Subgroups — C₁₃×#61944 #15748283

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3402	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#559	C₂²	1	2	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#559	C₂²	1	2	yes	complemented
25	Q₈²×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	C₂²	1	2	yes	—
28	C₁₃×#556	C₂²	1	2	yes	—
29	C₁₃×#556	C₂²	1	2	yes	complemented
30	C₁₃×#551	—	2	2	no	—
31	C₁₃×#551	—	2	2	no	—
32	D₄×Q₈×C₁₃	—	2	1	no	—
33	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
34	C₁₃×#542	—	2	1	no	—
35	C₁₃×#542	—	2	1	no	—
36	C₁₃×#542	—	2	2	no	—
37	C₁₃×#542	C₂²	1	2	yes	—
38	C₁₃×#542	C₂²	1	2	yes	—
39	C₁₃×#536	—	2	2	no	—
40	C₁₃×#536	C₂²	1	1	yes	characteristic
41	C₁₃×#535	C₂²	1	1	yes	characteristic
42	C₁₃×#533	C₂²	1	1	yes	characteristic
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#532	C₂²	1	1	yes	characteristic
45	C₁₃×#529	—	2	1	no	—
46	C₁₃×#529	—	2	1	no	—
47	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
48	C₁₃×#519	C₂²	1	1	yes	characteristic
49	C₁₃×#518	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	2	yes	—
52	C₁₃×#497	C₂²	1	2	yes	complemented
53	C₁₃×#496	C₂²	1	2	yes	—
54	C₁₃×#496	C₂²	1	2	yes	—
55	C₁₃×#495	C₂²	1	2	yes	—
56	C₁₃×#495	C₂²	1	2	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#489	C₂²	1	2	yes	complemented
61	C₁₃×#487	C₂²	1	2	yes	complemented
62	C₁₃×#486	C₂²	1	2	yes	—
63	C₁₃×#485	C₂²	1	2	yes	—
64	C₁₃×#482	C₂²	1	2	yes	—
65	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#477	C₂²	1	2	yes	complemented
67	C₁₃×#476	C₂²	1	2	yes	—
68	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#475	C₂²	1	2	yes	complemented
71	C₁₃×#474	C₂²	1	2	yes	—
72	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#464	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	complemented
77	C₁₃×#464	C₂²	1	2	yes	complemented
78	C₁₃×#464	C₂²	1	2	yes	complemented
79	C₁₃×#463	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×#463	C₂²	1	2	yes	—
84	C₁₃×#463	C₂²	1	2	yes	complemented
85	C₁₃×#462	C₂²	1	2	yes	complemented
86	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#461	C₂²	1	2	yes	complemented
88	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#460	C₂²	1	2	yes	—
90	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#459	C₂²	1	2	yes	—
92	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#452	C₂²	1	2	yes	—
94	C₁₃×#451	C₂²	1	2	yes	—
95	C₁₃×#450	C₂²	1	2	yes	—
96	C₁₃×#449	C₂²	1	2	yes	—
97	C₁₃×#448	C₂²	1	2	yes	—
98	C₁₃×#447	C₂²	1	2	yes	—
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#446	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#446	C₂²	1	2	yes	complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	complemented
105	C₁₃×#441	C₂²	1	2	yes	complemented
106	C₁₃×#441	C₂²	1	2	yes	complemented
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₁₃×#440	C₂²	1	2	yes	complemented
109	C₁₃×#440	C₂²	1	2	yes	complemented
110	C₁₃×#440	C₂²	1	2	yes	complemented
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×C₁₃×D₈	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	—	2	1	no	—
120	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₁₃	—	2	2	no	—
122	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
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×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×D₈	C₂³	1	2	yes	—
134	C₂×C₁₃×D₈	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	—	2	2	no	—
137	C₁₃×C₄⋊Q₈	—	2	2	no	—
138	C₁₃×C₄⋊Q₈	—	2	2	no	—
139	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
140	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
141	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₁₃×#127	C₂³	1	2	yes	—
148	C₁₃×#127	C₂³	1	1	yes	characteristic
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	2	no	—
157	C₁₃×#125	—	2	1	no	—
158	C₁₃×#125	D₄	1	1	yes	characteristic
159	C₁₃×#125	D₄	1	1	yes	characteristic
160	C₁₃×#124	—	2	2	no	—
161	C₁₃×#124	—	2	2	no	—
162	C₁₃×#124	—	2	2	no	—
163	C₁₃×#124	—	2	2	no	—
164	C₁₃×#124	—	2	2	no	—
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	—	2	1	no	—
167	C₁₃×#124	—	2	1	no	—
168	C₁₃×#124	C₂³	1	2	yes	—
169	C₁₃×#124	C₂³	1	2	yes	—
170	C₁₃×#124	C₂³	1	2	yes	—
171	C₁₃×#124	C₂³	1	2	yes	—
172	C₁₃×#124	C₂³	1	2	yes	—
173	C₁₃×#124	C₂³	1	2	yes	—
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	—	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	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	1	no	—
198	C₁₃×#121	—	2	1	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	C₂³	1	2	yes	—
201	C₁₃×#120	—	2	2	no	—
202	C₄×Q₈×C₁₃	—	2	2	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	1	yes	characteristic
211	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×D₄×C₁₃	—	2	1	no	—
216	C₄×D₄×C₁₃	—	2	1	no	—
217	C₄×D₄×C₁₃	—	2	1	no	—
218	C₄×D₄×C₁₃	—	2	1	no	—
219	C₄×D₄×C₁₃	—	2	2	no	—
220	C₄×D₄×C₁₃	—	2	2	no	—
221	C₄×D₄×C₁₃	—	2	2	no	—
222	C₄×D₄×C₁₃	—	2	1	no	—
223	C₄×D₄×C₁₃	C₂³	1	2	yes	—
224	C₄×D₄×C₁₃	C₂³	1	2	yes	—
225	C₄×D₄×C₁₃	C₂³	1	2	yes	—
226	C₄×D₄×C₁₃	C₂³	1	2	yes	—
227	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
237	C₁₃×#117	C₂³	1	1	yes	characteristic
238	C₁₃×#117	C₂³	1	1	yes	characteristic
239	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
241	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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×#107	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₄⋊C₈	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×#102	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
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	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#61944	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	4	1	no	—
283	C₁₃×#41	—	4	1	no	—
284	C₁₃×#41	—	8	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	—	2	1	no	—
290	C₂×Q₈×C₁₃	—	4	1	no	—
291	C₂×Q₈×C₁₃	—	4	1	no	—
292	C₂×Q₈×C₁₃	—	8	4	no	—
293	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
295	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×D₄×C₁₃	—	2	1	no	—
299	C₂×D₄×C₁₃	—	2	2	no	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	1	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	2	no	—
304	C₂×D₄×C₁₃	—	2	1	no	—
305	C₂×D₄×C₁₃	—	4	1	no	—
306	C₂×D₄×C₁₃	—	4	1	no	—
307	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃	—	2	1	no	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	1	no	—
314	C₂²×C₄×C₁₃	—	2	1	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₁₃×Q₁₆	—	4	2	no	—
323	C₁₃×Q₁₆	—	4	2	no	—
324	C₁₃×Q₁₆	—	4	2	no	—
325	C₁₃×SD₁₆	—	4	2	no	—
326	C₁₃×SD₁₆	—	4	2	no	—
327	C₁₃×SD₁₆	—	4	2	no	—
328	C₁₃×SD₁₆	—	4	2	no	—
329	C₁₃×SD₁₆	—	4	2	no	—
330	C₁₃×SD₁₆	—	4	2	no	—
331	C₁₃×D₈	—	4	2	no	—
332	C₁₃×D₈	—	4	2	no	—
333	C₁₃×D₈	—	4	2	no	—
334	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	1	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	1	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	2	no	—
354	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
358	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
368	C₁₃×C₂²⋊C₄	—	2	1	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	1	no	—
377	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
389	C₁₃×C₂²⋊C₄	—	2	2	no	—
390	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	—	2	1	no	—
394	C₄²×C₁₃	—	2	1	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	—	2	2	no	—
399	C₄²×C₁₃	—	2	2	no	—
400	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₁₃	C₂⁴	1	2	yes	—
403	C₄²×C₁₃	C₂⁴	1	2	yes	—
404	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
406	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3403	C₂×C₁₃	1	2	yes	complemented
409	#3402	C₂×C₁₃	1	2	yes	complemented
410	#3401	C₂×C₁₃	1	2	yes	complemented
411	#3401	C₂×C₁₃	1	2	yes	complemented
412	#3375	C₂×C₁₃	1	2	yes	complemented
413	#3373	C₂×C₁₃	1	2	yes	complemented
414	#3369	C₂×C₁₃	1	2	yes	complemented
415	#3367	C₂×C₁₃	1	2	yes	complemented
416	#3225	C₂×C₁₃	1	2	yes	complemented
417	#3224	C₂×C₁₃	1	2	yes	complemented
418	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#3121	C₂×C₁₃	1	2	yes	complemented
421	#3118	C₂×C₁₃	1	2	yes	complemented
422	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
423	#3115	C₂×C₁₃	1	1	yes	characteristic, complemented
424	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
425	C₂³×C₁₃	—	2	2	no	—
426	C₂³×C₁₃	—	2	2	no	—
427	C₂³×C₁₃	—	2	1	no	—
428	C₂³×C₁₃	—	4	2	no	—
429	C₂³×C₁₃	—	8	1	no	—
430	C₂³×C₁₃	—	8	1	no	—
431	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₁₃	—	2	2	no	—
433	Q₈×C₁₃	—	2	1	no	—
434	Q₈×C₁₃	—	2	2	no	—
435	Q₈×C₁₃	—	2	2	no	—
436	Q₈×C₁₃	—	2	2	no	—
437	Q₈×C₁₃	—	2	1	no	—
438	Q₈×C₁₃	—	4	2	no	—
439	Q₈×C₁₃	—	4	2	no	—
440	Q₈×C₁₃	—	4	2	no	—
441	Q₈×C₁₃	—	4	2	no	—
442	Q₈×C₁₃	—	8	2	no	—
443	Q₈×C₁₃	—	8	2	no	—
444	Q₈×C₁₃	—	8	1	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	1	no	—
447	D₄×C₁₃	—	2	2	no	—
448	D₄×C₁₃	—	2	2	no	—
449	D₄×C₁₃	—	2	2	no	—
450	D₄×C₁₃	—	2	1	no	—
451	D₄×C₁₃	—	4	2	no	—
452	D₄×C₁₃	—	4	2	no	—
453	D₄×C₁₃	—	4	2	no	—
454	D₄×C₁₃	—	8	2	no	—
455	D₄×C₁₃	—	8	2	no	—
456	D₄×C₁₃	—	8	1	no	—
457	D₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	2	1	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	1	no	—
461	C₂×C₄×C₁₃	—	2	1	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	4	1	no	—
468	C₂×C₄×C₁₃	—	4	1	no	—
469	C₂×C₄×C₁₃	—	4	4	no	—
470	C₂×C₄×C₁₃	—	4	2	no	—
471	C₂×C₄×C₁₃	—	4	2	no	—
472	C₂×C₄×C₁₃	—	8	1	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	1	no	—
475	C₂×C₄×C₁₃	—	8	2	no	—
476	C₂×C₄×C₁₃	—	8	2	no	—
477	C₂×C₄×C₁₃	—	8	2	no	—
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
488	C₈×C₁₃	—	2	2	no	—
489	C₈×C₁₃	—	2	2	no	—
490	C₈×C₁₃	—	2	2	no	—
491	C₈×C₁₃	—	2	2	no	—
492	#563	—	2	1	no	—
493	#563	—	2	1	no	—
494	#559	C₂²×C₁₃	1	2	yes	—
495	#559	C₂²×C₁₃	1	2	yes	—
496	#559	C₂²×C₁₃	1	2	yes	complemented
497	Q₈²	C₂²×C₁₃	1	2	yes	complemented
498	#556	—	2	1	no	—
499	#556	C₂²×C₁₃	1	2	yes	—
500	#556	C₂²×C₁₃	1	2	yes	—
501	#556	C₂²×C₁₃	1	2	yes	complemented
502	#551	—	2	2	no	—
503	#551	—	2	2	no	—
504	D₄×Q₈	—	2	1	no	—
505	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
506	#542	—	2	1	no	—
507	#542	—	2	1	no	—
508	#542	—	2	2	no	—
509	#542	C₂²×C₁₃	1	2	yes	—
510	#542	C₂²×C₁₃	1	2	yes	—
511	#536	—	2	2	no	—
512	#536	C₂²×C₁₃	1	1	yes	characteristic
513	#535	C₂²×C₁₃	1	1	yes	characteristic
514	#533	C₂²×C₁₃	1	1	yes	characteristic
515	#533	C₂²×C₁₃	1	1	yes	characteristic
516	#532	C₂²×C₁₃	1	1	yes	characteristic
517	#529	—	2	1	no	—
518	#529	—	2	1	no	—
519	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
520	#519	C₂²×C₁₃	1	1	yes	characteristic
521	#518	C₂²×C₁₃	1	1	yes	characteristic
522	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
523	#497	C₂²×C₁₃	1	2	yes	—
524	#497	C₂²×C₁₃	1	2	yes	complemented
525	#496	C₂²×C₁₃	1	2	yes	—
526	#496	C₂²×C₁₃	1	2	yes	—
527	#495	C₂²×C₁₃	1	2	yes	—
528	#495	C₂²×C₁₃	1	2	yes	complemented
529	#489	C₂²×C₁₃	1	2	yes	—
530	#489	C₂²×C₁₃	1	2	yes	—
531	#489	C₂²×C₁₃	1	2	yes	—
532	#489	C₂²×C₁₃	1	2	yes	complemented
533	#487	C₂²×C₁₃	1	2	yes	complemented
534	#486	C₂²×C₁₃	1	2	yes	—
535	#485	C₂²×C₁₃	1	2	yes	—
536	#482	C₂²×C₁₃	1	2	yes	—
537	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#477	C₂²×C₁₃	1	2	yes	complemented
539	#476	C₂²×C₁₃	1	2	yes	—
540	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
542	#475	C₂²×C₁₃	1	2	yes	complemented
543	#474	C₂²×C₁₃	1	2	yes	—
544	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
545	#464	C₂²×C₁₃	1	2	yes	—
546	#464	C₂²×C₁₃	1	2	yes	—
547	#464	C₂²×C₁₃	1	2	yes	—
548	#464	C₂²×C₁₃	1	2	yes	complemented
549	#464	C₂²×C₁₃	1	2	yes	complemented
550	#464	C₂²×C₁₃	1	2	yes	complemented
551	#463	C₂²×C₁₃	1	2	yes	—
552	#463	C₂²×C₁₃	1	2	yes	—
553	#463	C₂²×C₁₃	1	2	yes	—
554	#463	C₂²×C₁₃	1	2	yes	—
555	#463	C₂²×C₁₃	1	2	yes	—
556	#463	C₂²×C₁₃	1	2	yes	complemented
557	#462	C₂²×C₁₃	1	2	yes	complemented
558	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#461	C₂²×C₁₃	1	2	yes	complemented
560	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	#460	C₂²×C₁₃	1	2	yes	—
562	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#459	C₂²×C₁₃	1	2	yes	—
564	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#452	C₂²×C₁₃	1	2	yes	—
566	#451	C₂²×C₁₃	1	2	yes	—
567	#450	C₂²×C₁₃	1	2	yes	—
568	#449	C₂²×C₁₃	1	2	yes	—
569	#448	C₂²×C₁₃	1	2	yes	—
570	#447	C₂²×C₁₃	1	2	yes	—
571	#446	C₂²×C₁₃	1	2	yes	complemented
572	#446	C₂²×C₁₃	1	2	yes	complemented
573	#446	C₂²×C₁₃	1	2	yes	complemented
574	#446	C₂²×C₁₃	1	2	yes	complemented
575	#442	C₂²×C₁₃	1	2	yes	—
576	#442	C₂²×C₁₃	1	2	yes	complemented
577	#441	C₂²×C₁₃	1	2	yes	complemented
578	#441	C₂²×C₁₃	1	2	yes	complemented
579	#440	C₂²×C₁₃	1	2	yes	—
580	#440	C₂²×C₁₃	1	2	yes	complemented
581	#440	C₂²×C₁₃	1	2	yes	complemented
582	#440	C₂²×C₁₃	1	2	yes	complemented
583	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
584	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
585	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
586	C₄×D₈	C₂²×C₁₃	1	2	yes	—
587	#433	C₂²×C₁₃	1	2	yes	—
588	#433	C₂²×C₁₃	1	2	yes	—
589	#432	C₂²×C₁₃	1	1	yes	characteristic
590	#432	C₂²×C₁₃	1	1	yes	characteristic
591	C₂²×C₁₃	—	2	1	no	—
592	C₂²×C₁₃	—	2	1	no	—
593	C₂²×C₁₃	—	2	1	no	—
594	C₂²×C₁₃	—	4	2	no	—
595	C₂²×C₁₃	—	4	1	no	—
596	C₂²×C₁₃	—	4	2	no	—
597	C₂²×C₁₃	—	4	1	no	—
598	C₂²×C₁₃	—	4	2	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	—	4	1	no	—
601	C₂²×C₁₃	—	4	2	no	—
602	C₂²×C₁₃	—	4	2	no	—
603	C₂²×C₁₃	—	16	2	no	—
604	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
605	C₄×C₁₃	—	2	1	no	—
606	C₄×C₁₃	—	2	1	no	—
607	C₄×C₁₃	—	2	2	no	—
608	C₄×C₁₃	—	2	2	no	—
609	C₄×C₁₃	—	2	1	no	—
610	C₄×C₁₃	—	2	1	no	—
611	C₄×C₁₃	—	2	2	no	—
612	C₄×C₁₃	—	2	2	no	—
613	C₄×C₁₃	—	2	1	no	—
614	C₄×C₁₃	—	4	2	no	—
615	C₄×C₁₃	—	4	1	no	—
616	C₄×C₁₃	—	4	2	no	—
617	C₄×C₁₃	—	4	1	no	—
618	C₄×C₁₃	—	4	1	no	—
619	C₄×C₁₃	—	4	2	no	—
620	C₄×C₁₃	—	4	2	no	—
621	C₄×C₁₃	#585	1	1	yes	characteristic
622	C₄×C₁₃	#585	1	1	yes	characteristic
623	C₂×#41	—	2	1	no	—
624	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
625	C₂²×Q₈	—	2	2	no	—
626	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
629	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
630	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
637	C₂×D₈	C₂³×C₁₃	1	2	yes	—
638	C₂×D₈	C₂³×C₁₃	1	2	yes	—
639	C₂×D₈	C₂³×C₁₃	1	2	yes	—
640	C₄⋊Q₈	—	2	2	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
644	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
650	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
651	#127	C₂³×C₁₃	1	1	yes	characteristic
652	#127	C₂³×C₁₃	1	2	yes	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	D₄×C₁₃	1	1	yes	characteristic
663	#125	D₄×C₁₃	1	1	yes	characteristic
664	#124	—	2	2	no	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	1	no	—
670	#124	—	2	1	no	—
671	#124	—	2	1	no	—
672	#124	C₂³×C₁₃	1	2	yes	—
673	#124	C₂³×C₁₃	1	2	yes	—
674	#124	C₂³×C₁₃	1	2	yes	—
675	#124	C₂³×C₁₃	1	2	yes	—
676	#124	C₂³×C₁₃	1	2	yes	—
677	#124	C₂³×C₁₃	1	2	yes	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
699	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	C₂³×C₁₃	1	2	yes	—
705	#120	—	2	2	no	—
706	C₄×Q₈	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
711	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
713	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
714	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
715	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
716	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
718	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
728	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₁₃	1	2	yes	—
730	C₄×D₄	C₂³×C₁₃	1	2	yes	—
731	C₄×D₄	C₂³×C₁₃	1	2	yes	—
732	C₄×D₄	C₂³×C₁₃	1	2	yes	—
733	C₄×D₄	C₂³×C₁₃	1	2	yes	—
734	#117	—	2	1	no	—
735	#117	—	2	2	no	—
736	#117	—	2	2	no	—
737	#117	—	2	2	no	—
738	#117	—	2	2	no	—
739	#117	—	2	1	no	—
740	#117	C₂³×C₁₃	1	1	yes	characteristic
741	#117	C₂³×C₁₃	1	1	yes	characteristic
742	#117	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	—	2	1	no	—
744	C₂×C₂²⋊C₄	—	2	1	no	—
745	C₂×C₂²⋊C₄	—	2	2	no	—
746	C₂×C₄²	—	2	1	no	—
747	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
748	#107	C₂³×C₁₃	1	2	yes	—
749	#107	C₂³×C₁₃	1	2	yes	—
750	#106	C₂³×C₁₃	1	2	yes	—
751	#106	C₂³×C₁₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
753	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
754	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
760	#103	C₂³×C₁₃	1	2	yes	—
761	#103	C₂³×C₁₃	1	2	yes	—
762	#103	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#103	C₂³×C₁₃	1	2	yes	—
766	#103	C₂³×C₁₃	1	2	yes	—
767	#103	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	#102	C₂³×C₁₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
778	#97	C₂³×C₁₃	1	2	yes	—
779	#97	C₂³×C₁₃	1	2	yes	—
780	#97	C₂³×C₁₃	1	2	yes	—
781	#97	C₂³×C₁₃	1	2	yes	—
782	C₄×C₈	C₂³×C₁₃	1	2	yes	—
783	C₄×C₈	C₂³×C₁₃	1	2	yes	—
784	C₂×C₁₃	—	4	1	no	—
785	C₂×C₁₃	—	8	2	no	—
786	C₂×C₁₃	—	8	1	no	—
787	C₂×C₁₃	—	8	2	no	—
788	C₂×C₁₃	#3487	1	1	yes	characteristic
789	C₂×C₁₃	#3585	1	1	yes	characteristic
790	C₂×C₁₃	#3586	1	1	yes	characteristic
791	C₂⁴	—	2	1	no	—
792	#41	—	4	1	no	—
793	#41	—	4	1	no	—
794	#41	—	8	2	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	4	1	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	—	8	4	no	—
803	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
804	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
805	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	4	1	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
818	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
832	Q₁₆	—	4	2	no	—
833	Q₁₆	—	4	2	no	—
834	Q₁₆	—	4	2	no	—
835	SD₁₆	—	4	2	no	—
836	SD₁₆	—	4	2	no	—
837	SD₁₆	—	4	2	no	—
838	SD₁₆	—	4	2	no	—
839	SD₁₆	—	4	2	no	—
840	SD₁₆	—	4	2	no	—
841	D₈	—	4	2	no	—
842	D₈	—	4	2	no	—
843	D₈	—	4	2	no	—
844	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
845	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
846	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
847	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
866	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
872	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
873	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	1	no	—
887	C₂²⋊C₄	—	2	1	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
901	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
902	C₄²	—	2	1	no	—
903	C₄²	—	2	1	no	—
904	C₄²	—	2	1	no	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
911	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
912	C₄²	C₂⁴×C₁₃	1	2	yes	—
913	C₄²	C₂⁴×C₁₃	1	2	yes	—
914	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₁₃	#61944	1	1	yes	characteristic, direct product factor, Sylow
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	8	1	no	—
922	C₂³	—	8	1	no	—
923	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	Q₈	—	2	2	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	4	2	no	—
932	Q₈	—	4	2	no	—
933	Q₈	—	4	2	no	—
934	Q₈	—	8	2	no	—
935	Q₈	—	8	2	no	—
936	Q₈	—	8	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	1	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
972	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
979	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	2	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	16	2	no	—
997	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	4	2	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	2	no	—
1014	C₄	C₁₃×#585	1	1	yes	characteristic
1015	C₄	C₁₃×#585	1	1	yes	characteristic
1016	C₂	—	4	1	no	—
1017	C₂	—	8	2	no	—
1018	C₂	—	8	2	no	—
1019	C₂	—	8	1	no	—
1020	C₂	C₁₃×#3487	1	1	yes	characteristic
1021	C₂	C₁₃×#3585	1	1	yes	characteristic
1022	C₂	C₁₃×#3586	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
2. C₁₃×#3510	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3402	C₂	semidirect
5. C₁₃×#3401	C₂	semidirect
6. C₁₃×#3401	C₂	semidirect
7. C₁₃×#3375	C₂	semidirect
8. C₁₃×#3373	C₂	semidirect
9. C₁₃×#3369	C₂	semidirect
10. C₁₃×#3367	C₂	semidirect
11. C₁₃×#3225	C₂	semidirect
12. C₁₃×#3224	C₂	semidirect
13. C₁₃×#3215	C₂	semidirect
14. C₁₃×#3213	C₂	semidirect
15. C₁₃×#3121	C₂	semidirect
16. C₁₃×#3118	C₂	semidirect
17. C₁₃×#3116	C₂	semidirect
18. C₁₃×#3115	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
24. C₁₃×#559	C₂²	semidirect
25. Q₈²×C₁₃	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
33. D₄×Q₈×C₁₃	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
56. C₁₃×#495	C₂²	semidirect
60. C₁₃×#489	C₂²	semidirect
61. C₁₃×#487	C₂²	semidirect
65. C₁₃×#477	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
68. C₁₃×#476	C₂²	semidirect
69. C₁₃×#475	C₂²	semidirect
70. C₁₃×#475	C₂²	semidirect
72. C₁₃×#474	C₂²	semidirect
76. C₁₃×#464	C₂²	semidirect
77. C₁₃×#464	C₂²	semidirect
78. C₁₃×#464	C₂²	semidirect
84. C₁₃×#463	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
86. C₁₃×#462	C₂²	semidirect
87. C₁₃×#461	C₂²	semidirect
88. C₁₃×#461	C₂²	semidirect
90. C₁₃×#460	C₂²	semidirect
92. C₁₃×#459	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
100. C₁₃×#446	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
104. C₁₃×#442	C₂²	semidirect
105. C₁₃×#441	C₂²	semidirect
106. C₁₃×#441	C₂²	semidirect
108. C₁₃×#440	C₂²	semidirect
109. C₁₃×#440	C₂²	semidirect
110. C₁₃×#440	C₂²	semidirect
111. C₄×C₁₃×Q₁₆	C₂²	semidirect
113. C₄×C₁₃×SD₁₆	C₂²	semidirect
280. #61944	C₁₃	direct (N × H)
406. #3550	C₂×C₁₃	semidirect
407. #3510	C₂×C₁₃	semidirect
408. #3403	C₂×C₁₃	semidirect
409. #3402	C₂×C₁₃	semidirect
410. #3401	C₂×C₁₃	semidirect
411. #3401	C₂×C₁₃	semidirect
412. #3375	C₂×C₁₃	semidirect
413. #3373	C₂×C₁₃	semidirect
414. #3369	C₂×C₁₃	semidirect
415. #3367	C₂×C₁₃	semidirect
416. #3225	C₂×C₁₃	semidirect
417. #3224	C₂×C₁₃	semidirect
418. #3215	C₂×C₁₃	semidirect
419. #3213	C₂×C₁₃	semidirect
420. #3121	C₂×C₁₃	semidirect
421. #3118	C₂×C₁₃	semidirect
422. #3116	C₂×C₁₃	semidirect
423. #3115	C₂×C₁₃	semidirect
424. #2987	C₂×C₁₃	semidirect
496. #559	C₂²×C₁₃	semidirect
497. Q₈²	C₂²×C₁₃	semidirect
501. #556	C₂²×C₁₃	semidirect
505. D₄×Q₈	C₂²×C₁₃	semidirect
524. #497	C₂²×C₁₃	semidirect
528. #495	C₂²×C₁₃	semidirect
532. #489	C₂²×C₁₃	semidirect
533. #487	C₂²×C₁₃	semidirect
537. #477	C₂²×C₁₃	semidirect
538. #477	C₂²×C₁₃	semidirect
540. #476	C₂²×C₁₃	semidirect
541. #475	C₂²×C₁₃	semidirect
542. #475	C₂²×C₁₃	semidirect
544. #474	C₂²×C₁₃	semidirect
548. #464	C₂²×C₁₃	semidirect
549. #464	C₂²×C₁₃	semidirect
550. #464	C₂²×C₁₃	semidirect
556. #463	C₂²×C₁₃	semidirect
557. #462	C₂²×C₁₃	semidirect
558. #462	C₂²×C₁₃	semidirect
559. #461	C₂²×C₁₃	semidirect
560. #461	C₂²×C₁₃	semidirect
562. #460	C₂²×C₁₃	semidirect
564. #459	C₂²×C₁₃	semidirect
571. #446	C₂²×C₁₃	semidirect
572. #446	C₂²×C₁₃	semidirect
573. #446	C₂²×C₁₃	semidirect
574. #446	C₂²×C₁₃	semidirect
576. #442	C₂²×C₁₃	semidirect
577. #441	C₂²×C₁₃	semidirect
578. #441	C₂²×C₁₃	semidirect
580. #440	C₂²×C₁₃	semidirect
581. #440	C₂²×C₁₃	semidirect
582. #440	C₂²×C₁₃	semidirect
583. C₄×Q₁₆	C₂²×C₁₃	semidirect
585. C₄×SD₁₆	C₂²×C₁₃	semidirect
916. C₁₃	#61944	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×#3550	2
C₁₃×#3510	2
C₁₃×#3403	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3369	2
C₁₃×#3367	2
C₁₃×#3225	2
C₁₃×#3224	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3121	2
C₁₃×#3118	2
C₁₃×#3116	2
C₁₃×#3115	2
C₁₃×#2987	2
#61944	13

Subgroups — C13×#61944 #15748283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61944 #15748283