Subgroups — C₁₃×#61383 #15747722

Order 3328.

1726 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3387	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
8	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3163	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3084	C₂	1	2	yes	maximal
12	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2947	C₂	1	2	yes	maximal
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	Q₈²×C₁₃	—	2	1	no	—
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	Q₈²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#557	—	2	2	no	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	4	yes	—
27	C₁₃×#554	—	2	2	no	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₃	—	2	2	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#544	—	2	2	no	—
32	C₁₃×#544	—	2	2	no	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#544	C₂²	1	2	yes	—
35	C₁₃×#533	—	2	1	no	—
36	C₁₃×#533	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	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×#520	C₂²	1	2	yes	—
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#501	C₂²	1	4	yes	—
46	C₁₃×#501	C₂²	1	4	yes	—
47	C₁₃×#501	C₂²	1	4	yes	—
48	C₁₃×#500	C₂²	1	2	yes	—
49	C₁₃×#499	C₂²	1	4	yes	—
50	C₁₃×#498	C₂²	1	4	yes	—
51	C₁₃×#498	C₂²	1	2	yes	—
52	C₁₃×#479	C₂²	1	2	yes	—
53	C₁₃×#479	C₂²	1	4	yes	—
54	C₁₃×#479	C₂²	1	4	yes	—
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#478	C₂²	1	2	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	1	yes	characteristic
59	C₁₃×#477	C₂²	1	4	yes	—
60	C₁₃×#476	C₂²	1	1	yes	characteristic
61	C₁₃×#476	C₂²	1	4	yes	—
62	C₁₃×#475	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#475	C₂²	1	4	yes	—
65	C₁₃×#475	C₂²	1	1	yes	characteristic
66	C₁₃×#475	C₂²	1	4	yes	—
67	C₁₃×#475	C₂²	1	4	yes	—
68	C₁₃×#474	C₂²	1	1	yes	characteristic
69	C₁₃×#446	C₂²	1	2	yes	—
70	C₁₃×#446	C₂²	1	4	yes	—
71	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
72	C₁₃×#441	C₂²	1	2	yes	—
73	C₁₃×#441	C₂²	1	4	yes	—
74	C₁₃×#440	C₂²	1	4	yes	—
75	C₁₃×#440	C₂²	1	2	yes	—
76	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
77	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#428	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	2	yes	—
84	C₂×C₁₃×#106	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	—	2	1	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#137	Q₈	1	8	yes	complemented
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
103	C₁₃×C₄⋊Q₈	—	2	2	no	—
104	C₁₃×C₄⋊Q₈	—	2	2	no	—
105	C₁₃×C₄⋊Q₈	—	2	4	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	4	no	—
110	C₁₃×C₄⋊Q₈	—	2	4	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	D₄	1	2	yes	—
129	C₁₃×#125	C₂³	1	4	yes	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#125	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	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	2	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	4	no	—
148	C₄×Q₈×C₁₃	—	2	2	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	4	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	4	no	—
165	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₁₃	C₂³	1	4	yes	—
167	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
168	C₁₃×#117	—	2	2	no	—
169	C₁₃×#117	—	2	4	no	—
170	C₁₃×#117	—	2	1	no	—
171	C₁₃×#117	C₂³	1	2	yes	—
172	C₁₃×#117	C₂³	1	1	yes	characteristic
173	C₁₃×#117	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	—	2	1	no	—
181	C₂×C₄²×C₁₃	—	2	1	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	2	yes	—
185	C₁₃×#107	C₂³	1	2	yes	—
186	C₁₃×#107	C₂³	1	4	yes	—
187	C₁₃×#107	C₂³	1	4	yes	—
188	C₁₃×#106	C₂³	1	4	yes	—
189	C₁₃×#106	C₂³	1	4	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×#106	C₂³	1	2	yes	—
193	C₁₃×#106	C₂³	1	4	yes	—
194	C₁₃×#106	C₂³	1	4	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
196	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
197	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	2	yes	—
203	C₁₃×#103	C₂³	1	2	yes	—
204	C₁₃×#103	C₂³	1	2	yes	—
205	C₁₃×#103	C₂³	1	2	yes	—
206	C₁₃×#103	C₂³	1	2	yes	—
207	C₁₃×#102	C₂³	1	2	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	4	yes	—
212	C₄×C₈×C₁₃	C₂³	1	2	yes	—
213	C₄×C₈×C₁₃	C₂³	1	4	yes	—
214	#61383	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃×#41	—	2	2	no	—
216	C₁₃×#41	C₂×Q₈	1	4	yes	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	2	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	4	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	—	8	2	no	—
226	C₂×Q₈×C₁₃	—	8	4	no	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	complemented
230	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
231	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₁₃×Q₁₆	C₂×Q₈	1	8	yes	complemented
245	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
246	C₁₃×M₁₆	—	2	2	no	—
247	C₁₃×M₁₆	C₂×Q₈	1	4	yes	complemented
248	C₂×C₈×C₁₃	—	2	4	no	—
249	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	4	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	2	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	4	no	—
268	C₁₃×C₄⋊C₄	—	2	4	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
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	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	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	4	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
285	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₄²×C₁₃	—	2	1	no	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	C₄²×C₁₃	—	2	4	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	2	no	—
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₁₃	C₂⁴	1	4	yes	—
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	#3503	C₂×C₁₃	1	1	yes	characteristic
307	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3388	C₂×C₁₃	1	4	yes	complemented
309	#3387	C₂×C₁₃	1	2	yes	complemented
310	#3387	C₂×C₁₃	1	4	yes	complemented
311	#3386	C₂×C₁₃	1	2	yes	complemented
312	#3383	C₂×C₁₃	1	2	yes	complemented
313	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
314	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#3163	C₂×C₁₃	1	2	yes	complemented
316	#3084	C₂×C₁₃	1	2	yes	—
317	#3082	C₂×C₁₃	1	2	yes	complemented
318	#3076	C₂×C₁₃	1	1	yes	characteristic
319	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#2947	C₂×C₁₃	1	2	yes	—
322	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	4	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	1	no	—
329	Q₈×C₁₃	—	4	2	no	—
330	Q₈×C₁₃	—	4	2	no	—
331	Q₈×C₁₃	—	4	4	no	—
332	Q₈×C₁₃	—	8	1	no	—
333	Q₈×C₁₃	—	8	4	no	—
334	Q₈×C₁₃	—	8	2	no	—
335	Q₈×C₁₃	—	8	4	no	—
336	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
337	Q₈×C₁₃	C₂²×Q₈	1	2	yes	—
338	D₄×C₁₃	—	2	4	no	—
339	D₄×C₁₃	—	2	1	no	—
340	D₄×C₁₃	C₂²×Q₈	1	2	yes	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	4	1	no	—
353	C₂×C₄×C₁₃	—	4	2	no	—
354	C₂×C₄×C₁₃	—	4	2	no	—
355	C₂×C₄×C₁₃	—	8	4	no	—
356	C₂×C₄×C₁₃	—	8	1	no	—
357	C₂×C₄×C₁₃	—	8	2	no	—
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
366	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
367	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
368	C₈×C₁₃	—	2	2	no	—
369	C₈×C₁₃	—	2	2	no	—
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
372	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
373	Q₈²	—	2	1	no	—
374	Q₈²	C₂²×C₁₃	1	2	yes	—
375	Q₈²	C₂²×C₁₃	1	2	yes	—
376	#557	—	2	1	no	—
377	#557	—	2	2	no	—
378	#557	C₂²×C₁₃	1	2	yes	—
379	#557	C₂²×C₁₃	1	2	yes	—
380	#557	C₂²×C₁₃	1	4	yes	—
381	#554	—	2	2	no	—
382	#554	C₂²×C₁₃	1	2	yes	—
383	D₄×Q₈	—	2	2	no	—
384	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
385	#544	—	2	2	no	—
386	#544	—	2	2	no	—
387	#544	C₂²×C₁₃	1	2	yes	—
388	#544	C₂²×C₁₃	1	2	yes	—
389	#533	—	2	1	no	—
390	#533	—	2	2	no	—
391	#533	C₂²×C₁₃	1	1	yes	characteristic
392	#533	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₄⋊Q₈	—	2	1	no	—
394	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
395	#520	C₂²×C₁₃	1	2	yes	—
396	#519	C₂²×C₁₃	1	2	yes	—
397	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	#501	C₂²×C₁₃	1	4	yes	—
400	#501	C₂²×C₁₃	1	4	yes	—
401	#501	C₂²×C₁₃	1	4	yes	—
402	#500	C₂²×C₁₃	1	2	yes	—
403	#499	C₂²×C₁₃	1	4	yes	—
404	#498	C₂²×C₁₃	1	4	yes	—
405	#498	C₂²×C₁₃	1	2	yes	—
406	#479	C₂²×C₁₃	1	2	yes	—
407	#479	C₂²×C₁₃	1	4	yes	—
408	#479	C₂²×C₁₃	1	4	yes	—
409	#479	C₂²×C₁₃	1	4	yes	—
410	#478	C₂²×C₁₃	1	2	yes	—
411	#478	C₂²×C₁₃	1	4	yes	—
412	#477	C₂²×C₁₃	1	1	yes	characteristic
413	#477	C₂²×C₁₃	1	4	yes	—
414	#476	C₂²×C₁₃	1	1	yes	characteristic
415	#476	C₂²×C₁₃	1	4	yes	—
416	#475	C₂²×C₁₃	1	2	yes	—
417	#475	C₂²×C₁₃	1	2	yes	—
418	#475	C₂²×C₁₃	1	4	yes	—
419	#475	C₂²×C₁₃	1	1	yes	characteristic
420	#475	C₂²×C₁₃	1	4	yes	—
421	#475	C₂²×C₁₃	1	4	yes	—
422	#474	C₂²×C₁₃	1	1	yes	characteristic
423	#446	C₂²×C₁₃	1	2	yes	—
424	#446	C₂²×C₁₃	1	4	yes	—
425	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
426	#441	C₂²×C₁₃	1	2	yes	—
427	#441	C₂²×C₁₃	1	4	yes	—
428	#440	C₂²×C₁₃	1	4	yes	—
429	#440	C₂²×C₁₃	1	2	yes	—
430	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
432	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
433	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
434	#428	C₂²×C₁₃	1	2	yes	—
435	#428	C₂²×C₁₃	1	1	yes	characteristic
436	#428	C₂²×C₁₃	1	2	yes	—
437	#427	C₂²×C₁₃	1	2	yes	—
438	C₂×#106	C₂²×C₁₃	1	2	yes	—
439	#424	C₂²×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
441	#419	C₂²×C₁₃	1	1	yes	characteristic
442	#417	C₂²×C₁₃	1	1	yes	characteristic
443	#416	C₂²×C₁₃	1	2	yes	—
444	C₂×#103	C₂²×C₁₃	1	2	yes	—
445	#405	C₂²×C₁₃	1	2	yes	—
446	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
453	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₁₃	—	2	1	no	—
455	C₄×C₁₃	—	2	1	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	2	4	no	—
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	4	no	—
461	C₄×C₁₃	—	4	1	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	1	no	—
465	C₄×C₁₃	—	4	4	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	D₄×Q₈	1	2	yes	—
468	C₄×C₁₃	#577	1	2	yes	—
469	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
470	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×Q₈	—	2	2	no	—
473	C₂²×Q₈	—	2	1	no	—
474	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
475	#137	Q₈×C₁₃	1	8	yes	complemented
476	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
477	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
478	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
481	C₄⋊Q₈	—	2	2	no	—
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	—	2	4	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₁₃	1	2	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	4	yes	—
499	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	#125	—	2	2	no	—
501	#125	—	2	4	no	—
502	#125	—	2	4	no	—
503	#125	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	2	no	—
506	#125	D₄×C₁₃	1	2	yes	—
507	#125	C₂³×C₁₃	1	2	yes	—
508	#125	C₂³×C₁₃	1	4	yes	—
509	#125	C₂³×C₁₃	1	4	yes	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	1	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	4	no	—
515	C₂²⋊Q₈	—	2	4	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
519	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	4	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
532	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
533	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
534	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
536	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
537	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
538	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
539	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₄×D₄	C₂³×C₁₃	1	4	yes	—
546	#117	—	2	2	no	—
547	#117	—	2	4	no	—
548	#117	—	2	1	no	—
549	#117	C₂³×C₁₃	1	1	yes	characteristic
550	#117	C₂³×C₁₃	1	2	yes	—
551	#117	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	2	no	—
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
561	#107	C₂³×C₁₃	1	2	yes	—
562	#107	C₂³×C₁₃	1	2	yes	—
563	#107	C₂³×C₁₃	1	2	yes	—
564	#107	C₂³×C₁₃	1	4	yes	—
565	#107	C₂³×C₁₃	1	4	yes	—
566	#106	C₂³×C₁₃	1	4	yes	—
567	#106	C₂³×C₁₃	1	4	yes	—
568	#106	C₂³×C₁₃	1	2	yes	—
569	#106	C₂³×C₁₃	1	2	yes	—
570	#106	C₂³×C₁₃	1	2	yes	—
571	#106	C₂³×C₁₃	1	4	yes	—
572	#106	C₂³×C₁₃	1	4	yes	—
573	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
576	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
577	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
578	#103	C₂³×C₁₃	1	4	yes	—
579	#103	C₂³×C₁₃	1	4	yes	—
580	#103	C₂³×C₁₃	1	2	yes	—
581	#103	C₂³×C₁₃	1	2	yes	—
582	#103	C₂³×C₁₃	1	2	yes	—
583	#103	C₂³×C₁₃	1	2	yes	—
584	#103	C₂³×C₁₃	1	2	yes	—
585	#102	C₂³×C₁₃	1	2	yes	—
586	#102	C₂³×C₁₃	1	2	yes	—
587	#102	C₂³×C₁₃	1	2	yes	—
588	#97	C₂³×C₁₃	1	2	yes	—
589	#97	C₂³×C₁₃	1	4	yes	—
590	C₄×C₈	C₂³×C₁₃	1	2	yes	—
591	C₄×C₈	C₂³×C₁₃	1	4	yes	—
592	C₂×C₁₃	—	2	2	no	—
593	C₂×C₁₃	—	4	2	no	—
594	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
595	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
596	C₂×C₁₃	#3586	1	1	yes	characteristic
597	#41	—	2	2	no	—
598	#41	C₂×Q₈×C₁₃	1	4	yes	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	4	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	8	2	no	—
608	C₂×Q₈	—	8	4	no	—
609	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
610	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	complemented
612	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	Q₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
627	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
628	M₁₆	—	2	2	no	—
629	M₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
630	C₂×C₈	—	2	4	no	—
631	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
632	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
633	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
634	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
661	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
662	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
674	C₄²	—	2	1	no	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	2	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	2	no	—
683	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
684	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
685	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
686	C₄²	C₂⁴×C₁₃	1	4	yes	—
687	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₁₃	#61383	1	1	yes	characteristic, direct product factor, Sylow
689	C₂³	—	2	1	no	—
690	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	Q₈	—	2	4	no	—
692	Q₈	—	2	4	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	2	1	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	4	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	8	2	no	—
699	Q₈	—	8	4	no	—
700	Q₈	—	8	1	no	—
701	Q₈	—	8	4	no	—
702	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
703	Q₈	C₂²×Q₈×C₁₃	1	2	yes	—
704	D₄	—	2	4	no	—
705	D₄	—	2	1	no	—
706	D₄	C₂²×Q₈×C₁₃	1	2	yes	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	—	8	2	no	—
724	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
732	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
733	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	—	2	2	no	—
737	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
744	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
745	C₄	—	2	1	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	D₄×Q₈×C₁₃	1	2	yes	—
759	C₄	C₁₃×#577	1	2	yes	—
760	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
761	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
762	C₂	—	2	2	no	—
763	C₂	—	4	2	no	—
764	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
765	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
766	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	C₂×C₁₃×#41	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
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3388	C₂	semidirect
4. C₁₃×#3387	C₂	semidirect
5. C₁₃×#3387	C₂	semidirect
6. C₁₃×#3386	C₂	semidirect
7. C₁₃×#3383	C₂	semidirect
8. Q₈×C₁₃×SD₁₆	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3163	C₂	semidirect
12. C₁₃×#3082	C₂	semidirect
14. C₂×C₁₃×#475	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
97. C₁₃×#137	Q₈	semidirect
214. #61383	C₁₃	direct (N × H)
229. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
244. C₁₃×Q₁₆	C₂×Q₈	semidirect
245. C₁₃×SD₁₆	C₂×Q₈	semidirect
247. C₁₃×M₁₆	C₂×Q₈	semidirect
307. #3502	C₂×C₁₃	semidirect
308. #3388	C₂×C₁₃	semidirect
309. #3387	C₂×C₁₃	semidirect
310. #3387	C₂×C₁₃	semidirect
311. #3386	C₂×C₁₃	semidirect
312. #3383	C₂×C₁₃	semidirect
313. Q₈×SD₁₆	C₂×C₁₃	semidirect
314. #3165	C₂×C₁₃	semidirect
315. #3163	C₂×C₁₃	semidirect
317. #3082	C₂×C₁₃	semidirect
319. C₂×#475	C₂×C₁₃	semidirect
320. #2962	C₂×C₁₃	semidirect
475. #137	Q₈×C₁₃	semidirect
611. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
626. Q₁₆	C₂×Q₈×C₁₃	semidirect
627. SD₁₆	C₂×Q₈×C₁₃	semidirect
629. M₁₆	C₂×Q₈×C₁₃	semidirect
688. C₁₃	#61383	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×#3503	2
C₁₃×#3502	2
C₁₃×#3388	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3383	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3165	2
C₁₃×#3163	2
C₁₃×#3084	2
C₁₃×#3082	2
C₁₃×#3076	2
C₂×C₁₃×#475	2
C₁₃×#2962	2
C₁₃×#2947	2
C₄×C₁₃×#137	2
#61383	13

Subgroups — C13×#61383 #15747722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61383 #15747722