Subgroups — C₁₃×#60930 #15747269

Order 3328.

1804 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3262	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3249	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#554	—	2	1	no	—
24	C₁₃×#553	—	2	2	no	—
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	4	yes	—
31	C₁₃×#541	—	2	1	no	—
32	C₁₃×#541	C₂²	1	2	yes	—
33	C₁₃×#539	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#537	C₂²	1	2	yes	—
36	C₁₃×#536	C₂²	1	1	yes	characteristic
37	C₁₃×#536	C₂²	1	1	yes	characteristic
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	C₂²	1	2	yes	—
40	C₁₃×#533	C₂²	1	2	yes	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	2	yes	—
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#529	—	2	1	no	—
46	C₁₃×#529	C₂²	1	2	yes	—
47	C₁₃×#520	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#479	C₂²	1	4	yes	—
52	C₁₃×#478	C₂²	1	4	yes	—
53	C₁₃×#477	C₂²	1	4	yes	—
54	C₁₃×#477	C₂²	1	4	yes	—
55	C₁₃×#477	C₂²	1	2	yes	—
56	C₁₃×#477	C₂²	1	2	yes	—
57	C₁₃×#477	C₂²	1	2	yes	—
58	C₁₃×#476	C₂²	1	2	yes	—
59	C₁₃×#475	C₂²	1	2	yes	—
60	C₁₃×#474	C₂²	1	2	yes	—
61	C₁₃×#474	C₂²	1	4	yes	—
62	C₁₃×#470	C₂²	1	4	yes	—
63	C₁₃×#468	C₂²	1	4	yes	—
64	C₁₃×#468	C₂²	1	4	yes	—
65	C₁₃×#468	C₂²	1	4	yes	—
66	C₁₃×#467	C₂²	1	4	yes	—
67	C₁₃×#467	C₂²	1	4	yes	—
68	C₁₃×#466	C₂²	1	4	yes	—
69	C₁₃×#465	C₂²	1	4	yes	—
70	C₁₃×#464	C₂²	1	4	yes	—
71	C₁₃×#464	C₂²	1	4	yes	—
72	C₁₃×#464	C₂²	1	2	yes	—
73	C₁₃×#463	C₂²	1	2	yes	—
74	C₁₃×#463	C₂²	1	4	yes	—
75	C₁₃×#462	C₂²	1	1	yes	characteristic
76	C₁₃×#462	C₂²	1	2	yes	—
77	C₁₃×#462	C₂²	1	4	yes	—
78	C₁₃×#461	C₂²	1	1	yes	characteristic
79	C₁₃×#461	C₂²	1	4	yes	—
80	C₁₃×#460	C₂²	1	1	yes	characteristic
81	C₁₃×#460	C₂²	1	2	yes	—
82	C₁₃×#459	C₂²	1	1	yes	characteristic
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₂×C₁₃×#107	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	4	yes	—
86	C₁₃×#424	C₂²	1	2	yes	—
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	—	2	1	no	—
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#137	—	4	4	no	—
102	C₁₃×#135	—	4	4	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	2	yes	—
109	C₁₃×#131	—	4	4	no	—
110	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
111	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
112	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₁₃×#127	C₂³	1	1	yes	characteristic
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	4	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#124	—	2	1	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	4	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	C₂³	1	2	yes	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	1	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	4	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	—	2	1	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	C₂³	1	4	yes	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	2	no	—
172	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	4	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	1	no	—
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	4	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	—	2	1	no	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#107	C₂³	1	4	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	2	yes	—
225	C₁₃×#103	C₂³	1	4	yes	—
226	C₁₃×#103	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×#102	C₂³	1	4	yes	—
231	#60930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	8	4	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	8	2	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₁₃×Q₁₆	—	4	2	no	—
275	C₁₃×Q₁₆	—	4	4	no	—
276	C₁₃×SD₁₆	—	4	2	no	—
277	C₁₃×SD₁₆	—	4	2	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×D₈	—	4	2	no	—
280	C₁₃×M₁₆	—	2	4	no	—
281	C₁₃×M₁₆	—	4	4	no	—
282	C₂×C₈×C₁₃	—	2	4	no	—
283	C₂×C₈×C₁₃	—	4	4	no	—
284	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
285	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	4	no	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₄²×C₁₃	C₂⁴	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3461	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3262	C₂×C₁₃	1	4	yes	complemented
348	#3258	C₂×C₁₃	1	4	yes	complemented
349	#3254	C₂×C₁₃	1	2	yes	complemented
350	#3252	C₂×C₁₃	1	2	yes	complemented
351	#3249	C₂×C₁₃	1	2	yes	complemented
352	#3247	C₂×C₁₃	1	2	yes	complemented
353	#3083	C₂×C₁₃	1	2	yes	complemented
354	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3063	C₂×C₁₃	1	2	yes	complemented
357	#3061	C₂×C₁₃	1	2	yes	complemented
358	#3046	C₂×C₁₃	1	2	yes	complemented
359	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	1	no	—
373	Q₈×C₁₃	—	4	4	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	—	8	2	no	—
376	Q₈×C₁₃	—	8	2	no	—
377	D₄×C₁₃	—	2	4	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	8	2	no	—
388	D₄×C₁₃	—	8	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	4	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	8	1	no	—
407	C₂×C₄×C₁₃	—	8	4	no	—
408	C₂×C₄×C₁₃	—	8	1	no	—
409	C₂×C₄×C₁₃	—	8	2	no	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
419	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	2	no	—
423	C₈×C₁₃	—	2	4	no	—
424	C₂×#137	C₂²×C₁₃	1	2	yes	—
425	C₂×#135	C₂²×C₁₃	1	2	yes	—
426	C₂×#131	C₂²×C₁₃	1	2	yes	—
427	#556	—	2	1	no	—
428	#555	—	2	1	no	—
429	#554	—	2	1	no	—
430	#553	—	2	2	no	—
431	#548	—	2	2	no	—
432	#547	—	2	1	no	—
433	#544	C₂²×C₁₃	1	1	yes	characteristic
434	#542	—	2	1	no	—
435	#542	C₂²×C₁₃	1	2	yes	—
436	#542	C₂²×C₁₃	1	4	yes	—
437	#541	—	2	1	no	—
438	#541	C₂²×C₁₃	1	2	yes	—
439	#539	—	2	2	no	—
440	#537	C₂²×C₁₃	1	1	yes	characteristic
441	#537	C₂²×C₁₃	1	2	yes	—
442	#536	C₂²×C₁₃	1	1	yes	characteristic
443	#536	C₂²×C₁₃	1	1	yes	characteristic
444	#533	—	2	1	no	—
445	#533	C₂²×C₁₃	1	2	yes	—
446	#533	C₂²×C₁₃	1	2	yes	—
447	#532	C₂²×C₁₃	1	1	yes	characteristic
448	#532	C₂²×C₁₃	1	2	yes	—
449	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	#529	—	2	2	no	—
451	#529	—	2	1	no	—
452	#529	C₂²×C₁₃	1	2	yes	—
453	#520	C₂²×C₁₃	1	2	yes	—
454	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
455	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	#479	C₂²×C₁₃	1	4	yes	—
458	#478	C₂²×C₁₃	1	4	yes	—
459	#477	C₂²×C₁₃	1	2	yes	—
460	#477	C₂²×C₁₃	1	2	yes	—
461	#477	C₂²×C₁₃	1	4	yes	—
462	#477	C₂²×C₁₃	1	2	yes	—
463	#477	C₂²×C₁₃	1	4	yes	—
464	#476	C₂²×C₁₃	1	2	yes	—
465	#475	C₂²×C₁₃	1	2	yes	—
466	#474	C₂²×C₁₃	1	2	yes	—
467	#474	C₂²×C₁₃	1	4	yes	—
468	#470	C₂²×C₁₃	1	4	yes	—
469	#468	C₂²×C₁₃	1	4	yes	—
470	#468	C₂²×C₁₃	1	4	yes	—
471	#468	C₂²×C₁₃	1	4	yes	—
472	#467	C₂²×C₁₃	1	4	yes	—
473	#467	C₂²×C₁₃	1	4	yes	—
474	#466	C₂²×C₁₃	1	4	yes	—
475	#465	C₂²×C₁₃	1	4	yes	—
476	#464	C₂²×C₁₃	1	4	yes	—
477	#464	C₂²×C₁₃	1	2	yes	—
478	#464	C₂²×C₁₃	1	4	yes	—
479	#463	C₂²×C₁₃	1	4	yes	—
480	#463	C₂²×C₁₃	1	2	yes	—
481	#462	C₂²×C₁₃	1	1	yes	characteristic
482	#462	C₂²×C₁₃	1	2	yes	—
483	#462	C₂²×C₁₃	1	4	yes	—
484	#461	C₂²×C₁₃	1	1	yes	characteristic
485	#461	C₂²×C₁₃	1	4	yes	—
486	#460	C₂²×C₁₃	1	2	yes	—
487	#460	C₂²×C₁₃	1	1	yes	characteristic
488	#459	C₂²×C₁₃	1	1	yes	characteristic
489	#428	C₂²×C₁₃	1	2	yes	—
490	C₂×#107	C₂²×C₁₃	1	2	yes	—
491	#424	C₂²×C₁₃	1	2	yes	—
492	#424	C₂²×C₁₃	1	4	yes	—
493	#423	C₂²×C₁₃	1	1	yes	characteristic
494	#423	C₂²×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
497	#417	C₂²×C₁₃	1	2	yes	—
498	#417	C₂²×C₁₃	1	2	yes	—
499	#416	C₂²×C₁₃	1	2	yes	—
500	C₂×#103	C₂²×C₁₃	1	2	yes	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	#537	1	2	yes	—
513	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	4	4	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	1	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	#537	1	2	yes	—
528	C₄×C₁₃	#578	1	2	yes	—
529	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	C₂×#41	—	2	2	no	—
532	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×#41	C₂³×C₁₃	1	2	yes	—
534	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	#137	—	4	4	no	—
538	#135	—	4	4	no	—
539	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
540	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
542	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
544	C₂×D₈	C₂³×C₁₃	1	2	yes	—
545	#131	—	4	4	no	—
546	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
547	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
548	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
549	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
559	#127	C₂³×C₁₃	1	1	yes	characteristic
560	#126	—	2	2	no	—
561	#126	—	2	4	no	—
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#126	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	2	1	no	—
567	#125	—	2	2	no	—
568	#125	—	2	2	no	—
569	#125	—	2	2	no	—
570	#125	C₂³×C₁₃	1	2	yes	—
571	#124	—	2	1	no	—
572	#124	—	2	2	no	—
573	#124	—	2	4	no	—
574	#124	—	2	2	no	—
575	#124	C₂³×C₁₃	1	2	yes	—
576	#124	C₂³×C₁₃	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	4	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
595	#121	—	2	2	no	—
596	#121	—	2	1	no	—
597	#121	—	2	2	no	—
598	#121	—	2	4	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	C₂³×C₁₃	1	2	yes	—
603	#121	C₂³×C₁₃	1	4	yes	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
609	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
611	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
612	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	D₄×C₁₃	1	2	yes	—
623	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
624	C₄×D₄	D₄×C₁₃	1	2	yes	—
625	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
626	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₁₃	1	4	yes	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	C₂³×C₁₃	1	1	yes	characteristic
635	#117	C₂³×C₁₃	1	1	yes	characteristic
636	#117	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
646	#107	C₂³×C₁₃	1	4	yes	—
647	#107	C₂³×C₁₃	1	4	yes	—
648	#107	C₂³×C₁₃	1	4	yes	—
649	#106	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
652	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
654	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
655	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
656	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#103	C₂³×C₁₃	1	2	yes	—
660	#103	C₂³×C₁₃	1	2	yes	—
661	#103	C₂³×C₁₃	1	4	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	#102	C₂³×C₁₃	1	2	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	#102	C₂³×C₁₃	1	4	yes	—
667	C₂×C₁₃	—	2	2	no	—
668	C₂×C₁₃	—	4	2	no	—
669	C₂×C₁₃	—	8	2	no	—
670	C₂×C₁₃	—	8	1	no	—
671	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
672	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
673	C₂×C₁₃	#3585	1	1	yes	characteristic
674	#41	—	2	2	no	—
675	#41	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	2	4	no	—
678	#41	—	2	2	no	—
679	#41	—	2	4	no	—
680	#41	—	8	4	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	8	2	no	—
688	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
690	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	Q₁₆	—	4	2	no	—
717	Q₁₆	—	4	4	no	—
718	SD₁₆	—	4	2	no	—
719	SD₁₆	—	4	2	no	—
720	SD₁₆	—	4	4	no	—
721	D₈	—	4	2	no	—
722	M₁₆	—	2	4	no	—
723	M₁₆	—	4	4	no	—
724	C₂×C₈	—	2	4	no	—
725	C₂×C₈	—	4	4	no	—
726	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
727	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
728	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	4	no	—
780	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₄²	C₂×D₄×C₁₃	1	2	yes	—
784	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₁₃	1	2	yes	—
786	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₁₃	#60930	1	1	yes	characteristic, direct product factor, Sylow
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
791	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	1	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	Q₈	—	8	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	1	no	—
833	C₂×C₄	—	8	4	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
845	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
846	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
847	C₈	—	2	2	no	—
848	C₈	—	2	2	no	—
849	C₈	—	2	4	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	C₁₃×#537	1	2	yes	—
862	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	4	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₄	C₁₃×#537	1	2	yes	—
877	C₄	C₁₃×#578	1	2	yes	—
878	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
879	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	8	1	no	—
883	C₂	—	8	2	no	—
884	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
885	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
886	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3461	C₂	semidirect
3. C₁₃×#3262	C₂	semidirect
4. C₁₃×#3258	C₂	semidirect
5. C₁₃×#3254	C₂	semidirect
6. C₁₃×#3252	C₂	semidirect
7. C₁₃×#3249	C₂	semidirect
8. C₁₃×#3247	C₂	semidirect
9. C₁₃×#3083	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₂×C₁₃×#477	C₂	semidirect
12. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3061	C₂	semidirect
14. C₁₃×#3046	C₂	semidirect
15. C₁₃×#3037	C₂	semidirect
16. C₁₃×#3035	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
231. #60930	C₁₃	direct (N × H)
345. #3511	C₂×C₁₃	semidirect
346. #3461	C₂×C₁₃	semidirect
347. #3262	C₂×C₁₃	semidirect
348. #3258	C₂×C₁₃	semidirect
349. #3254	C₂×C₁₃	semidirect
350. #3252	C₂×C₁₃	semidirect
351. #3249	C₂×C₁₃	semidirect
352. #3247	C₂×C₁₃	semidirect
353. #3083	C₂×C₁₃	semidirect
354. #3079	C₂×C₁₃	semidirect
355. C₂×#477	C₂×C₁₃	semidirect
356. #3063	C₂×C₁₃	semidirect
357. #3061	C₂×C₁₃	semidirect
358. #3046	C₂×C₁₃	semidirect
359. #3037	C₂×C₁₃	semidirect
360. #3035	C₂×C₁₃	semidirect
361. #2906	C₂×C₁₃	semidirect
787. C₁₃	#60930	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×#3511	2
C₁₃×#3461	2
C₁₃×#3262	2
C₁₃×#3258	2
C₁₃×#3254	2
C₁₃×#3252	2
C₁₃×#3249	2
C₁₃×#3247	2
C₁₃×#3083	2
C₁₃×#3079	2
C₂×C₁₃×#477	2
C₁₃×#3063	2
C₁₃×#3061	2
C₁₃×#3046	2
C₁₃×#3037	2
C₁₃×#3035	2
C₁₃×#2906	2
#60930	13

Subgroups — C13×#60930 #15747269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60930 #15747269