Subgroups — C₁₃×#61371 #15747710

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3381	C₂	1	4	yes	maximal, complemented
8	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3081	C₂	1	2	yes	maximal
13	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2949	C₂	1	2	yes	maximal
17	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	Q₈²×C₁₃	—	2	1	no	—
20	Q₈²×C₁₃	C₂²	1	2	yes	complemented
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	2	no	—
23	C₁₃×#557	C₂²	1	2	yes	complemented
24	C₁₃×#557	C₂²	1	4	yes	complemented
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#554	—	2	2	no	—
27	C₁₃×#554	C₂²	1	2	yes	—
28	C₁₃×#554	C₂²	1	4	yes	—
29	D₄×Q₈×C₁₃	—	2	1	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	C₂²	1	2	yes	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#543	—	2	2	no	—
35	C₁₃×#533	—	2	2	no	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
40	C₁₃×#519	C₂²	1	2	yes	—
41	C₁₃×#518	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#501	C₂²	1	4	yes	complemented
45	C₁₃×#501	C₂²	1	4	yes	complemented
46	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#499	C₂²	1	2	yes	complemented
49	C₁₃×#499	C₂²	1	4	yes	complemented
50	C₁₃×#499	C₂²	1	2	yes	complemented
51	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#498	C₂²	1	4	yes	complemented
53	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#479	C₂²	1	4	yes	complemented
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#479	C₂²	1	4	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#477	C₂²	1	4	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	4	yes	—
64	C₁₃×#475	C₂²	1	2	yes	complemented
65	C₁₃×#475	C₂²	1	4	yes	complemented
66	C₁₃×#474	C₂²	1	2	yes	—
67	C₁₃×#474	C₂²	1	4	yes	—
68	C₁₃×#446	C₂²	1	2	yes	complemented
69	C₁₃×#446	C₂²	1	2	yes	complemented
70	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
71	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
72	C₁₃×#440	C₂²	1	4	yes	—
73	C₁₃×#440	C₂²	1	4	yes	—
74	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
75	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
77	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	2	yes	—
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	2	yes	—
84	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₁₃×#423	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	2	yes	—
88	C₁₃×#418	C₂²	1	2	yes	—
89	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	—	2	2	no	—
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₂×C₁₃×SD₁₆	Q₈	1	8	yes	complemented
98	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	4	no	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	4	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#125	—	2	4	no	—
118	C₁₃×#125	—	2	4	no	—
119	C₁₃×#125	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	2	no	—
122	C₁₃×#125	D₄	1	2	yes	—
123	C₁₃×#125	C₂³	1	2	yes	—
124	C₁₃×#125	C₂³	1	4	yes	—
125	C₁₃×#125	C₂³	1	2	yes	—
126	C₁₃×#125	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	1	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	4	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	—	2	1	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×Q₈×C₁₃	—	2	1	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	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₄×D₄×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	C₂³	1	4	yes	—
166	C₄×D₄×C₁₃	C₂³	1	4	yes	—
167	C₁₃×#117	—	2	4	no	—
168	C₁₃×#117	C₂³	1	2	yes	—
169	C₁₃×#117	C₂³	1	2	yes	—
170	C₁₃×#117	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₂×C₄²×C₁₃	—	2	1	no	—
179	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₁₃×#107	C₂³	1	2	yes	—
181	C₁₃×#107	C₂³	1	2	yes	—
182	C₁₃×#107	C₂³	1	2	yes	—
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	4	yes	—
185	C₁₃×#107	C₂³	1	4	yes	—
186	C₁₃×#106	C₂³	1	2	yes	—
187	C₁₃×#106	C₂³	1	2	yes	—
188	C₁₃×#106	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×#106	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#97	C₂³	1	4	yes	—
207	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₃	C₂³	1	4	yes	—
212	#61371	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	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	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	4	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	8	4	no	—
223	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	complemented
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
230	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	2	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	8	2	no	—
239	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
243	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
244	C₁₃×M₁₆	—	2	4	no	—
245	C₂×C₈×C₁₃	—	2	2	no	—
246	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
247	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
250	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	4	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
273	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	4	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	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	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
291	C₄²×C₁₃	—	2	2	no	—
292	C₄²×C₁₃	—	2	2	no	—
293	C₄²×C₁₃	—	2	4	no	—
294	C₄²×C₁₃	—	2	4	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₁₃	C₂⁴	1	4	yes	—
302	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#3501	C₂×C₁₃	1	1	yes	characteristic
304	#3388	C₂×C₁₃	1	4	yes	complemented
305	#3386	C₂×C₁₃	1	2	yes	complemented
306	#3385	C₂×C₁₃	1	2	yes	complemented
307	#3381	C₂×C₁₃	1	2	yes	complemented
308	#3381	C₂×C₁₃	1	4	yes	complemented
309	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
310	#3163	C₂×C₁₃	1	2	yes	complemented
311	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3082	C₂×C₁₃	1	2	yes	complemented
313	#3081	C₂×C₁₃	1	2	yes	—
314	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3077	C₂×C₁₃	1	1	yes	characteristic
316	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#2949	C₂×C₁₃	1	2	yes	—
318	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	4	no	—
321	C₂³×C₁₃	—	8	1	no	—
322	C₂³×C₁₃	—	8	1	no	—
323	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₃	—	2	4	no	—
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	4	2	no	—
328	Q₈×C₁₃	—	4	2	no	—
329	Q₈×C₁₃	—	4	2	no	—
330	Q₈×C₁₃	—	8	1	no	—
331	Q₈×C₁₃	—	8	1	no	—
332	Q₈×C₁₃	—	8	4	no	—
333	Q₈×C₁₃	—	8	4	no	—
334	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
335	D₄×C₁₃	—	2	4	no	—
336	D₄×C₁₃	—	2	2	no	—
337	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	4	no	—
349	C₂×C₄×C₁₃	—	8	4	no	—
350	C₂×C₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	1	no	—
353	C₂×C₄×C₁₃	—	8	1	no	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
356	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
362	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₁₃	—	2	1	no	—
365	C₈×C₁₃	—	2	1	no	—
366	C₈×C₁₃	—	2	4	no	—
367	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
368	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
369	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
370	Q₈²	—	2	1	no	—
371	Q₈²	C₂²×C₁₃	1	2	yes	complemented
372	#557	—	2	1	no	—
373	#557	—	2	2	no	—
374	#557	C₂²×C₁₃	1	2	yes	complemented
375	#557	C₂²×C₁₃	1	4	yes	complemented
376	#554	—	2	1	no	—
377	#554	—	2	2	no	—
378	#554	C₂²×C₁₃	1	2	yes	—
379	#554	C₂²×C₁₃	1	4	yes	—
380	D₄×Q₈	—	2	1	no	—
381	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
382	#544	—	2	2	no	—
383	#544	C₂²×C₁₃	1	2	yes	—
384	#544	C₂²×C₁₃	1	2	yes	—
385	#543	—	2	2	no	—
386	#533	—	2	2	no	—
387	#533	C₂²×C₁₃	1	1	yes	characteristic
388	#533	C₂²×C₁₃	1	1	yes	characteristic
389	#533	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊Q₈	—	2	2	no	—
391	#519	C₂²×C₁₃	1	2	yes	—
392	#518	C₂²×C₁₃	1	2	yes	—
393	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
395	#501	C₂²×C₁₃	1	4	yes	complemented
396	#501	C₂²×C₁₃	1	4	yes	complemented
397	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
399	#499	C₂²×C₁₃	1	2	yes	complemented
400	#499	C₂²×C₁₃	1	4	yes	complemented
401	#499	C₂²×C₁₃	1	2	yes	complemented
402	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#498	C₂²×C₁₃	1	4	yes	complemented
404	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
405	#479	C₂²×C₁₃	1	4	yes	complemented
406	#479	C₂²×C₁₃	1	4	yes	complemented
407	#479	C₂²×C₁₃	1	4	yes	complemented
408	#478	C₂²×C₁₃	1	4	yes	—
409	#478	C₂²×C₁₃	1	4	yes	—
410	#478	C₂²×C₁₃	1	4	yes	—
411	#477	C₂²×C₁₃	1	2	yes	complemented
412	#477	C₂²×C₁₃	1	4	yes	complemented
413	#476	C₂²×C₁₃	1	2	yes	—
414	#476	C₂²×C₁₃	1	4	yes	—
415	#475	C₂²×C₁₃	1	2	yes	complemented
416	#475	C₂²×C₁₃	1	4	yes	complemented
417	#474	C₂²×C₁₃	1	2	yes	—
418	#474	C₂²×C₁₃	1	4	yes	—
419	#446	C₂²×C₁₃	1	2	yes	complemented
420	#446	C₂²×C₁₃	1	2	yes	complemented
421	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
422	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
423	#440	C₂²×C₁₃	1	4	yes	—
424	#440	C₂²×C₁₃	1	4	yes	—
425	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
426	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
427	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
428	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
429	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
430	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
431	#428	C₂²×C₁₃	1	2	yes	—
432	#428	C₂²×C₁₃	1	2	yes	—
433	#427	C₂²×C₁₃	1	2	yes	—
434	#427	C₂²×C₁₃	1	2	yes	—
435	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
436	#424	C₂²×C₁₃	1	2	yes	—
437	#423	C₂²×C₁₃	1	1	yes	characteristic
438	#419	C₂²×C₁₃	1	2	yes	—
439	#418	C₂²×C₁₃	1	2	yes	—
440	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
442	#405	C₂²×C₁₃	1	2	yes	—
443	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	4	no	—
447	C₂²×C₁₃	—	4	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	8	4	no	—
450	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
451	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	4	no	—
458	C₄×C₁₃	—	4	2	no	—
459	C₄×C₁₃	—	4	2	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	D₄×Q₈	1	2	yes	—
465	C₄×C₁₃	#577	1	2	yes	—
466	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
467	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	—	2	1	no	—
472	C₂×SD₁₆	Q₈×C₁₃	1	8	yes	complemented
473	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
474	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
475	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₄⋊Q₈	—	2	2	no	—
479	C₄⋊Q₈	—	2	4	no	—
480	C₄⋊Q₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	4	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
485	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
486	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
488	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
492	#125	—	2	4	no	—
493	#125	—	2	4	no	—
494	#125	—	2	4	no	—
495	#125	—	2	2	no	—
496	#125	—	2	2	no	—
497	#125	D₄×C₁₃	1	2	yes	—
498	#125	C₂³×C₁₃	1	2	yes	—
499	#125	C₂³×C₁₃	1	2	yes	—
500	#125	C₂³×C₁₃	1	4	yes	—
501	#125	C₂³×C₁₃	1	4	yes	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	—	2	1	no	—
505	C₂²⋊Q₈	—	2	1	no	—
506	C₂²⋊Q₈	—	2	1	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	2	no	—
509	C₂²⋊Q₈	—	2	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
516	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	4	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
529	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
530	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
531	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
532	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	C₂³×C₁₃	1	2	yes	—
539	C₄×D₄	C₂³×C₁₃	1	2	yes	—
540	C₄×D₄	C₂³×C₁₃	1	4	yes	—
541	C₄×D₄	C₂³×C₁₃	1	4	yes	—
542	#117	—	2	4	no	—
543	#117	C₂³×C₁₃	1	2	yes	—
544	#117	C₂³×C₁₃	1	2	yes	—
545	#117	C₂³×C₁₃	1	2	yes	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	2	no	—
549	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	4	no	—
553	C₂×C₄²	—	2	1	no	—
554	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
555	#107	C₂³×C₁₃	1	2	yes	—
556	#107	C₂³×C₁₃	1	2	yes	—
557	#107	C₂³×C₁₃	1	2	yes	—
558	#107	C₂³×C₁₃	1	2	yes	—
559	#107	C₂³×C₁₃	1	4	yes	—
560	#107	C₂³×C₁₃	1	4	yes	—
561	#106	C₂³×C₁₃	1	2	yes	—
562	#106	C₂³×C₁₃	1	2	yes	—
563	#106	C₂³×C₁₃	1	2	yes	—
564	#106	C₂³×C₁₃	1	2	yes	—
565	#106	C₂³×C₁₃	1	2	yes	—
566	#106	C₂³×C₁₃	1	2	yes	—
567	#106	C₂³×C₁₃	1	4	yes	—
568	#106	C₂³×C₁₃	1	4	yes	—
569	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
570	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
571	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
572	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
573	#103	C₂³×C₁₃	1	2	yes	—
574	#103	C₂³×C₁₃	1	2	yes	—
575	#103	C₂³×C₁₃	1	4	yes	—
576	#103	C₂³×C₁₃	1	4	yes	—
577	#102	C₂³×C₁₃	1	2	yes	—
578	#102	C₂³×C₁₃	1	2	yes	—
579	#102	C₂³×C₁₃	1	4	yes	—
580	#102	C₂³×C₁₃	1	4	yes	—
581	#97	C₂³×C₁₃	1	4	yes	—
582	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₁₃	1	4	yes	—
587	C₂×C₁₃	—	2	2	no	—
588	C₂×C₁₃	—	4	4	no	—
589	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
590	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
591	C₂×C₁₃	#3584	1	1	yes	characteristic
592	C₂⁴	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	4	no	—
599	C₂×Q₈	—	2	4	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	8	4	no	—
602	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
603	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
604	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	complemented
605	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
609	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
622	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
623	M₁₆	—	2	4	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
626	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
629	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
658	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
679	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₄²	C₂⁴×C₁₃	1	4	yes	—
681	C₁₃	#61371	1	1	yes	characteristic, direct product factor, Sylow
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	Q₈	—	2	4	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	4	2	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	8	4	no	—
694	Q₈	—	8	1	no	—
695	Q₈	—	8	1	no	—
696	Q₈	—	8	4	no	—
697	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	8	2	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	—	8	4	no	—
715	C₂×C₄	—	8	1	no	—
716	C₂×C₄	—	8	1	no	—
717	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
720	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
725	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
726	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	—	2	4	no	—
730	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
731	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	4	no	—
738	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
739	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	4	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	4	no	—
745	C₄	—	2	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	2	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	D₄×Q₈×C₁₃	1	2	yes	—
753	C₄	C₁₃×#577	1	2	yes	—
754	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
755	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
756	C₂	—	2	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
759	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
760	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
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×#3502	C₂	semidirect
3. C₁₃×#3388	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3385	C₂	semidirect
6. C₁₃×#3381	C₂	semidirect
7. C₁₃×#3381	C₂	semidirect
8. Q₈×C₁₃×SD₁₆	C₂	semidirect
9. C₁₃×#3163	C₂	semidirect
10. C₁₃×#3160	C₂	semidirect
11. C₁₃×#3082	C₂	semidirect
13. C₁₃×#3078	C₂	semidirect
15. C₁₃×#2960	C₂	semidirect
20. Q₈²×C₁₃	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
24. C₁₃×#557	C₂²	semidirect
44. C₁₃×#501	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#500	C₂²	semidirect
47. C₁₃×#500	C₂²	semidirect
48. C₁₃×#499	C₂²	semidirect
49. C₁₃×#499	C₂²	semidirect
50. C₁₃×#499	C₂²	semidirect
51. C₁₃×#498	C₂²	semidirect
52. C₁₃×#498	C₂²	semidirect
53. C₁₃×#498	C₂²	semidirect
54. C₁₃×#479	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#479	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
64. C₁₃×#475	C₂²	semidirect
65. C₁₃×#475	C₂²	semidirect
68. C₁₃×#446	C₂²	semidirect
69. C₁₃×#446	C₂²	semidirect
70. C₈×Q₈×C₁₃	C₂²	semidirect
71. C₈×Q₈×C₁₃	C₂²	semidirect
97. C₂×C₁₃×SD₁₆	Q₈	semidirect
212. #61371	C₁₃	direct (N × H)
225. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
242. C₁₃×SD₁₆	C₂×Q₈	semidirect
243. C₁₃×SD₁₆	C₂×Q₈	semidirect
246. C₂×C₈×C₁₃	C₂×Q₈	semidirect
302. #3502	C₂×C₁₃	semidirect
304. #3388	C₂×C₁₃	semidirect
305. #3386	C₂×C₁₃	semidirect
306. #3385	C₂×C₁₃	semidirect
307. #3381	C₂×C₁₃	semidirect
308. #3381	C₂×C₁₃	semidirect
309. Q₈×SD₁₆	C₂×C₁₃	semidirect
310. #3163	C₂×C₁₃	semidirect
311. #3160	C₂×C₁₃	semidirect
312. #3082	C₂×C₁₃	semidirect
314. #3078	C₂×C₁₃	semidirect
316. #2960	C₂×C₁₃	semidirect
371. Q₈²	C₂²×C₁₃	semidirect
374. #557	C₂²×C₁₃	semidirect
375. #557	C₂²×C₁₃	semidirect
395. #501	C₂²×C₁₃	semidirect
396. #501	C₂²×C₁₃	semidirect
397. #500	C₂²×C₁₃	semidirect
398. #500	C₂²×C₁₃	semidirect
399. #499	C₂²×C₁₃	semidirect
400. #499	C₂²×C₁₃	semidirect
401. #499	C₂²×C₁₃	semidirect
402. #498	C₂²×C₁₃	semidirect
403. #498	C₂²×C₁₃	semidirect
404. #498	C₂²×C₁₃	semidirect
405. #479	C₂²×C₁₃	semidirect
406. #479	C₂²×C₁₃	semidirect
407. #479	C₂²×C₁₃	semidirect
411. #477	C₂²×C₁₃	semidirect
412. #477	C₂²×C₁₃	semidirect
415. #475	C₂²×C₁₃	semidirect
416. #475	C₂²×C₁₃	semidirect
419. #446	C₂²×C₁₃	semidirect
420. #446	C₂²×C₁₃	semidirect
421. C₈×Q₈	C₂²×C₁₃	semidirect
422. C₈×Q₈	C₂²×C₁₃	semidirect
472. C₂×SD₁₆	Q₈×C₁₃	semidirect
604. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
621. SD₁₆	C₂×Q₈×C₁₃	semidirect
622. SD₁₆	C₂×Q₈×C₁₃	semidirect
625. C₂×C₈	C₂×Q₈×C₁₃	semidirect
681. C₁₃	#61371	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×#3502	2
C₁₃×#3501	2
C₁₃×#3388	2
C₁₃×#3386	2
C₁₃×#3385	2
C₁₃×#3381	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3163	2
C₁₃×#3160	2
C₁₃×#3082	2
C₁₃×#3081	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#2960	2
C₁₃×#2949	2
C₂×C₄×C₁₃×SD₁₆	2
#61371	13

Subgroups — C13×#61371 #15747710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61371 #15747710