Subgroups — C₁₃×#61894 #15748233

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 802 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	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	2	yes	complemented
17	C₁₃×#557	C₂²	1	2	yes	complemented
18	C₁₃×#556	—	2	2	no	—
19	C₁₃×#556	—	2	2	no	—
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#556	C₂²	1	4	yes	—
22	C₁₃×#556	C₂²	1	4	yes	—
23	C₁₃×#556	C₂²	1	2	yes	complemented
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#539	—	2	1	no	—
27	C₁₃×#539	—	2	1	no	—
28	C₁₃×#536	—	2	1	no	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	2	yes	—
33	C₁₃×#529	C₂²	1	2	yes	—
34	C₂×C₁₃×#126	—	2	1	no	—
35	C₂×C₁₃×#126	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
39	C₁₃×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#117	—	2	1	no	—
45	C₁₃×#497	C₂²	1	2	yes	—
46	C₁₃×#497	C₂²	1	4	yes	complemented
47	C₁₃×#496	C₂²	1	2	yes	—
48	C₁₃×#495	C₂²	1	4	yes	—
49	C₁₃×#491	C₂²	1	4	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	—
51	C₁₃×#489	C₂²	1	2	yes	—
52	C₁₃×#488	C₂²	1	4	yes	—
53	C₁₃×#483	C₂²	1	2	yes	—
54	C₁₃×#480	C₂²	1	2	yes	—
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#478	C₂²	1	4	yes	—
57	C₁₃×#477	C₂²	1	2	yes	complemented
58	C₁₃×#475	C₂²	1	2	yes	complemented
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	4	yes	—
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	—
63	C₁₃×#463	C₂²	1	4	yes	—
64	C₁₃×#463	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	2	yes	—
70	C₁₃×#451	C₂²	1	2	yes	—
71	C₁₃×#450	C₂²	1	2	yes	—
72	C₁₃×#448	C₂²	1	2	yes	—
73	C₁₃×#448	C₂²	1	2	yes	—
74	C₁₃×#447	C₂²	1	2	yes	—
75	C₁₃×#446	C₂²	1	4	yes	complemented
76	C₁₃×#446	C₂²	1	4	yes	complemented
77	C₁₃×#442	C₂²	1	4	yes	—
78	C₁₃×#441	C₂²	1	4	yes	complemented
79	C₁₃×#440	C₂²	1	4	yes	—
80	C₁₃×#440	C₂²	1	4	yes	complemented
81	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
82	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
83	C₁₃×#432	C₂²	1	1	yes	characteristic
84	C₁₃×#432	C₂²	1	1	yes	characteristic
85	C₁₃×#432	C₂²	1	2	yes	—
86	C₁₃×#431	C₂²	1	2	yes	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	—	2	1	no	—
93	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	4	yes	—
99	C₁₃×C₄⋊Q₈	—	2	2	no	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×#127	C₂³	1	1	yes	characteristic
106	C₁₃×#126	—	2	4	no	—
107	C₁₃×#126	—	2	4	no	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	2	no	—
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#126	—	2	2	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	—	2	2	no	—
116	C₁₃×#125	—	2	1	no	—
117	C₁₃×#125	C₂³	1	2	yes	—
118	C₁₃×#125	C₂³	1	2	yes	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	—	2	1	no	—
122	C₁₃×#124	—	2	1	no	—
123	C₁₃×#124	—	2	1	no	—
124	C₁₃×#124	C₂³	1	2	yes	—
125	C₁₃×#124	C₂³	1	2	yes	—
126	C₁₃×#124	C₂³	1	4	yes	—
127	C₁₃×#124	C₂³	1	2	yes	—
128	C₁₃×#124	C₂³	1	2	yes	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	2	no	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	C₂³	1	2	yes	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	D₄	1	2	yes	—
149	C₄×Q₈×C₁₃	D₄	1	2	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	4	yes	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₁₃×#117	—	2	1	no	—
168	C₁₃×#117	—	2	4	no	—
169	C₁₃×#117	—	2	4	no	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	2	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
180	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₄²×C₁₃	—	2	1	no	—
188	C₂×C₄²×C₁₃	—	2	1	no	—
189	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#107	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×#97	C₂³	1	4	yes	—
209	C₁₃×#97	C₂³	1	2	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	4	yes	—
212	#61894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	—	2	1	no	—
214	C₁₃×#41	—	4	4	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	4	2	no	—
220	C₂×Q₈×C₁₃	—	4	2	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	4	2	no	—
232	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	4	4	no	—
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₁₃×Q₁₆	—	4	4	no	—
250	C₁₃×Q₁₆	—	4	4	no	—
251	C₁₃×SD₁₆	—	4	4	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₁₃×D₈	—	4	4	no	—
255	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
256	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	2	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	—	2	2	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	C₂×D₄	1	2	yes	—
307	C₄²×C₁₃	C₂×D₄	1	2	yes	—
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂⁴	1	2	yes	—
311	C₄²×C₁₃	C₂⁴	1	2	yes	—
312	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
314	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3402	C₂×C₁₃	1	4	yes	complemented
317	#3401	C₂×C₁₃	1	4	yes	complemented
318	#3377	C₂×C₁₃	1	4	yes	complemented
319	#3376	C₂×C₁₃	1	4	yes	complemented
320	#3218	C₂×C₁₃	1	2	yes	complemented
321	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3213	C₂×C₁₃	1	1	yes	characteristic
323	#3211	C₂×C₁₃	1	2	yes	complemented
324	#3114	C₂×C₁₃	1	2	yes	complemented
325	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
327	#3108	C₂×C₁₃	1	2	yes	complemented
328	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂³×C₁₃	—	2	2	no	—
330	C₂³×C₁₃	—	2	2	no	—
331	C₂³×C₁₃	—	4	2	no	—
332	C₂³×C₁₃	—	4	2	no	—
333	C₂³×C₁₃	—	4	2	no	—
334	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₁₃	—	2	2	no	—
336	Q₈×C₁₃	—	2	4	no	—
337	Q₈×C₁₃	—	2	4	no	—
338	Q₈×C₁₃	—	2	2	no	—
339	Q₈×C₁₃	—	4	2	no	—
340	Q₈×C₁₃	—	4	2	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	Q₈×C₁₃	—	4	2	no	—
343	Q₈×C₁₃	—	4	2	no	—
344	Q₈×C₁₃	—	8	1	no	—
345	D₄×C₁₃	—	2	4	no	—
346	D₄×C₁₃	—	2	4	no	—
347	D₄×C₁₃	—	4	2	no	—
348	D₄×C₁₃	—	4	2	no	—
349	D₄×C₁₃	—	4	4	no	—
350	D₄×C₁₃	—	8	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	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	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	8	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	2	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	8	2	no	—
370	C₂×C₄×C₁₃	—	8	2	no	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
381	C₈×C₁₃	—	2	4	no	—
382	C₈×C₁₃	—	2	4	no	—
383	#559	C₂²×C₁₃	1	2	yes	complemented
384	#557	C₂²×C₁₃	1	2	yes	complemented
385	#556	—	2	2	no	—
386	#556	—	2	2	no	—
387	#556	—	2	2	no	—
388	#556	C₂²×C₁₃	1	4	yes	—
389	#556	C₂²×C₁₃	1	4	yes	—
390	#556	C₂²×C₁₃	1	2	yes	complemented
391	#554	C₂²×C₁₃	1	2	yes	complemented
392	#552	—	2	2	no	—
393	#539	—	2	1	no	—
394	#539	—	2	1	no	—
395	#536	—	2	1	no	—
396	#533	C₂²×C₁₃	1	1	yes	characteristic
397	#532	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	#529	C₂²×C₁₃	1	2	yes	—
400	#529	C₂²×C₁₃	1	2	yes	—
401	C₂×#126	—	2	1	no	—
402	C₂×#126	—	2	1	no	—
403	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	—	2	1	no	—
406	#520	—	2	1	no	—
407	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#117	—	2	1	no	—
412	#497	C₂²×C₁₃	1	2	yes	—
413	#497	C₂²×C₁₃	1	4	yes	complemented
414	#496	C₂²×C₁₃	1	2	yes	—
415	#495	C₂²×C₁₃	1	4	yes	—
416	#491	C₂²×C₁₃	1	4	yes	complemented
417	#489	C₂²×C₁₃	1	2	yes	—
418	#489	C₂²×C₁₃	1	2	yes	—
419	#488	C₂²×C₁₃	1	4	yes	—
420	#483	C₂²×C₁₃	1	2	yes	—
421	#480	C₂²×C₁₃	1	2	yes	—
422	#479	C₂²×C₁₃	1	4	yes	complemented
423	#478	C₂²×C₁₃	1	4	yes	—
424	#477	C₂²×C₁₃	1	2	yes	complemented
425	#475	C₂²×C₁₃	1	2	yes	complemented
426	#464	C₂²×C₁₃	1	4	yes	—
427	#464	C₂²×C₁₃	1	4	yes	—
428	#464	C₂²×C₁₃	1	4	yes	complemented
429	#463	C₂²×C₁₃	1	4	yes	—
430	#463	C₂²×C₁₃	1	4	yes	—
431	#463	C₂²×C₁₃	1	4	yes	—
432	#462	C₂²×C₁₃	1	2	yes	complemented
433	#462	C₂²×C₁₃	1	4	yes	complemented
434	#461	C₂²×C₁₃	1	4	yes	complemented
435	#460	C₂²×C₁₃	1	2	yes	complemented
436	#451	C₂²×C₁₃	1	2	yes	—
437	#451	C₂²×C₁₃	1	2	yes	—
438	#450	C₂²×C₁₃	1	2	yes	—
439	#448	C₂²×C₁₃	1	2	yes	—
440	#448	C₂²×C₁₃	1	2	yes	—
441	#447	C₂²×C₁₃	1	2	yes	—
442	#446	C₂²×C₁₃	1	4	yes	complemented
443	#446	C₂²×C₁₃	1	4	yes	complemented
444	#442	C₂²×C₁₃	1	4	yes	—
445	#441	C₂²×C₁₃	1	4	yes	complemented
446	#440	C₂²×C₁₃	1	4	yes	—
447	#440	C₂²×C₁₃	1	4	yes	complemented
448	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
449	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
450	#432	C₂²×C₁₃	1	1	yes	characteristic
451	#432	C₂²×C₁₃	1	1	yes	characteristic
452	#432	C₂²×C₁₃	1	2	yes	—
453	#431	C₂²×C₁₃	1	2	yes	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	8	4	no	—
463	C₂²×C₁₃	#575	1	2	yes	—
464	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	2	2	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	2	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	1	no	—
473	C₄×C₁₃	—	2	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	2	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	2	no	—
479	C₄×C₁₃	—	4	2	no	—
480	C₄×C₁₃	#585	1	2	yes	—
481	C₂×#41	—	2	1	no	—
482	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
483	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
488	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×D₈	C₂³×C₁₃	1	4	yes	—
493	C₄⋊Q₈	—	2	2	no	—
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
496	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	#127	C₂³×C₁₃	1	1	yes	characteristic
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#126	—	2	4	no	—
503	#126	—	2	4	no	—
504	#126	—	2	2	no	—
505	#126	—	2	2	no	—
506	#126	—	2	2	no	—
507	#126	—	2	2	no	—
508	#125	—	2	2	no	—
509	#125	—	2	2	no	—
510	#125	—	2	1	no	—
511	#125	C₂³×C₁₃	1	2	yes	—
512	#125	C₂³×C₁₃	1	2	yes	—
513	#124	—	2	2	no	—
514	#124	—	2	2	no	—
515	#124	—	2	1	no	—
516	#124	—	2	1	no	—
517	#124	—	2	1	no	—
518	#124	C₂³×C₁₃	1	2	yes	—
519	#124	C₂³×C₁₃	1	4	yes	—
520	#124	C₂³×C₁₃	1	2	yes	—
521	#124	C₂³×C₁₃	1	2	yes	—
522	#124	C₂³×C₁₃	1	2	yes	—
523	#123	—	2	2	no	—
524	#123	—	2	2	no	—
525	#123	—	2	2	no	—
526	#123	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
535	#121	—	2	1	no	—
536	#121	C₂³×C₁₃	1	2	yes	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	D₄×C₁₃	1	2	yes	—
543	C₄×Q₈	D₄×C₁₃	1	2	yes	—
544	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
549	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
550	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	C₂³×C₁₃	1	4	yes	—
558	C₄×D₄	C₂³×C₁₃	1	2	yes	—
559	C₄×D₄	C₂³×C₁₃	1	2	yes	—
560	C₄×D₄	C₂³×C₁₃	1	2	yes	—
561	#117	—	2	1	no	—
562	#117	—	2	4	no	—
563	#117	—	2	4	no	—
564	#117	—	2	2	no	—
565	#117	—	2	2	no	—
566	#117	—	2	2	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₄²	—	2	1	no	—
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
586	#107	C₂³×C₁₃	1	4	yes	—
587	#106	C₂³×C₁₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
589	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
590	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
591	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
592	#103	C₂³×C₁₃	1	4	yes	—
593	#103	C₂³×C₁₃	1	4	yes	—
594	#103	C₂³×C₁₃	1	4	yes	—
595	#103	C₂³×C₁₃	1	4	yes	—
596	#103	C₂³×C₁₃	1	4	yes	—
597	#102	C₂³×C₁₃	1	4	yes	—
598	#102	C₂³×C₁₃	1	4	yes	—
599	#102	C₂³×C₁₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
602	#97	C₂³×C₁₃	1	4	yes	—
603	#97	C₂³×C₁₃	1	2	yes	—
604	#97	C₂³×C₁₃	1	2	yes	—
605	C₄×C₈	C₂³×C₁₃	1	4	yes	—
606	C₂×C₁₃	—	2	2	no	—
607	C₂×C₁₃	—	8	2	no	—
608	C₂×C₁₃	—	8	2	no	—
609	C₂×C₁₃	#3487	1	1	yes	characteristic
610	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
611	C₂×C₁₃	#3586	1	1	yes	characteristic
612	C₂⁴	—	2	1	no	—
613	#41	—	4	4	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	4	2	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
622	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	4	4	no	—
641	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
648	Q₁₆	—	4	4	no	—
649	Q₁₆	—	4	4	no	—
650	SD₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	4	4	no	—
654	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
655	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	C₂×D₄×C₁₃	1	2	yes	—
706	C₄²	C₂×D₄×C₁₃	1	2	yes	—
707	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
708	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₄²	C₂⁴×C₁₃	1	2	yes	—
710	C₄²	C₂⁴×C₁₃	1	2	yes	—
711	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₁₃	#61894	1	1	yes	characteristic, direct product factor, Sylow
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	2	4	no	—
722	Q₈	—	2	4	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	C₂²×D₄×C₁₃	1	2	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	C₂²×D₄×C₁₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
765	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
766	C₈	—	2	4	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	8	4	no	—
777	C₂²	C₁₃×#575	1	2	yes	—
778	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
779	C₄	—	2	2	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	C₁₃×#585	1	2	yes	—
795	C₂	—	2	2	no	—
796	C₂	—	8	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₁₃×#3487	1	1	yes	characteristic
799	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
800	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×#3213	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3377	C₂	semidirect
6. C₁₃×#3376	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3215	C₂	semidirect
10. C₁₃×#3211	C₂	semidirect
11. C₁₃×#3114	C₂	semidirect
12. C₁₃×#3113	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3108	C₂	semidirect
15. C₁₃×#2983	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
17. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
46. C₁₃×#497	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#475	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
75. C₁₃×#446	C₂²	semidirect
76. C₁₃×#446	C₂²	semidirect
78. C₁₃×#441	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₄×C₁₃×Q₁₆	C₂²	semidirect
82. C₄×C₁₃×SD₁₆	C₂²	semidirect
212. #61894	C₁₃	direct (N × H)
314. #3507	C₂×C₁₃	semidirect
315. C₂×#556	C₂×C₁₃	semidirect
316. #3402	C₂×C₁₃	semidirect
317. #3401	C₂×C₁₃	semidirect
318. #3377	C₂×C₁₃	semidirect
319. #3376	C₂×C₁₃	semidirect
320. #3218	C₂×C₁₃	semidirect
321. #3215	C₂×C₁₃	semidirect
323. #3211	C₂×C₁₃	semidirect
324. #3114	C₂×C₁₃	semidirect
325. #3113	C₂×C₁₃	semidirect
326. #3112	C₂×C₁₃	semidirect
327. #3108	C₂×C₁₃	semidirect
328. #2983	C₂×C₁₃	semidirect
383. #559	C₂²×C₁₃	semidirect
384. #557	C₂²×C₁₃	semidirect
390. #556	C₂²×C₁₃	semidirect
391. #554	C₂²×C₁₃	semidirect
413. #497	C₂²×C₁₃	semidirect
416. #491	C₂²×C₁₃	semidirect
422. #479	C₂²×C₁₃	semidirect
424. #477	C₂²×C₁₃	semidirect
425. #475	C₂²×C₁₃	semidirect
428. #464	C₂²×C₁₃	semidirect
432. #462	C₂²×C₁₃	semidirect
433. #462	C₂²×C₁₃	semidirect
434. #461	C₂²×C₁₃	semidirect
435. #460	C₂²×C₁₃	semidirect
442. #446	C₂²×C₁₃	semidirect
443. #446	C₂²×C₁₃	semidirect
445. #441	C₂²×C₁₃	semidirect
447. #440	C₂²×C₁₃	semidirect
448. C₄×Q₁₆	C₂²×C₁₃	semidirect
449. C₄×SD₁₆	C₂²×C₁₃	semidirect
713. C₁₃	#61894	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
C₂×C₁₃×#556	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3377	2
C₁₃×#3376	2
C₁₃×#3218	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3114	2
C₁₃×#3113	2
C₁₃×#3112	2
C₁₃×#3108	2
C₁₃×#2983	2
#61894	13

Subgroups — C13×#61894 #15748233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61894 #15748233