Subgroups — C₁₃×#61491 #15747830

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3516	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#552	—	2	2	no	—
30	C₁₃×#552	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#548	C₂²	1	2	yes	—
33	C₁₃×#548	C₂²	1	2	yes	—
34	C₁₃×#542	—	2	2	no	—
35	C₁₃×#542	C₂²	1	2	yes	—
36	C₁₃×#541	—	2	2	no	—
37	C₁₃×#541	C₂²	1	2	yes	—
38	C₁₃×#529	—	2	2	no	—
39	C₁₃×#529	—	2	2	no	—
40	C₁₃×#529	C₂²	1	2	yes	—
41	C₁₃×#529	C₂²	1	1	yes	characteristic
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₁₃×#519	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₁₃×#501	C₂²	1	2	yes	—
46	C₁₃×#499	C₂²	1	1	yes	characteristic
47	C₁₃×#497	C₂²	1	2	yes	—
48	C₁₃×#495	C₂²	1	1	yes	characteristic
49	C₁₃×#488	C₂²	1	2	yes	—
50	C₁₃×#488	C₂²	1	2	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#485	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	2	yes	—
55	C₁₃×#484	C₂²	1	2	yes	—
56	C₁₃×#481	C₂²	1	2	yes	—
57	C₁₃×#480	C₂²	1	2	yes	—
58	C₁₃×#479	C₂²	1	2	yes	—
59	C₁₃×#479	C₂²	1	2	yes	—
60	C₁₃×#479	C₂²	1	2	yes	—
61	C₁₃×#479	C₂²	1	2	yes	—
62	C₁₃×#477	C₂²	1	2	yes	—
63	C₁₃×#474	C₂²	1	2	yes	—
64	C₁₃×#470	C₂²	1	2	yes	—
65	C₁₃×#468	C₂²	1	2	yes	—
66	C₁₃×#467	C₂²	1	1	yes	characteristic
67	C₁₃×#467	C₂²	1	2	yes	—
68	C₁₃×#466	C₂²	1	1	yes	characteristic
69	C₁₃×#465	C₂²	1	2	yes	—
70	C₁₃×#465	C₂²	1	2	yes	—
71	C₁₃×#464	C₂²	1	2	yes	—
72	C₁₃×#464	C₂²	1	2	yes	—
73	C₁₃×#464	C₂²	1	2	yes	—
74	C₁₃×#463	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	2	yes	—
76	C₁₃×#462	C₂²	1	2	yes	—
77	C₁₃×#452	C₂²	1	2	yes	—
78	C₁₃×#451	C₂²	1	2	yes	—
79	C₁₃×#451	C₂²	1	2	yes	—
80	C₁₃×#451	C₂²	1	2	yes	—
81	C₁₃×#449	C₂²	1	2	yes	—
82	C₁₃×#448	C₂²	1	2	yes	—
83	C₁₃×#446	C₂²	1	1	yes	characteristic
84	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
85	C₁₃×#441	C₂²	1	2	yes	—
86	C₁₃×#441	C₂²	1	2	yes	—
87	C₁₃×#441	C₂²	1	2	yes	—
88	C₁₃×#440	C₂²	1	2	yes	—
89	C₁₃×#440	C₂²	1	2	yes	—
90	C₁₃×#440	C₂²	1	2	yes	—
91	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
92	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
93	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
94	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
96	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
97	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
100	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
101	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
102	C₁₃×#436	C₂²	1	1	yes	characteristic
103	C₁₃×#435	C₂²	1	2	yes	—
104	C₈×D₄×C₁₃	C₂²	1	2	yes	—
105	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
106	C₁₃×#433	C₂²	1	2	yes	—
107	C₁₃×#432	C₂²	1	1	yes	characteristic
108	C₁₃×#428	C₂²	1	2	yes	—
109	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
110	C₁₃×#416	C₂²	1	2	yes	—
111	C₂×C₁₃×#103	C₂²	1	2	yes	—
112	C₂×C₁₃×#103	C₂²	1	2	yes	—
113	C₁₃×#405	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
118	C₁₃×#137	—	2	8	no	—
119	C₂×C₁₃×Q₁₆	—	2	4	no	—
120	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	D₄	1	2	yes	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	D₄	1	1	yes	characteristic
154	C₁₃×#125	C₂³	1	2	yes	—
155	C₁₃×#125	C₂³	1	2	yes	—
156	C₁₃×#124	—	2	2	no	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	—	2	2	no	—
159	C₁₃×#124	D₄	1	1	yes	characteristic
160	C₁₃×#124	C₂³	1	2	yes	—
161	C₁₃×#124	C₂³	1	2	yes	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	D₄	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	—	2	2	no	—
182	C₁₃×#121	—	2	2	no	—
183	C₁₃×#121	D₄	1	1	yes	characteristic
184	C₁₃×#121	C₂³	1	2	yes	—
185	C₁₃×#121	C₂³	1	2	yes	—
186	C₄×Q₈×C₁₃	—	2	2	no	—
187	C₄×Q₈×C₁₃	—	2	2	no	—
188	C₄×Q₈×C₁₃	—	2	2	no	—
189	C₄×Q₈×C₁₃	—	2	2	no	—
190	C₄×Q₈×C₁₃	—	2	2	no	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
194	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
195	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
196	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
197	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
198	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₁₃	—	2	2	no	—
201	C₄×D₄×C₁₃	—	2	2	no	—
202	C₄×D₄×C₁₃	—	2	2	no	—
203	C₄×D₄×C₁₃	—	2	2	no	—
204	C₄×D₄×C₁₃	—	2	2	no	—
205	C₄×D₄×C₁₃	—	2	2	no	—
206	C₄×D₄×C₁₃	—	2	2	no	—
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	C₂³	1	2	yes	—
209	C₄×D₄×C₁₃	C₂³	1	2	yes	—
210	C₄×D₄×C₁₃	C₂³	1	2	yes	—
211	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
212	C₁₃×#117	—	2	2	no	—
213	C₁₃×#117	—	2	2	no	—
214	C₁₃×#117	—	2	2	no	—
215	C₁₃×#117	—	2	2	no	—
216	C₁₃×#117	—	2	2	no	—
217	C₁₃×#117	—	2	2	no	—
218	C₁₃×#117	C₂³	1	2	yes	—
219	C₁₃×#117	C₂³	1	2	yes	—
220	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
223	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
224	C₂×C₄²×C₁₃	—	2	2	no	—
225	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₁₃×#107	C₂³	1	1	yes	characteristic
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	2	yes	—
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	1	yes	characteristic
231	C₁₃×#107	C₂³	1	1	yes	characteristic
232	C₁₃×#107	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×#106	C₂³	1	2	yes	—
235	C₁₃×#106	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
237	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×#102	C₂³	1	2	yes	—
255	C₁₃×#102	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	2	yes	—
266	#61491	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₁₃×#41	—	2	4	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₂×Q₈×C₁₃	—	2	2	no	—
270	C₂×Q₈×C₁₃	—	2	2	no	—
271	C₂×Q₈×C₁₃	—	2	2	no	—
272	C₂×Q₈×C₁₃	—	2	4	no	—
273	C₂×Q₈×C₁₃	—	2	4	no	—
274	C₂×Q₈×C₁₃	—	4	2	no	—
275	C₂×Q₈×C₁₃	—	4	2	no	—
276	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₁₃×Q₁₆	—	2	4	no	—
298	C₁₃×Q₁₆	—	2	4	no	—
299	C₁₃×Q₁₆	—	2	2	no	—
300	C₁₃×Q₁₆	—	4	1	no	—
301	C₁₃×Q₁₆	—	4	2	no	—
302	C₁₃×Q₁₆	#41	1	4	yes	—
303	C₁₃×SD₁₆	—	2	4	no	—
304	C₁₃×SD₁₆	—	2	4	no	—
305	C₁₃×SD₁₆	—	4	2	no	—
306	C₁₃×D₈	—	4	1	no	—
307	C₁₃×M₁₆	—	2	4	no	—
308	C₂×C₈×C₁₃	—	2	2	no	—
309	C₂×C₈×C₁₃	—	4	1	no	—
310	C₂×C₈×C₁₃	—	4	2	no	—
311	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
342	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
344	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	2	yes	—
380	#3516	C₂×C₁₃	1	2	yes	complemented
381	#3402	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#3390	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3364	C₂×C₁₃	1	2	yes	complemented
384	#3352	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3346	C₂×C₁₃	1	2	yes	complemented
386	#3301	C₂×C₁₃	1	2	yes	complemented
387	#3300	C₂×C₁₃	1	2	yes	complemented
388	#3299	C₂×C₁₃	1	2	yes	complemented
389	#3277	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3270	C₂×C₁₃	1	2	yes	complemented
391	#3178	C₂×C₁₃	1	2	yes	complemented
392	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#3127	C₂×C₁₃	1	2	yes	complemented
394	#3124	C₂×C₁₃	1	2	yes	complemented
395	#3117	C₂×C₁₃	1	2	yes	complemented
396	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#2947	C₂×C₁₃	1	2	yes	complemented
398	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
399	C₂³×C₁₃	—	2	2	no	—
400	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₁₃	—	2	2	no	—
403	Q₈×C₁₃	—	2	2	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	4	1	no	—
408	Q₈×C₁₃	—	4	4	no	—
409	Q₈×C₁₃	—	4	4	no	—
410	Q₈×C₁₃	—	8	2	no	—
411	Q₈×C₁₃	C₂×#41	1	4	yes	—
412	D₄×C₁₃	—	2	4	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	4	1	no	—
416	D₄×C₁₃	—	4	4	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	8	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	4	1	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	4	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	8	2	no	—
436	C₂×C₄×C₁₃	—	8	2	no	—
437	C₂×C₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
448	C₈×C₁₃	—	2	1	no	—
449	C₈×C₁₃	—	2	2	no	—
450	C₈×C₁₃	—	2	1	no	—
451	C₈×C₁₃	—	2	1	no	—
452	C₈×C₁₃	—	2	2	no	—
453	C₈×C₁₃	C₂×#41	1	2	yes	—
454	C₂×#137	C₂²×C₁₃	1	2	yes	—
455	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
456	#557	C₂²×C₁₃	1	2	yes	—
457	#556	—	2	2	no	—
458	#556	C₂²×C₁₃	1	2	yes	—
459	#554	—	2	2	no	—
460	#554	C₂²×C₁₃	1	2	yes	—
461	#553	—	2	2	no	—
462	#553	C₂²×C₁₃	1	2	yes	—
463	#552	—	2	2	no	—
464	#552	C₂²×C₁₃	1	2	yes	—
465	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
466	#548	C₂²×C₁₃	1	2	yes	—
467	#548	C₂²×C₁₃	1	2	yes	—
468	#542	—	2	2	no	—
469	#542	C₂²×C₁₃	1	2	yes	—
470	#541	—	2	2	no	—
471	#541	C₂²×C₁₃	1	2	yes	—
472	#529	—	2	2	no	—
473	#529	—	2	2	no	—
474	#529	C₂²×C₁₃	1	2	yes	—
475	#529	C₂²×C₁₃	1	1	yes	characteristic
476	#520	C₂²×C₁₃	1	2	yes	—
477	#519	C₂²×C₁₃	1	2	yes	—
478	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
479	#501	C₂²×C₁₃	1	2	yes	—
480	#499	C₂²×C₁₃	1	1	yes	characteristic
481	#497	C₂²×C₁₃	1	2	yes	—
482	#495	C₂²×C₁₃	1	1	yes	characteristic
483	#488	C₂²×C₁₃	1	2	yes	—
484	#488	C₂²×C₁₃	1	2	yes	—
485	#487	C₂²×C₁₃	1	2	yes	—
486	#485	C₂²×C₁₃	1	2	yes	—
487	#485	C₂²×C₁₃	1	2	yes	—
488	#484	C₂²×C₁₃	1	2	yes	—
489	#484	C₂²×C₁₃	1	2	yes	—
490	#481	C₂²×C₁₃	1	2	yes	—
491	#480	C₂²×C₁₃	1	2	yes	—
492	#479	C₂²×C₁₃	1	2	yes	—
493	#479	C₂²×C₁₃	1	2	yes	—
494	#479	C₂²×C₁₃	1	2	yes	—
495	#479	C₂²×C₁₃	1	2	yes	—
496	#477	C₂²×C₁₃	1	2	yes	—
497	#474	C₂²×C₁₃	1	2	yes	—
498	#470	C₂²×C₁₃	1	2	yes	—
499	#468	C₂²×C₁₃	1	2	yes	—
500	#467	C₂²×C₁₃	1	1	yes	characteristic
501	#467	C₂²×C₁₃	1	2	yes	—
502	#466	C₂²×C₁₃	1	1	yes	characteristic
503	#465	C₂²×C₁₃	1	2	yes	—
504	#465	C₂²×C₁₃	1	2	yes	—
505	#464	C₂²×C₁₃	1	2	yes	—
506	#464	C₂²×C₁₃	1	2	yes	—
507	#464	C₂²×C₁₃	1	2	yes	—
508	#463	C₂²×C₁₃	1	2	yes	—
509	#462	C₂²×C₁₃	1	2	yes	—
510	#462	C₂²×C₁₃	1	2	yes	—
511	#452	C₂²×C₁₃	1	2	yes	—
512	#451	C₂²×C₁₃	1	2	yes	—
513	#451	C₂²×C₁₃	1	2	yes	—
514	#451	C₂²×C₁₃	1	2	yes	—
515	#449	C₂²×C₁₃	1	2	yes	—
516	#448	C₂²×C₁₃	1	2	yes	—
517	#446	C₂²×C₁₃	1	1	yes	characteristic
518	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
519	#441	C₂²×C₁₃	1	2	yes	—
520	#441	C₂²×C₁₃	1	2	yes	—
521	#441	C₂²×C₁₃	1	2	yes	—
522	#440	C₂²×C₁₃	1	2	yes	—
523	#440	C₂²×C₁₃	1	2	yes	—
524	#440	C₂²×C₁₃	1	2	yes	—
525	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
526	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
527	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
528	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
529	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
530	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
531	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
532	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
533	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
534	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
535	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
536	#436	C₂²×C₁₃	1	1	yes	characteristic
537	#435	C₂²×C₁₃	1	2	yes	—
538	C₈×D₄	C₂²×C₁₃	1	2	yes	—
539	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
540	#433	C₂²×C₁₃	1	2	yes	—
541	#432	C₂²×C₁₃	1	1	yes	characteristic
542	#428	C₂²×C₁₃	1	2	yes	—
543	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
544	#416	C₂²×C₁₃	1	2	yes	—
545	C₂×#103	C₂²×C₁₃	1	2	yes	—
546	C₂×#103	C₂²×C₁₃	1	2	yes	—
547	#405	C₂²×C₁₃	1	2	yes	—
548	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	#578	1	2	yes	—
558	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₁₃	—	2	1	no	—
560	C₄×C₁₃	—	2	1	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	1	no	—
564	C₄×C₁₃	—	2	4	no	—
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
575	C₄×C₁₃	#585	1	1	yes	characteristic
576	C₂×#41	C₂³×C₁₃	1	2	yes	—
577	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
579	#137	—	2	8	no	—
580	C₂×Q₁₆	—	2	4	no	—
581	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
582	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
583	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
590	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
592	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
595	C₄⋊Q₈	—	2	2	no	—
596	C₄⋊Q₈	—	2	2	no	—
597	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	D₄×C₁₃	1	2	yes	—
608	#125	—	2	2	no	—
609	#125	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	D₄×C₁₃	1	1	yes	characteristic
615	#125	C₂³×C₁₃	1	2	yes	—
616	#125	C₂³×C₁₃	1	2	yes	—
617	#124	—	2	2	no	—
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	D₄×C₁₃	1	1	yes	characteristic
621	#124	C₂³×C₁₃	1	2	yes	—
622	#124	C₂³×C₁₃	1	2	yes	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	D₄×C₁₃	1	2	yes	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
637	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	D₄×C₁₃	1	1	yes	characteristic
645	#121	C₂³×C₁₃	1	2	yes	—
646	#121	C₂³×C₁₃	1	2	yes	—
647	C₄×Q₈	—	2	2	no	—
648	C₄×Q₈	—	2	2	no	—
649	C₄×Q₈	—	2	2	no	—
650	C₄×Q₈	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	C₂³×C₁₃	1	2	yes	—
680	#117	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄⋊C₄	—	2	2	no	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄²	—	2	2	no	—
686	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
687	#107	C₂³×C₁₃	1	1	yes	characteristic
688	#107	C₂³×C₁₃	1	1	yes	characteristic
689	#107	C₂³×C₁₃	1	2	yes	—
690	#107	C₂³×C₁₃	1	2	yes	—
691	#107	C₂³×C₁₃	1	1	yes	characteristic
692	#107	C₂³×C₁₃	1	1	yes	characteristic
693	#107	C₂³×C₁₃	1	2	yes	—
694	#106	C₂³×C₁₃	1	2	yes	—
695	#106	C₂³×C₁₃	1	2	yes	—
696	#106	C₂³×C₁₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
699	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
701	#103	C₂³×C₁₃	1	2	yes	—
702	#103	C₂³×C₁₃	1	2	yes	—
703	#103	C₂³×C₁₃	1	2	yes	—
704	#103	C₂³×C₁₃	1	2	yes	—
705	#103	C₂³×C₁₃	1	2	yes	—
706	#103	C₂³×C₁₃	1	2	yes	—
707	#103	C₂³×C₁₃	1	2	yes	—
708	#103	C₂³×C₁₃	1	2	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#103	C₂³×C₁₃	1	2	yes	—
712	#103	C₂³×C₁₃	1	2	yes	—
713	#102	C₂³×C₁₃	1	2	yes	—
714	#102	C₂³×C₁₃	1	2	yes	—
715	#102	C₂³×C₁₃	1	2	yes	—
716	#102	C₂³×C₁₃	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
720	#97	C₂³×C₁₃	1	2	yes	—
721	#97	C₂³×C₁₃	1	2	yes	—
722	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄×C₈	C₂³×C₁₃	1	2	yes	—
727	C₂×C₁₃	—	2	2	no	—
728	C₂×C₁₃	—	4	2	no	—
729	C₂×C₁₃	—	8	2	no	—
730	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
731	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
732	C₂×C₁₃	#3584	1	1	yes	characteristic
733	#41	—	2	4	no	—
734	#41	—	4	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	2	4	no	—
739	C₂×Q₈	—	2	4	no	—
740	C₂×Q₈	—	4	2	no	—
741	C₂×Q₈	—	4	2	no	—
742	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
744	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
745	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
763	Q₁₆	—	2	4	no	—
764	Q₁₆	—	2	4	no	—
765	Q₁₆	—	2	2	no	—
766	Q₁₆	—	4	1	no	—
767	Q₁₆	—	4	2	no	—
768	Q₁₆	C₁₃×#41	1	4	yes	—
769	SD₁₆	—	2	4	no	—
770	SD₁₆	—	2	4	no	—
771	SD₁₆	—	4	2	no	—
772	D₈	—	4	1	no	—
773	M₁₆	—	2	4	no	—
774	C₂×C₈	—	2	2	no	—
775	C₂×C₈	—	4	1	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
781	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
782	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
807	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
809	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
810	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
813	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
828	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
829	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
842	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
843	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
845	C₄²	C₂⁴×C₁₃	1	2	yes	—
846	C₁₃	#61491	1	1	yes	characteristic, direct product factor, Sylow
847	C₂³	—	2	2	no	—
848	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
849	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	4	1	no	—
856	Q₈	—	4	4	no	—
857	Q₈	—	4	4	no	—
858	Q₈	—	8	2	no	—
859	Q₈	C₂×C₁₃×#41	1	4	yes	—
860	D₄	—	2	4	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	1	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	4	no	—
866	D₄	—	8	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
896	C₈	—	2	1	no	—
897	C₈	—	2	2	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	1	no	—
900	C₈	—	2	2	no	—
901	C₈	C₂×C₁₃×#41	1	2	yes	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	C₁₃×#578	1	2	yes	—
911	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	4	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
928	C₄	C₁₃×#585	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	2	no	—
932	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
933	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
934	C₂	C₁₃×#3584	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 ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3516	C₂	semidirect
2. C₁₃×#3402	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3352	C₂	semidirect
6. C₁₃×#3346	C₂	semidirect
7. C₁₃×#3301	C₂	semidirect
8. C₁₃×#3300	C₂	semidirect
9. C₁₃×#3299	C₂	semidirect
10. C₁₃×#3277	C₂	semidirect
11. C₁₃×#3270	C₂	semidirect
12. C₁₃×#3178	C₂	semidirect
13. C₁₃×#3168	C₂	semidirect
14. C₁₃×#3127	C₂	semidirect
15. C₁₃×#3124	C₂	semidirect
16. C₁₃×#3117	C₂	semidirect
17. C₁₃×#2966	C₂	semidirect
18. C₁₃×#2947	C₂	semidirect
19. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
266. #61491	C₁₃	direct (N × H)
380. #3516	C₂×C₁₃	semidirect
381. #3402	C₂×C₁₃	semidirect
382. #3390	C₂×C₁₃	semidirect
383. #3364	C₂×C₁₃	semidirect
384. #3352	C₂×C₁₃	semidirect
385. #3346	C₂×C₁₃	semidirect
386. #3301	C₂×C₁₃	semidirect
387. #3300	C₂×C₁₃	semidirect
388. #3299	C₂×C₁₃	semidirect
389. #3277	C₂×C₁₃	semidirect
390. #3270	C₂×C₁₃	semidirect
391. #3178	C₂×C₁₃	semidirect
392. #3168	C₂×C₁₃	semidirect
393. #3127	C₂×C₁₃	semidirect
394. #3124	C₂×C₁₃	semidirect
395. #3117	C₂×C₁₃	semidirect
396. #2966	C₂×C₁₃	semidirect
397. #2947	C₂×C₁₃	semidirect
398. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
846. C₁₃	#61491	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×#3516	2
C₁₃×#3402	2
C₁₃×#3390	2
C₁₃×#3364	2
C₁₃×#3352	2
C₁₃×#3346	2
C₁₃×#3301	2
C₁₃×#3300	2
C₁₃×#3299	2
C₁₃×#3277	2
C₁₃×#3270	2
C₁₃×#3178	2
C₁₃×#3168	2
C₁₃×#3127	2
C₁₃×#3124	2
C₁₃×#3117	2
C₁₃×#2966	2
C₁₃×#2947	2
C₂×C₄×C₁₃×Q₁₆	2
#61491	13

Subgroups — C13×#61491 #15747830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61491 #15747830