Subgroups — C₁₃×#61941 #15748280

Order 3328.

1646 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3219	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	2	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#557	C₂²	1	1	yes	characteristic
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	—	2	1	no	—
28	C₁₃×#556	C₂²	1	2	yes	—
29	C₁₃×#556	C₂²	1	1	yes	characteristic
30	C₁₃×#556	C₂²	1	2	yes	—
31	C₁₃×#556	C₂²	1	2	yes	—
32	C₁₃×#554	—	2	1	no	—
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#552	—	2	2	no	—
35	C₁₃×#552	—	2	1	no	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#542	C₂²	1	2	yes	—
38	C₁₃×#541	—	2	1	no	—
39	C₁₃×#541	—	2	2	no	—
40	C₁₃×#541	C₂²	1	2	yes	—
41	C₁₃×#539	—	2	1	no	—
42	C₁₃×#539	—	2	1	no	—
43	C₁₃×#536	C₂²	1	2	yes	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	—	2	2	no	—
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	2	yes	—
53	C₁₃×#497	C₂²	1	2	yes	—
54	C₁₃×#497	C₂²	1	2	yes	—
55	C₁₃×#496	C₂²	1	1	yes	characteristic
56	C₁₃×#495	C₂²	1	2	yes	—
57	C₁₃×#494	C₂²	1	2	yes	—
58	C₁₃×#491	C₂²	1	1	yes	characteristic
59	C₁₃×#491	C₂²	1	2	yes	—
60	C₁₃×#490	C₂²	1	1	yes	characteristic
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	2	yes	—
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#487	C₂²	1	2	yes	—
65	C₁₃×#484	C₂²	1	1	yes	characteristic
66	C₁₃×#483	C₂²	1	2	yes	—
67	C₁₃×#481	C₂²	1	1	yes	characteristic
68	C₁₃×#479	C₂²	1	2	yes	—
69	C₁₃×#479	C₂²	1	2	yes	—
70	C₁₃×#478	C₂²	1	2	yes	—
71	C₁₃×#476	C₂²	1	2	yes	—
72	C₁₃×#475	C₂²	1	2	yes	—
73	C₁₃×#475	C₂²	1	2	yes	—
74	C₁₃×#464	C₂²	1	2	yes	—
75	C₁₃×#464	C₂²	1	2	yes	—
76	C₁₃×#464	C₂²	1	2	yes	—
77	C₁₃×#464	C₂²	1	2	yes	—
78	C₁₃×#464	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	—
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#463	C₂²	1	2	yes	—
82	C₁₃×#463	C₂²	1	2	yes	—
83	C₁₃×#462	C₂²	1	2	yes	—
84	C₁₃×#462	C₂²	1	2	yes	—
85	C₁₃×#462	C₂²	1	2	yes	—
86	C₁₃×#462	C₂²	1	2	yes	—
87	C₁₃×#462	C₂²	1	2	yes	—
88	C₁₃×#462	C₂²	1	2	yes	—
89	C₁₃×#461	C₂²	1	2	yes	—
90	C₁₃×#461	C₂²	1	2	yes	—
91	C₁₃×#460	C₂²	1	2	yes	—
92	C₁₃×#452	C₂²	1	2	yes	—
93	C₁₃×#452	C₂²	1	2	yes	—
94	C₁₃×#452	C₂²	1	2	yes	—
95	C₁₃×#451	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	1	yes	characteristic
97	C₁₃×#449	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#446	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	—
102	C₁₃×#446	C₂²	1	2	yes	—
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#441	C₂²	1	2	yes	—
105	C₁₃×#441	C₂²	1	2	yes	—
106	C₁₃×#441	C₂²	1	2	yes	—
107	C₁₃×#441	C₂²	1	2	yes	—
108	C₁₃×#441	C₂²	1	2	yes	—
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	2	yes	—
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
115	C₁₃×#433	C₂²	1	2	yes	—
116	C₁₃×#433	C₂²	1	2	yes	—
117	C₁₃×#432	C₂²	1	1	yes	characteristic
118	C₁₃×#432	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	C₂³	1	2	yes	—
120	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×D₈	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	1	no	—
136	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×#127	C₂³	1	1	yes	characteristic
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	—	2	2	no	—
149	C₁₃×#126	—	2	2	no	—
150	C₁₃×#126	—	2	2	no	—
151	C₁₃×#126	—	2	2	no	—
152	C₁₃×#126	—	2	2	no	—
153	C₁₃×#126	—	2	2	no	—
154	C₁₃×#126	—	2	2	no	—
155	C₁₃×#126	—	2	2	no	—
156	C₁₃×#126	—	2	1	no	—
157	C₁₃×#125	—	2	2	no	—
158	C₁₃×#125	—	2	2	no	—
159	C₁₃×#125	—	2	2	no	—
160	C₁₃×#125	—	2	2	no	—
161	C₁₃×#125	—	2	2	no	—
162	C₁₃×#125	—	2	2	no	—
163	C₁₃×#125	—	2	2	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	1	no	—
167	C₁₃×#125	D₄	1	2	yes	—
168	C₁₃×#125	C₂³	1	2	yes	—
169	C₁₃×#125	C₂³	1	1	yes	characteristic
170	C₁₃×#124	—	2	2	no	—
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#124	C₂³	1	2	yes	—
174	C₁₃×#124	C₂³	1	2	yes	—
175	C₁₃×#124	C₂³	1	2	yes	—
176	C₁₃×#124	C₂³	1	1	yes	characteristic
177	C₁₃×#123	—	2	1	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	1	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₁₃×#121	—	2	1	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₁₃	—	2	2	no	—
202	C₄×Q₈×C₁₃	—	2	1	no	—
203	C₄×Q₈×C₁₃	—	2	1	no	—
204	C₄×Q₈×C₁₃	—	2	2	no	—
205	C₄×Q₈×C₁₃	—	2	1	no	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	—	2	2	no	—
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	2	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	C₂³	1	2	yes	—
228	C₄×D₄×C₁₃	C₂³	1	2	yes	—
229	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
230	C₁₃×#117	—	2	1	no	—
231	C₁₃×#117	—	2	2	no	—
232	C₁₃×#117	—	2	2	no	—
233	C₁₃×#117	—	2	2	no	—
234	C₁₃×#117	—	2	2	no	—
235	C₁₃×#117	—	2	1	no	—
236	C₁₃×#117	—	2	1	no	—
237	C₁₃×#117	C₂³	1	2	yes	—
238	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₁₃	—	2	1	no	—
243	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
244	C₁₃×#107	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₃×#97	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	1	yes	characteristic
275	C₁₃×#97	C₂³	1	1	yes	characteristic
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#61941	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	4	2	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₂×Q₈×C₁₃	—	2	1	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	2	2	no	—
286	C₂×Q₈×C₁₃	—	4	2	no	—
287	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
290	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₁₃	—	2	2	no	—
295	C₂×D₄×C₁₃	—	2	1	no	—
296	C₂×D₄×C₁₃	—	2	1	no	—
297	C₂×D₄×C₁₃	—	2	1	no	—
298	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	—	2	1	no	—
301	C₂²×C₄×C₁₃	—	2	1	no	—
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	2	no	—
304	C₂²×C₄×C₁₃	—	2	2	no	—
305	C₂²×C₄×C₁₃	—	2	2	no	—
306	C₂²×C₄×C₁₃	—	2	2	no	—
307	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₁₃×Q₁₆	—	4	2	no	—
311	C₁₃×Q₁₆	—	4	2	no	—
312	C₁₃×Q₁₆	—	4	2	no	—
313	C₁₃×Q₁₆	—	4	2	no	—
314	C₁₃×Q₁₆	—	4	2	no	—
315	C₁₃×Q₁₆	—	4	2	no	—
316	C₁₃×SD₁₆	—	4	2	no	—
317	C₁₃×SD₁₆	—	4	2	no	—
318	C₁₃×SD₁₆	—	4	2	no	—
319	C₁₃×SD₁₆	—	4	2	no	—
320	C₁₃×SD₁₆	—	4	2	no	—
321	C₁₃×D₈	—	4	2	no	—
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
326	C₁₃×C₄⋊C₄	—	2	1	no	—
327	C₁₃×C₄⋊C₄	—	2	1	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	1	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	1	no	—
338	C₁₃×C₄⋊C₄	—	2	1	no	—
339	C₁₃×C₄⋊C₄	—	2	1	no	—
340	C₁₃×C₄⋊C₄	—	2	1	no	—
341	C₁₃×C₄⋊C₄	—	2	1	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	2	no	—
352	C₁₃×C₄⋊C₄	—	2	2	no	—
353	C₁₃×C₄⋊C₄	—	2	1	no	—
354	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	—	2	1	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	1	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	1	no	—
374	C₁₃×C₂²⋊C₄	—	2	1	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	1	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
385	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	—	2	2	no	—
389	C₄²×C₁₃	—	2	2	no	—
390	C₄²×C₁₃	—	2	2	no	—
391	C₄²×C₁₃	—	2	1	no	—
392	C₄²×C₁₃	—	2	2	no	—
393	C₄²×C₁₃	—	2	2	no	—
394	C₄²×C₁₃	—	2	2	no	—
395	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₁₃	C₂⁴	1	2	yes	—
398	C₄²×C₁₃	C₂⁴	1	2	yes	—
399	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
403	#3402	C₂×C₁₃	1	2	yes	complemented
404	#3401	C₂×C₁₃	1	2	yes	complemented
405	#3398	C₂×C₁₃	1	2	yes	complemented
406	#3398	C₂×C₁₃	1	2	yes	complemented
407	#3376	C₂×C₁₃	1	2	yes	complemented
408	#3374	C₂×C₁₃	1	2	yes	complemented
409	#3371	C₂×C₁₃	1	2	yes	complemented
410	#3369	C₂×C₁₃	1	2	yes	complemented
411	#3225	C₂×C₁₃	1	2	yes	complemented
412	#3223	C₂×C₁₃	1	2	yes	complemented
413	#3219	C₂×C₁₃	1	1	yes	characteristic
414	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3125	C₂×C₁₃	1	2	yes	complemented
416	#3120	C₂×C₁₃	1	2	yes	complemented
417	#3117	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
420	C₂³×C₁₃	—	2	1	no	—
421	C₂³×C₁₃	—	2	2	no	—
422	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	Q₈×C₁₃	—	2	2	no	—
424	Q₈×C₁₃	—	2	2	no	—
425	Q₈×C₁₃	—	2	2	no	—
426	Q₈×C₁₃	—	2	2	no	—
427	Q₈×C₁₃	—	2	2	no	—
428	Q₈×C₁₃	—	2	2	no	—
429	Q₈×C₁₃	—	2	2	no	—
430	Q₈×C₁₃	—	4	1	no	—
431	Q₈×C₁₃	—	4	1	no	—
432	Q₈×C₁₃	—	4	2	no	—
433	Q₈×C₁₃	—	4	2	no	—
434	Q₈×C₁₃	—	8	1	no	—
435	Q₈×C₁₃	—	8	2	no	—
436	D₄×C₁₃	—	2	2	no	—
437	D₄×C₁₃	—	2	2	no	—
438	D₄×C₁₃	—	2	2	no	—
439	D₄×C₁₃	—	4	2	no	—
440	D₄×C₁₃	—	4	4	no	—
441	D₄×C₁₃	—	8	1	no	—
442	D₄×C₁₃	—	8	1	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	1	no	—
450	C₂×C₄×C₁₃	—	2	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	4	1	no	—
453	C₂×C₄×C₁₃	—	4	1	no	—
454	C₂×C₄×C₁₃	—	4	2	no	—
455	C₂×C₄×C₁₃	—	4	4	no	—
456	C₂×C₄×C₁₃	—	4	2	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	8	2	no	—
459	C₂×C₄×C₁₃	—	8	2	no	—
460	C₂×C₄×C₁₃	—	8	1	no	—
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
471	C₈×C₁₃	—	2	2	no	—
472	C₈×C₁₃	—	2	2	no	—
473	C₈×C₁₃	—	2	2	no	—
474	C₈×C₁₃	—	2	2	no	—
475	#563	—	2	2	no	—
476	#559	C₂²×C₁₃	1	2	yes	—
477	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
478	#557	C₂²×C₁₃	1	2	yes	—
479	#557	C₂²×C₁₃	1	1	yes	characteristic
480	#557	C₂²×C₁₃	1	2	yes	—
481	#556	—	2	1	no	—
482	#556	—	2	1	no	—
483	#556	C₂²×C₁₃	1	2	yes	—
484	#556	C₂²×C₁₃	1	2	yes	—
485	#556	C₂²×C₁₃	1	2	yes	—
486	#556	C₂²×C₁₃	1	1	yes	characteristic
487	#554	—	2	1	no	—
488	#554	C₂²×C₁₃	1	1	yes	characteristic
489	#552	—	2	2	no	—
490	#552	—	2	1	no	—
491	#544	—	2	1	no	—
492	#542	C₂²×C₁₃	1	2	yes	—
493	#541	—	2	1	no	—
494	#541	—	2	2	no	—
495	#541	C₂²×C₁₃	1	2	yes	—
496	#539	—	2	1	no	—
497	#539	—	2	1	no	—
498	#536	C₂²×C₁₃	1	2	yes	—
499	#533	C₂²×C₁₃	1	1	yes	characteristic
500	#533	C₂²×C₁₃	1	1	yes	characteristic
501	#532	C₂²×C₁₃	1	1	yes	characteristic
502	#529	—	2	2	no	—
503	#529	C₂²×C₁₃	1	1	yes	characteristic
504	#520	C₂²×C₁₃	1	2	yes	—
505	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
506	#497	C₂²×C₁₃	1	1	yes	characteristic
507	#497	C₂²×C₁₃	1	2	yes	—
508	#497	C₂²×C₁₃	1	2	yes	—
509	#497	C₂²×C₁₃	1	2	yes	—
510	#496	C₂²×C₁₃	1	1	yes	characteristic
511	#495	C₂²×C₁₃	1	2	yes	—
512	#494	C₂²×C₁₃	1	2	yes	—
513	#491	C₂²×C₁₃	1	1	yes	characteristic
514	#491	C₂²×C₁₃	1	2	yes	—
515	#490	C₂²×C₁₃	1	1	yes	characteristic
516	#489	C₂²×C₁₃	1	2	yes	—
517	#489	C₂²×C₁₃	1	2	yes	—
518	#488	C₂²×C₁₃	1	2	yes	—
519	#487	C₂²×C₁₃	1	2	yes	—
520	#484	C₂²×C₁₃	1	1	yes	characteristic
521	#483	C₂²×C₁₃	1	2	yes	—
522	#481	C₂²×C₁₃	1	1	yes	characteristic
523	#479	C₂²×C₁₃	1	2	yes	—
524	#479	C₂²×C₁₃	1	2	yes	—
525	#478	C₂²×C₁₃	1	2	yes	—
526	#476	C₂²×C₁₃	1	2	yes	—
527	#475	C₂²×C₁₃	1	2	yes	—
528	#475	C₂²×C₁₃	1	2	yes	—
529	#464	C₂²×C₁₃	1	2	yes	—
530	#464	C₂²×C₁₃	1	2	yes	—
531	#464	C₂²×C₁₃	1	2	yes	—
532	#464	C₂²×C₁₃	1	2	yes	—
533	#464	C₂²×C₁₃	1	2	yes	—
534	#464	C₂²×C₁₃	1	2	yes	—
535	#463	C₂²×C₁₃	1	2	yes	—
536	#463	C₂²×C₁₃	1	2	yes	—
537	#463	C₂²×C₁₃	1	2	yes	—
538	#462	C₂²×C₁₃	1	2	yes	—
539	#462	C₂²×C₁₃	1	2	yes	—
540	#462	C₂²×C₁₃	1	2	yes	—
541	#462	C₂²×C₁₃	1	2	yes	—
542	#462	C₂²×C₁₃	1	2	yes	—
543	#462	C₂²×C₁₃	1	2	yes	—
544	#461	C₂²×C₁₃	1	2	yes	—
545	#461	C₂²×C₁₃	1	2	yes	—
546	#460	C₂²×C₁₃	1	2	yes	—
547	#452	C₂²×C₁₃	1	2	yes	—
548	#452	C₂²×C₁₃	1	2	yes	—
549	#452	C₂²×C₁₃	1	2	yes	—
550	#451	C₂²×C₁₃	1	2	yes	—
551	#451	C₂²×C₁₃	1	1	yes	characteristic
552	#449	C₂²×C₁₃	1	2	yes	—
553	#448	C₂²×C₁₃	1	1	yes	characteristic
554	#446	C₂²×C₁₃	1	2	yes	—
555	#446	C₂²×C₁₃	1	2	yes	—
556	#446	C₂²×C₁₃	1	2	yes	—
557	#446	C₂²×C₁₃	1	2	yes	—
558	#442	C₂²×C₁₃	1	2	yes	—
559	#441	C₂²×C₁₃	1	2	yes	—
560	#441	C₂²×C₁₃	1	2	yes	—
561	#441	C₂²×C₁₃	1	2	yes	—
562	#441	C₂²×C₁₃	1	2	yes	—
563	#441	C₂²×C₁₃	1	2	yes	—
564	#440	C₂²×C₁₃	1	2	yes	—
565	#440	C₂²×C₁₃	1	2	yes	—
566	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
567	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
569	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
570	#433	C₂²×C₁₃	1	2	yes	—
571	#433	C₂²×C₁₃	1	2	yes	—
572	#432	C₂²×C₁₃	1	1	yes	characteristic
573	#432	C₂²×C₁₃	1	1	yes	characteristic
574	C₂²×C₁₃	—	2	1	no	—
575	C₂²×C₁₃	—	2	1	no	—
576	C₂²×C₁₃	—	2	1	no	—
577	C₂²×C₁₃	—	4	1	no	—
578	C₂²×C₁₃	—	4	2	no	—
579	C₂²×C₁₃	—	4	1	no	—
580	C₂²×C₁₃	—	4	2	no	—
581	C₂²×C₁₃	—	4	2	no	—
582	C₂²×C₁₃	—	4	1	no	—
583	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₁₃	—	2	1	no	—
585	C₄×C₁₃	—	2	1	no	—
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	1	no	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	2	2	no	—
590	C₄×C₁₃	—	2	2	no	—
591	C₄×C₁₃	—	2	2	no	—
592	C₄×C₁₃	—	2	1	no	—
593	C₄×C₁₃	—	4	1	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	1	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	—	4	2	no	—
599	C₄×C₁₃	—	4	2	no	—
600	C₄×C₁₃	—	4	1	no	—
601	C₄×C₁₃	#585	1	2	yes	—
602	C₂×#41	C₂³×C₁₃	1	2	yes	—
603	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
605	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
607	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
608	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
609	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
610	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
613	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
614	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
615	C₂×D₈	C₂³×C₁₃	1	2	yes	—
616	C₄⋊Q₈	—	2	2	no	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	1	no	—
619	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
620	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
624	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
625	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
628	#127	C₂³×C₁₃	1	1	yes	characteristic
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	1	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	D₄×C₁₃	1	2	yes	—
651	#125	C₂³×C₁₃	1	1	yes	characteristic
652	#125	C₂³×C₁₃	1	2	yes	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	C₂³×C₁₃	1	1	yes	characteristic
656	#124	C₂³×C₁₃	1	2	yes	—
657	#124	C₂³×C₁₃	1	2	yes	—
658	#124	C₂³×C₁₃	1	2	yes	—
659	#124	C₂³×C₁₃	1	2	yes	—
660	#123	—	2	1	no	—
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	1	no	—
669	C₂²⋊Q₈	—	2	1	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	1	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
677	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
678	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
679	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	C₂³×C₁₃	1	1	yes	characteristic
684	C₄×Q₈	—	2	2	no	—
685	C₄×Q₈	—	2	1	no	—
686	C₄×Q₈	—	2	1	no	—
687	C₄×Q₈	—	2	2	no	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	—	2	1	no	—
691	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
692	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
695	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
697	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
698	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
701	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	2	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	C₂³×C₁₃	1	2	yes	—
710	C₄×D₄	C₂³×C₁₃	1	2	yes	—
711	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₄×D₄	C₂³×C₁₃	1	2	yes	—
713	#117	—	2	1	no	—
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	—	2	2	no	—
718	#117	—	2	1	no	—
719	#117	—	2	1	no	—
720	#117	C₂³×C₁₃	1	2	yes	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	2	no	—
723	C₂×C₄⋊C₄	—	2	1	no	—
724	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×C₄²	—	2	1	no	—
726	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
727	#107	C₂³×C₁₃	1	2	yes	—
728	#106	C₂³×C₁₃	1	2	yes	—
729	#106	C₂³×C₁₃	1	2	yes	—
730	#106	C₂³×C₁₃	1	2	yes	—
731	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
732	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
733	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
734	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
735	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
736	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
737	#103	C₂³×C₁₃	1	2	yes	—
738	#103	C₂³×C₁₃	1	2	yes	—
739	#103	C₂³×C₁₃	1	2	yes	—
740	#103	C₂³×C₁₃	1	2	yes	—
741	#103	C₂³×C₁₃	1	2	yes	—
742	#103	C₂³×C₁₃	1	2	yes	—
743	#103	C₂³×C₁₃	1	2	yes	—
744	#103	C₂³×C₁₃	1	2	yes	—
745	#103	C₂³×C₁₃	1	2	yes	—
746	#103	C₂³×C₁₃	1	2	yes	—
747	#103	C₂³×C₁₃	1	2	yes	—
748	#102	C₂³×C₁₃	1	2	yes	—
749	#102	C₂³×C₁₃	1	2	yes	—
750	#102	C₂³×C₁₃	1	2	yes	—
751	#102	C₂³×C₁₃	1	2	yes	—
752	#102	C₂³×C₁₃	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
754	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
756	#97	C₂³×C₁₃	1	2	yes	—
757	#97	C₂³×C₁₃	1	1	yes	characteristic
758	#97	C₂³×C₁₃	1	1	yes	characteristic
759	#97	C₂³×C₁₃	1	2	yes	—
760	#97	C₂³×C₁₃	1	2	yes	—
761	C₄×C₈	C₂³×C₁₃	1	2	yes	—
762	C₄×C₈	C₂³×C₁₃	1	2	yes	—
763	C₂×C₁₃	—	4	1	no	—
764	C₂×C₁₃	—	8	1	no	—
765	C₂×C₁₃	—	8	2	no	—
766	C₂×C₁₃	#3487	1	1	yes	characteristic
767	C₂×C₁₃	#3586	1	1	yes	characteristic
768	C₂×C₁₃	#3586	1	1	yes	characteristic
769	#41	—	4	2	no	—
770	#41	—	4	2	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	4	2	no	—
775	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
778	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
798	Q₁₆	—	4	2	no	—
799	Q₁₆	—	4	2	no	—
800	Q₁₆	—	4	2	no	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	SD₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	SD₁₆	—	4	2	no	—
807	SD₁₆	—	4	2	no	—
808	SD₁₆	—	4	2	no	—
809	D₈	—	4	2	no	—
810	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
811	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
812	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
813	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
845	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
846	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
847	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
848	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
849	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	1	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
873	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	1	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
884	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₄²	C₂⁴×C₁₃	1	2	yes	—
886	C₄²	C₂⁴×C₁₃	1	2	yes	—
887	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₁₃	#61941	1	1	yes	characteristic, direct product factor, Sylow
890	C₂³	—	2	1	no	—
891	C₂³	—	2	2	no	—
892	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	4	1	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	4	2	no	—
903	Q₈	—	4	2	no	—
904	Q₈	—	8	1	no	—
905	Q₈	—	8	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	2	2	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	4	no	—
911	D₄	—	8	1	no	—
912	D₄	—	8	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
930	C₂×C₄	—	8	1	no	—
931	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
935	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
938	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
939	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
940	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₈	—	2	2	no	—
944	C₈	—	2	2	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	C₁₃×#585	1	2	yes	—
973	C₂	—	4	1	no	—
974	C₂	—	8	1	no	—
975	C₂	—	8	2	no	—
976	C₂	C₁₃×#3487	1	1	yes	characteristic
977	C₂	C₁₃×#3586	1	1	yes	characteristic
978	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3219	C₂
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×#3555	C₂	semidirect
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3398	C₂	semidirect
6. C₁₃×#3398	C₂	semidirect
7. C₁₃×#3376	C₂	semidirect
8. C₁₃×#3374	C₂	semidirect
9. C₁₃×#3371	C₂	semidirect
10. C₁₃×#3369	C₂	semidirect
11. C₁₃×#3225	C₂	semidirect
12. C₁₃×#3223	C₂	semidirect
14. C₁₃×#3216	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3120	C₂	semidirect
17. C₁₃×#3117	C₂	semidirect
18. C₁₃×#3113	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
280. #61941	C₁₃	direct (N × H)
401. #3555	C₂×C₁₃	semidirect
402. #3507	C₂×C₁₃	semidirect
403. #3402	C₂×C₁₃	semidirect
404. #3401	C₂×C₁₃	semidirect
405. #3398	C₂×C₁₃	semidirect
406. #3398	C₂×C₁₃	semidirect
407. #3376	C₂×C₁₃	semidirect
408. #3374	C₂×C₁₃	semidirect
409. #3371	C₂×C₁₃	semidirect
410. #3369	C₂×C₁₃	semidirect
411. #3225	C₂×C₁₃	semidirect
412. #3223	C₂×C₁₃	semidirect
414. #3216	C₂×C₁₃	semidirect
415. #3125	C₂×C₁₃	semidirect
416. #3120	C₂×C₁₃	semidirect
417. #3117	C₂×C₁₃	semidirect
418. #3113	C₂×C₁₃	semidirect
419. #2987	C₂×C₁₃	semidirect
889. C₁₃	#61941	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×#3555	2
C₁₃×#3507	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3398	2
C₁₃×#3376	2
C₁₃×#3374	2
C₁₃×#3371	2
C₁₃×#3369	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3219	2
C₁₃×#3216	2
C₁₃×#3125	2
C₁₃×#3120	2
C₁₃×#3117	2
C₁₃×#3113	2
C₁₃×#2987	2
#61941	13

Subgroups — C13×#61941 #15748280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61941 #15748280