482	C₂²	1	2	yes	—
57	C₁₃×#482	C₂²	1	2	yes	complemented
58	C₁₃×#479	C₂²	1	2	yes	complemented
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#478	C₂²	1	2	yes	complemented
61	C₁₃×#478	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	complemented
63	C₁₃×#474	C₂²	1	2	yes	complemented
64	C₁₃×#470	C₂²	1	2	yes	complemented
65	C₁₃×#468	C₂²	1	2	yes	—
66	C₁₃×#467	C₂²	1	2	yes	complemented
67	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#466	C₂²	1	1	yes	characteristic
69	C₁₃×#465	C₂²	1	2	yes	—
70	C₁₃×#465	C₂²	1	2	yes	complemented
71	C₁₃×#464	C₂²	1	2	yes	complemented
72	C₁₃×#463	C₂²	1	2	yes	—
73	C₁₃×#463	C₂²	1	2	yes	—
74	C₁₃×#463	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	2	yes	complemented
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	2	yes	—
79	C₁₃×#452	C₂²	1	2	yes	complemented
80	C₁₃×#450	C₂²	1	2	yes	complemented
81	C₁₃×#449	C₂²	1	2	yes	—
82	C₁₃×#447	C₂²	1	2	yes	—
83	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
84	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#442	C₂²	1	2	yes	—
86	C₁₃×#442	C₂²	1	2	yes	—
87	C₁₃×#441	C₂²	1	2	yes	complemented
88	C₁₃×#440	C₂²	1	2	yes	complemented
89	C₁₃×#440	C₂²	1	2	yes	complemented
90	C₁₃×#440	C₂²	1	2	yes	complemented
91	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
95	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
96	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
97	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
98	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×D₈	C₂²	1	2	yes	—
100	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
102	C₁₃×#436	C₂²	1	1	yes	characteristic
103	C₁₃×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
105	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₁₃×#433	C₂²	1	2	yes	complemented
107	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
108	C₁₃×#428	C₂²	1	2	yes	complemented
109	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#416	C₂²	1	2	yes	—
111	C₁₃×#416	C₂²	1	2	yes	complemented
112	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
113	C₁₃×#405	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂×C₁₃×#41	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
119	C₁₃×#135	—	2	4	no	—
120	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×#126	—	2	2	no	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	D₄	1	2	yes	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	D₄	1	1	yes	characteristic
151	C₁₃×#125	C₂³	1	2	yes	—
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#124	—	2	2	no	—
154	C₁₃×#124	—	2	2	no	—
155	C₁₃×#124	D₄	1	1	yes	characteristic
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#124	C₂³	1	2	yes	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	D₄	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
173	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	2	no	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	D₄	1	1	yes	characteristic
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#120	—	2	2	no	—
185	C₁₃×#120	—	2	2	no	—
186	C₄×Q₈×C₁₃	—	2	2	no	—
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	2	no	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	2	yes	—
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	2	yes	—
205	C₄×D₄×C₁₃	C₂³	1	2	yes	—
206	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	—	2	2	no	—
210	C₁₃×#117	—	2	2	no	—
211	C₁₃×#117	—	2	2	no	—
212	C₁₃×#117	—	2	2	no	—
213	C₁₃×#117	C₂³	1	2	yes	—
214	C₁₃×#117	C₂³	1	2	yes	—
215	C₁₃×#117	C₂³	1	2	yes	—
216	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
217	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₄²×C₁₃	—	2	2	no	—
225	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₁₃×#107	C₂³	1	1	yes	characteristic
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	—
229	C₁₃×#107	C₂³	1	1	yes	characteristic
230	C₁₃×#107	C₂³	1	1	yes	characteristic
231	C₁₃×#107	C₂³	1	2	yes	—
232	C₁₃×#106	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×#106	C₂³	1	2	yes	—
235	C₁₃×#106	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×#102	C₂³	1	2	yes	—
255	C₁₃×#102	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	2	yes	—
266	#61501	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂⁴×C₁₃	—	2	2	no	—
268	C₁₃×#41	—	2	4	no	—
269	C₁₃×#41	—	2	4	no	—
270	C₁₃×#41	—	4	2	no	—
271	C₁₃×#41	—	4	2	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	—	2	4	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	4	2	no	—
283	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₁₃×Q₁₆	—	2	2	no	—
301	C₁₃×Q₁₆	—	4	1	no	—
302	C₁₃×Q₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	—	2	4	no	—
304	C₁₃×SD₁₆	—	2	4	no	—
305	C₁₃×SD₁₆	—	2	4	no	—
306	C₁₃×SD₁₆	—	4	2	no	—
307	C₁₃×D₈	—	2	4	no	—
308	C₁₃×D₈	—	4	1	no	—
309	C₁₃×D₈	#41	1	4	yes	—
310	C₁₃×M₁₆	—	2	4	no	—
311	C₂×C₈×C₁₃	—	2	2	no	—
312	C₂×C₈×C₁₃	—	4	1	no	—
313	C₂×C₈×C₁₃	—	4	2	no	—
314	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
341	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
342	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
368	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	2	yes	—
380	#3521	C₂×C₁₃	1	2	yes	complemented
381	#3402	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#3389	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3360	C₂×C₁₃	1	2	yes	complemented
384	#3352	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3350	C₂×C₁₃	1	2	yes	complemented
386	#3302	C₂×C₁₃	1	2	yes	complemented
387	#3297	C₂×C₁₃	1	2	yes	complemented
388	#3296	C₂×C₁₃	1	2	yes	complemented
389	#3273	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3267	C₂×C₁₃	1	2	yes	complemented
391	#3178	C₂×C₁₃	1	2	yes	complemented
392	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#3120	C₂×C₁₃	1	2	yes	complemented
394	#3118	C₂×C₁₃	1	2	yes	complemented
395	#3111	C₂×C₁₃	1	2	yes	complemented
396	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#2946	C₂×C₁₃	1	2	yes	complemented
398	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
399	C₂³×C₁₃	—	2	2	no	—
400	C₂³×C₁₃	—	2	2	no	—
401	C₂³×C₁₃	—	4	4	no	—
402	C₂³×C₁₃	—	8	2	no	—
403	C₂³×C₁₃	—	8	2	no	—
404	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	2	2	no	—
408	Q₈×C₁₃	—	2	2	no	—
409	Q₈×C₁₃	—	2	2	no	—
410	Q₈×C₁₃	—	4	1	no	—
411	Q₈×C₁₃	—	8	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	4	1	no	—
416	D₄×C₁₃	—	4	2	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	8	2	no	—
421	D₄×C₁₃	—	8	2	no	—
422	D₄×C₁₃	C₂×#41	1	4	yes	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	4	1	no	—
434	C₂×C₄×C₁₃	—	4	1	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	—	8	2	no	—
440	C₂×C₄×C₁₃	—	8	2	no	—
441	C₂×C₄×C₁₃	—	8	2	no	—
442	C₂×C₄×C₁₃	—	8	2	no	—
443	C₂×C₄×C₁₃	—	8	2	no	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
453	C₈×C₁₃	—	2	1	no	—
454	C₈×C₁₃	—	2	2	no	—
455	C₈×C₁₃	—	2	1	no	—
456	C₈×C₁₃	—	2	1	no	—
457	C₈×C₁₃	—	2	2	no	—
458	C₈×C₁₃	C₂×#41	1	2	yes	—
459	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
460	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
461	#556	C₂²×C₁₃	1	2	yes	complemented
462	#556	C₂²×C₁₃	1	2	yes	complemented
463	#554	C₂²×C₁₃	1	2	yes	complemented
464	#553	—	2	2	no	—
465	#553	C₂²×C₁₃	1	2	yes	—
466	#552	—	2	2	no	—
467	#552	C₂²×C₁₃	1	2	yes	—
468	#551	—	2	2	no	—
469	#551	—	2	2	no	—
470	#547	C₂²×C₁₃	1	2	yes	—
471	#546	C₂²×C₁₃	1	2	yes	—
472	#546	C₂²×C₁₃	1	2	yes	complemented
473	#542	C₂²×C₁₃	1	2	yes	—
474	#541	C₂²×C₁₃	1	2	yes	complemented
475	#539	—	2	2	no	—
476	#538	—	2	2	no	—
477	#529	—	2	2	no	—
478	#529	C₂²×C₁₃	1	1	yes	characteristic
479	#529	C₂²×C₁₃	1	2	yes	complemented
480	C₂×#126	—	2	2	no	—
481	#520	C₂²×C₁₃	1	2	yes	—
482	#518	C₂²×C₁₃	1	2	yes	complemented
483	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
484	#501	C₂²×C₁₃	1	2	yes	complemented
485	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	#497	C₂²×C₁₃	1	2	yes	complemented
487	#495	C₂²×C₁₃	1	1	yes	characteristic
488	#488	C₂²×C₁₃	1	2	yes	complemented
489	#488	C₂²×C₁₃	1	2	yes	complemented
490	#487	C₂²×C₁₃	1	2	yes	complemented
491	#485	C₂²×C₁₃	1	2	yes	complemented
492	#485	C₂²×C₁₃	1	2	yes	complemented
493	#484	C₂²×C₁₃	1	2	yes	complemented
494	#483	C₂²×C₁₃	1	2	yes	complemented
495	#482	C₂²×C₁₃	1	2	yes	—
496	#482	C₂²×C₁₃	1	2	yes	complemented
497	#479	C₂²×C₁₃	1	2	yes	complemented
498	#479	C₂²×C₁₃	1	2	yes	complemented
499	#478	C₂²×C₁₃	1	2	yes	complemented
500	#478	C₂²×C₁₃	1	2	yes	complemented
501	#476	C₂²×C₁₃	1	2	yes	complemented
502	#474	C₂²×C₁₃	1	2	yes	complemented
503	#470	C₂²×C₁₃	1	2	yes	complemented
504	#468	C₂²×C₁₃	1	2	yes	—
505	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	#467	C₂²×C₁₃	1	2	yes	complemented
507	#466	C₂²×C₁₃	1	1	yes	characteristic
508	#465	C₂²×C₁₃	1	2	yes	—
509	#465	C₂²×C₁₃	1	2	yes	complemented
510	#464	C₂²×C₁₃	1	2	yes	complemented
511	#463	C₂²×C₁₃	1	2	yes	—
512	#463	C₂²×C₁₃	1	2	yes	—
513	#463	C₂²×C₁₃	1	2	yes	—
514	#462	C₂²×C₁₃	1	2	yes	complemented
515	#461	C₂²×C₁₃	1	2	yes	complemented
516	#452	C₂²×C₁₃	1	2	yes	—
517	#452	C₂²×C₁₃	1	2	yes	—
518	#452	C₂²×C₁₃	1	2	yes	complemented
519	#450	C₂²×C₁₃	1	2	yes	complemented
520	#449	C₂²×C₁₃	1	2	yes	—
521	#447	C₂²×C₁₃	1	2	yes	—
522	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#442	C₂²×C₁₃	1	2	yes	—
525	#442	C₂²×C₁₃	1	2	yes	—
526	#441	C₂²×C₁₃	1	2	yes	complemented
527	#440	C₂²×C₁₃	1	2	yes	complemented
528	#440	C₂²×C₁₃	1	2	yes	complemented
529	#440	C₂²×C₁₃	1	2	yes	complemented
530	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
534	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
535	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
536	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
537	C₄×D₈	C₂²×C₁₃	1	2	yes	—
538	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
540	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
541	#436	C₂²×C₁₃	1	1	yes	characteristic
542	#435	C₂²×C₁₃	1	2	yes	complemented
543	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
544	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
545	#433	C₂²×C₁₃	1	2	yes	complemented
546	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
547	#428	C₂²×C₁₃	1	2	yes	complemented
548	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
549	#416	C₂²×C₁₃	1	2	yes	—
550	#416	C₂²×C₁₃	1	2	yes	complemented
551	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
552	#405	C₂²×C₁₃	1	2	yes	complemented
553	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	2	1	no	—
556	C₂²×C₁₃	—	2	2	no	—
557	C₂²×C₁₃	—	2	2	no	—
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	2	no	—
560	C₂²×C₁₃	—	2	4	no	—
561	C₂²×C₁₃	—	4	2	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	16	4	no	—
567	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	1	no	—
571	C₄×C₁₃	—	2	1	no	—
572	C₄×C₁₃	—	2	2	no	—
573	C₄×C₁₃	—	2	2	no	—
574	C₄×C₁₃	—	2	1	no	—
575	C₄×C₁₃	—	2	2	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
583	C₄×C₁₃	#585	1	1	yes	characteristic
584	C₂×#41	C₂³×C₁₃	1	2	yes	—
585	C₂×#41	C₂³×C₁₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
587	AGL(1,ℤ/8)	—	2	8	no	—
588	#135	—	2	4	no	—
589	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
593	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
596	C₂×D₈	C₂³×C₁₃	1	2	yes	—
597	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	D₄×C₁₃	1	2	yes	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	D₄×C₁₃	1	1	yes	characteristic
620	#125	C₂³×C₁₃	1	2	yes	—
621	#125	C₂³×C₁₃	1	2	yes	—
622	#124	—	2	2	no	—
623	#124	—	2	2	no	—
624	#124	D₄×C₁₃	1	1	yes	characteristic
625	#124	C₂³×C₁₃	1	2	yes	—
626	#124	C₂³×C₁₃	1	2	yes	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	D₄×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
642	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	D₄×C₁₃	1	1	yes	characteristic
651	#121	C₂³×C₁₃	1	2	yes	—
652	#121	C₂³×C₁₃	1	2	yes	—
653	#120	—	2	2	no	—
654	#120	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	2	yes	—
672	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	C₄×D₄	C₂³×C₁₃	1	2	yes	—
674	C₄×D₄	C₂³×C₁₃	1	2	yes	—
675	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₄×D₄	C₂³×C₁₃	1	2	yes	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	C₂³×C₁₃	1	2	yes	—
683	#117	C₂³×C₁₃	1	2	yes	—
684	#117	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	—	2	2	no	—
686	C₂×C₄⋊C₄	—	2	2	no	—
687	C₂×C₄⋊C₄	—	2	2	no	—
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
689	C₂×C₂²⋊C₄	—	2	2	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	—	2	2	no	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₄²	—	2	2	no	—
694	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
695	#107	C₂³×C₁₃	1	1	yes	characteristic
696	#107	C₂³×C₁₃	1	1	yes	characteristic
697	#107	C₂³×C₁₃	1	2	yes	—
698	#107	C₂³×C₁₃	1	1	yes	characteristic
699	#107	C₂³×C₁₃	1	1	yes	characteristic
700	#107	C₂³×C₁₃	1	2	yes	—
701	#106	C₂³×C₁₃	1	2	yes	—
702	#106	C₂³×C₁₃	1	2	yes	—
703	#106	C₂³×C₁₃	1	2	yes	—
704	#106	C₂³×C₁₃	1	2	yes	—
705	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
706	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
707	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
708	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#103	C₂³×C₁₃	1	2	yes	—
712	#103	C₂³×C₁₃	1	2	yes	—
713	#103	C₂³×C₁₃	1	2	yes	—
714	#103	C₂³×C₁₃	1	2	yes	—
715	#103	C₂³×C₁₃	1	2	yes	—
716	#103	C₂³×C₁₃	1	2	yes	—
717	#102	C₂³×C₁₃	1	2	yes	—
718	#102	C₂³×C₁₃	1	2	yes	—
719	#102	C₂³×C₁₃	1	2	yes	—
720	#102	C₂³×C₁₃	1	2	yes	—
721	#102	C₂³×C₁₃	1	2	yes	—
722	#102	C₂³×C₁₃	1	2	yes	—
723	#102	C₂³×C₁₃	1	2	yes	—
724	#102	C₂³×C₁₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
728	#97	C₂³×C₁₃	1	2	yes	—
729	#97	C₂³×C₁₃	1	2	yes	—
730	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₁₃	1	2	yes	—
735	C₂×C₁₃	—	4	1	no	—
736	C₂×C₁₃	—	4	2	no	—
737	C₂×C₁₃	—	4	4	no	—
738	C₂×C₁₃	—	8	2	no	—
739	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
740	C₂×C₁₃	#3584	1	1	yes	characteristic
741	C₂×C₁₃	#3584	1	1	yes	characteristic
742	C₂⁴	—	2	2	no	—
743	#41	—	2	4	no	—
744	#41	—	2	4	no	—
745	#41	—	4	2	no	—
746	#41	—	4	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
750	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
760	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
775	Q₁₆	—	2	2	no	—
776	Q₁₆	—	4	1	no	—
777	Q₁₆	—	4	2	no	—
778	SD₁₆	—	2	4	no	—
779	SD₁₆	—	2	4	no	—
780	SD₁₆	—	2	4	no	—
781	SD₁₆	—	4	2	no	—
782	D₈	—	2	4	no	—
783	D₈	—	4	1	no	—
784	D₈	C₁₃×#41	1	4	yes	—
785	M₁₆	—	2	4	no	—
786	C₂×C₈	—	2	2	no	—
787	C₂×C₈	—	4	1	no	—
788	C₂×C₈	—	4	2	no	—
789	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
793	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
794	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
812	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
840	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
851	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
852	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
854	C₄²	C₂⁴×C₁₃	1	2	yes	—
855	C₁₃	#61501	1	1	yes	characteristic, direct product factor, Sylow
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	8	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
862	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	Q₈	—	2	2	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	1	no	—
868	Q₈	—	8	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	1	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	C₂×C₁₃×#41	1	4	yes	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
909	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
910	C₈	—	2	1	no	—
911	C₈	—	2	2	no	—
912	C₈	—	2	1	no	—
913	C₈	—	2	1	no	—
914	C₈	—	2	2	no	—
915	C₈	C₂×C₁₃×#41	1	2	yes	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	16	4	no	—
929	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
945	C₄	C₁₃×#585	1	1	yes	characteristic
946	C₂	—	4	2	no	—
947	C₂	—	4	1	no	—
948	C₂	—	4	4	no	—
949	C₂	—	8	2	no	—
950	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
951	C₂	C₁₃×#3584	1	1	yes	characteristic
952	C₂	C₁₃×#3584	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3521	C₂	semidirect
2. C₁₃×#3402	C₂	semidirect
3. C₁₃×#3389	C₂	semidirect
4. C₁₃×#3360	C₂	semidirect
5. C₁₃×#3352	C₂	semidirect
6. C₁₃×#3350	C₂	semidirect
7. C₁₃×#3302	C₂	semidirect
8. C₁₃×#3297	C₂	semidirect
9. C₁₃×#3296	C₂	semidirect
10. C₁₃×#3273	C₂	semidirect
11. C₁₃×#3267	C₂	semidirect
12. C₁₃×#3178	C₂	semidirect
13. C₁₃×#3168	C₂	semidirect
14. C₁₃×#3120	C₂	semidirect
15. C₁₃×#3118	C₂	semidirect
16. C₁₃×#3111	C₂	semidirect
17. C₁₃×#2966	C₂	semidirect
18. C₁₃×#2946	C₂	semidirect
19. C₄×C₁₃×#135	C₂	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
33. C₁₃×#546	C₂²	semidirect
35. C₁₃×#541	C₂²	semidirect
40. C₁₃×#529	C₂²	semidirect
43. C₁₃×#518	C₂²	semidirect
44. C₄×C₁₃×#41	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#499	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#488	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
55. C₁₃×#483	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#470	C₂²	semidirect
66. C₁₃×#467	C₂²	semidirect
67. C₁₃×#467	C₂²	semidirect
70. C₁₃×#465	C₂²	semidirect
71. C₁₃×#464	C₂²	semidirect
75. C₁₃×#462	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
79. C₁₃×#452	C₂²	semidirect
80. C₁₃×#450	C₂²	semidirect
83. C₁₃×#446	C₂²	semidirect
84. C₈×Q₈×C₁₃	C₂²	semidirect
87. C₁₃×#441	C₂²	semidirect
88. C₁₃×#440	C₂²	semidirect
89. C₁₃×#440	C₂²	semidirect
90. C₁₃×#440	C₂²	semidirect
91. C₄×C₁₃×Q₁₆	C₂²	semidirect
92. C₄×C₁₃×Q₁₆	C₂²	semidirect
93. C₄×C₁₃×Q₁₆	C₂²	semidirect
94. C₄×C₁₃×SD₁₆	C₂²	semidirect
95. C₄×C₁₃×SD₁₆	C₂²	semidirect
96. C₄×C₁₃×SD₁₆	C₂²	semidirect
97. C₄×C₁₃×SD₁₆	C₂²	semidirect
103. C₁₃×#435	C₂²	semidirect
105. C₈×D₄×C₁₃	C₂²	semidirect
106. C₁₃×#433	C₂²	semidirect
107. C₁₃×#432	C₂²	semidirect
108. C₁₃×#428	C₂²	semidirect
109. C₁₃×#427	C₂²	semidirect
111. C₁₃×#416	C₂²	semidirect
112. C₂×C₁₃×#102	C₂²	semidirect
113. C₁₃×#405	C₂²	semidirect
114. C₂×C₄×C₈×C₁₃	C₂²	semidirect
266. #61501	C₁₃	direct (N × H)
380. #3521	C₂×C₁₃	semidirect
381. #3402	C₂×C₁₃	semidirect
382. #3389	C₂×C₁₃	semidirect
383. #3360	C₂×C₁₃	semidirect
384. #3352	C₂×C₁₃	semidirect
385. #3350	C₂×C₁₃	semidirect
386. #3302	C₂×C₁₃	semidirect
387. #3297	C₂×C₁₃	semidirect
388. #3296	C₂×C₁₃	semidirect
389. #3273	C₂×C₁₃	semidirect
390. #3267	C₂×C₁₃	semidirect
391. #3178	C₂×C₁₃	semidirect
392. #3168	C₂×C₁₃	semidirect
393. #3120	C₂×C₁₃	semidirect
394. #3118	C₂×C₁₃	semidirect
395. #3111	C₂×C₁₃	semidirect
396. #2966	C₂×C₁₃	semidirect
397. #2946	C₂×C₁₃	semidirect
398. C₄×#135	C₂×C₁₃	semidirect
461. #556	C₂²×C₁₃	semidirect
462. #556	C₂²×C₁₃	semidirect
463. #554	C₂²×C₁₃	semidirect
472. #546	C₂²×C₁₃	semidirect
474. #541	C₂²×C₁₃	semidirect
479. #529	C₂²×C₁₃	semidirect
482. #518	C₂²×C₁₃	semidirect
483. C₄×#41	C₂²×C₁₃	semidirect
484. #501	C₂²×C₁₃	semidirect
485. #499	C₂²×C₁₃	semidirect
486. #497	C₂²×C₁₃	semidirect
488. #488	C₂²×C₁₃	semidirect
489. #488	C₂²×C₁₃	semidirect
490. #487	C₂²×C₁₃	semidirect
491. #485	C₂²×C₁₃	semidirect
492. #485	C₂²×C₁₃	semidirect
493. #484	C₂²×C₁₃	semidirect
494. #483	C₂²×C₁₃	semidirect
496. #482	C₂²×C₁₃	semidirect
497. #479	C₂²×C₁₃	semidirect
498. #479	C₂²×C₁₃	semidirect
499. #478	C₂²×C₁₃	semidirect
500. #478	C₂²×C₁₃	semidirect
501. #476	C₂²×C₁₃	semidirect
502. #474	C₂²×C₁₃	semidirect
503. #470	C₂²×C₁₃	semidirect
505. #467	C₂²×C₁₃	semidirect
506. #467	C₂²×C₁₃	semidirect
509. #465	C₂²×C₁₃	semidirect
510. #464	C₂²×C₁₃	semidirect
514. #462	C₂²×C₁₃	semidirect
515. #461	C₂²×C₁₃	semidirect
518. #452	C₂²×C₁₃	semidirect
519. #450	C₂²×C₁₃	semidirect
522. #446	C₂²×C₁₃	semidirect
523. C₈×Q₈	C₂²×C₁₃	semidirect
526. #441	C₂²×C₁₃	semidirect
527. #440	C₂²×C₁₃	semidirect
528. #440	C₂²×C₁₃	semidirect
529. #440	C₂²×C₁₃	semidirect
530. C₄×Q₁₆	C₂²×C₁₃	semidirect
531. C₄×Q₁₆	C₂²×C₁₃	semidirect
532. C₄×Q₁₆	C₂²×C₁₃	semidirect
533. C₄×SD₁₆	C₂²×C₁₃	semidirect
534. C₄×SD₁₆	C₂²×C₁₃	semidirect
535. C₄×SD₁₆	C₂²×C₁₃	semidirect
536. C₄×SD₁₆	C₂²×C₁₃	semidirect
542. #435	C₂²×C₁₃	semidirect
544. C₈×D₄	C₂²×C₁₃	semidirect
545. #433	C₂²×C₁₃	semidirect
546. #432	C₂²×C₁₃	semidirect
547. #428	C₂²×C₁₃	semidirect
548. #427	C₂²×C₁₃	semidirect
550. #416	C₂²×C₁₃	semidirect
551. C₂×#102	C₂²×C₁₃	semidirect
552. #405	C₂²×C₁₃	semidirect
553. C₂×C₄×C₈	C₂²×C₁₃	semidirect
855. C₁₃	#61501	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×#3521	2
C₁₃×#3402	2
C₁₃×#3389	2
C₁₃×#3360	2
C₁₃×#3352	2
C₁₃×#3350	2
C₁₃×#3302	2
C₁₃×#3297	2
C₁₃×#3296	2
C₁₃×#3273	2
C₁₃×#3267	2
C₁₃×#3178	2
C₁₃×#3168	2
C₁₃×#3120	2
C₁₃×#3118	2
C₁₃×#3111	2
C₁₃×#2966	2
C₁₃×#2946	2
C₄×C₁₃×#135	2
#61501	13

Subgroups — C13×#61501 #15747840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61501 #15747840