Subgroups — C₁₃×#61637 #15747976

Order 3328.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3287	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3220	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3198	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3191	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#135	C₂²	1	2	yes	—
24	C₂×C₁₃×#135	C₂²	1	2	yes	—
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₁₃×#560	—	2	2	no	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#553	C₂²	1	2	yes	complemented
29	C₁₃×#552	C₂²	1	2	yes	complemented
30	C₁₃×#550	—	2	2	no	—
31	C₁₃×#550	C₂²	1	2	yes	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	C₁₃×#550	C₂²	1	2	yes	complemented
34	C₁₃×#548	—	2	2	no	—
35	C₁₃×#548	C₂²	1	2	yes	—
36	C₁₃×#548	C₂²	1	2	yes	—
37	C₁₃×#547	C₂²	1	2	yes	complemented
38	C₁₃×#541	C₂²	1	1	yes	characteristic
39	C₁₃×#540	—	2	2	no	—
40	C₁₃×#540	C₂²	1	1	yes	characteristic
41	C₁₃×#539	—	2	2	no	—
42	C₁₃×#537	C₂²	1	2	yes	—
43	C₁₃×#535	—	2	2	no	—
44	C₁₃×#535	C₂²	1	1	yes	characteristic
45	C₁₃×#535	C₂²	1	1	yes	characteristic
46	C₁₃×#525	—	2	2	no	—
47	C₁₃×#525	C₂²	1	2	yes	—
48	C₁₃×#525	C₂²	1	1	yes	characteristic
49	C₁₃×#525	C₂²	1	1	yes	characteristic
50	C₁₃×#519	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#496	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#490	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#485	C₂²	1	2	yes	—
60	C₁₃×#485	C₂²	1	2	yes	complemented
61	C₁₃×#482	C₂²	1	2	yes	—
62	C₁₃×#482	C₂²	1	2	yes	complemented
63	C₁₃×#481	C₂²	1	2	yes	complemented
64	C₁₃×#480	C₂²	1	2	yes	complemented
65	C₁₃×#479	C₂²	1	2	yes	complemented
66	C₁₃×#479	C₂²	1	2	yes	complemented
67	C₁₃×#469	C₂²	1	2	yes	complemented
68	C₁₃×#468	C₂²	1	2	yes	complemented
69	C₁₃×#467	C₂²	1	2	yes	complemented
70	C₁₃×#466	C₂²	1	2	yes	complemented
71	C₁₃×#466	C₂²	1	2	yes	complemented
72	C₁₃×#465	C₂²	1	2	yes	complemented
73	C₁₃×#465	C₂²	1	2	yes	complemented
74	C₁₃×#465	C₂²	1	2	yes	complemented
75	C₁₃×#464	C₂²	1	2	yes	complemented
76	C₁₃×#463	C₂²	1	2	yes	complemented
77	C₁₃×#462	C₂²	1	2	yes	complemented
78	C₁₃×#460	C₂²	1	2	yes	complemented
79	C₁₃×#460	C₂²	1	2	yes	complemented
80	C₁₃×#459	C₂²	1	2	yes	complemented
81	C₁₃×#452	C₂²	1	2	yes	—
82	C₁₃×#452	C₂²	1	2	yes	—
83	C₁₃×#452	C₂²	1	2	yes	—
84	C₁₃×#452	C₂²	1	2	yes	complemented
85	C₁₃×#452	C₂²	1	2	yes	complemented
86	C₁₃×#451	C₂²	1	2	yes	—
87	C₁₃×#451	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	—
89	C₁₃×#449	C₂²	1	2	yes	—
90	C₁₃×#449	C₂²	1	2	yes	—
91	C₁₃×#449	C₂²	1	2	yes	—
92	C₁₃×#449	C₂²	1	2	yes	complemented
93	C₁₃×#449	C₂²	1	2	yes	complemented
94	C₁₃×#449	C₂²	1	2	yes	complemented
95	C₁₃×#449	C₂²	1	2	yes	complemented
96	C₁₃×#448	C₂²	1	2	yes	—
97	C₁₃×#448	C₂²	1	2	yes	complemented
98	C₁₃×#447	C₂²	1	2	yes	—
99	C₁₃×#441	C₂²	1	2	yes	complemented
100	C₁₃×#440	C₂²	1	2	yes	complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
103	C₁₃×#435	C₂²	1	2	yes	complemented
104	C₁₃×#435	C₂²	1	2	yes	complemented
105	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
107	C₁₃×#433	C₂²	1	1	yes	characteristic
108	C₁₃×#433	C₂²	1	1	yes	characteristic
109	C₁₃×#417	C₂²	1	2	yes	complemented
110	C₁₃×#416	C₂²	1	2	yes	—
111	C₁₃×#416	C₂²	1	2	yes	—
112	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
113	C₁₃×#408	C₂²	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
115	C₁₃×2₋¹⁺⁴	—	4	4	no	—
116	C₂×C₁₃×#41	—	2	2	no	—
117	C₂×C₁₃×#41	—	2	1	no	—
118	C₂×C₁₃×#41	—	2	2	no	—
119	C₂×C₁₃×#41	—	4	4	no	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂×C₁₃×#41	C₂³	1	2	yes	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×#41	C₂³	1	2	yes	—
125	C₂×C₁₃×#41	C₂³	1	2	yes	—
126	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₁₃	—	2	1	no	—
128	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₁₃	—	2	1	no	—
131	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃	—	2	1	no	—
133	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×#137	—	4	4	no	—
135	C₁₃×#135	—	4	4	no	—
136	C₁₃×#135	—	4	4	no	—
137	C₁₃×#135	—	4	4	no	—
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×D₈	C₂³	1	2	yes	—
148	C₂×C₁₃×D₈	C₂³	1	2	yes	—
149	C₂×C₁₃×D₈	C₂³	1	2	yes	—
150	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
151	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×#127	—	2	2	no	—
156	C₁₃×#127	—	2	2	no	—
157	C₁₃×#127	—	2	1	no	—
158	C₁₃×#127	—	2	2	no	—
159	C₁₃×#127	C₂³	1	1	yes	characteristic
160	C₁₃×#127	C₂³	1	1	yes	characteristic
161	C₁₃×#127	C₂³	1	1	yes	characteristic
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#125	—	2	2	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	C₂³	1	1	yes	characteristic
168	C₁₃×#125	C₂³	1	1	yes	characteristic
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	—	2	2	no	—
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	C₂³	1	1	yes	characteristic
173	C₁₃×#124	C₂³	1	1	yes	characteristic
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	1	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	D₄	1	2	yes	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₃×#121	—	2	2	no	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	2	no	—
193	C₁₃×#121	—	2	2	no	—
194	C₁₃×#121	—	2	2	no	—
195	C₁₃×#121	—	2	2	no	—
196	C₁₃×#121	—	2	2	no	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	D₄	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#121	C₂³	1	2	yes	—
209	C₁₃×#121	C₂³	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₁₃×#120	—	2	1	no	—
213	C₁₃×#120	—	2	2	no	—
214	C₁₃×#120	—	2	2	no	—
215	C₁₃×#120	—	2	2	no	—
216	C₁₃×#120	D₄	1	2	yes	—
217	C₄×Q₈×C₁₃	—	2	2	no	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
221	C₄×D₄×C₁₃	—	2	2	no	—
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	2	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	2	no	—
226	C₄×D₄×C₁₃	—	2	2	no	—
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	C₂³	1	2	yes	—
231	C₄×D₄×C₁₃	C₂³	1	2	yes	—
232	C₄×D₄×C₁₃	C₂³	1	2	yes	—
233	C₁₃×#117	—	2	2	no	—
234	C₁₃×#117	—	2	2	no	—
235	C₁₃×#117	C₂³	1	2	yes	—
236	C₁₃×#117	C₂³	1	1	yes	characteristic
237	C₁₃×#117	C₂³	1	1	yes	characteristic
238	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#102	C₂³	1	2	yes	—
255	C₁₃×#102	C₂³	1	2	yes	—
256	C₁₃×#102	C₂³	1	2	yes	—
257	C₁₃×#102	C₂³	1	2	yes	—
258	C₁₃×#102	C₂³	1	2	yes	—
259	C₁₃×#102	C₂³	1	2	yes	—
260	C₁₃×#102	C₂³	1	2	yes	—
261	C₁₃×#102	C₂³	1	2	yes	—
262	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₁₃×#97	C₂³	1	1	yes	characteristic
269	C₁₃×#97	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
272	#61637	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂⁴×C₁₃	—	2	1	no	—
274	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₁₃×#41	—	2	4	no	—
276	C₁₃×#41	—	2	4	no	—
277	C₁₃×#41	—	2	4	no	—
278	C₁₃×#41	—	4	2	no	—
279	C₁₃×#41	—	4	2	no	—
280	C₁₃×#41	—	4	2	no	—
281	C₁₃×#41	—	4	2	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	8	no	—
284	C₁₃×#41	—	4	2	no	—
285	C₁₃×#41	—	4	2	no	—
286	C₁₃×#41	—	4	2	no	—
287	C₁₃×#41	—	4	2	no	—
288	C₁₃×#41	—	4	8	no	—
289	C₁₃×#41	—	4	4	no	—
290	C₂×Q₈×C₁₃	—	2	4	no	—
291	C₂×Q₈×C₁₃	—	2	1	no	—
292	C₂×Q₈×C₁₃	—	2	2	no	—
293	C₂×Q₈×C₁₃	—	2	4	no	—
294	C₂×Q₈×C₁₃	—	4	2	no	—
295	C₂×Q₈×C₁₃	—	4	4	no	—
296	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	2	no	—
304	C₂×D₄×C₁₃	—	2	2	no	—
305	C₂×D₄×C₁₃	—	2	2	no	—
306	C₂×D₄×C₁₃	—	2	2	no	—
307	C₂×D₄×C₁₃	—	2	2	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	2	2	no	—
310	C₂×D₄×C₁₃	—	2	2	no	—
311	C₂×D₄×C₁₃	—	2	2	no	—
312	C₂×D₄×C₁₃	—	2	1	no	—
313	C₂×D₄×C₁₃	—	2	2	no	—
314	C₂×D₄×C₁₃	—	2	2	no	—
315	C₂×D₄×C₁₃	—	2	2	no	—
316	C₂×D₄×C₁₃	—	4	2	no	—
317	C₂×D₄×C₁₃	—	4	4	no	—
318	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
319	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₁₃	—	2	1	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	2	no	—
329	C₂²×C₄×C₁₃	—	2	2	no	—
330	C₂²×C₄×C₁₃	—	2	1	no	—
331	C₂²×C₄×C₁₃	—	2	2	no	—
332	C₂²×C₄×C₁₃	—	2	2	no	—
333	C₂²×C₄×C₁₃	—	2	2	no	—
334	C₂²×C₄×C₁₃	—	2	2	no	—
335	C₂²×C₄×C₁₃	—	2	2	no	—
336	C₂²×C₄×C₁₃	—	4	2	no	—
337	C₂²×C₄×C₁₃	—	4	4	no	—
338	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
339	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
343	C₁₃×Q₁₆	—	2	4	no	—
344	C₁₃×Q₁₆	—	2	4	no	—
345	C₁₃×Q₁₆	—	4	2	no	—
346	C₁₃×SD₁₆	—	2	4	no	—
347	C₁₃×SD₁₆	—	2	4	no	—
348	C₁₃×SD₁₆	—	4	2	no	—
349	C₁₃×SD₁₆	—	4	2	no	—
350	C₁₃×SD₁₆	—	4	2	no	—
351	C₁₃×SD₁₆	—	4	2	no	—
352	C₁₃×D₈	—	4	2	no	—
353	C₁₃×D₈	—	4	2	no	—
354	C₁₃×D₈	—	4	2	no	—
355	C₁₃×M₁₆	—	4	2	no	—
356	C₂×C₈×C₁₃	—	4	2	no	—
357	C₂×C₈×C₁₃	—	4	2	no	—
358	C₂×C₈×C₁₃	—	4	2	no	—
359	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
360	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
375	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
379	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
389	C₁₃×C₂²⋊C₄	—	2	2	no	—
390	C₁₃×C₂²⋊C₄	—	2	2	no	—
391	C₁₃×C₂²⋊C₄	—	2	2	no	—
392	C₁₃×C₂²⋊C₄	—	2	2	no	—
393	C₁₃×C₂²⋊C₄	—	2	2	no	—
394	C₁₃×C₂²⋊C₄	—	2	2	no	—
395	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
396	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
397	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
398	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
400	C₄²×C₁₃	—	2	2	no	—
401	C₄²×C₁₃	—	2	2	no	—
402	C₄²×C₁₃	—	2	2	no	—
403	C₄²×C₁₃	—	2	2	no	—
404	C₄²×C₁₃	—	2	1	no	—
405	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
407	#3539	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3487	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3317	C₂×C₁₃	1	2	yes	complemented
410	#3309	C₂×C₁₃	1	2	yes	complemented
411	#3301	C₂×C₁₃	1	2	yes	complemented
412	#3300	C₂×C₁₃	1	2	yes	complemented
413	#3287	C₂×C₁₃	1	2	yes	complemented
414	#3284	C₂×C₁₃	1	2	yes	complemented
415	#3271	C₂×C₁₃	1	2	yes	complemented
416	#3269	C₂×C₁₃	1	2	yes	complemented
417	#3222	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3220	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3198	C₂×C₁₃	1	2	yes	complemented
420	#3191	C₂×C₁₃	1	2	yes	complemented
421	#3127	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#3126	C₂×C₁₃	1	1	yes	characteristic, complemented
423	#3013	C₂×C₁₃	1	2	yes	complemented
424	#3002	C₂×C₁₃	1	2	yes	complemented
425	#2977	C₂×C₁₃	1	1	yes	characteristic, complemented
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	1	no	—
428	C₂³×C₁₃	—	2	1	no	—
429	C₂³×C₁₃	—	2	1	no	—
430	C₂³×C₁₃	—	4	1	no	—
431	C₂³×C₁₃	—	4	2	no	—
432	C₂³×C₁₃	—	4	2	no	—
433	C₂³×C₁₃	—	8	2	no	—
434	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
436	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
437	Q₈×C₁₃	—	2	4	no	—
438	Q₈×C₁₃	—	2	2	no	—
439	Q₈×C₁₃	—	2	2	no	—
440	Q₈×C₁₃	—	2	2	no	—
441	Q₈×C₁₃	—	2	2	no	—
442	Q₈×C₁₃	—	4	1	no	—
443	Q₈×C₁₃	—	4	4	no	—
444	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	2	2	no	—
448	D₄×C₁₃	—	2	2	no	—
449	D₄×C₁₃	—	2	2	no	—
450	D₄×C₁₃	—	4	2	no	—
451	D₄×C₁₃	—	4	2	no	—
452	D₄×C₁₃	—	4	1	no	—
453	D₄×C₁₃	—	4	2	no	—
454	D₄×C₁₃	—	4	4	no	—
455	D₄×C₁₃	—	4	4	no	—
456	D₄×C₁₃	—	4	4	no	—
457	D₄×C₁₃	—	4	2	no	—
458	D₄×C₁₃	—	4	2	no	—
459	D₄×C₁₃	—	8	2	no	—
460	D₄×C₁₃	—	8	2	no	—
461	D₄×C₁₃	—	8	2	no	—
462	D₄×C₁₃	—	8	2	no	—
463	D₄×C₁₃	—	8	2	no	—
464	D₄×C₁₃	—	8	2	no	—
465	D₄×C₁₃	—	8	2	no	—
466	D₄×C₁₃	—	8	2	no	—
467	D₄×C₁₃	—	8	2	no	—
468	D₄×C₁₃	—	8	2	no	—
469	D₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	—	2	4	no	—
471	C₂×C₄×C₁₃	—	2	2	no	—
472	C₂×C₄×C₁₃	—	2	2	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	2	no	—
475	C₂×C₄×C₁₃	—	2	2	no	—
476	C₂×C₄×C₁₃	—	2	2	no	—
477	C₂×C₄×C₁₃	—	2	2	no	—
478	C₂×C₄×C₁₃	—	2	2	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	4	1	no	—
483	C₂×C₄×C₁₃	—	4	2	no	—
484	C₂×C₄×C₁₃	—	4	4	no	—
485	C₂×C₄×C₁₃	—	4	4	no	—
486	C₂×C₄×C₁₃	—	4	4	no	—
487	C₂×C₄×C₁₃	—	4	4	no	—
488	C₂×C₄×C₁₃	—	4	2	no	—
489	C₂×C₄×C₁₃	—	8	2	no	—
490	C₂×C₄×C₁₃	—	8	2	no	—
491	C₂×C₄×C₁₃	—	8	2	no	—
492	C₂×C₄×C₁₃	—	8	2	no	—
493	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
499	C₈×C₁₃	—	2	2	no	—
500	C₈×C₁₃	—	2	2	no	—
501	C₈×C₁₃	—	2	2	no	—
502	C₈×C₁₃	—	2	2	no	—
503	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
504	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
505	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
506	C₂×#135	C₂²×C₁₃	1	2	yes	—
507	C₂×#135	C₂²×C₁₃	1	2	yes	—
508	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
509	#560	—	2	2	no	—
510	#553	—	2	2	no	—
511	#553	C₂²×C₁₃	1	2	yes	complemented
512	#552	C₂²×C₁₃	1	2	yes	complemented
513	#550	—	2	2	no	—
514	#550	C₂²×C₁₃	1	2	yes	—
515	#550	C₂²×C₁₃	1	2	yes	—
516	#550	C₂²×C₁₃	1	2	yes	complemented
517	#548	—	2	2	no	—
518	#548	C₂²×C₁₃	1	2	yes	—
519	#548	C₂²×C₁₃	1	2	yes	—
520	#547	C₂²×C₁₃	1	2	yes	complemented
521	#541	C₂²×C₁₃	1	1	yes	characteristic
522	#540	—	2	2	no	—
523	#540	C₂²×C₁₃	1	1	yes	characteristic
524	#539	—	2	2	no	—
525	#537	C₂²×C₁₃	1	2	yes	—
526	#535	—	2	2	no	—
527	#535	C₂²×C₁₃	1	1	yes	characteristic
528	#535	C₂²×C₁₃	1	1	yes	characteristic
529	#525	—	2	2	no	—
530	#525	C₂²×C₁₃	1	1	yes	characteristic
531	#525	C₂²×C₁₃	1	2	yes	—
532	#525	C₂²×C₁₃	1	1	yes	characteristic
533	#519	C₂²×C₁₃	1	1	yes	characteristic
534	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
536	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
539	#490	C₂²×C₁₃	1	1	yes	characteristic, complemented
540	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
542	#485	C₂²×C₁₃	1	2	yes	—
543	#485	C₂²×C₁₃	1	2	yes	complemented
544	#482	C₂²×C₁₃	1	2	yes	—
545	#482	C₂²×C₁₃	1	2	yes	complemented
546	#481	C₂²×C₁₃	1	2	yes	complemented
547	#480	C₂²×C₁₃	1	2	yes	complemented
548	#479	C₂²×C₁₃	1	2	yes	complemented
549	#479	C₂²×C₁₃	1	2	yes	complemented
550	#469	C₂²×C₁₃	1	2	yes	complemented
551	#468	C₂²×C₁₃	1	2	yes	complemented
552	#467	C₂²×C₁₃	1	2	yes	complemented
553	#466	C₂²×C₁₃	1	2	yes	complemented
554	#466	C₂²×C₁₃	1	2	yes	complemented
555	#465	C₂²×C₁₃	1	2	yes	complemented
556	#465	C₂²×C₁₃	1	2	yes	complemented
557	#465	C₂²×C₁₃	1	2	yes	complemented
558	#464	C₂²×C₁₃	1	2	yes	complemented
559	#463	C₂²×C₁₃	1	2	yes	complemented
560	#462	C₂²×C₁₃	1	2	yes	complemented
561	#460	C₂²×C₁₃	1	2	yes	complemented
562	#460	C₂²×C₁₃	1	2	yes	complemented
563	#459	C₂²×C₁₃	1	2	yes	complemented
564	#452	C₂²×C₁₃	1	2	yes	—
565	#452	C₂²×C₁₃	1	2	yes	—
566	#452	C₂²×C₁₃	1	2	yes	—
567	#452	C₂²×C₁₃	1	2	yes	complemented
568	#452	C₂²×C₁₃	1	2	yes	complemented
569	#451	C₂²×C₁₃	1	2	yes	—
570	#451	C₂²×C₁₃	1	2	yes	complemented
571	#450	C₂²×C₁₃	1	2	yes	—
572	#449	C₂²×C₁₃	1	2	yes	—
573	#449	C₂²×C₁₃	1	2	yes	—
574	#449	C₂²×C₁₃	1	2	yes	—
575	#449	C₂²×C₁₃	1	2	yes	complemented
576	#449	C₂²×C₁₃	1	2	yes	complemented
577	#449	C₂²×C₁₃	1	2	yes	complemented
578	#449	C₂²×C₁₃	1	2	yes	complemented
579	#448	C₂²×C₁₃	1	2	yes	—
580	#448	C₂²×C₁₃	1	2	yes	complemented
581	#447	C₂²×C₁₃	1	2	yes	—
582	#441	C₂²×C₁₃	1	2	yes	complemented
583	#440	C₂²×C₁₃	1	2	yes	complemented
584	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
585	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
586	#435	C₂²×C₁₃	1	2	yes	complemented
587	#435	C₂²×C₁₃	1	2	yes	complemented
588	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
589	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
590	#433	C₂²×C₁₃	1	1	yes	characteristic
591	#433	C₂²×C₁₃	1	1	yes	characteristic
592	#417	C₂²×C₁₃	1	2	yes	complemented
593	#416	C₂²×C₁₃	1	2	yes	—
594	#416	C₂²×C₁₃	1	2	yes	—
595	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
596	#408	C₂²×C₁₃	1	2	yes	—
597	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
598	C₂²×C₁₃	—	2	2	no	—
599	C₂²×C₁₃	—	2	2	no	—
600	C₂²×C₁₃	—	2	2	no	—
601	C₂²×C₁₃	—	2	2	no	—
602	C₂²×C₁₃	—	2	2	no	—
603	C₂²×C₁₃	—	2	1	no	—
604	C₂²×C₁₃	—	2	2	no	—
605	C₂²×C₁₃	—	2	2	no	—
606	C₂²×C₁₃	—	4	2	no	—
607	C₂²×C₁₃	—	4	2	no	—
608	C₂²×C₁₃	—	4	2	no	—
609	C₂²×C₁₃	—	4	2	no	—
610	C₂²×C₁₃	—	4	2	no	—
611	C₂²×C₁₃	—	4	1	no	—
612	C₂²×C₁₃	—	4	1	no	—
613	C₂²×C₁₃	—	4	1	no	—
614	C₂²×C₁₃	—	4	2	no	—
615	C₂²×C₁₃	—	8	2	no	—
616	C₂²×C₁₃	—	8	4	no	—
617	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₁₃	—	2	2	no	—
619	C₄×C₁₃	—	2	2	no	—
620	C₄×C₁₃	—	2	4	no	—
621	C₄×C₁₃	—	2	2	no	—
622	C₄×C₁₃	—	2	1	no	—
623	C₄×C₁₃	—	2	2	no	—
624	C₄×C₁₃	—	4	2	no	—
625	C₄×C₁₃	—	4	2	no	—
626	C₄×C₁₃	—	4	2	no	—
627	C₄×C₁₃	—	4	1	no	—
628	C₄×C₁₃	—	4	2	no	—
629	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
630	2₋¹⁺⁴	—	4	4	no	—
631	C₂×#41	—	2	2	no	—
632	C₂×#41	—	2	1	no	—
633	C₂×#41	—	2	2	no	—
634	C₂×#41	—	4	4	no	—
635	C₂×#41	C₂³×C₁₃	1	2	yes	—
636	C₂×#41	C₂³×C₁₃	1	2	yes	—
637	C₂×#41	C₂³×C₁₃	1	2	yes	—
638	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×#41	C₂³×C₁₃	1	2	yes	—
640	C₂×#41	C₂³×C₁₃	1	2	yes	—
641	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
642	C₂²×Q₈	—	2	1	no	—
643	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
644	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
645	C₂²×D₄	—	2	1	no	—
646	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
649	#137	—	4	4	no	—
650	#135	—	4	4	no	—
651	#135	—	4	4	no	—
652	#135	—	4	4	no	—
653	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
662	C₂×D₈	C₂³×C₁₃	1	2	yes	—
663	C₂×D₈	C₂³×C₁₃	1	2	yes	—
664	C₂×D₈	C₂³×C₁₃	1	2	yes	—
665	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
666	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
667	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
668	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
669	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
670	#127	—	2	2	no	—
671	#127	—	2	2	no	—
672	#127	—	2	1	no	—
673	#127	—	2	2	no	—
674	#127	C₂³×C₁₃	1	1	yes	characteristic
675	#127	C₂³×C₁₃	1	1	yes	characteristic
676	#127	C₂³×C₁₃	1	1	yes	characteristic
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#125	—	2	2	no	—
681	#125	—	2	2	no	—
682	#125	C₂³×C₁₃	1	1	yes	characteristic
683	#125	C₂³×C₁₃	1	1	yes	characteristic
684	#124	—	2	1	no	—
685	#124	—	2	2	no	—
686	#124	—	2	2	no	—
687	#124	C₂³×C₁₃	1	1	yes	characteristic
688	#124	C₂³×C₁₃	1	1	yes	characteristic
689	#123	—	2	2	no	—
690	#123	—	2	1	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	D₄×C₁₃	1	2	yes	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	D₄×C₁₃	1	2	yes	—
721	#121	C₂³×C₁₃	1	2	yes	—
722	#121	C₂³×C₁₃	1	2	yes	—
723	#121	C₂³×C₁₃	1	2	yes	—
724	#121	C₂³×C₁₃	1	2	yes	—
725	#121	C₂³×C₁₃	1	2	yes	—
726	#121	C₂³×C₁₃	1	2	yes	—
727	#120	—	2	1	no	—
728	#120	—	2	2	no	—
729	#120	—	2	2	no	—
730	#120	—	2	2	no	—
731	#120	D₄×C₁₃	1	2	yes	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
734	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
735	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	2	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	C₂³×C₁₃	1	2	yes	—
746	C₄×D₄	C₂³×C₁₃	1	2	yes	—
747	C₄×D₄	C₂³×C₁₃	1	2	yes	—
748	#117	—	2	2	no	—
749	#117	—	2	2	no	—
750	#117	C₂³×C₁₃	1	1	yes	characteristic
751	#117	C₂³×C₁₃	1	2	yes	—
752	#117	C₂³×C₁₃	1	1	yes	characteristic
753	C₂×C₄⋊C₄	—	2	2	no	—
754	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
755	#107	C₂³×C₁₃	1	2	yes	—
756	#107	C₂³×C₁₃	1	2	yes	—
757	#106	C₂³×C₁₃	1	2	yes	—
758	#106	C₂³×C₁₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
761	#103	C₂³×C₁₃	1	2	yes	—
762	#103	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#103	C₂³×C₁₃	1	2	yes	—
766	#103	C₂³×C₁₃	1	2	yes	—
767	#103	C₂³×C₁₃	1	2	yes	—
768	#103	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	#102	C₂³×C₁₃	1	2	yes	—
776	#102	C₂³×C₁₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
783	#97	C₂³×C₁₃	1	1	yes	characteristic
784	#97	C₂³×C₁₃	1	1	yes	characteristic
785	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₂×C₁₃	—	4	2	no	—
788	C₂×C₁₃	—	4	2	no	—
789	C₂×C₁₃	—	4	1	no	—
790	C₂×C₁₃	—	8	2	no	—
791	C₂×C₁₃	—	8	1	no	—
792	C₂×C₁₃	—	8	1	no	—
793	C₂×C₁₃	—	8	1	no	—
794	C₂×C₁₃	#3484	1	1	yes	characteristic
795	C₂×C₁₃	#3584	1	2	yes	—
796	C₂⁴	—	2	1	no	—
797	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
798	#41	—	2	4	no	—
799	#41	—	2	4	no	—
800	#41	—	2	4	no	—
801	#41	—	4	2	no	—
802	#41	—	4	2	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	8	no	—
807	#41	—	4	2	no	—
808	#41	—	4	2	no	—
809	#41	—	4	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	8	no	—
812	#41	—	4	4	no	—
813	C₂×Q₈	—	2	4	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	4	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	4	no	—
819	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
821	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
822	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	4	no	—
841	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
842	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
845	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
847	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	4	no	—
861	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
862	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
866	Q₁₆	—	2	4	no	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	4	2	no	—
869	SD₁₆	—	2	4	no	—
870	SD₁₆	—	2	4	no	—
871	SD₁₆	—	4	2	no	—
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	D₈	—	4	2	no	—
876	D₈	—	4	2	no	—
877	D₈	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	—	4	2	no	—
881	C₂×C₈	—	4	2	no	—
882	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
883	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
884	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
885	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
898	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
899	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
902	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
903	C₂²⋊C₄	—	2	1	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
920	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	1	no	—
928	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₁₃	#61637	1	1	yes	characteristic, direct product factor, Sylow
931	C₂³	—	2	2	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	4	1	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	2	no	—
939	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
940	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
941	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
942	Q₈	—	2	4	no	—
943	Q₈	—	2	2	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	4	1	no	—
948	Q₈	—	4	4	no	—
949	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
950	D₄	—	2	2	no	—
951	D₄	—	2	2	no	—
952	D₄	—	2	2	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	2	no	—
955	D₄	—	4	2	no	—
956	D₄	—	4	2	no	—
957	D₄	—	4	1	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	4	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	4	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	2	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	2	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	2	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	4	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	—	4	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	2	no	—
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	8	2	no	—
1026	C₂²	—	8	4	no	—
1027	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1028	C₄	—	2	2	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	2	no	—
1039	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1040	C₂	—	4	1	no	—
1041	C₂	—	4	2	no	—
1042	C₂	—	4	2	no	—
1043	C₂	—	8	1	no	—
1044	C₂	—	8	1	no	—
1045	C₂	—	8	2	no	—
1046	C₂	—	8	1	no	—
1047	C₂	C₁₃×#3484	1	1	yes	characteristic
1048	C₂	C₁₃×#3584	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3539	C₂	semidirect
2. C₁₃×#3487	C₂	semidirect
3. C₁₃×#3317	C₂	semidirect
4. C₁₃×#3309	C₂	semidirect
5. C₁₃×#3301	C₂	semidirect
6. C₁₃×#3300	C₂	semidirect
7. C₁₃×#3287	C₂	semidirect
8. C₁₃×#3284	C₂	semidirect
9. C₁₃×#3271	C₂	semidirect
10. C₁₃×#3269	C₂	semidirect
11. C₁₃×#3222	C₂	semidirect
12. C₁₃×#3220	C₂	semidirect
13. C₁₃×#3198	C₂	semidirect
14. C₁₃×#3191	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
16. C₁₃×#3126	C₂	semidirect
17. C₁₃×#3013	C₂	semidirect
18. C₁₃×#3002	C₂	semidirect
19. C₁₃×#2977	C₂	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#496	C₂²	semidirect
53. C₁₃×#493	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
55. C₁₃×#490	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#488	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
60. C₁₃×#485	C₂²	semidirect
62. C₁₃×#482	C₂²	semidirect
63. C₁₃×#481	C₂²	semidirect
64. C₁₃×#480	C₂²	semidirect
65. C₁₃×#479	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
67. C₁₃×#469	C₂²	semidirect
68. C₁₃×#468	C₂²	semidirect
69. C₁₃×#467	C₂²	semidirect
70. C₁₃×#466	C₂²	semidirect
71. C₁₃×#466	C₂²	semidirect
72. C₁₃×#465	C₂²	semidirect
73. C₁₃×#465	C₂²	semidirect
74. C₁₃×#465	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#463	C₂²	semidirect
77. C₁₃×#462	C₂²	semidirect
78. C₁₃×#460	C₂²	semidirect
79. C₁₃×#460	C₂²	semidirect
80. C₁₃×#459	C₂²	semidirect
84. C₁₃×#452	C₂²	semidirect
85. C₁₃×#452	C₂²	semidirect
87. C₁₃×#451	C₂²	semidirect
92. C₁₃×#449	C₂²	semidirect
93. C₁₃×#449	C₂²	semidirect
94. C₁₃×#449	C₂²	semidirect
95. C₁₃×#449	C₂²	semidirect
97. C₁₃×#448	C₂²	semidirect
99. C₁₃×#441	C₂²	semidirect
100. C₁₃×#440	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
102. C₄×C₁₃×SD₁₆	C₂²	semidirect
103. C₁₃×#435	C₂²	semidirect
104. C₁₃×#435	C₂²	semidirect
105. C₈×D₄×C₁₃	C₂²	semidirect
106. C₈×D₄×C₁₃	C₂²	semidirect
109. C₁₃×#417	C₂²	semidirect
112. C₂×C₁₃×#103	C₂²	semidirect
272. #61637	C₁₃	direct (N × H)
407. #3539	C₂×C₁₃	semidirect
408. #3487	C₂×C₁₃	semidirect
409. #3317	C₂×C₁₃	semidirect
410. #3309	C₂×C₁₃	semidirect
411. #3301	C₂×C₁₃	semidirect
412. #3300	C₂×C₁₃	semidirect
413. #3287	C₂×C₁₃	semidirect
414. #3284	C₂×C₁₃	semidirect
415. #3271	C₂×C₁₃	semidirect
416. #3269	C₂×C₁₃	semidirect
417. #3222	C₂×C₁₃	semidirect
418. #3220	C₂×C₁₃	semidirect
419. #3198	C₂×C₁₃	semidirect
420. #3191	C₂×C₁₃	semidirect
421. #3127	C₂×C₁₃	semidirect
422. #3126	C₂×C₁₃	semidirect
423. #3013	C₂×C₁₃	semidirect
424. #3002	C₂×C₁₃	semidirect
425. #2977	C₂×C₁₃	semidirect
505. C₂×#137	C₂²×C₁₃	semidirect
508. C₂×#135	C₂²×C₁₃	semidirect
511. #553	C₂²×C₁₃	semidirect
512. #552	C₂²×C₁₃	semidirect
516. #550	C₂²×C₁₃	semidirect
520. #547	C₂²×C₁₃	semidirect
534. #497	C₂²×C₁₃	semidirect
535. #496	C₂²×C₁₃	semidirect
536. #493	C₂²×C₁₃	semidirect
537. #492	C₂²×C₁₃	semidirect
538. #490	C₂²×C₁₃	semidirect
539. #490	C₂²×C₁₃	semidirect
540. #488	C₂²×C₁₃	semidirect
541. #488	C₂²×C₁₃	semidirect
543. #485	C₂²×C₁₃	semidirect
545. #482	C₂²×C₁₃	semidirect
546. #481	C₂²×C₁₃	semidirect
547. #480	C₂²×C₁₃	semidirect
548. #479	C₂²×C₁₃	semidirect
549. #479	C₂²×C₁₃	semidirect
550. #469	C₂²×C₁₃	semidirect
551. #468	C₂²×C₁₃	semidirect
552. #467	C₂²×C₁₃	semidirect
553. #466	C₂²×C₁₃	semidirect
554. #466	C₂²×C₁₃	semidirect
555. #465	C₂²×C₁₃	semidirect
556. #465	C₂²×C₁₃	semidirect
557. #465	C₂²×C₁₃	semidirect
558. #464	C₂²×C₁₃	semidirect
559. #463	C₂²×C₁₃	semidirect
560. #462	C₂²×C₁₃	semidirect
561. #460	C₂²×C₁₃	semidirect
562. #460	C₂²×C₁₃	semidirect
563. #459	C₂²×C₁₃	semidirect
567. #452	C₂²×C₁₃	semidirect
568. #452	C₂²×C₁₃	semidirect
570. #451	C₂²×C₁₃	semidirect
575. #449	C₂²×C₁₃	semidirect
576. #449	C₂²×C₁₃	semidirect
577. #449	C₂²×C₁₃	semidirect
578. #449	C₂²×C₁₃	semidirect
580. #448	C₂²×C₁₃	semidirect
582. #441	C₂²×C₁₃	semidirect
583. #440	C₂²×C₁₃	semidirect
584. C₄×Q₁₆	C₂²×C₁₃	semidirect
585. C₄×SD₁₆	C₂²×C₁₃	semidirect
586. #435	C₂²×C₁₃	semidirect
587. #435	C₂²×C₁₃	semidirect
588. C₈×D₄	C₂²×C₁₃	semidirect
589. C₈×D₄	C₂²×C₁₃	semidirect
592. #417	C₂²×C₁₃	semidirect
595. C₂×#103	C₂²×C₁₃	semidirect
930. C₁₃	#61637	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×#3539	2
C₁₃×#3487	2
C₁₃×#3317	2
C₁₃×#3309	2
C₁₃×#3301	2
C₁₃×#3300	2
C₁₃×#3287	2
C₁₃×#3284	2
C₁₃×#3271	2
C₁₃×#3269	2
C₁₃×#3222	2
C₁₃×#3220	2
C₁₃×#3198	2
C₁₃×#3191	2
C₁₃×#3127	2
C₁₃×#3126	2
C₁₃×#3013	2
C₁₃×#3002	2
C₁₃×#2977	2
#61637	13

Subgroups — C13×#61637 #15747976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61637 #15747976