Subgroups — C₁₃×#61899 #15748238

Order 3328.

1780 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3397	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3103	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#559	C₂²	1	2	yes	complemented
20	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	—	2	2	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	4	yes	—
27	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#554	C₂²	1	2	yes	complemented
29	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#548	—	2	1	no	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	—	2	2	no	—
33	C₁₃×#542	—	2	1	no	—
34	C₁₃×#542	—	2	2	no	—
35	C₁₃×#532	C₂²	1	2	yes	—
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₁₃×#529	C₂²	1	1	yes	characteristic
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₂×C₁₃×#126	—	2	2	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₁₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	—	2	1	no	—
48	C₁₃×#497	C₂²	1	2	yes	complemented
49	C₁₃×#496	C₂²	1	4	yes	—
50	C₁₃×#495	C₂²	1	4	yes	—
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	2	yes	complemented
53	C₁₃×#489	C₂²	1	4	yes	—
54	C₁₃×#488	C₂²	1	4	yes	—
55	C₁₃×#487	C₂²	1	2	yes	complemented
56	C₁₃×#484	C₂²	1	1	yes	characteristic
57	C₁₃×#481	C₂²	1	1	yes	characteristic
58	C₁₃×#481	C₂²	1	2	yes	—
59	C₁₃×#479	C₂²	1	4	yes	complemented
60	C₁₃×#478	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	2	yes	—
67	C₁₃×#463	C₂²	1	4	yes	—
68	C₁₃×#463	C₂²	1	4	yes	—
69	C₁₃×#462	C₂²	1	2	yes	complemented
70	C₁₃×#461	C₂²	1	2	yes	complemented
71	C₁₃×#461	C₂²	1	4	yes	complemented
72	C₁₃×#460	C₂²	1	4	yes	complemented
73	C₁₃×#459	C₂²	1	2	yes	—
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#450	C₂²	1	1	yes	characteristic
76	C₁₃×#448	C₂²	1	2	yes	—
77	C₁₃×#448	C₂²	1	2	yes	—
78	C₁₃×#448	C₂²	1	2	yes	—
79	C₁₃×#447	C₂²	1	1	yes	characteristic
80	C₁₃×#447	C₂²	1	2	yes	—
81	C₁₃×#446	C₂²	1	2	yes	complemented
82	C₁₃×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
84	C₁₃×#442	C₂²	1	4	yes	—
85	C₁₃×#441	C₂²	1	4	yes	complemented
86	C₁₃×#440	C₂²	1	4	yes	complemented
87	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
88	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
89	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
90	C₄×C₁₃×D₈	C₂²	1	2	yes	—
91	C₁₃×#432	C₂²	1	1	yes	characteristic
92	C₁₃×#432	C₂²	1	2	yes	—
93	C₁₃×#431	C₂²	1	2	yes	—
94	C₁₃×#431	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×D₈	C₂³	1	2	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	2	yes	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#126	—	2	1	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#125	C₂³	1	1	yes	characteristic
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×#124	—	2	1	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	C₂³	1	4	yes	—
134	C₁₃×#124	C₂³	1	1	yes	characteristic
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	1	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	C₂³	1	1	yes	characteristic
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₁₃	D₄	1	2	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	—	2	4	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	2	no	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	2	no	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#106	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	2	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₁₃×#97	C₂³	1	4	yes	—
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₁₃	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	4	yes	—
228	#61899	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	8	4	no	—
232	C₁₃×#41	—	8	2	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	4	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
242	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	4	4	no	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₁₃×Q₁₆	—	4	4	no	—
270	C₁₃×SD₁₆	—	4	4	no	—
271	C₁₃×SD₁₆	—	4	4	no	—
272	C₁₃×SD₁₆	—	4	4	no	—
273	C₁₃×SD₁₆	—	4	2	no	—
274	C₁₃×D₈	—	4	2	no	—
275	C₁₃×D₈	—	4	4	no	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	4	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₄²×C₁₃	—	2	4	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	2	yes	—
336	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3401	C₂×C₁₃	1	4	yes	complemented
339	#3397	C₂×C₁₃	1	2	yes	complemented
340	#3394	C₂×C₁₃	1	2	yes	complemented
341	#3376	C₂×C₁₃	1	4	yes	complemented
342	#3369	C₂×C₁₃	1	2	yes	complemented
343	#3360	C₂×C₁₃	1	2	yes	complemented
344	#3218	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3213	C₂×C₁₃	1	2	yes	complemented
346	#3211	C₂×C₁₃	1	2	yes	complemented
347	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3117	C₂×C₁₃	1	2	yes	complemented
349	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3103	C₂×C₁₃	1	2	yes	complemented
352	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	4	2	no	—
357	C₂³×C₁₃	—	4	2	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	4	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	Q₈×C₁₃	—	4	4	no	—
367	Q₈×C₁₃	—	8	2	no	—
368	Q₈×C₁₃	—	8	1	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	4	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	8	2	no	—
379	D₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	4	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	4	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	4	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	8	2	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
410	C₈×C₁₃	—	2	2	no	—
411	C₈×C₁₃	—	2	4	no	—
412	C₈×C₁₃	—	2	2	no	—
413	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#559	C₂²×C₁₃	1	2	yes	complemented
415	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#556	—	2	1	no	—
417	#556	—	2	1	no	—
418	#556	—	2	2	no	—
419	#556	C₂²×C₁₃	1	2	yes	—
420	#556	C₂²×C₁₃	1	2	yes	—
421	#556	C₂²×C₁₃	1	4	yes	—
422	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#554	C₂²×C₁₃	1	2	yes	complemented
424	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	#548	—	2	1	no	—
426	#547	—	2	1	no	—
427	#547	—	2	2	no	—
428	#542	—	2	1	no	—
429	#542	—	2	2	no	—
430	#532	C₂²×C₁₃	1	2	yes	—
431	#532	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
433	#529	C₂²×C₁₃	1	1	yes	characteristic
434	#529	C₂²×C₁₃	1	2	yes	—
435	C₂×#126	—	2	2	no	—
436	C₂×#124	C₂²×C₁₃	1	2	yes	—
437	C₂×C₂²⋊Q₈	—	2	1	no	—
438	#520	—	2	1	no	—
439	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
440	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×#117	—	2	1	no	—
443	#497	C₂²×C₁₃	1	2	yes	complemented
444	#496	C₂²×C₁₃	1	4	yes	—
445	#495	C₂²×C₁₃	1	4	yes	—
446	#492	C₂²×C₁₃	1	2	yes	complemented
447	#491	C₂²×C₁₃	1	2	yes	complemented
448	#489	C₂²×C₁₃	1	4	yes	—
449	#488	C₂²×C₁₃	1	4	yes	—
450	#487	C₂²×C₁₃	1	2	yes	complemented
451	#484	C₂²×C₁₃	1	1	yes	characteristic
452	#481	C₂²×C₁₃	1	1	yes	characteristic
453	#481	C₂²×C₁₃	1	2	yes	—
454	#479	C₂²×C₁₃	1	4	yes	complemented
455	#478	C₂²×C₁₃	1	2	yes	—
456	#476	C₂²×C₁₃	1	2	yes	—
457	#475	C₂²×C₁₃	1	4	yes	complemented
458	#464	C₂²×C₁₃	1	4	yes	—
459	#464	C₂²×C₁₃	1	4	yes	complemented
460	#463	C₂²×C₁₃	1	4	yes	—
461	#463	C₂²×C₁₃	1	2	yes	—
462	#463	C₂²×C₁₃	1	4	yes	—
463	#463	C₂²×C₁₃	1	4	yes	—
464	#462	C₂²×C₁₃	1	2	yes	complemented
465	#461	C₂²×C₁₃	1	2	yes	complemented
466	#461	C₂²×C₁₃	1	4	yes	complemented
467	#460	C₂²×C₁₃	1	4	yes	complemented
468	#459	C₂²×C₁₃	1	2	yes	—
469	#451	C₂²×C₁₃	1	2	yes	—
470	#450	C₂²×C₁₃	1	1	yes	characteristic
471	#448	C₂²×C₁₃	1	2	yes	—
472	#448	C₂²×C₁₃	1	2	yes	—
473	#448	C₂²×C₁₃	1	2	yes	—
474	#447	C₂²×C₁₃	1	1	yes	characteristic
475	#447	C₂²×C₁₃	1	2	yes	—
476	#446	C₂²×C₁₃	1	2	yes	complemented
477	#446	C₂²×C₁₃	1	4	yes	complemented
478	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
479	#442	C₂²×C₁₃	1	4	yes	—
480	#441	C₂²×C₁₃	1	4	yes	complemented
481	#440	C₂²×C₁₃	1	4	yes	complemented
482	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
483	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
484	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
485	C₄×D₈	C₂²×C₁₃	1	2	yes	—
486	#432	C₂²×C₁₃	1	1	yes	characteristic
487	#432	C₂²×C₁₃	1	2	yes	—
488	#431	C₂²×C₁₃	1	2	yes	—
489	#431	C₂²×C₁₃	1	1	yes	characteristic
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	2	no	—
494	C₂²×C₁₃	—	4	1	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	8	4	no	—
502	C₂²×C₁₃	#577	1	2	yes	—
503	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	2	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	4	4	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	#575	1	2	yes	—
519	C₄×C₁₃	#585	1	2	yes	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	2	1	no	—
523	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
524	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
528	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
529	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
530	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
532	C₂×D₈	C₂³×C₁₃	1	2	yes	—
533	C₂×D₈	C₂³×C₁₃	1	4	yes	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	2	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	#127	C₂³×C₁₃	1	1	yes	characteristic
543	#127	C₂³×C₁₃	1	2	yes	—
544	#126	—	2	4	no	—
545	#126	—	2	4	no	—
546	#126	—	2	4	no	—
547	#126	—	2	4	no	—
548	#126	—	2	1	no	—
549	#126	—	2	2	no	—
550	#125	C₂³×C₁₃	1	1	yes	characteristic
551	#125	C₂³×C₁₃	1	2	yes	—
552	#124	—	2	1	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	1	no	—
557	#124	—	2	2	no	—
558	#124	C₂³×C₁₃	1	4	yes	—
559	#124	C₂³×C₁₃	1	4	yes	—
560	#124	C₂³×C₁₃	1	1	yes	characteristic
561	#124	C₂³×C₁₃	1	2	yes	—
562	#123	—	2	2	no	—
563	#123	—	2	1	no	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
576	#121	—	2	1	no	—
577	#121	—	2	2	no	—
578	#121	—	2	1	no	—
579	#121	—	2	2	no	—
580	#121	C₂³×C₁₃	1	1	yes	characteristic
581	#121	C₂³×C₁₃	1	2	yes	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
587	C₄×Q₈	D₄×C₁₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₁₃	1	2	yes	—
607	C₄×D₄	C₂³×C₁₃	1	2	yes	—
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	2	yes	—
610	#117	—	2	2	no	—
611	#117	—	2	2	no	—
612	#117	—	2	4	no	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	—	2	2	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₄²	—	2	2	no	—
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
629	#107	C₂³×C₁₃	1	2	yes	—
630	#106	C₂³×C₁₃	1	2	yes	—
631	#106	C₂³×C₁₃	1	4	yes	—
632	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
633	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
634	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
635	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
636	#103	C₂³×C₁₃	1	2	yes	—
637	#103	C₂³×C₁₃	1	4	yes	—
638	#103	C₂³×C₁₃	1	4	yes	—
639	#103	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	2	yes	—
642	#102	C₂³×C₁₃	1	2	yes	—
643	#102	C₂³×C₁₃	1	2	yes	—
644	#102	C₂³×C₁₃	1	4	yes	—
645	#102	C₂³×C₁₃	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
647	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
649	#97	C₂³×C₁₃	1	4	yes	—
650	#97	C₂³×C₁₃	1	2	yes	—
651	C₄×C₈	C₂³×C₁₃	1	2	yes	—
652	C₄×C₈	C₂³×C₁₃	1	4	yes	—
653	C₂×C₁₃	—	2	2	no	—
654	C₂×C₁₃	—	8	2	no	—
655	C₂×C₁₃	—	8	1	no	—
656	C₂×C₁₃	—	8	2	no	—
657	C₂×C₁₃	#3487	1	1	yes	characteristic
658	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
659	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
660	C₂⁴	—	2	1	no	—
661	#41	—	4	4	no	—
662	#41	—	8	4	no	—
663	#41	—	8	2	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
670	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
673	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	4	2	no	—
682	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	Q₁₆	—	4	4	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	4	no	—
703	SD₁₆	—	4	4	no	—
704	SD₁₆	—	4	2	no	—
705	D₈	—	4	2	no	—
706	D₈	—	4	4	no	—
707	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
709	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
730	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
732	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₄²	C₂×D₄×C₁₃	1	2	yes	—
761	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₁₃	1	2	yes	—
763	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₄²	C₂⁴×C₁₃	1	2	yes	—
765	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₁₃	1	2	yes	—
767	C₁₃	#61899	1	1	yes	characteristic, direct product factor, Sylow
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	4	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	4	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
825	C₈	—	2	2	no	—
826	C₈	—	2	4	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	8	4	no	—
840	C₂²	C₁₃×#577	1	2	yes	—
841	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	4	no	—
855	C₄	—	4	1	no	—
856	C₄	C₁₃×#575	1	2	yes	—
857	C₄	C₁₃×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₁₃×#3487	1	1	yes	characteristic
863	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
864	C₂	C₂×C₁₃×#577	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3522	C₂	semidirect
2. C₂×C₁₃×#556	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3397	C₂	semidirect
5. C₁₃×#3394	C₂	semidirect
6. C₁₃×#3376	C₂	semidirect
7. C₁₃×#3369	C₂	semidirect
8. C₁₃×#3360	C₂	semidirect
9. C₁₃×#3218	C₂	semidirect
10. C₁₃×#3213	C₂	semidirect
11. C₁₃×#3211	C₂	semidirect
12. C₁₃×#3206	C₂	semidirect
13. C₁₃×#3117	C₂	semidirect
14. C₁₃×#3109	C₂	semidirect
15. C₁₃×#3105	C₂	semidirect
16. C₁₃×#3103	C₂	semidirect
17. C₁₃×#2984	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#559	C₂²	semidirect
20. Q₈²×C₁₃	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
48. C₁₃×#497	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
55. C₁₃×#487	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
71. C₁₃×#461	C₂²	semidirect
72. C₁₃×#460	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₈×Q₈×C₁₃	C₂²	semidirect
85. C₁₃×#441	C₂²	semidirect
86. C₁₃×#440	C₂²	semidirect
88. C₄×C₁₃×SD₁₆	C₂²	semidirect
89. C₄×C₁₃×SD₁₆	C₂²	semidirect
228. #61899	C₁₃	direct (N × H)
336. #3522	C₂×C₁₃	semidirect
337. C₂×#556	C₂×C₁₃	semidirect
338. #3401	C₂×C₁₃	semidirect
339. #3397	C₂×C₁₃	semidirect
340. #3394	C₂×C₁₃	semidirect
341. #3376	C₂×C₁₃	semidirect
342. #3369	C₂×C₁₃	semidirect
343. #3360	C₂×C₁₃	semidirect
344. #3218	C₂×C₁₃	semidirect
345. #3213	C₂×C₁₃	semidirect
346. #3211	C₂×C₁₃	semidirect
347. #3206	C₂×C₁₃	semidirect
348. #3117	C₂×C₁₃	semidirect
349. #3109	C₂×C₁₃	semidirect
350. #3105	C₂×C₁₃	semidirect
351. #3103	C₂×C₁₃	semidirect
352. #2984	C₂×C₁₃	semidirect
413. #559	C₂²×C₁₃	semidirect
414. #559	C₂²×C₁₃	semidirect
415. Q₈²	C₂²×C₁₃	semidirect
422. #554	C₂²×C₁₃	semidirect
423. #554	C₂²×C₁₃	semidirect
424. #550	C₂²×C₁₃	semidirect
443. #497	C₂²×C₁₃	semidirect
446. #492	C₂²×C₁₃	semidirect
447. #491	C₂²×C₁₃	semidirect
450. #487	C₂²×C₁₃	semidirect
454. #479	C₂²×C₁₃	semidirect
457. #475	C₂²×C₁₃	semidirect
459. #464	C₂²×C₁₃	semidirect
464. #462	C₂²×C₁₃	semidirect
465. #461	C₂²×C₁₃	semidirect
466. #461	C₂²×C₁₃	semidirect
467. #460	C₂²×C₁₃	semidirect
476. #446	C₂²×C₁₃	semidirect
477. #446	C₂²×C₁₃	semidirect
478. C₈×Q₈	C₂²×C₁₃	semidirect
480. #441	C₂²×C₁₃	semidirect
481. #440	C₂²×C₁₃	semidirect
483. C₄×SD₁₆	C₂²×C₁₃	semidirect
484. C₄×SD₁₆	C₂²×C₁₃	semidirect
767. C₁₃	#61899	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×#3522	2
C₂×C₁₃×#556	2
C₁₃×#3401	2
C₁₃×#3397	2
C₁₃×#3394	2
C₁₃×#3376	2
C₁₃×#3369	2
C₁₃×#3360	2
C₁₃×#3218	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3206	2
C₁₃×#3117	2
C₁₃×#3109	2
C₁₃×#3105	2
C₁₃×#3103	2
C₁₃×#2984	2
#61899	13

Subgroups — C13×#61899 #15748238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61899 #15748238