Subgroups — C₁₃×#61875 #15748214

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 942 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
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	2	yes	maximal
12	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3240	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3121	C₂	1	2	yes	maximal
17	C₁₃×#3117	C₂	1	1	yes	maximal, characteristic
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	Q₈²×C₁₃	—	2	1	no	—
22	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
23	Q₈²×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#557	—	2	1	no	—
25	C₁₃×#557	—	2	2	no	—
26	C₁₃×#557	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	2	yes	—
28	C₁₃×#557	C₂²	1	2	yes	—
29	C₁₃×#557	C₂²	1	2	yes	—
30	C₁₃×#557	C₂²	1	2	yes	—
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	2	yes	—
33	C₁₃×#556	C₂²	1	1	yes	characteristic
34	C₁₃×#554	C₂²	1	1	yes	characteristic
35	C₁₃×#552	—	2	1	no	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	—	2	1	no	—
38	C₁₃×#544	—	2	1	no	—
39	C₁₃×#544	C₂²	1	2	yes	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#541	—	2	1	no	—
42	C₁₃×#541	—	2	2	no	—
43	C₁₃×#541	C₂²	1	2	yes	—
44	C₁₃×#533	—	2	2	no	—
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	1	yes	characteristic
52	C₁₃×#501	C₂²	1	2	yes	—
53	C₁₃×#501	C₂²	1	2	yes	—
54	C₁₃×#501	C₂²	1	2	yes	—
55	C₁₃×#501	C₂²	1	1	yes	characteristic
56	C₁₃×#499	C₂²	1	2	yes	—
57	C₁₃×#498	C₂²	1	2	yes	—
58	C₁₃×#491	C₂²	1	2	yes	—
59	C₁₃×#491	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	1	yes	characteristic
61	C₁₃×#489	C₂²	1	2	yes	—
62	C₁₃×#489	C₂²	1	1	yes	characteristic
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#487	C₂²	1	2	yes	—
65	C₁₃×#485	C₂²	1	2	yes	—
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#484	C₂²	1	1	yes	characteristic
69	C₁₃×#483	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#481	C₂²	1	1	yes	characteristic
72	C₁₃×#479	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	—
74	C₁₃×#479	C₂²	1	2	yes	—
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#479	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	2	yes	—
79	C₁₃×#478	C₂²	1	2	yes	—
80	C₁₃×#478	C₂²	1	2	yes	—
81	C₁₃×#477	C₂²	1	2	yes	—
82	C₁₃×#477	C₂²	1	2	yes	—
83	C₁₃×#477	C₂²	1	2	yes	—
84	C₁₃×#476	C₂²	1	2	yes	—
85	C₁₃×#475	C₂²	1	2	yes	—
86	C₁₃×#475	C₂²	1	2	yes	—
87	C₁₃×#475	C₂²	1	2	yes	—
88	C₁₃×#475	C₂²	1	2	yes	—
89	C₁₃×#475	C₂²	1	2	yes	—
90	C₁₃×#464	C₂²	1	2	yes	—
91	C₁₃×#464	C₂²	1	2	yes	—
92	C₁₃×#464	C₂²	1	2	yes	—
93	C₁₃×#462	C₂²	1	2	yes	—
94	C₁₃×#462	C₂²	1	2	yes	—
95	C₁₃×#462	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	2	yes	—
97	C₁₃×#451	C₂²	1	1	yes	characteristic
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×#441	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×Q₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×Q₁₆	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₁₃×C₄⋊Q₈	—	2	2	no	—
125	C₁₃×C₄⋊Q₈	—	2	2	no	—
126	C₁₃×C₄⋊Q₈	—	2	2	no	—
127	C₁₃×C₄⋊Q₈	—	2	2	no	—
128	C₁₃×C₄⋊Q₈	—	2	2	no	—
129	C₁₃×C₄⋊Q₈	—	2	2	no	—
130	C₁₃×C₄⋊Q₈	—	2	1	no	—
131	C₁₃×C₄⋊Q₈	—	2	2	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
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	1	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	2	no	—
157	C₁₃×#125	—	2	2	no	—
158	C₁₃×#125	—	2	1	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	1	no	—
165	C₁₃×#125	D₄	1	2	yes	—
166	C₁₃×#125	C₂³	1	2	yes	—
167	C₁₃×#125	C₂³	1	2	yes	—
168	C₁₃×#125	C₂³	1	2	yes	—
169	C₁₃×#125	C₂³	1	2	yes	—
170	C₁₃×#125	C₂³	1	1	yes	characteristic
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#124	C₂³	1	1	yes	characteristic
174	C₁₃×#123	—	2	1	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×C₂²⋊Q₈	—	2	1	no	—
177	C₁₃×C₂²⋊Q₈	—	2	1	no	—
178	C₁₃×C₂²⋊Q₈	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	1	no	—
180	C₁₃×C₂²⋊Q₈	—	2	1	no	—
181	C₁₃×C₂²⋊Q₈	—	2	1	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
191	C₁₃×#121	C₂³	1	1	yes	characteristic
192	C₄×Q₈×C₁₃	—	2	2	no	—
193	C₄×Q₈×C₁₃	—	2	1	no	—
194	C₄×Q₈×C₁₃	—	2	1	no	—
195	C₄×Q₈×C₁₃	—	2	2	no	—
196	C₄×Q₈×C₁₃	—	2	2	no	—
197	C₄×Q₈×C₁₃	—	2	2	no	—
198	C₄×Q₈×C₁₃	—	2	2	no	—
199	C₄×Q₈×C₁₃	—	2	2	no	—
200	C₄×Q₈×C₁₃	—	2	2	no	—
201	C₄×Q₈×C₁₃	—	2	1	no	—
202	C₄×Q₈×C₁₃	—	2	1	no	—
203	C₄×Q₈×C₁₃	—	2	1	no	—
204	C₄×Q₈×C₁₃	—	2	1	no	—
205	C₄×Q₈×C₁₃	—	2	1	no	—
206	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
223	C₁₃×#117	—	2	1	no	—
224	C₁₃×#117	—	2	2	no	—
225	C₁₃×#117	—	2	1	no	—
226	C₁₃×#117	—	2	2	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	—	2	1	no	—
229	C₁₃×#117	C₂³	1	2	yes	—
230	C₁₃×#117	C₂³	1	2	yes	—
231	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₁₃	—	2	1	no	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₁₃×#107	C₂³	1	2	yes	—
237	C₁₃×#107	C₂³	1	2	yes	—
238	C₁₃×#107	C₂³	1	2	yes	—
239	C₁₃×#107	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#106	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×#106	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×#103	C₂³	1	2	yes	—
266	C₁₃×#103	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	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
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	#61875	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂×Q₈×C₁₃	—	2	4	no	—
282	C₂×Q₈×C₁₃	—	2	1	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	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
290	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
295	C₂×D₄×C₁₃	—	2	1	no	—
296	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	—	2	1	no	—
298	C₂²×C₄×C₁₃	—	2	1	no	—
299	C₂²×C₄×C₁₃	—	2	1	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×Q₁₆	—	2	4	no	—
305	C₁₃×Q₁₆	—	2	4	no	—
306	C₁₃×Q₁₆	—	2	4	no	—
307	C₁₃×SD₁₆	—	2	4	no	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
310	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
317	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
324	C₁₃×C₄⋊C₄	—	2	1	no	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	2	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	1	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	—	2	1	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
346	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
347	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
348	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
349	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
350	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
352	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
353	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
354	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
356	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	1	no	—
364	C₁₃×C₂²⋊C₄	—	2	1	no	—
365	C₁₃×C₂²⋊C₄	—	2	1	no	—
366	C₁₃×C₂²⋊C₄	—	2	1	no	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	—	2	2	no	—
369	C₁₃×C₂²⋊C₄	—	2	1	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
372	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	—	2	2	no	—
376	C₄²×C₁₃	—	2	1	no	—
377	C₄²×C₁₃	—	2	2	no	—
378	C₄²×C₁₃	—	2	2	no	—
379	C₄²×C₁₃	—	2	2	no	—
380	C₄²×C₁₃	—	2	2	no	—
381	C₄²×C₁₃	—	2	2	no	—
382	C₄²×C₁₃	—	2	2	no	—
383	C₄²×C₁₃	—	2	2	no	—
384	C₄²×C₁₃	—	2	2	no	—
385	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₁₃	C₂⁴	1	2	yes	—
388	C₄²×C₁₃	C₂⁴	1	2	yes	—
389	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
391	#3555	C₂×C₁₃	1	1	yes	characteristic
392	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#3390	C₂×C₁₃	1	2	yes	complemented
394	#3388	C₂×C₁₃	1	2	yes	complemented
395	#3387	C₂×C₁₃	1	2	yes	complemented
396	#3387	C₂×C₁₃	1	2	yes	complemented
397	#3377	C₂×C₁₃	1	2	yes	complemented
398	#3377	C₂×C₁₃	1	2	yes	complemented
399	#3374	C₂×C₁₃	1	2	yes	complemented
400	#3369	C₂×C₁₃	1	2	yes	complemented
401	#3244	C₂×C₁₃	1	2	yes	—
402	#3242	C₂×C₁₃	1	2	yes	complemented
403	#3240	C₂×C₁₃	1	1	yes	characteristic
404	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3127	C₂×C₁₃	1	2	yes	complemented
406	#3121	C₂×C₁₃	1	2	yes	—
407	#3117	C₂×C₁₃	1	1	yes	characteristic
408	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
410	C₂³×C₁₃	—	2	1	no	—
411	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₁₃	—	2	4	no	—
413	Q₈×C₁₃	—	2	2	no	—
414	Q₈×C₁₃	—	2	2	no	—
415	Q₈×C₁₃	—	2	2	no	—
416	Q₈×C₁₃	—	2	2	no	—
417	Q₈×C₁₃	—	4	1	no	—
418	Q₈×C₁₃	—	4	1	no	—
419	Q₈×C₁₃	—	4	2	no	—
420	Q₈×C₁₃	—	4	2	no	—
421	Q₈×C₁₃	—	8	1	no	—
422	Q₈×C₁₃	—	8	1	no	—
423	Q₈×C₁₃	—	8	2	no	—
424	Q₈×C₁₃	—	8	2	no	—
425	Q₈×C₁₃	—	8	2	no	—
426	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
427	D₄×C₁₃	—	2	2	no	—
428	D₄×C₁₃	—	8	1	no	—
429	C₂×C₄×C₁₃	—	2	4	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	1	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	4	1	no	—
441	C₂×C₄×C₁₃	—	4	1	no	—
442	C₂×C₄×C₁₃	—	4	2	no	—
443	C₂×C₄×C₁₃	—	8	2	no	—
444	C₂×C₄×C₁₃	—	8	1	no	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
455	C₈×C₁₃	—	2	2	no	—
456	C₈×C₁₃	—	2	2	no	—
457	C₈×C₁₃	—	2	2	no	—
458	C₈×C₁₃	—	2	2	no	—
459	#563	—	2	2	no	—
460	Q₈²	—	2	1	no	—
461	Q₈²	C₂²×C₁₃	1	2	yes	—
462	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
463	#557	—	2	1	no	—
464	#557	—	2	2	no	—
465	#557	C₂²×C₁₃	1	1	yes	characteristic
466	#557	C₂²×C₁₃	1	2	yes	—
467	#557	C₂²×C₁₃	1	2	yes	—
468	#557	C₂²×C₁₃	1	2	yes	—
469	#557	C₂²×C₁₃	1	2	yes	—
470	#556	—	2	1	no	—
471	#556	C₂²×C₁₃	1	2	yes	—
472	#556	C₂²×C₁₃	1	1	yes	characteristic
473	#554	C₂²×C₁₃	1	1	yes	characteristic
474	#552	—	2	1	no	—
475	#544	—	2	1	no	—
476	#544	—	2	1	no	—
477	#544	—	2	1	no	—
478	#544	C₂²×C₁₃	1	2	yes	—
479	#542	C₂²×C₁₃	1	2	yes	—
480	#541	—	2	1	no	—
481	#541	—	2	2	no	—
482	#541	C₂²×C₁₃	1	2	yes	—
483	#533	—	2	2	no	—
484	#533	C₂²×C₁₃	1	1	yes	characteristic
485	#533	C₂²×C₁₃	1	1	yes	characteristic
486	#533	C₂²×C₁₃	1	1	yes	characteristic
487	#529	C₂²×C₁₃	1	1	yes	characteristic
488	#519	C₂²×C₁₃	1	2	yes	—
489	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
490	#501	C₂²×C₁₃	1	1	yes	characteristic
491	#501	C₂²×C₁₃	1	2	yes	—
492	#501	C₂²×C₁₃	1	2	yes	—
493	#501	C₂²×C₁₃	1	2	yes	—
494	#501	C₂²×C₁₃	1	1	yes	characteristic
495	#499	C₂²×C₁₃	1	2	yes	—
496	#498	C₂²×C₁₃	1	2	yes	—
497	#491	C₂²×C₁₃	1	2	yes	—
498	#491	C₂²×C₁₃	1	2	yes	—
499	#489	C₂²×C₁₃	1	1	yes	characteristic
500	#489	C₂²×C₁₃	1	2	yes	—
501	#489	C₂²×C₁₃	1	1	yes	characteristic
502	#488	C₂²×C₁₃	1	2	yes	—
503	#487	C₂²×C₁₃	1	2	yes	—
504	#485	C₂²×C₁₃	1	2	yes	—
505	#485	C₂²×C₁₃	1	2	yes	—
506	#485	C₂²×C₁₃	1	2	yes	—
507	#484	C₂²×C₁₃	1	1	yes	characteristic
508	#483	C₂²×C₁₃	1	2	yes	—
509	#482	C₂²×C₁₃	1	2	yes	—
510	#481	C₂²×C₁₃	1	1	yes	characteristic
511	#479	C₂²×C₁₃	1	2	yes	—
512	#479	C₂²×C₁₃	1	2	yes	—
513	#479	C₂²×C₁₃	1	2	yes	—
514	#479	C₂²×C₁₃	1	2	yes	—
515	#479	C₂²×C₁₃	1	2	yes	—
516	#479	C₂²×C₁₃	1	2	yes	—
517	#479	C₂²×C₁₃	1	2	yes	—
518	#478	C₂²×C₁₃	1	2	yes	—
519	#478	C₂²×C₁₃	1	2	yes	—
520	#477	C₂²×C₁₃	1	2	yes	—
521	#477	C₂²×C₁₃	1	2	yes	—
522	#477	C₂²×C₁₃	1	2	yes	—
523	#476	C₂²×C₁₃	1	2	yes	—
524	#475	C₂²×C₁₃	1	2	yes	—
525	#475	C₂²×C₁₃	1	2	yes	—
526	#475	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	#462	C₂²×C₁₃	1	2	yes	—
533	#462	C₂²×C₁₃	1	2	yes	—
534	#462	C₂²×C₁₃	1	2	yes	—
535	#451	C₂²×C₁₃	1	2	yes	—
536	#451	C₂²×C₁₃	1	1	yes	characteristic
537	#448	C₂²×C₁₃	1	1	yes	characteristic
538	#446	C₂²×C₁₃	1	2	yes	—
539	#446	C₂²×C₁₃	1	2	yes	—
540	#446	C₂²×C₁₃	1	2	yes	—
541	#446	C₂²×C₁₃	1	2	yes	—
542	#441	C₂²×C₁₃	1	2	yes	—
543	#441	C₂²×C₁₃	1	2	yes	—
544	#441	C₂²×C₁₃	1	2	yes	—
545	#441	C₂²×C₁₃	1	2	yes	—
546	#441	C₂²×C₁₃	1	2	yes	—
547	#441	C₂²×C₁₃	1	2	yes	—
548	#440	C₂²×C₁₃	1	2	yes	—
549	#440	C₂²×C₁₃	1	2	yes	—
550	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
551	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
552	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
553	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
554	#433	C₂²×C₁₃	1	2	yes	—
555	#433	C₂²×C₁₃	1	2	yes	—
556	#432	C₂²×C₁₃	1	1	yes	characteristic
557	#432	C₂²×C₁₃	1	1	yes	characteristic
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	1	no	—
560	C₂²×C₁₃	—	2	1	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	1	no	—
563	C₂²×C₁₃	—	4	1	no	—
564	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	2	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	2	2	no	—
573	C₄×C₁₃	—	2	4	no	—
574	C₄×C₁₃	—	2	1	no	—
575	C₄×C₁₃	—	4	1	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	1	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	1	no	—
583	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
584	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₄⋊Q₈	—	2	2	no	—
590	C₄⋊Q₈	—	2	2	no	—
591	C₄⋊Q₈	—	2	2	no	—
592	C₄⋊Q₈	—	2	2	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	—	2	2	no	—
597	C₄⋊Q₈	—	2	2	no	—
598	C₄⋊Q₈	—	2	2	no	—
599	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
600	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
607	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
608	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	1	no	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	—	2	2	no	—
622	#125	—	2	2	no	—
623	#125	—	2	1	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	—	2	1	no	—
630	#125	D₄×C₁₃	1	2	yes	—
631	#125	C₂³×C₁₃	1	1	yes	characteristic
632	#125	C₂³×C₁₃	1	2	yes	—
633	#125	C₂³×C₁₃	1	2	yes	—
634	#125	C₂³×C₁₃	1	2	yes	—
635	#125	C₂³×C₁₃	1	2	yes	—
636	#124	—	2	2	no	—
637	#124	C₂³×C₁₃	1	1	yes	characteristic
638	#124	C₂³×C₁₃	1	2	yes	—
639	#123	—	2	1	no	—
640	#123	—	2	2	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	2	no	—
651	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
652	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
653	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
654	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
655	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
656	#121	C₂³×C₁₃	1	1	yes	characteristic
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	2	no	—
661	C₄×Q₈	—	2	2	no	—
662	C₄×Q₈	—	2	2	no	—
663	C₄×Q₈	—	2	2	no	—
664	C₄×Q₈	—	2	2	no	—
665	C₄×Q₈	—	2	2	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	—	2	1	no	—
669	C₄×Q₈	—	2	1	no	—
670	C₄×Q₈	—	2	1	no	—
671	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
672	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
673	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
674	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
675	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
676	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
677	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
679	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
680	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
684	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
687	C₄×D₄	C₂³×C₁₃	1	2	yes	—
688	#117	—	2	1	no	—
689	#117	—	2	2	no	—
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	1	no	—
694	#117	C₂³×C₁₃	1	2	yes	—
695	#117	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄⋊C₄	—	2	1	no	—
697	C₂×C₄⋊C₄	—	2	1	no	—
698	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
701	#107	C₂³×C₁₃	1	2	yes	—
702	#107	C₂³×C₁₃	1	2	yes	—
703	#107	C₂³×C₁₃	1	2	yes	—
704	#107	C₂³×C₁₃	1	2	yes	—
705	#107	C₂³×C₁₃	1	2	yes	—
706	#106	C₂³×C₁₃	1	2	yes	—
707	#106	C₂³×C₁₃	1	2	yes	—
708	#106	C₂³×C₁₃	1	2	yes	—
709	#106	C₂³×C₁₃	1	2	yes	—
710	#106	C₂³×C₁₃	1	2	yes	—
711	#106	C₂³×C₁₃	1	2	yes	—
712	#106	C₂³×C₁₃	1	2	yes	—
713	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
714	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
715	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
716	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
717	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
719	#103	C₂³×C₁₃	1	2	yes	—
720	#103	C₂³×C₁₃	1	2	yes	—
721	#103	C₂³×C₁₃	1	2	yes	—
722	#103	C₂³×C₁₃	1	2	yes	—
723	#103	C₂³×C₁₃	1	2	yes	—
724	#103	C₂³×C₁₃	1	2	yes	—
725	#103	C₂³×C₁₃	1	2	yes	—
726	#103	C₂³×C₁₃	1	2	yes	—
727	#103	C₂³×C₁₃	1	2	yes	—
728	#103	C₂³×C₁₃	1	2	yes	—
729	#103	C₂³×C₁₃	1	2	yes	—
730	#103	C₂³×C₁₃	1	2	yes	—
731	#103	C₂³×C₁₃	1	2	yes	—
732	#102	C₂³×C₁₃	1	2	yes	—
733	#102	C₂³×C₁₃	1	2	yes	—
734	#102	C₂³×C₁₃	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
738	#97	C₂³×C₁₃	1	2	yes	—
739	#97	C₂³×C₁₃	1	1	yes	characteristic
740	#97	C₂³×C₁₃	1	1	yes	characteristic
741	#97	C₂³×C₁₃	1	2	yes	—
742	#97	C₂³×C₁₃	1	2	yes	—
743	C₄×C₈	C₂³×C₁₃	1	2	yes	—
744	C₄×C₈	C₂³×C₁₃	1	2	yes	—
745	C₂×C₁₃	—	4	1	no	—
746	C₂×C₁₃	—	8	1	no	—
747	C₂×C₁₃	#3486	1	1	yes	characteristic
748	C₂×C₁₃	#3586	1	1	yes	characteristic
749	C₂×C₁₃	#3586	1	1	yes	characteristic
750	C₂×Q₈	—	2	4	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	2	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
759	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
762	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
763	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
771	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	Q₁₆	—	2	4	no	—
774	Q₁₆	—	2	4	no	—
775	Q₁₆	—	2	4	no	—
776	SD₁₆	—	2	4	no	—
777	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
778	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
780	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	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	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	1	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	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
818	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
823	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	1	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	1	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
856	C₄²	C₂⁴×C₁₃	1	2	yes	—
857	C₄²	C₂⁴×C₁₃	1	2	yes	—
858	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₁₃	#61875	1	1	yes	characteristic, direct product factor, Sylow
861	C₂³	—	2	1	no	—
862	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	Q₈	—	2	4	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	1	no	—
870	Q₈	—	4	2	no	—
871	Q₈	—	4	2	no	—
872	Q₈	—	8	1	no	—
873	Q₈	—	8	1	no	—
874	Q₈	—	8	2	no	—
875	Q₈	—	8	2	no	—
876	Q₈	—	8	2	no	—
877	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
878	D₄	—	2	2	no	—
879	D₄	—	8	1	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
902	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
905	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
906	C₈	—	2	2	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₈	—	2	2	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	4	no	—
926	C₄	—	2	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	1	no	—
935	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
936	C₂	—	4	1	no	—
937	C₂	—	8	1	no	—
938	C₂	C₁₃×#3486	1	1	yes	characteristic
939	C₂	C₁₃×#3586	1	1	yes	characteristic
940	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×#121	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×#3390	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3387	C₂	semidirect
6. C₁₃×#3387	C₂	semidirect
7. C₁₃×#3377	C₂	semidirect
8. C₁₃×#3377	C₂	semidirect
9. C₁₃×#3374	C₂	semidirect
10. C₁₃×#3369	C₂	semidirect
12. C₁₃×#3242	C₂	semidirect
14. C₁₃×#3237	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
18. C₁₃×#3113	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
280. #61875	C₁₃	direct (N × H)
392. #3502	C₂×C₁₃	semidirect
393. #3390	C₂×C₁₃	semidirect
394. #3388	C₂×C₁₃	semidirect
395. #3387	C₂×C₁₃	semidirect
396. #3387	C₂×C₁₃	semidirect
397. #3377	C₂×C₁₃	semidirect
398. #3377	C₂×C₁₃	semidirect
399. #3374	C₂×C₁₃	semidirect
400. #3369	C₂×C₁₃	semidirect
402. #3242	C₂×C₁₃	semidirect
404. #3237	C₂×C₁₃	semidirect
405. #3127	C₂×C₁₃	semidirect
408. #3113	C₂×C₁₃	semidirect
409. #2987	C₂×C₁₃	semidirect
860. C₁₃	#61875	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×#3502	2
C₁₃×#3390	2
C₁₃×#3388	2
C₁₃×#3387	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3369	2
C₁₃×#3244	2
C₁₃×#3242	2
C₁₃×#3240	2
C₁₃×#3237	2
C₁₃×#3127	2
C₁₃×#3121	2
C₁₃×#3117	2
C₁₃×#3113	2
C₁₃×#2987	2
#61875	13

Subgroups — C13×#61875 #15748214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61875 #15748214