Subgroups — C₁₃×#62572 #15748911

Order 3328.

1652 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3554	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3331	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#564	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#562	—	2	2	no	—
23	C₁₃×#559	—	2	1	no	—
24	C₁₃×#559	C₂²	1	1	yes	characteristic
25	C₁₃×#557	C₂²	1	1	yes	characteristic
26	C₁₃×#557	C₂²	1	2	yes	—
27	C₁₃×#554	—	2	1	no	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#552	—	2	2	no	—
30	C₁₃×#552	C₂²	1	2	yes	—
31	C₁₃×#552	C₂²	1	2	yes	—
32	C₁₃×#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#548	C₂²	1	2	yes	—
35	C₁₃×#547	C₂²	1	2	yes	—
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	C₂²	1	2	yes	—
38	C₁₃×#542	—	2	1	no	—
39	C₁₃×#542	C₂²	1	2	yes	—
40	C₁₃×#541	—	2	2	no	—
41	C₁₃×#541	C₂²	1	2	yes	—
42	C₁₃×#540	—	2	1	no	—
43	C₁₃×#539	—	2	2	no	—
44	C₁₃×#539	—	2	1	no	—
45	C₁₃×#536	C₂²	1	2	yes	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	—
52	C₁₃×#498	C₂²	1	1	yes	characteristic
53	C₁₃×#497	C₂²	1	2	yes	—
54	C₁₃×#494	C₂²	1	1	yes	characteristic
55	C₁₃×#491	C₂²	1	2	yes	—
56	C₁₃×#491	C₂²	1	2	yes	—
57	C₁₃×#491	C₂²	1	2	yes	—
58	C₁₃×#490	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	2	yes	—
61	C₁₃×#488	C₂²	1	2	yes	—
62	C₁₃×#488	C₂²	1	2	yes	—
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#487	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	1	yes	characteristic
66	C₁₃×#487	C₂²	1	1	yes	characteristic
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#484	C₂²	1	1	yes	characteristic
69	C₁₃×#484	C₂²	1	1	yes	characteristic
70	C₁₃×#483	C₂²	1	2	yes	—
71	C₁₃×#483	C₂²	1	1	yes	characteristic
72	C₁₃×#483	C₂²	1	1	yes	characteristic
73	C₁₃×#482	C₂²	1	2	yes	—
74	C₁₃×#481	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×#478	C₂²	1	2	yes	—
79	C₁₃×#476	C₂²	1	2	yes	—
80	C₁₃×#475	C₂²	1	2	yes	—
81	C₁₃×#470	C₂²	1	2	yes	—
82	C₁₃×#470	C₂²	1	2	yes	—
83	C₁₃×#470	C₂²	1	2	yes	—
84	C₁₃×#468	C₂²	1	2	yes	—
85	C₁₃×#467	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	2	yes	—
90	C₁₃×#462	C₂²	1	2	yes	—
91	C₁₃×#462	C₂²	1	2	yes	—
92	C₁₃×#460	C₂²	1	2	yes	—
93	C₁₃×#452	C₂²	1	2	yes	—
94	C₁₃×#452	C₂²	1	2	yes	—
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	—
97	C₁₃×#451	C₂²	1	2	yes	—
98	C₁₃×#451	C₂²	1	2	yes	—
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#441	C₂²	1	2	yes	—
101	C₁₃×#441	C₂²	1	2	yes	—
102	C₁₃×#441	C₂²	1	2	yes	—
103	C₁₃×#440	C₂²	1	2	yes	—
104	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
106	C₁₃×#436	C₂²	1	2	yes	—
107	C₁₃×#435	C₂²	1	2	yes	—
108	C₁₃×#435	C₂²	1	2	yes	—
109	C₁₃×#433	C₂²	1	2	yes	—
110	C₁₃×#432	C₂²	1	1	yes	characteristic
111	C₁₃×#419	C₂²	1	2	yes	—
112	C₁₃×#417	C₂²	1	2	yes	—
113	C₁₃×#417	C₂²	1	2	yes	—
114	C₁₃×#417	C₂²	1	2	yes	—
115	C₁₃×#416	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	2	yes	—
117	C₁₃×#405	C₂²	1	2	yes	—
118	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	C₂³	1	2	yes	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	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×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
130	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	—	2	2	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₁₃×#127	—	2	1	no	—
142	C₁₃×#127	C₂³	1	1	yes	characteristic
143	C₁₃×#126	—	2	2	no	—
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	D₄	1	2	yes	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	1	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	2	no	—
159	C₁₃×#125	—	2	1	no	—
160	C₁₃×#125	—	2	1	no	—
161	C₁₃×#125	—	2	1	no	—
162	C₁₃×#125	—	2	1	no	—
163	C₁₃×#125	D₄	1	1	yes	characteristic
164	C₁₃×#125	C₂³	1	2	yes	—
165	C₁₃×#125	C₂³	1	2	yes	—
166	C₁₃×#125	C₂³	1	2	yes	—
167	C₁₃×#124	—	2	1	no	—
168	C₁₃×#124	—	2	2	no	—
169	C₁₃×#124	—	2	2	no	—
170	C₁₃×#124	D₄	1	1	yes	characteristic
171	C₁₃×#124	C₂³	1	2	yes	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#123	—	2	2	no	—
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	2	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	D₄	1	2	yes	—
182	C₁₃×C₂²⋊Q₈	—	2	1	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	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	1	yes	characteristic
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	D₄	1	1	yes	characteristic
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	2	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
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	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₁₃	—	2	2	no	—
219	C₄×D₄×C₁₃	—	2	1	no	—
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	—	2	1	no	—
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	1	no	—
225	C₄×D₄×C₁₃	C₂³	1	2	yes	—
226	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₁₃	C₂³	1	2	yes	—
228	C₁₃×#117	—	2	1	no	—
229	C₁₃×#117	—	2	1	no	—
230	C₁₃×#117	—	2	2	no	—
231	C₁₃×#117	—	2	2	no	—
232	C₁₃×#117	C₂³	1	2	yes	—
233	C₁₃×#117	C₂³	1	2	yes	—
234	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	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×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	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×#102	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	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	2	yes	—
275	C₁₃×#97	C₂³	1	2	yes	—
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62572	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	4	2	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	4	2	no	—
285	C₂×Q₈×C₁₃	—	2	1	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	—	4	2	no	—
290	C₂×Q₈×C₁₃	—	4	2	no	—
291	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×D₄×C₁₃	—	2	2	no	—
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	1	no	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
302	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃	—	2	1	no	—
305	C₂²×C₄×C₁₃	—	2	1	no	—
306	C₂²×C₄×C₁₃	—	2	2	no	—
307	C₂²×C₄×C₁₃	—	2	2	no	—
308	C₂²×C₄×C₁₃	—	2	2	no	—
309	C₂²×C₄×C₁₃	—	2	2	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
315	C₁₃×Q₁₆	—	4	2	no	—
316	C₁₃×Q₁₆	—	4	2	no	—
317	C₁₃×Q₁₆	—	4	2	no	—
318	C₁₃×Q₁₆	—	4	2	no	—
319	C₁₃×SD₁₆	—	4	2	no	—
320	C₁₃×SD₁₆	—	4	2	no	—
321	C₁₃×M₁₆	—	4	2	no	—
322	C₁₃×M₁₆	—	4	2	no	—
323	C₂×C₈×C₁₃	—	4	2	no	—
324	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
328	C₁₃×C₄⋊C₄	—	2	1	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	1	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	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	1	no	—
373	C₁₃×C₂²⋊C₄	—	2	1	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	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	2	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	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₄²×C₁₃	—	2	2	no	—
390	C₄²×C₁₃	—	2	2	no	—
391	C₄²×C₁₃	—	2	1	no	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	—	2	2	no	—
394	C₄²×C₁₃	—	2	2	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₁₃	C₂⁴	1	2	yes	—
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	#3563	C₂×C₁₃	1	1	yes	characteristic, complemented
402	#3554	C₂×C₁₃	1	1	yes	characteristic
403	#3374	C₂×C₁₃	1	2	yes	complemented
404	#3371	C₂×C₁₃	1	2	yes	complemented
405	#3331	C₂×C₁₃	1	2	yes	complemented
406	#3327	C₂×C₁₃	1	2	yes	complemented
407	#3317	C₂×C₁₃	1	2	yes	complemented
408	#3316	C₂×C₁₃	1	2	yes	complemented
409	#3315	C₂×C₁₃	1	2	yes	complemented
410	#3312	C₂×C₁₃	1	2	yes	complemented
411	#3244	C₂×C₁₃	1	2	yes	complemented
412	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
413	#3223	C₂×C₁₃	1	2	yes	complemented
414	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
416	#3178	C₂×C₁₃	1	2	yes	complemented
417	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3137	C₂×C₁₃	1	2	yes	complemented
419	#2967	C₂×C₁₃	1	1	yes	characteristic, complemented
420	C₂³×C₁₃	—	2	2	no	—
421	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
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	—	4	1	no	—
430	Q₈×C₁₃	—	8	1	no	—
431	Q₈×C₁₃	—	8	1	no	—
432	Q₈×C₁₃	—	8	2	no	—
433	Q₈×C₁₃	—	8	2	no	—
434	D₄×C₁₃	—	2	2	no	—
435	D₄×C₁₃	—	2	2	no	—
436	D₄×C₁₃	—	4	1	no	—
437	D₄×C₁₃	—	4	2	no	—
438	D₄×C₁₃	—	4	2	no	—
439	D₄×C₁₃	—	8	1	no	—
440	D₄×C₁₃	—	8	2	no	—
441	D₄×C₁₃	—	8	2	no	—
442	D₄×C₁₃	—	8	2	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	2	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	1	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	4	1	no	—
456	C₂×C₄×C₁₃	—	4	1	no	—
457	C₂×C₄×C₁₃	—	4	2	no	—
458	C₂×C₄×C₁₃	—	8	2	no	—
459	C₂×C₄×C₁₃	—	8	2	no	—
460	C₂×C₄×C₁₃	—	8	2	no	—
461	C₂×C₄×C₁₃	—	8	1	no	—
462	C₂×C₄×C₁₃	—	8	2	no	—
463	C₂×C₄×C₁₃	—	8	2	no	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
473	C₈×C₁₃	—	2	2	no	—
474	C₈×C₁₃	—	2	2	no	—
475	C₈×C₁₃	—	2	2	no	—
476	C₈×C₁₃	—	2	2	no	—
477	#564	—	2	1	no	—
478	#563	—	2	1	no	—
479	#562	—	2	2	no	—
480	#559	—	2	1	no	—
481	#559	C₂²×C₁₃	1	1	yes	characteristic
482	#557	C₂²×C₁₃	1	1	yes	characteristic
483	#557	C₂²×C₁₃	1	2	yes	—
484	#554	—	2	1	no	—
485	#554	C₂²×C₁₃	1	2	yes	—
486	#552	—	2	2	no	—
487	#552	C₂²×C₁₃	1	2	yes	—
488	#552	C₂²×C₁₃	1	2	yes	—
489	#550	C₂²×C₁₃	1	1	yes	characteristic
490	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
491	#548	C₂²×C₁₃	1	2	yes	—
492	#547	C₂²×C₁₃	1	2	yes	—
493	#544	—	2	1	no	—
494	#544	C₂²×C₁₃	1	2	yes	—
495	#542	—	2	1	no	—
496	#542	C₂²×C₁₃	1	2	yes	—
497	#541	—	2	2	no	—
498	#541	C₂²×C₁₃	1	2	yes	—
499	#540	—	2	1	no	—
500	#539	—	2	2	no	—
501	#539	—	2	1	no	—
502	#536	C₂²×C₁₃	1	2	yes	—
503	#533	C₂²×C₁₃	1	1	yes	characteristic
504	#533	C₂²×C₁₃	1	1	yes	characteristic
505	#532	C₂²×C₁₃	1	1	yes	characteristic
506	#529	C₂²×C₁₃	1	1	yes	characteristic
507	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
508	#501	C₂²×C₁₃	1	2	yes	—
509	#498	C₂²×C₁₃	1	1	yes	characteristic
510	#497	C₂²×C₁₃	1	2	yes	—
511	#494	C₂²×C₁₃	1	1	yes	characteristic
512	#491	C₂²×C₁₃	1	2	yes	—
513	#491	C₂²×C₁₃	1	2	yes	—
514	#491	C₂²×C₁₃	1	2	yes	—
515	#490	C₂²×C₁₃	1	2	yes	—
516	#489	C₂²×C₁₃	1	2	yes	—
517	#489	C₂²×C₁₃	1	2	yes	—
518	#488	C₂²×C₁₃	1	2	yes	—
519	#488	C₂²×C₁₃	1	2	yes	—
520	#488	C₂²×C₁₃	1	2	yes	—
521	#487	C₂²×C₁₃	1	2	yes	—
522	#487	C₂²×C₁₃	1	1	yes	characteristic
523	#487	C₂²×C₁₃	1	1	yes	characteristic
524	#485	C₂²×C₁₃	1	2	yes	—
525	#484	C₂²×C₁₃	1	1	yes	characteristic
526	#484	C₂²×C₁₃	1	1	yes	characteristic
527	#483	C₂²×C₁₃	1	1	yes	characteristic
528	#483	C₂²×C₁₃	1	2	yes	—
529	#483	C₂²×C₁₃	1	1	yes	characteristic
530	#482	C₂²×C₁₃	1	2	yes	—
531	#481	C₂²×C₁₃	1	2	yes	—
532	#479	C₂²×C₁₃	1	2	yes	—
533	#479	C₂²×C₁₃	1	2	yes	—
534	#479	C₂²×C₁₃	1	2	yes	—
535	#478	C₂²×C₁₃	1	2	yes	—
536	#476	C₂²×C₁₃	1	2	yes	—
537	#475	C₂²×C₁₃	1	2	yes	—
538	#470	C₂²×C₁₃	1	2	yes	—
539	#470	C₂²×C₁₃	1	2	yes	—
540	#470	C₂²×C₁₃	1	2	yes	—
541	#468	C₂²×C₁₃	1	2	yes	—
542	#467	C₂²×C₁₃	1	2	yes	—
543	#465	C₂²×C₁₃	1	2	yes	—
544	#464	C₂²×C₁₃	1	2	yes	—
545	#464	C₂²×C₁₃	1	2	yes	—
546	#462	C₂²×C₁₃	1	2	yes	—
547	#462	C₂²×C₁₃	1	2	yes	—
548	#462	C₂²×C₁₃	1	2	yes	—
549	#460	C₂²×C₁₃	1	2	yes	—
550	#452	C₂²×C₁₃	1	2	yes	—
551	#452	C₂²×C₁₃	1	2	yes	—
552	#452	C₂²×C₁₃	1	2	yes	—
553	#452	C₂²×C₁₃	1	2	yes	—
554	#451	C₂²×C₁₃	1	2	yes	—
555	#451	C₂²×C₁₃	1	2	yes	—
556	#446	C₂²×C₁₃	1	2	yes	—
557	#441	C₂²×C₁₃	1	2	yes	—
558	#441	C₂²×C₁₃	1	2	yes	—
559	#441	C₂²×C₁₃	1	2	yes	—
560	#440	C₂²×C₁₃	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
562	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
563	#436	C₂²×C₁₃	1	2	yes	—
564	#435	C₂²×C₁₃	1	2	yes	—
565	#435	C₂²×C₁₃	1	2	yes	—
566	#433	C₂²×C₁₃	1	2	yes	—
567	#432	C₂²×C₁₃	1	1	yes	characteristic
568	#419	C₂²×C₁₃	1	2	yes	—
569	#417	C₂²×C₁₃	1	2	yes	—
570	#417	C₂²×C₁₃	1	2	yes	—
571	#417	C₂²×C₁₃	1	2	yes	—
572	#416	C₂²×C₁₃	1	2	yes	—
573	C₂×#103	C₂²×C₁₃	1	2	yes	—
574	#405	C₂²×C₁₃	1	2	yes	—
575	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
576	C₂²×C₁₃	—	2	1	no	—
577	C₂²×C₁₃	—	2	1	no	—
578	C₂²×C₁₃	—	2	2	no	—
579	C₂²×C₁₃	—	2	2	no	—
580	C₂²×C₁₃	—	2	2	no	—
581	C₂²×C₁₃	—	2	1	no	—
582	C₂²×C₁₃	—	4	2	no	—
583	C₂²×C₁₃	—	4	2	no	—
584	C₂²×C₁₃	—	4	2	no	—
585	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	1	no	—
588	C₄×C₁₃	—	2	1	no	—
589	C₄×C₁₃	—	2	1	no	—
590	C₄×C₁₃	—	2	2	no	—
591	C₄×C₁₃	—	2	2	no	—
592	C₄×C₁₃	—	2	1	no	—
593	C₄×C₁₃	—	2	2	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	1	no	—
596	C₄×C₁₃	—	4	2	no	—
597	C₄×C₁₃	—	4	2	no	—
598	C₄×C₁₃	—	4	1	no	—
599	C₄×C₁₃	—	4	1	no	—
600	C₄×C₁₃	—	4	2	no	—
601	C₄×C₁₃	—	4	1	no	—
602	C₄×C₁₃	—	4	2	no	—
603	C₄×C₁₃	#585	1	2	yes	—
604	C₂×#41	C₂³×C₁₃	1	2	yes	—
605	C₂×#41	C₂³×C₁₃	1	2	yes	—
606	C₂²×Q₈	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×Q₁₆	C₂³×C₁₃	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
613	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
614	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
615	C₂²×C₈	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	C₂³×C₁₃	1	1	yes	characteristic
620	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
622	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
623	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
626	#127	—	2	1	no	—
627	#127	C₂³×C₁₃	1	1	yes	characteristic
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	D₄×C₁₃	1	2	yes	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	1	no	—
645	#125	—	2	1	no	—
646	#125	—	2	1	no	—
647	#125	—	2	1	no	—
648	#125	D₄×C₁₃	1	1	yes	characteristic
649	#125	C₂³×C₁₃	1	2	yes	—
650	#125	C₂³×C₁₃	1	2	yes	—
651	#125	C₂³×C₁₃	1	2	yes	—
652	#124	—	2	1	no	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	D₄×C₁₃	1	1	yes	characteristic
656	#124	C₂³×C₁₃	1	2	yes	—
657	#124	C₂³×C₁₃	1	2	yes	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	#123	—	2	2	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	#123	D₄×C₁₃	1	2	yes	—
667	C₂²⋊Q₈	—	2	1	no	—
668	C₂²⋊Q₈	—	2	1	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
679	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
682	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
683	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
684	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
685	#121	—	2	2	no	—
686	#121	—	2	2	no	—
687	#121	—	2	1	no	—
688	#121	—	2	1	no	—
689	#121	—	2	2	no	—
690	#121	D₄×C₁₃	1	1	yes	characteristic
691	#121	C₂³×C₁₃	1	2	yes	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	2	no	—
694	C₄×Q₈	—	2	1	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
701	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
702	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	1	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	2	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	C₂³×C₁₃	1	2	yes	—
711	C₄×D₄	C₂³×C₁₃	1	2	yes	—
712	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
713	#117	—	2	1	no	—
714	#117	—	2	1	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	C₂³×C₁₃	1	2	yes	—
718	#117	C₂³×C₁₃	1	2	yes	—
719	C₂×C₄⋊C₄	—	2	1	no	—
720	C₂×C₄⋊C₄	—	2	1	no	—
721	C₂×C₄⋊C₄	—	2	2	no	—
722	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
725	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
726	#107	C₂³×C₁₃	1	2	yes	—
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	#106	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	#103	C₂³×C₁₃	1	2	yes	—
736	#103	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	#103	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	#102	C₂³×C₁₃	1	2	yes	—
754	#102	C₂³×C₁₃	1	2	yes	—
755	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
759	#97	C₂³×C₁₃	1	2	yes	—
760	#97	C₂³×C₁₃	1	2	yes	—
761	#97	C₂³×C₁₃	1	2	yes	—
762	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
763	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₄×C₈	C₂³×C₁₃	1	2	yes	—
765	C₂×C₁₃	—	4	1	no	—
766	C₂×C₁₃	—	4	2	no	—
767	C₂×C₁₃	—	8	2	no	—
768	C₂×C₁₃	#3500	1	1	yes	characteristic
769	C₂×C₁₃	#3586	1	1	yes	characteristic
770	C₂×C₁₃	#3586	1	1	yes	characteristic
771	#41	—	4	2	no	—
772	#41	—	4	2	no	—
773	#41	—	4	2	no	—
774	#41	—	4	2	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	2	no	—
778	C₂×Q₈	—	2	2	no	—
779	C₂×Q₈	—	4	2	no	—
780	C₂×Q₈	—	4	2	no	—
781	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
784	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
805	Q₁₆	—	4	2	no	—
806	Q₁₆	—	4	2	no	—
807	Q₁₆	—	4	2	no	—
808	Q₁₆	—	4	2	no	—
809	SD₁₆	—	4	2	no	—
810	SD₁₆	—	4	2	no	—
811	M₁₆	—	4	2	no	—
812	M₁₆	—	4	2	no	—
813	C₂×C₈	—	4	2	no	—
814	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
815	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	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	2	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	1	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
854	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	1	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	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
875	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
877	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
888	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₄²	C₂⁴×C₁₃	1	2	yes	—
890	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
891	C₁₃	#62572	1	1	yes	characteristic, direct product factor, Sylow
892	C₂³	—	2	2	no	—
893	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
894	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	—	2	2	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	8	2	no	—
903	Q₈	—	8	1	no	—
904	Q₈	—	8	1	no	—
905	Q₈	—	8	2	no	—
906	D₄	—	2	2	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	1	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	2	no	—
911	D₄	—	8	1	no	—
912	D₄	—	8	2	no	—
913	D₄	—	8	2	no	—
914	D₄	—	8	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	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	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	8	2	no	—
931	C₂×C₄	—	8	2	no	—
932	C₂×C₄	—	8	2	no	—
933	C₂×C₄	—	8	1	no	—
934	C₂×C₄	—	8	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
939	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
940	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
941	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
944	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
945	C₈	—	2	2	no	—
946	C₈	—	2	2	no	—
947	C₈	—	2	2	no	—
948	C₈	—	2	2	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	2	no	—
976	C₄	C₁₃×#585	1	2	yes	—
977	C₂	—	4	1	no	—
978	C₂	—	4	2	no	—
979	C₂	—	8	2	no	—
980	C₂	C₁₃×#3500	1	1	yes	characteristic
981	C₂	C₁₃×#3586	1	1	yes	characteristic
982	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×#3554	C₂
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×#3563	C₂	semidirect
3. C₁₃×#3374	C₂	semidirect
4. C₁₃×#3371	C₂	semidirect
5. C₁₃×#3331	C₂	semidirect
6. C₁₃×#3327	C₂	semidirect
7. C₁₃×#3317	C₂	semidirect
8. C₁₃×#3316	C₂	semidirect
9. C₁₃×#3315	C₂	semidirect
10. C₁₃×#3312	C₂	semidirect
11. C₁₃×#3244	C₂	semidirect
12. C₁₃×#3236	C₂	semidirect
13. C₁₃×#3223	C₂	semidirect
14. C₁₃×#3216	C₂	semidirect
15. C₁₃×#3185	C₂	semidirect
16. C₁₃×#3178	C₂	semidirect
17. C₁₃×#3142	C₂	semidirect
18. C₁₃×#3137	C₂	semidirect
19. C₁₃×#2967	C₂	semidirect
280. #62572	C₁₃	direct (N × H)
401. #3563	C₂×C₁₃	semidirect
403. #3374	C₂×C₁₃	semidirect
404. #3371	C₂×C₁₃	semidirect
405. #3331	C₂×C₁₃	semidirect
406. #3327	C₂×C₁₃	semidirect
407. #3317	C₂×C₁₃	semidirect
408. #3316	C₂×C₁₃	semidirect
409. #3315	C₂×C₁₃	semidirect
410. #3312	C₂×C₁₃	semidirect
411. #3244	C₂×C₁₃	semidirect
412. #3236	C₂×C₁₃	semidirect
413. #3223	C₂×C₁₃	semidirect
414. #3216	C₂×C₁₃	semidirect
415. #3185	C₂×C₁₃	semidirect
416. #3178	C₂×C₁₃	semidirect
417. #3142	C₂×C₁₃	semidirect
418. #3137	C₂×C₁₃	semidirect
419. #2967	C₂×C₁₃	semidirect
891. C₁₃	#62572	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×#3563	2
C₁₃×#3554	2
C₁₃×#3374	2
C₁₃×#3371	2
C₁₃×#3331	2
C₁₃×#3327	2
C₁₃×#3317	2
C₁₃×#3316	2
C₁₃×#3315	2
C₁₃×#3312	2
C₁₃×#3244	2
C₁₃×#3236	2
C₁₃×#3223	2
C₁₃×#3216	2
C₁₃×#3185	2
C₁₃×#3178	2
C₁₃×#3142	2
C₁₃×#3137	2
C₁₃×#2967	2
#62572	13

Subgroups — C13×#62572 #15748911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62572 #15748911