Subgroups — C₁₃×#61346 #15747685

Order 3328.

1782 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3369	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2952	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	2	yes	—
21	Q₈²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#556	C₂²	1	4	yes	—
26	C₁₃×#554	—	2	1	no	—
27	C₁₃×#554	—	2	2	no	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#552	—	2	2	no	—
30	D₄×Q₈×C₁₃	—	2	2	no	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#544	—	2	2	no	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#539	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₁₃×#529	—	2	2	no	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#520	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#491	C₂²	1	4	yes	—
47	C₁₃×#489	C₂²	1	4	yes	—
48	C₁₃×#489	C₂²	1	4	yes	—
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	4	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#486	C₂²	1	2	yes	—
53	C₁₃×#479	C₂²	1	4	yes	—
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#476	C₂²	1	4	yes	—
56	C₁₃×#475	C₂²	1	2	yes	—
57	C₁₃×#475	C₂²	1	4	yes	—
58	C₁₃×#475	C₂²	1	2	yes	—
59	C₁₃×#475	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	2	yes	—
61	C₁₃×#464	C₂²	1	4	yes	—
62	C₁₃×#463	C₂²	1	2	yes	—
63	C₁₃×#463	C₂²	1	4	yes	—
64	C₁₃×#462	C₂²	1	1	yes	characteristic
65	C₁₃×#462	C₂²	1	4	yes	—
66	C₁₃×#461	C₂²	1	1	yes	characteristic
67	C₁₃×#461	C₂²	1	4	yes	—
68	C₁₃×#460	C₂²	1	1	yes	characteristic
69	C₁₃×#459	C₂²	1	1	yes	characteristic
70	C₁₃×#446	C₂²	1	4	yes	—
71	C₁₃×#446	C₂²	1	2	yes	—
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
73	C₁₃×#442	C₂²	1	4	yes	—
74	C₁₃×#441	C₂²	1	2	yes	—
75	C₁₃×#441	C₂²	1	4	yes	—
76	C₁₃×#440	C₂²	1	2	yes	—
77	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#106	C₂²	1	2	yes	—
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₃×#419	C₂²	1	1	yes	characteristic
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₁₃×#417	C₂²	1	2	yes	—
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	—	2	2	no	—
96	C₂²×Q₈×C₁₃	—	2	1	no	—
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#137	—	2	4	no	—
99	C₁₃×#135	—	2	8	no	—
100	C₂×C₁₃×Q₁₆	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	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×D₈	C₂³	1	2	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×#127	C₂³	1	1	yes	characteristic
123	C₁₃×#126	—	2	4	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	4	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	D₄	1	2	yes	—
130	C₁₃×#125	C₂³	1	4	yes	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	C₂³	1	4	yes	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	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	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	1	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	4	no	—
165	C₄×D₄×C₁₃	—	2	4	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	C₂³	1	4	yes	—
170	C₄×D₄×C₁₃	C₂³	1	4	yes	—
171	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
172	C₁₃×#117	—	2	2	no	—
173	C₁₃×#117	—	2	2	no	—
174	C₁₃×#117	—	2	4	no	—
175	C₁₃×#117	—	2	1	no	—
176	C₁₃×#117	C₂³	1	1	yes	characteristic
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₃	—	2	1	no	—
186	C₂×C₄²×C₁₃	—	2	1	no	—
187	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	4	yes	—
190	C₁₃×#106	C₂³	1	4	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	2	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	#61346	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃×#41	—	2	2	no	—
217	C₁₃×#41	—	2	4	no	—
218	C₁₃×#41	—	2	4	no	—
219	C₁₃×#41	#41	1	4	yes	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	8	2	no	—
227	C₂×Q₈×C₁₃	—	8	4	no	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	4	no	—
247	C₂²×C₄×C₁₃	—	2	4	no	—
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×Q₁₆	—	2	4	no	—
252	C₁₃×Q₁₆	—	2	4	no	—
253	C₁₃×SD₁₆	—	2	4	no	—
254	C₁₃×SD₁₆	—	2	4	no	—
255	C₁₃×SD₁₆	—	2	4	no	—
256	C₁₃×D₈	—	2	4	no	—
257	C₁₃×M₁₆	—	2	2	no	—
258	C₁₃×M₁₆	—	2	2	no	—
259	C₂×C₈×C₁₃	—	2	4	no	—
260	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
285	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
287	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
288	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
289	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
290	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	4	no	—
297	C₁₃×C₂²⋊C₄	—	2	4	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	4	no	—
300	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	—	2	1	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	4	no	—
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₄²×C₁₃	C₂⁴	1	4	yes	—
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3376	C₂×C₁₃	1	4	yes	complemented
316	#3374	C₂×C₁₃	1	2	yes	complemented
317	#3373	C₂×C₁₃	1	2	yes	complemented
318	#3369	C₂×C₁₃	1	4	yes	complemented
319	#3365	C₂×C₁₃	1	2	yes	complemented
320	#3359	C₂×C₁₃	1	2	yes	complemented
321	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3137	C₂×C₁₃	1	2	yes	complemented
323	#3084	C₂×C₁₃	1	2	yes	complemented
324	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
325	#3046	C₂×C₁₃	1	2	yes	complemented
326	#3035	C₂×C₁₃	1	1	yes	characteristic
327	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#2952	C₂×C₁₃	1	2	yes	complemented
329	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
330	C₂³×C₁₃	—	2	1	no	—
331	C₂³×C₁₃	—	2	2	no	—
332	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₁₃	—	2	4	no	—
334	Q₈×C₁₃	—	2	1	no	—
335	Q₈×C₁₃	—	2	2	no	—
336	Q₈×C₁₃	—	2	2	no	—
337	Q₈×C₁₃	—	2	2	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	4	2	no	—
340	Q₈×C₁₃	—	4	2	no	—
341	Q₈×C₁₃	—	4	4	no	—
342	Q₈×C₁₃	—	8	2	no	—
343	Q₈×C₁₃	—	8	4	no	—
344	Q₈×C₁₃	C₂×#41	1	2	yes	—
345	D₄×C₁₃	—	2	4	no	—
346	D₄×C₁₃	—	2	2	no	—
347	D₄×C₁₃	—	2	1	no	—
348	D₄×C₁₃	—	2	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	4	2	no	—
351	D₄×C₁₃	—	8	1	no	—
352	D₄×C₁₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	2	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	8	4	no	—
368	C₂×C₄×C₁₃	—	8	4	no	—
369	C₂×C₄×C₁₃	—	8	1	no	—
370	C₂×C₄×C₁₃	—	8	2	no	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
375	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
379	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
380	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
381	C₈×C₁₃	—	2	2	no	—
382	C₈×C₁₃	—	2	2	no	—
383	C₈×C₁₃	—	2	2	no	—
384	C₈×C₁₃	—	2	2	no	—
385	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#135	C₂²×C₁₃	1	2	yes	—
387	#559	C₂²×C₁₃	1	2	yes	—
388	Q₈²	C₂²×C₁₃	1	2	yes	—
389	#557	C₂²×C₁₃	1	2	yes	—
390	#557	C₂²×C₁₃	1	2	yes	—
391	#556	—	2	1	no	—
392	#556	C₂²×C₁₃	1	4	yes	—
393	#554	—	2	1	no	—
394	#554	—	2	2	no	—
395	#554	C₂²×C₁₃	1	2	yes	—
396	#552	—	2	2	no	—
397	D₄×Q₈	—	2	2	no	—
398	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
399	#544	—	2	2	no	—
400	#544	C₂²×C₁₃	1	2	yes	—
401	#539	—	2	2	no	—
402	#536	C₂²×C₁₃	1	2	yes	—
403	#533	—	2	1	no	—
404	#533	C₂²×C₁₃	1	1	yes	characteristic
405	#532	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊Q₈	—	2	1	no	—
407	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
408	#529	—	2	2	no	—
409	#520	C₂²×C₁₃	1	2	yes	—
410	#520	C₂²×C₁₃	1	2	yes	—
411	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
413	#491	C₂²×C₁₃	1	4	yes	—
414	#489	C₂²×C₁₃	1	4	yes	—
415	#489	C₂²×C₁₃	1	4	yes	—
416	#488	C₂²×C₁₃	1	4	yes	—
417	#487	C₂²×C₁₃	1	4	yes	—
418	#487	C₂²×C₁₃	1	2	yes	—
419	#486	C₂²×C₁₃	1	2	yes	—
420	#479	C₂²×C₁₃	1	4	yes	—
421	#478	C₂²×C₁₃	1	4	yes	—
422	#476	C₂²×C₁₃	1	4	yes	—
423	#475	C₂²×C₁₃	1	2	yes	—
424	#475	C₂²×C₁₃	1	4	yes	—
425	#475	C₂²×C₁₃	1	2	yes	—
426	#475	C₂²×C₁₃	1	4	yes	—
427	#464	C₂²×C₁₃	1	4	yes	—
428	#464	C₂²×C₁₃	1	2	yes	—
429	#463	C₂²×C₁₃	1	4	yes	—
430	#463	C₂²×C₁₃	1	2	yes	—
431	#462	C₂²×C₁₃	1	4	yes	—
432	#462	C₂²×C₁₃	1	1	yes	characteristic
433	#461	C₂²×C₁₃	1	1	yes	characteristic
434	#461	C₂²×C₁₃	1	4	yes	—
435	#460	C₂²×C₁₃	1	1	yes	characteristic
436	#459	C₂²×C₁₃	1	1	yes	characteristic
437	#446	C₂²×C₁₃	1	4	yes	—
438	#446	C₂²×C₁₃	1	2	yes	—
439	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
440	#442	C₂²×C₁₃	1	4	yes	—
441	#441	C₂²×C₁₃	1	2	yes	—
442	#441	C₂²×C₁₃	1	4	yes	—
443	#440	C₂²×C₁₃	1	2	yes	—
444	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
445	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
446	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
447	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
448	#428	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#106	C₂²×C₁₃	1	2	yes	—
450	#424	C₂²×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
452	#419	C₂²×C₁₃	1	1	yes	characteristic
453	#417	C₂²×C₁₃	1	2	yes	—
454	#417	C₂²×C₁₃	1	2	yes	—
455	#417	C₂²×C₁₃	1	1	yes	characteristic
456	#416	C₂²×C₁₃	1	2	yes	—
457	C₂×#103	C₂²×C₁₃	1	2	yes	—
458	#405	C₂²×C₁₃	1	2	yes	—
459	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	—	4	1	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	#548	1	2	yes	—
469	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	4	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	4	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	4	no	—
482	C₄×C₁₃	#548	1	2	yes	—
483	C₄×C₁₃	#577	1	2	yes	—
484	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
485	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
486	C₂×#41	C₂³×C₁₃	1	2	yes	—
487	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×Q₈	—	2	2	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
491	#137	—	2	4	no	—
492	#135	—	2	8	no	—
493	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
494	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
497	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
498	C₂×D₈	C₂³×C₁₃	1	2	yes	—
499	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	2	no	—
505	C₄⋊Q₈	—	2	4	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
509	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
515	#127	C₂³×C₁₃	1	1	yes	characteristic
516	#126	—	2	4	no	—
517	#126	—	2	4	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	4	no	—
521	#125	—	2	4	no	—
522	#125	D₄×C₁₃	1	2	yes	—
523	#125	C₂³×C₁₃	1	4	yes	—
524	#124	—	2	2	no	—
525	#124	C₂³×C₁₃	1	2	yes	—
526	#124	C₂³×C₁₃	1	4	yes	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
538	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
551	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
552	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
553	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	4	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₁₃	1	4	yes	—
564	C₄×D₄	C₂³×C₁₃	1	4	yes	—
565	#117	—	2	2	no	—
566	#117	—	2	2	no	—
567	#117	—	2	4	no	—
568	#117	—	2	1	no	—
569	#117	C₂³×C₁₃	1	1	yes	characteristic
570	#117	C₂³×C₁₃	1	2	yes	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
578	C₂×C₄²	—	2	1	no	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
581	#107	C₂³×C₁₃	1	2	yes	—
582	#106	C₂³×C₁₃	1	4	yes	—
583	#106	C₂³×C₁₃	1	4	yes	—
584	#106	C₂³×C₁₃	1	2	yes	—
585	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
589	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
590	#103	C₂³×C₁₃	1	4	yes	—
591	#103	C₂³×C₁₃	1	4	yes	—
592	#103	C₂³×C₁₃	1	2	yes	—
593	#103	C₂³×C₁₃	1	2	yes	—
594	#103	C₂³×C₁₃	1	2	yes	—
595	#103	C₂³×C₁₃	1	4	yes	—
596	#103	C₂³×C₁₃	1	4	yes	—
597	#103	C₂³×C₁₃	1	2	yes	—
598	#103	C₂³×C₁₃	1	2	yes	—
599	#102	C₂³×C₁₃	1	2	yes	—
600	#102	C₂³×C₁₃	1	2	yes	—
601	#102	C₂³×C₁₃	1	2	yes	—
602	#102	C₂³×C₁₃	1	4	yes	—
603	#102	C₂³×C₁₃	1	4	yes	—
604	#97	C₂³×C₁₃	1	2	yes	—
605	#97	C₂³×C₁₃	1	4	yes	—
606	C₄×C₈	C₂³×C₁₃	1	2	yes	—
607	C₄×C₈	C₂³×C₁₃	1	4	yes	—
608	C₂×C₁₃	—	2	2	no	—
609	C₂×C₁₃	—	4	2	no	—
610	C₂×C₁₃	—	8	2	no	—
611	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
612	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
613	C₂×C₁₃	#3586	1	1	yes	characteristic
614	#41	—	2	2	no	—
615	#41	—	2	4	no	—
616	#41	—	2	4	no	—
617	#41	C₁₃×#41	1	4	yes	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	4	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	8	2	no	—
625	C₂×Q₈	—	8	4	no	—
626	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
627	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
628	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
629	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
649	Q₁₆	—	2	4	no	—
650	Q₁₆	—	2	4	no	—
651	SD₁₆	—	2	4	no	—
652	SD₁₆	—	2	4	no	—
653	SD₁₆	—	2	4	no	—
654	D₈	—	2	4	no	—
655	M₁₆	—	2	2	no	—
656	M₁₆	—	2	2	no	—
657	C₂×C₈	—	2	4	no	—
658	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
659	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
660	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
661	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
683	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
685	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
687	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	4	no	—
705	C₄²	—	2	4	no	—
706	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
708	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₃	1	4	yes	—
710	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₁₃	#61346	1	1	yes	characteristic, direct product factor, Sylow
712	C₂³	—	2	1	no	—
713	C₂³	—	2	2	no	—
714	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
715	Q₈	—	2	4	no	—
716	Q₈	—	2	1	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	4	4	no	—
724	Q₈	—	8	2	no	—
725	Q₈	—	8	4	no	—
726	Q₈	C₂×C₁₃×#41	1	2	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	C₂×C₁₃×#41	1	2	yes	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	8	4	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	1	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
754	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
756	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
760	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
761	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
762	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
763	C₈	—	2	2	no	—
764	C₈	—	2	2	no	—
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	C₁₃×#548	1	2	yes	—
776	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
777	C₄	—	2	1	no	—
778	C₄	—	2	4	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	4	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	4	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	C₁₃×#548	1	2	yes	—
790	C₄	C₁₃×#577	1	2	yes	—
791	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
792	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
793	C₂	—	2	2	no	—
794	C₂	—	4	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
797	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
798	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3035	C₂
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×#3507	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3376	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3373	C₂	semidirect
6. C₁₃×#3369	C₂	semidirect
7. C₁₃×#3365	C₂	semidirect
8. C₁₃×#3359	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3084	C₂	semidirect
12. C₂×C₁₃×#475	C₂	semidirect
13. C₁₃×#3046	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2952	C₂	semidirect
17. C₄×C₁₃×#137	C₂	semidirect
215. #61346	C₁₃	direct (N × H)
313. #3507	C₂×C₁₃	semidirect
314. #3503	C₂×C₁₃	semidirect
315. #3376	C₂×C₁₃	semidirect
316. #3374	C₂×C₁₃	semidirect
317. #3373	C₂×C₁₃	semidirect
318. #3369	C₂×C₁₃	semidirect
319. #3365	C₂×C₁₃	semidirect
320. #3359	C₂×C₁₃	semidirect
321. #3141	C₂×C₁₃	semidirect
322. #3137	C₂×C₁₃	semidirect
323. #3084	C₂×C₁₃	semidirect
324. C₂×#475	C₂×C₁₃	semidirect
325. #3046	C₂×C₁₃	semidirect
327. #2962	C₂×C₁₃	semidirect
328. #2952	C₂×C₁₃	semidirect
329. C₄×#137	C₂×C₁₃	semidirect
711. C₁₃	#61346	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×#3507	2
C₁₃×#3503	2
C₁₃×#3376	2
C₁₃×#3374	2
C₁₃×#3373	2
C₁₃×#3369	2
C₁₃×#3365	2
C₁₃×#3359	2
C₁₃×#3141	2
C₁₃×#3137	2
C₁₃×#3084	2
C₂×C₁₃×#475	2
C₁₃×#3046	2
C₁₃×#3035	2
C₁₃×#2962	2
C₁₃×#2952	2
C₄×C₁₃×#137	2
#61346	13

Subgroups — C13×#61346 #15747685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61346 #15747685