Subgroups — C₁₃×#61937 #15748276

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3373	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×#3224	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3118	C₂	1	4	yes	maximal, complemented
15	C₁₃×#3107	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×#563	—	2	2	no	—
19	C₁₃×#559	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	2	yes	—
21	C₁₃×#559	C₂²	1	2	yes	complemented
22	Q₈²×C₁₃	C₂²	1	2	yes	complemented
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	C₂²	1	2	yes	complemented
25	C₁₃×#550	C₂²	1	2	yes	—
26	C₁₃×#550	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₃	—	2	1	no	—
28	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#546	—	2	2	no	—
30	C₁₃×#546	—	2	2	no	—
31	C₁₃×#542	—	2	2	no	—
32	C₁₃×#542	C₂²	1	4	yes	—
33	C₁₃×#540	—	2	2	no	—
34	C₁₃×#536	—	2	2	no	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	—	2	1	no	—
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
42	C₁₃×#518	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#496	C₂²	1	4	yes	complemented
45	C₁₃×#495	C₂²	1	4	yes	complemented
46	C₁₃×#493	C₂²	1	2	yes	—
47	C₁₃×#492	C₂²	1	2	yes	—
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#486	C₂²	1	2	yes	—
50	C₁₃×#486	C₂²	1	2	yes	—
51	C₁₃×#486	C₂²	1	4	yes	complemented
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#482	C₂²	1	2	yes	—
54	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#476	C₂²	1	4	yes	complemented
57	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#474	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#460	C₂²	1	2	yes	—
67	C₁₃×#460	C₂²	1	2	yes	—
68	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#460	C₂²	1	4	yes	complemented
70	C₁₃×#459	C₂²	1	2	yes	—
71	C₁₃×#459	C₂²	1	2	yes	—
72	C₁₃×#459	C₂²	1	4	yes	complemented
73	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#452	C₂²	1	2	yes	—
75	C₁₃×#450	C₂²	1	4	yes	—
76	C₁₃×#449	C₂²	1	2	yes	—
77	C₁₃×#447	C₂²	1	4	yes	—
78	C₁₃×#446	C₂²	1	2	yes	complemented
79	C₁₃×#446	C₂²	1	2	yes	complemented
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
82	C₁₃×#442	C₂²	1	4	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
87	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
88	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
89	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
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	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×D₈	C₂³	1	4	yes	—
107	C₂×C₁₃×D₈	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	4	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	—	2	1	no	—
118	C₁₃×#127	—	2	1	no	—
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#127	C₂³	1	4	yes	—
121	C₁₃×#127	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#126	—	2	4	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#125	—	2	1	no	—
126	C₁₃×#125	D₄	1	2	yes	—
127	C₁₃×#124	—	2	2	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	4	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	C₂³	1	4	yes	—
133	C₁₃×#124	C₂³	1	4	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	4	no	—
152	C₁₃×#121	—	2	4	no	—
153	C₁₃×#121	C₂³	1	2	yes	—
154	C₁₃×#120	—	2	4	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₄×D₄×C₁₃	C₂³	1	4	yes	—
174	C₄×D₄×C₁₃	C₂³	1	4	yes	—
175	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	C₂³	1	4	yes	—
177	C₁₃×#117	—	2	1	no	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	1	no	—
180	C₁₃×#117	C₂³	1	1	yes	characteristic
181	C₁₃×#117	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×#107	C₂³	1	2	yes	—
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#106	C₂³	1	2	yes	—
188	C₁₃×#106	C₂³	1	2	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×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#102	C₂³	1	2	yes	—
200	C₁₃×#102	C₂³	1	2	yes	—
201	C₁₃×#102	C₂³	1	4	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	#61937	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	2	no	—
215	C₁₃×#41	—	4	1	no	—
216	C₁₃×#41	—	4	1	no	—
217	C₁₃×#41	—	8	2	no	—
218	C₁₃×#41	—	8	4	no	—
219	C₁₃×#41	—	8	4	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	8	4	no	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
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	2	no	—
234	C₂×D₄×C₁₃	—	2	4	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	2	no	—
241	C₂×D₄×C₁₃	—	8	2	no	—
242	C₂×D₄×C₁₃	—	8	2	no	—
243	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	2	4	no	—
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₁₃×Q₁₆	—	4	2	no	—
257	C₁₃×SD₁₆	—	4	2	no	—
258	C₁₃×SD₁₆	—	4	4	no	—
259	C₁₃×SD₁₆	—	4	2	no	—
260	C₁₃×SD₁₆	—	4	4	no	—
261	C₁₃×D₈	—	4	4	no	—
262	C₁₃×D₈	—	4	4	no	—
263	C₁₃×D₈	—	4	2	no	—
264	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
287	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	1	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	4	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	4	yes	—
312	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3399	C₂×C₁₃	1	2	yes	complemented
315	#3397	C₂×C₁₃	1	2	yes	complemented
316	#3396	C₂×C₁₃	1	2	yes	complemented
317	#3394	C₂×C₁₃	1	2	yes	complemented
318	#3375	C₂×C₁₃	1	2	yes	complemented
319	#3373	C₂×C₁₃	1	2	yes	complemented
320	#3362	C₂×C₁₃	1	2	yes	complemented
321	#3358	C₂×C₁₃	1	2	yes	complemented
322	#3224	C₂×C₁₃	1	4	yes	complemented
323	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3118	C₂×C₁₃	1	4	yes	complemented
326	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	4	no	—
331	C₂³×C₁₃	—	2	1	no	—
332	C₂³×C₁₃	—	4	4	no	—
333	C₂³×C₁₃	—	8	2	no	—
334	C₂³×C₁₃	—	8	2	no	—
335	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₁₃	—	2	4	no	—
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	2	2	no	—
340	Q₈×C₁₃	—	2	1	no	—
341	Q₈×C₁₃	—	2	1	no	—
342	Q₈×C₁₃	—	4	2	no	—
343	Q₈×C₁₃	—	8	4	no	—
344	Q₈×C₁₃	—	8	1	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	2	4	no	—
349	D₄×C₁₃	—	2	4	no	—
350	D₄×C₁₃	—	2	1	no	—
351	D₄×C₁₃	—	4	4	no	—
352	D₄×C₁₃	—	4	2	no	—
353	D₄×C₁₃	—	4	4	no	—
354	D₄×C₁₃	—	4	2	no	—
355	D₄×C₁₃	—	4	4	no	—
356	D₄×C₁₃	—	8	2	no	—
357	D₄×C₁₃	—	8	2	no	—
358	D₄×C₁₃	—	8	1	no	—
359	D₄×C₁₃	—	8	4	no	—
360	D₄×C₁₃	—	8	4	no	—
361	D₄×C₁₃	—	8	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	4	2	no	—
373	C₂×C₄×C₁₃	—	4	4	no	—
374	C₂×C₄×C₁₃	—	4	2	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	8	4	no	—
377	C₂×C₄×C₁₃	—	8	4	no	—
378	C₂×C₄×C₁₃	—	8	4	no	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	2	2	no	—
389	C₈×C₁₃	—	2	2	no	—
390	C₈×C₁₃	—	2	2	no	—
391	#563	—	2	2	no	—
392	#559	C₂²×C₁₃	1	2	yes	—
393	#559	C₂²×C₁₃	1	2	yes	—
394	#559	C₂²×C₁₃	1	2	yes	complemented
395	Q₈²	C₂²×C₁₃	1	2	yes	complemented
396	#556	—	2	1	no	—
397	#556	C₂²×C₁₃	1	2	yes	complemented
398	#550	C₂²×C₁₃	1	2	yes	—
399	#550	C₂²×C₁₃	1	2	yes	—
400	D₄×Q₈	—	2	1	no	—
401	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
402	#546	—	2	2	no	—
403	#546	—	2	2	no	—
404	#542	—	2	2	no	—
405	#542	C₂²×C₁₃	1	4	yes	—
406	#540	—	2	2	no	—
407	#536	—	2	2	no	—
408	#535	C₂²×C₁₃	1	2	yes	—
409	#533	C₂²×C₁₃	1	1	yes	characteristic
410	#533	C₂²×C₁₃	1	1	yes	characteristic
411	#532	—	2	1	no	—
412	#532	—	2	1	no	—
413	#532	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
415	#518	C₂²×C₁₃	1	2	yes	—
416	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
417	#496	C₂²×C₁₃	1	4	yes	complemented
418	#495	C₂²×C₁₃	1	4	yes	complemented
419	#493	C₂²×C₁₃	1	2	yes	—
420	#492	C₂²×C₁₃	1	2	yes	—
421	#489	C₂²×C₁₃	1	4	yes	complemented
422	#486	C₂²×C₁₃	1	2	yes	—
423	#486	C₂²×C₁₃	1	2	yes	—
424	#486	C₂²×C₁₃	1	4	yes	complemented
425	#485	C₂²×C₁₃	1	2	yes	—
426	#482	C₂²×C₁₃	1	2	yes	—
427	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	#476	C₂²×C₁₃	1	4	yes	complemented
430	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#474	C₂²×C₁₃	1	4	yes	complemented
433	#464	C₂²×C₁₃	1	4	yes	complemented
434	#463	C₂²×C₁₃	1	4	yes	complemented
435	#463	C₂²×C₁₃	1	4	yes	complemented
436	#463	C₂²×C₁₃	1	4	yes	complemented
437	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#460	C₂²×C₁₃	1	2	yes	—
440	#460	C₂²×C₁₃	1	2	yes	—
441	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	#460	C₂²×C₁₃	1	4	yes	complemented
443	#459	C₂²×C₁₃	1	2	yes	—
444	#459	C₂²×C₁₃	1	2	yes	—
445	#459	C₂²×C₁₃	1	4	yes	complemented
446	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#452	C₂²×C₁₃	1	2	yes	—
448	#450	C₂²×C₁₃	1	4	yes	—
449	#449	C₂²×C₁₃	1	2	yes	—
450	#447	C₂²×C₁₃	1	4	yes	—
451	#446	C₂²×C₁₃	1	2	yes	complemented
452	#446	C₂²×C₁₃	1	2	yes	complemented
453	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
454	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
455	#442	C₂²×C₁₃	1	4	yes	complemented
456	#440	C₂²×C₁₃	1	4	yes	complemented
457	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
458	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
459	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
460	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
461	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
462	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
463	#433	C₂²×C₁₃	1	4	yes	—
464	#431	C₂²×C₁₃	1	1	yes	characteristic
465	#431	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×C₁₃	—	2	1	no	—
467	C₂²×C₁₃	—	2	1	no	—
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	—	4	1	no	—
470	C₂²×C₁₃	—	4	4	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	1	no	—
474	C₂²×C₁₃	—	4	4	no	—
475	C₂²×C₁₃	—	4	1	no	—
476	C₂²×C₁₃	—	4	4	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	16	4	no	—
479	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	2	1	no	—
484	C₄×C₁₃	—	2	4	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	4	2	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	2	no	—
489	C₄×C₁₃	—	4	2	no	—
490	C₄×C₁₃	—	4	1	no	—
491	C₄×C₁₃	#576	1	2	yes	—
492	C₄×C₁₃	#577	1	2	yes	—
493	C₄×C₁₃	#585	1	1	yes	characteristic
494	C₄×C₁₃	#585	1	1	yes	characteristic
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×Q₈	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
503	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
505	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
506	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
507	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
508	C₂×D₈	C₂³×C₁₃	1	4	yes	—
509	C₂×D₈	C₂³×C₁₃	1	2	yes	—
510	C₂×D₈	C₂³×C₁₃	1	4	yes	—
511	C₄⋊Q₈	—	2	4	no	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
514	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
519	#127	—	2	1	no	—
520	#127	—	2	1	no	—
521	#127	C₂³×C₁₃	1	2	yes	—
522	#127	C₂³×C₁₃	1	2	yes	—
523	#127	C₂³×C₁₃	1	1	yes	characteristic
524	#127	C₂³×C₁₃	1	4	yes	—
525	#126	—	2	4	no	—
526	#126	—	2	4	no	—
527	#125	—	2	1	no	—
528	#125	D₄×C₁₃	1	2	yes	—
529	#124	—	2	2	no	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	—	2	4	no	—
533	#124	—	2	1	no	—
534	#124	C₂³×C₁₃	1	4	yes	—
535	#124	C₂³×C₁₃	1	4	yes	—
536	#123	—	2	4	no	—
537	#123	—	2	4	no	—
538	#123	—	2	4	no	—
539	#123	—	2	4	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	4	no	—
544	C₂²⋊Q₈	—	2	4	no	—
545	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
546	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
547	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
548	#121	—	2	1	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	4	no	—
554	#121	—	2	4	no	—
555	#121	C₂³×C₁₃	1	2	yes	—
556	#120	—	2	4	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
562	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
563	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
564	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₄×D₄	C₂³×C₁₃	1	4	yes	—
576	C₄×D₄	C₂³×C₁₃	1	4	yes	—
577	C₄×D₄	C₂³×C₁₃	1	2	yes	—
578	C₄×D₄	C₂³×C₁₃	1	4	yes	—
579	#117	—	2	1	no	—
580	#117	—	2	2	no	—
581	#117	—	2	1	no	—
582	#117	C₂³×C₁₃	1	1	yes	characteristic
583	#117	C₂³×C₁₃	1	2	yes	—
584	C₂×C₂²⋊C₄	—	2	4	no	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
587	#107	C₂³×C₁₃	1	2	yes	—
588	#107	C₂³×C₁₃	1	2	yes	—
589	#106	C₂³×C₁₃	1	2	yes	—
590	#106	C₂³×C₁₃	1	2	yes	—
591	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
596	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
597	#103	C₂³×C₁₃	1	2	yes	—
598	#103	C₂³×C₁₃	1	2	yes	—
599	#103	C₂³×C₁₃	1	2	yes	—
600	#103	C₂³×C₁₃	1	2	yes	—
601	#102	C₂³×C₁₃	1	2	yes	—
602	#102	C₂³×C₁₃	1	2	yes	—
603	#102	C₂³×C₁₃	1	4	yes	—
604	#102	C₂³×C₁₃	1	2	yes	—
605	#102	C₂³×C₁₃	1	4	yes	—
606	#102	C₂³×C₁₃	1	2	yes	—
607	#102	C₂³×C₁₃	1	4	yes	—
608	#102	C₂³×C₁₃	1	4	yes	—
609	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
610	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
611	#97	C₂³×C₁₃	1	4	yes	—
612	C₄×C₈	C₂³×C₁₃	1	2	yes	—
613	C₄×C₈	C₂³×C₁₃	1	2	yes	—
614	C₄×C₈	C₂³×C₁₃	1	4	yes	—
615	C₂×C₁₃	—	4	1	no	—
616	C₂×C₁₃	—	8	1	no	—
617	C₂×C₁₃	—	8	2	no	—
618	C₂×C₁₃	—	8	4	no	—
619	C₂×C₁₃	#3487	1	1	yes	characteristic
620	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
621	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
622	C₂⁴	—	2	2	no	—
623	#41	—	4	1	no	—
624	#41	—	4	1	no	—
625	#41	—	8	2	no	—
626	#41	—	8	4	no	—
627	#41	—	8	4	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	4	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	8	4	no	—
632	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
633	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	8	2	no	—
650	C₂×D₄	—	8	2	no	—
651	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
652	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
664	Q₁₆	—	4	2	no	—
665	SD₁₆	—	4	2	no	—
666	SD₁₆	—	4	4	no	—
667	SD₁₆	—	4	2	no	—
668	SD₁₆	—	4	4	no	—
669	D₈	—	4	4	no	—
670	D₈	—	4	4	no	—
671	D₈	—	4	2	no	—
672	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
673	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
674	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	4	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
687	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
688	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
691	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
692	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
694	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	4	no	—
715	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₁₃	1	4	yes	—
720	C₁₃	#61937	1	1	yes	characteristic, direct product factor, Sylow
721	C₂³	—	2	2	no	—
722	C₂³	—	2	4	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	8	2	no	—
726	C₂³	—	8	2	no	—
727	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	Q₈	—	2	4	no	—
729	Q₈	—	2	4	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	1	no	—
733	Q₈	—	2	1	no	—
734	Q₈	—	4	2	no	—
735	Q₈	—	8	4	no	—
736	Q₈	—	8	1	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	1	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	4	no	—
742	D₄	—	2	1	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	2	no	—
745	D₄	—	4	4	no	—
746	D₄	—	4	4	no	—
747	D₄	—	4	2	no	—
748	D₄	—	8	2	no	—
749	D₄	—	8	2	no	—
750	D₄	—	8	1	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	D₄	—	8	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	4	2	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	8	4	no	—
769	C₂×C₄	—	8	4	no	—
770	C₂×C₄	—	8	4	no	—
771	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
773	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
776	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
778	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	2	no	—
782	C₈	—	2	2	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	2	1	no	—
785	C₂²	—	2	1	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	4	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	16	4	no	—
796	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
797	C₄	—	2	1	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	1	no	—
800	C₄	—	2	4	no	—
801	C₄	—	2	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	C₁₃×#576	1	2	yes	—
809	C₄	C₁₃×#577	1	2	yes	—
810	C₄	C₁₃×#585	1	1	yes	characteristic
811	C₄	C₁₃×#585	1	1	yes	characteristic
812	C₂	—	4	1	no	—
813	C₂	—	8	4	no	—
814	C₂	—	8	2	no	—
815	C₂	—	8	1	no	—
816	C₂	C₁₃×#3487	1	1	yes	characteristic
817	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
818	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×#3550	C₂	semidirect
2. C₁₃×#3508	C₂	semidirect
3. C₁₃×#3399	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3396	C₂	semidirect
6. C₁₃×#3394	C₂	semidirect
7. C₁₃×#3375	C₂	semidirect
8. C₁₃×#3373	C₂	semidirect
9. C₁₃×#3362	C₂	semidirect
10. C₁₃×#3358	C₂	semidirect
11. C₁₃×#3224	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3205	C₂	semidirect
14. C₁₃×#3118	C₂	semidirect
15. C₁₃×#3107	C₂	semidirect
16. C₁₃×#3106	C₂	semidirect
17. C₁₃×#2986	C₂	semidirect
21. C₁₃×#559	C₂²	semidirect
22. Q₈²×C₁₃	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
44. C₁₃×#496	C₂²	semidirect
45. C₁₃×#495	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
51. C₁₃×#486	C₂²	semidirect
54. C₁₃×#477	C₂²	semidirect
55. C₁₃×#476	C₂²	semidirect
56. C₁₃×#476	C₂²	semidirect
57. C₁₃×#475	C₂²	semidirect
58. C₁₃×#474	C₂²	semidirect
59. C₁₃×#474	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
78. C₁₃×#446	C₂²	semidirect
79. C₁₃×#446	C₂²	semidirect
80. C₈×Q₈×C₁₃	C₂²	semidirect
81. C₈×Q₈×C₁₃	C₂²	semidirect
82. C₁₃×#442	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₄×C₁₃×SD₁₆	C₂²	semidirect
87. C₄×C₁₃×SD₁₆	C₂²	semidirect
88. C₄×C₁₃×D₈	C₂²	semidirect
89. C₄×C₁₃×D₈	C₂²	semidirect
213. #61937	C₁₃	direct (N × H)
312. #3550	C₂×C₁₃	semidirect
313. #3508	C₂×C₁₃	semidirect
314. #3399	C₂×C₁₃	semidirect
315. #3397	C₂×C₁₃	semidirect
316. #3396	C₂×C₁₃	semidirect
317. #3394	C₂×C₁₃	semidirect
318. #3375	C₂×C₁₃	semidirect
319. #3373	C₂×C₁₃	semidirect
320. #3362	C₂×C₁₃	semidirect
321. #3358	C₂×C₁₃	semidirect
322. #3224	C₂×C₁₃	semidirect
323. #3208	C₂×C₁₃	semidirect
324. #3205	C₂×C₁₃	semidirect
325. #3118	C₂×C₁₃	semidirect
326. #3107	C₂×C₁₃	semidirect
327. #3106	C₂×C₁₃	semidirect
328. #2986	C₂×C₁₃	semidirect
394. #559	C₂²×C₁₃	semidirect
395. Q₈²	C₂²×C₁₃	semidirect
397. #556	C₂²×C₁₃	semidirect
401. D₄×Q₈	C₂²×C₁₃	semidirect
417. #496	C₂²×C₁₃	semidirect
418. #495	C₂²×C₁₃	semidirect
421. #489	C₂²×C₁₃	semidirect
424. #486	C₂²×C₁₃	semidirect
427. #477	C₂²×C₁₃	semidirect
428. #476	C₂²×C₁₃	semidirect
429. #476	C₂²×C₁₃	semidirect
430. #475	C₂²×C₁₃	semidirect
431. #474	C₂²×C₁₃	semidirect
432. #474	C₂²×C₁₃	semidirect
433. #464	C₂²×C₁₃	semidirect
434. #463	C₂²×C₁₃	semidirect
435. #463	C₂²×C₁₃	semidirect
436. #463	C₂²×C₁₃	semidirect
437. #462	C₂²×C₁₃	semidirect
438. #461	C₂²×C₁₃	semidirect
441. #460	C₂²×C₁₃	semidirect
442. #460	C₂²×C₁₃	semidirect
445. #459	C₂²×C₁₃	semidirect
446. #459	C₂²×C₁₃	semidirect
451. #446	C₂²×C₁₃	semidirect
452. #446	C₂²×C₁₃	semidirect
453. C₈×Q₈	C₂²×C₁₃	semidirect
454. C₈×Q₈	C₂²×C₁₃	semidirect
455. #442	C₂²×C₁₃	semidirect
456. #440	C₂²×C₁₃	semidirect
457. C₄×Q₁₆	C₂²×C₁₃	semidirect
458. C₄×SD₁₆	C₂²×C₁₃	semidirect
459. C₄×SD₁₆	C₂²×C₁₃	semidirect
460. C₄×SD₁₆	C₂²×C₁₃	semidirect
461. C₄×D₈	C₂²×C₁₃	semidirect
462. C₄×D₈	C₂²×C₁₃	semidirect
720. C₁₃	#61937	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×#3550	2
C₁₃×#3508	2
C₁₃×#3399	2
C₁₃×#3397	2
C₁₃×#3396	2
C₁₃×#3394	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3224	2
C₁₃×#3208	2
C₁₃×#3205	2
C₁₃×#3118	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#2986	2
#61937	13

Subgroups — C13×#61937 #15748276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61937 #15748276