Subgroups — C₁₃×#62139 #15748478

Order 3328.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3236	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#557	—	2	1	no	—
26	C₁₃×#557	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	1	yes	characteristic
28	C₁₃×#554	—	2	1	no	—
29	C₁₃×#554	—	2	2	no	—
30	C₁₃×#554	C₂²	1	1	yes	characteristic
31	C₁₃×#554	C₂²	1	1	yes	characteristic
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#554	C₂²	1	2	yes	—
34	C₁₃×#553	C₂²	1	2	yes	—
35	C₁₃×#552	—	2	2	no	—
36	C₁₃×#552	—	2	1	no	—
37	C₁₃×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
40	C₁₃×#547	—	2	1	no	—
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#541	—	2	1	no	—
43	C₁₃×#539	—	2	2	no	—
44	C₁₃×#533	—	2	2	no	—
45	C₁₃×#533	—	2	1	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	2	yes	—
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₂×C₁₃×#125	C₂²	1	2	yes	—
52	C₁₃×#520	—	2	1	no	—
53	C₄×C₁₃×#41	—	2	1	no	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#500	C₂²	1	1	yes	characteristic
60	C₁₃×#498	C₂²	1	1	yes	characteristic
61	C₁₃×#491	C₂²	1	2	yes	—
62	C₁₃×#491	C₂²	1	2	yes	—
63	C₁₃×#487	C₂²	1	1	yes	characteristic
64	C₁₃×#487	C₂²	1	1	yes	characteristic
65	C₁₃×#485	C₂²	1	2	yes	—
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#484	C₂²	1	2	yes	—
68	C₁₃×#484	C₂²	1	2	yes	—
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	2	yes	—
71	C₁₃×#483	C₂²	1	2	yes	—
72	C₁₃×#483	C₂²	1	1	yes	characteristic
73	C₁₃×#481	C₂²	1	2	yes	—
74	C₁₃×#480	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#479	C₂²	1	1	yes	characteristic
78	C₁₃×#479	C₂²	1	2	yes	—
79	C₁₃×#479	C₂²	1	2	yes	—
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#479	C₂²	1	2	yes	—
83	C₁₃×#479	C₂²	1	2	yes	—
84	C₁₃×#479	C₂²	1	1	yes	characteristic
85	C₁₃×#479	C₂²	1	2	yes	—
86	C₁₃×#477	C₂²	1	1	yes	characteristic
87	C₁₃×#477	C₂²	1	1	yes	characteristic
88	C₁₃×#477	C₂²	1	1	yes	characteristic
89	C₁₃×#476	C₂²	1	1	yes	characteristic
90	C₁₃×#475	C₂²	1	1	yes	characteristic
91	C₁₃×#475	C₂²	1	1	yes	characteristic
92	C₁₃×#475	C₂²	1	2	yes	—
93	C₁₃×#474	C₂²	1	2	yes	—
94	C₁₃×#470	C₂²	1	2	yes	—
95	C₁₃×#468	C₂²	1	2	yes	—
96	C₁₃×#467	C₂²	1	2	yes	—
97	C₁₃×#467	C₂²	1	2	yes	—
98	C₁₃×#465	C₂²	1	2	yes	—
99	C₁₃×#465	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	1	yes	characteristic
101	C₁₃×#464	C₂²	1	1	yes	characteristic
102	C₁₃×#464	C₂²	1	2	yes	—
103	C₁₃×#462	C₂²	1	1	yes	characteristic
104	C₁₃×#462	C₂²	1	2	yes	—
105	C₁₃×#461	C₂²	1	1	yes	characteristic
106	C₁₃×#461	C₂²	1	2	yes	—
107	C₁₃×#451	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	1	yes	characteristic
109	C₁₃×#448	C₂²	1	2	yes	—
110	C₁₃×#448	C₂²	1	1	yes	characteristic
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#441	C₂²	1	2	yes	—
114	C₁₃×#441	C₂²	1	2	yes	—
115	C₁₃×#440	C₂²	1	2	yes	—
116	C₁₃×#440	C₂²	1	2	yes	—
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#435	C₂²	1	2	yes	—
122	C₁₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
125	C₁₃×#432	C₂²	1	2	yes	—
126	C₁₃×#431	C₂²	1	1	yes	characteristic
127	C₁₃×#428	C₂²	1	2	yes	—
128	C₂×C₁₃×#107	C₂²	1	2	yes	—
129	C₂×C₁₃×#106	C₂²	1	2	yes	—
130	C₁₃×#423	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
132	C₁₃×#419	C₂²	1	2	yes	—
133	C₂×C₁₃×#103	C₂²	1	2	yes	—
134	C₂×C₁₃×#103	C₂²	1	2	yes	—
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
146	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
148	C₁₃×C₄⋊Q₈	—	2	1	no	—
149	C₁₃×C₄⋊Q₈	—	2	1	no	—
150	C₁₃×C₄⋊Q₈	—	2	2	no	—
151	C₁₃×C₄⋊Q₈	—	2	1	no	—
152	C₁₃×C₄⋊Q₈	—	2	2	no	—
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	—	2	1	no	—
163	C₁₃×#125	—	2	1	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	1	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	1	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	C₂³	1	1	yes	characteristic
175	C₁₃×#125	C₂³	1	2	yes	—
176	C₁₃×#125	C₂³	1	2	yes	—
177	C₁₃×#125	C₂³	1	2	yes	—
178	C₁₃×#124	C₂³	1	1	yes	characteristic
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	1	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	1	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	C₂³	1	2	yes	—
205	C₁₃×#121	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₁₃	D₄	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₁₃×#117	—	2	2	no	—
243	C₁₃×#117	—	2	1	no	—
244	C₁₃×#117	—	2	2	no	—
245	C₁₃×#117	—	2	1	no	—
246	C₁₃×#117	—	2	2	no	—
247	C₁₃×#117	D₄	1	1	yes	characteristic
248	C₁₃×#117	D₄	1	2	yes	—
249	C₁₃×#117	C₂³	1	2	yes	—
250	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
253	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₁₃	—	2	2	no	—
260	C₂×C₄²×C₁₃	—	2	1	no	—
261	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
262	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
263	C₁₃×#107	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	2	yes	—
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	1	yes	characteristic
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#103	C₂³	1	2	yes	—
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	#62139	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	4	no	—
314	C₁₃×#41	—	4	4	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	—	2	2	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	4	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	4	2	no	—
324	C₂×Q₈×C₁₃	—	4	1	no	—
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	—	2	1	no	—
336	C₂²×C₄×C₁₃	—	2	2	no	—
337	C₂²×C₄×C₁₃	—	2	2	no	—
338	C₂²×C₄×C₁₃	—	2	1	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	2	no	—
343	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₁₃×Q₁₆	—	2	2	no	—
350	C₁₃×Q₁₆	—	4	1	no	—
351	C₁₃×Q₁₆	—	4	2	no	—
352	C₁₃×SD₁₆	—	2	2	no	—
353	C₁₃×SD₁₆	—	4	1	no	—
354	C₁₃×SD₁₆	—	4	2	no	—
355	C₁₃×M₁₆	—	4	2	no	—
356	C₂×C₈×C₁₃	—	4	2	no	—
357	C₂×C₈×C₁₃	—	4	2	no	—
358	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	1	no	—
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	2	no	—
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	1	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	1	no	—
417	C₁₃×C₂²⋊C₄	—	2	1	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₄²×C₁₃	—	2	1	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	1	no	—
427	C₄²×C₁₃	—	2	2	no	—
428	C₄²×C₁₃	—	2	1	no	—
429	C₄²×C₁₃	—	2	2	no	—
430	C₄²×C₁₃	—	2	1	no	—
431	C₄²×C₁₃	—	2	2	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	1	no	—
434	C₄²×C₁₃	C₂×D₄	1	2	yes	—
435	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₁₃	C₂×D₄	1	2	yes	—
438	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₁₃	C₂⁴	1	2	yes	—
440	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
441	#3515	C₂×C₁₃	1	1	yes	characteristic
442	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
443	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3346	C₂×C₁₃	1	2	yes	complemented
448	#3344	C₂×C₁₃	1	2	yes	complemented
449	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3335	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3320	C₂×C₁₃	1	2	yes	complemented
452	#3312	C₂×C₁₃	1	2	yes	complemented
453	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3252	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3248	C₂×C₁₃	1	2	yes	complemented
457	#3236	C₂×C₁₃	1	2	yes	complemented
458	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3117	C₂×C₁₃	1	2	yes	complemented
460	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
462	C₂×#479	C₂×C₁₃	1	2	yes	complemented
463	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
464	C₂³×C₁₃	—	2	1	no	—
465	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
467	Q₈×C₁₃	—	2	2	no	—
468	Q₈×C₁₃	—	2	1	no	—
469	Q₈×C₁₃	—	2	1	no	—
470	Q₈×C₁₃	—	2	2	no	—
471	Q₈×C₁₃	—	2	1	no	—
472	Q₈×C₁₃	—	2	1	no	—
473	Q₈×C₁₃	—	2	2	no	—
474	Q₈×C₁₃	—	2	1	no	—
475	Q₈×C₁₃	—	4	4	no	—
476	Q₈×C₁₃	—	4	2	no	—
477	Q₈×C₁₃	—	4	2	no	—
478	Q₈×C₁₃	—	8	2	no	—
479	Q₈×C₁₃	—	8	1	no	—
480	Q₈×C₁₃	—	8	1	no	—
481	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
482	D₄×C₁₃	—	2	4	no	—
483	D₄×C₁₃	—	2	1	no	—
484	D₄×C₁₃	—	2	1	no	—
485	D₄×C₁₃	—	4	4	no	—
486	D₄×C₁₃	—	8	1	no	—
487	D₄×C₁₃	#137	1	4	yes	—
488	C₂×C₄×C₁₃	—	2	4	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	2	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	2	no	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	2	no	—
500	C₂×C₄×C₁₃	—	2	2	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	2	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	4	2	no	—
506	C₂×C₄×C₁₃	—	4	1	no	—
507	C₂×C₄×C₁₃	—	4	4	no	—
508	C₂×C₄×C₁₃	—	4	2	no	—
509	C₂×C₄×C₁₃	—	4	4	no	—
510	C₂×C₄×C₁₃	—	4	2	no	—
511	C₂×C₄×C₁₃	—	8	2	no	—
512	C₂×C₄×C₁₃	—	8	2	no	—
513	C₂×C₄×C₁₃	—	8	1	no	—
514	C₂×C₄×C₁₃	—	8	2	no	—
515	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
524	C₈×C₁₃	—	2	1	no	—
525	C₈×C₁₃	—	2	1	no	—
526	C₈×C₁₃	—	2	1	no	—
527	C₈×C₁₃	—	2	1	no	—
528	C₈×C₁₃	—	2	2	no	—
529	C₈×C₁₃	—	2	2	no	—
530	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
531	#557	—	2	1	no	—
532	#557	C₂²×C₁₃	1	1	yes	characteristic
533	#557	C₂²×C₁₃	1	1	yes	characteristic
534	#554	—	2	1	no	—
535	#554	—	2	2	no	—
536	#554	C₂²×C₁₃	1	1	yes	characteristic
537	#554	C₂²×C₁₃	1	1	yes	characteristic
538	#554	C₂²×C₁₃	1	1	yes	characteristic
539	#554	C₂²×C₁₃	1	2	yes	—
540	#553	C₂²×C₁₃	1	2	yes	—
541	#552	—	2	2	no	—
542	#552	—	2	1	no	—
543	#552	C₂²×C₁₃	1	2	yes	—
544	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
545	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
546	#547	—	2	1	no	—
547	#547	C₂²×C₁₃	1	1	yes	characteristic
548	#541	—	2	1	no	—
549	#539	—	2	2	no	—
550	#533	—	2	2	no	—
551	#533	—	2	1	no	—
552	#533	C₂²×C₁₃	1	1	yes	characteristic
553	#533	C₂²×C₁₃	1	2	yes	—
554	#533	C₂²×C₁₃	1	1	yes	characteristic
555	#529	C₂²×C₁₃	1	1	yes	characteristic
556	#529	C₂²×C₁₃	1	2	yes	—
557	C₂×#125	C₂²×C₁₃	1	2	yes	—
558	#520	—	2	1	no	—
559	C₄×#41	—	2	1	no	—
560	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
561	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
562	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
563	#501	C₂²×C₁₃	1	2	yes	—
564	#501	C₂²×C₁₃	1	2	yes	—
565	#500	C₂²×C₁₃	1	1	yes	characteristic
566	#498	C₂²×C₁₃	1	1	yes	characteristic
567	#491	C₂²×C₁₃	1	2	yes	—
568	#491	C₂²×C₁₃	1	2	yes	—
569	#487	C₂²×C₁₃	1	1	yes	characteristic
570	#487	C₂²×C₁₃	1	1	yes	characteristic
571	#485	C₂²×C₁₃	1	2	yes	—
572	#485	C₂²×C₁₃	1	2	yes	—
573	#484	C₂²×C₁₃	1	2	yes	—
574	#484	C₂²×C₁₃	1	2	yes	—
575	#484	C₂²×C₁₃	1	2	yes	—
576	#483	C₂²×C₁₃	1	2	yes	—
577	#483	C₂²×C₁₃	1	1	yes	characteristic
578	#483	C₂²×C₁₃	1	2	yes	—
579	#481	C₂²×C₁₃	1	2	yes	—
580	#480	C₂²×C₁₃	1	1	yes	characteristic
581	#479	C₂²×C₁₃	1	1	yes	characteristic
582	#479	C₂²×C₁₃	1	2	yes	—
583	#479	C₂²×C₁₃	1	2	yes	—
584	#479	C₂²×C₁₃	1	2	yes	—
585	#479	C₂²×C₁₃	1	2	yes	—
586	#479	C₂²×C₁₃	1	2	yes	—
587	#479	C₂²×C₁₃	1	2	yes	—
588	#479	C₂²×C₁₃	1	2	yes	—
589	#479	C₂²×C₁₃	1	2	yes	—
590	#479	C₂²×C₁₃	1	1	yes	characteristic
591	#479	C₂²×C₁₃	1	2	yes	—
592	#477	C₂²×C₁₃	1	1	yes	characteristic
593	#477	C₂²×C₁₃	1	1	yes	characteristic
594	#477	C₂²×C₁₃	1	1	yes	characteristic
595	#476	C₂²×C₁₃	1	1	yes	characteristic
596	#475	C₂²×C₁₃	1	1	yes	characteristic
597	#475	C₂²×C₁₃	1	1	yes	characteristic
598	#475	C₂²×C₁₃	1	2	yes	—
599	#474	C₂²×C₁₃	1	2	yes	—
600	#470	C₂²×C₁₃	1	2	yes	—
601	#468	C₂²×C₁₃	1	2	yes	—
602	#467	C₂²×C₁₃	1	2	yes	—
603	#467	C₂²×C₁₃	1	2	yes	—
604	#465	C₂²×C₁₃	1	2	yes	—
605	#465	C₂²×C₁₃	1	2	yes	—
606	#464	C₂²×C₁₃	1	1	yes	characteristic
607	#464	C₂²×C₁₃	1	1	yes	characteristic
608	#464	C₂²×C₁₃	1	2	yes	—
609	#462	C₂²×C₁₃	1	2	yes	—
610	#462	C₂²×C₁₃	1	1	yes	characteristic
611	#461	C₂²×C₁₃	1	2	yes	—
612	#461	C₂²×C₁₃	1	1	yes	characteristic
613	#451	C₂²×C₁₃	1	1	yes	characteristic
614	#451	C₂²×C₁₃	1	2	yes	—
615	#448	C₂²×C₁₃	1	1	yes	characteristic
616	#448	C₂²×C₁₃	1	2	yes	—
617	#446	C₂²×C₁₃	1	1	yes	characteristic
618	#446	C₂²×C₁₃	1	1	yes	characteristic
619	#441	C₂²×C₁₃	1	2	yes	—
620	#441	C₂²×C₁₃	1	2	yes	—
621	#440	C₂²×C₁₃	1	2	yes	—
622	#440	C₂²×C₁₃	1	2	yes	—
623	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
624	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
625	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
626	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
627	#435	C₂²×C₁₃	1	2	yes	—
628	#435	C₂²×C₁₃	1	2	yes	—
629	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
630	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
631	#432	C₂²×C₁₃	1	2	yes	—
632	#431	C₂²×C₁₃	1	1	yes	characteristic
633	#428	C₂²×C₁₃	1	2	yes	—
634	C₂×#107	C₂²×C₁₃	1	2	yes	—
635	C₂×#106	C₂²×C₁₃	1	2	yes	—
636	#423	C₂²×C₁₃	1	1	yes	characteristic
637	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
638	#419	C₂²×C₁₃	1	2	yes	—
639	C₂×#103	C₂²×C₁₃	1	2	yes	—
640	C₂×#103	C₂²×C₁₃	1	2	yes	—
641	C₂²×C₁₃	—	2	2	no	—
642	C₂²×C₁₃	—	2	2	no	—
643	C₂²×C₁₃	—	2	1	no	—
644	C₂²×C₁₃	—	2	1	no	—
645	C₂²×C₁₃	—	2	1	no	—
646	C₂²×C₁₃	—	4	1	no	—
647	C₂²×C₁₃	—	4	1	no	—
648	C₂²×C₁₃	—	4	1	no	—
649	C₂²×C₁₃	C₂×#137	1	4	yes	—
650	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
651	C₄×C₁₃	—	2	1	no	—
652	C₄×C₁₃	—	2	2	no	—
653	C₄×C₁₃	—	2	1	no	—
654	C₄×C₁₃	—	2	2	no	—
655	C₄×C₁₃	—	2	1	no	—
656	C₄×C₁₃	—	2	2	no	—
657	C₄×C₁₃	—	2	1	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	4	1	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	—	4	2	no	—
662	C₄×C₁₃	—	4	2	no	—
663	C₄×C₁₃	—	4	1	no	—
664	C₄×C₁₃	—	4	2	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	1	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	2	no	—
669	C₄×C₁₃	C₂×#137	1	2	yes	—
670	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
671	C₄×C₁₃	#585	1	1	yes	characteristic
672	C₂×#41	—	2	1	no	—
673	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
674	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
675	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
682	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
683	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
684	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
685	C₄⋊Q₈	—	2	1	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	2	no	—
688	C₄⋊Q₈	—	2	1	no	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
692	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
695	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	1	no	—
700	#125	—	2	1	no	—
701	#125	—	2	2	no	—
702	#125	—	2	1	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	1	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	1	no	—
710	#125	—	2	2	no	—
711	#125	C₂³×C₁₃	1	1	yes	characteristic
712	#125	C₂³×C₁₃	1	2	yes	—
713	#125	C₂³×C₁₃	1	2	yes	—
714	#125	C₂³×C₁₃	1	2	yes	—
715	#124	C₂³×C₁₃	1	1	yes	characteristic
716	#123	—	2	2	no	—
717	#123	—	2	1	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
737	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
738	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
739	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
740	#121	—	2	2	no	—
741	#121	C₂³×C₁₃	1	2	yes	—
742	#121	C₂³×C₁₃	1	1	yes	characteristic
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
757	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
759	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
760	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
762	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
763	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
774	C₄×D₄	D₄×C₁₃	1	2	yes	—
775	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₁₃	1	2	yes	—
777	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
778	C₄×D₄	C₂³×C₁₃	1	2	yes	—
779	#117	—	2	2	no	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	2	1	no	—
783	#117	—	2	2	no	—
784	#117	D₄×C₁₃	1	1	yes	characteristic
785	#117	D₄×C₁₃	1	2	yes	—
786	#117	C₂³×C₁₃	1	2	yes	—
787	C₂×C₄⋊C₄	—	2	2	no	—
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	2	no	—
790	C₂×C₄⋊C₄	—	2	2	no	—
791	C₂×C₄⋊C₄	—	2	1	no	—
792	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
795	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
796	C₂×C₄²	—	2	2	no	—
797	C₂×C₄²	—	2	1	no	—
798	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
799	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
800	#107	C₂³×C₁₃	1	1	yes	characteristic
801	#107	C₂³×C₁₃	1	2	yes	—
802	#107	C₂³×C₁₃	1	2	yes	—
803	#107	C₂³×C₁₃	1	2	yes	—
804	#107	C₂³×C₁₃	1	2	yes	—
805	#107	C₂³×C₁₃	1	1	yes	characteristic
806	#107	C₂³×C₁₃	1	2	yes	—
807	#106	C₂³×C₁₃	1	1	yes	characteristic
808	#106	C₂³×C₁₃	1	2	yes	—
809	#106	C₂³×C₁₃	1	2	yes	—
810	#106	C₂³×C₁₃	1	2	yes	—
811	#106	C₂³×C₁₃	1	2	yes	—
812	#106	C₂³×C₁₃	1	1	yes	characteristic
813	#106	C₂³×C₁₃	1	2	yes	—
814	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
818	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
821	#103	C₂³×C₁₃	1	1	yes	characteristic
822	#103	C₂³×C₁₃	1	1	yes	characteristic
823	#103	C₂³×C₁₃	1	2	yes	—
824	#103	C₂³×C₁₃	1	2	yes	—
825	#103	C₂³×C₁₃	1	2	yes	—
826	#103	C₂³×C₁₃	1	2	yes	—
827	#103	C₂³×C₁₃	1	2	yes	—
828	#103	C₂³×C₁₃	1	2	yes	—
829	#103	C₂³×C₁₃	1	2	yes	—
830	#103	C₂³×C₁₃	1	2	yes	—
831	#103	C₂³×C₁₃	1	1	yes	characteristic
832	#103	C₂³×C₁₃	1	1	yes	characteristic
833	#103	C₂³×C₁₃	1	1	yes	characteristic
834	#103	C₂³×C₁₃	1	1	yes	characteristic
835	#103	C₂³×C₁₃	1	2	yes	—
836	#103	C₂³×C₁₃	1	2	yes	—
837	#103	C₂³×C₁₃	1	2	yes	—
838	#102	C₂³×C₁₃	1	1	yes	characteristic
839	#102	C₂³×C₁₃	1	1	yes	characteristic
840	#102	C₂³×C₁₃	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
842	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
845	#97	C₂³×C₁₃	1	2	yes	—
846	#97	C₂³×C₁₃	1	2	yes	—
847	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
849	C₂×C₁₃	—	2	4	no	—
850	C₂×C₁₃	—	4	1	no	—
851	C₂×C₁₃	—	8	1	no	—
852	C₂×C₁₃	#3489	1	1	yes	characteristic
853	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
854	C₂×C₁₃	#3584	1	1	yes	characteristic
855	#41	—	2	4	no	—
856	#41	—	4	4	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	4	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	1	no	—
867	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
869	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
875	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
886	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
887	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
888	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
891	Q₁₆	—	2	2	no	—
892	Q₁₆	—	4	1	no	—
893	Q₁₆	—	4	2	no	—
894	SD₁₆	—	2	2	no	—
895	SD₁₆	—	4	1	no	—
896	SD₁₆	—	4	2	no	—
897	M₁₆	—	4	2	no	—
898	C₂×C₈	—	4	2	no	—
899	C₂×C₈	—	4	2	no	—
900	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
905	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
964	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
965	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	C₂×D₄×C₁₃	1	2	yes	—
977	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
978	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
979	C₄²	C₂×D₄×C₁₃	1	2	yes	—
980	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
981	C₄²	C₂⁴×C₁₃	1	2	yes	—
982	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₁₃	#62139	1	1	yes	characteristic, direct product factor, Sylow
984	C₂³	—	2	1	no	—
985	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
986	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
987	Q₈	—	2	2	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	4	4	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	1	no	—
1001	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	4	4	no	—
1006	D₄	—	8	1	no	—
1007	D₄	C₁₃×#137	1	4	yes	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	1	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1041	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	2	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	C₂×C₁₃×#137	1	4	yes	—
1059	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	C₂×C₁₃×#137	1	2	yes	—
1079	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1080	C₄	C₁₃×#585	1	1	yes	characteristic
1081	C₂	—	2	4	no	—
1082	C₂	—	4	1	no	—
1083	C₂	—	8	1	no	—
1084	C₂	C₁₃×#3489	1	1	yes	characteristic
1085	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
1086	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3372	C₂	semidirect
7. C₁₃×#3346	C₂	semidirect
8. C₁₃×#3344	C₂	semidirect
9. C₁₃×#3338	C₂	semidirect
10. C₁₃×#3335	C₂	semidirect
11. C₁₃×#3320	C₂	semidirect
12. C₁₃×#3312	C₂	semidirect
13. C₁₃×#3299	C₂	semidirect
14. C₁₃×#3298	C₂	semidirect
15. C₁₃×#3252	C₂	semidirect
16. C₁₃×#3248	C₂	semidirect
17. C₁₃×#3236	C₂	semidirect
18. C₁₃×#3231	C₂	semidirect
19. C₁₃×#3117	C₂	semidirect
20. C₁₃×#3108	C₂	semidirect
21. C₁₃×#3078	C₂	semidirect
22. C₂×C₁₃×#479	C₂	semidirect
23. C₁₃×#2990	C₂	semidirect
312. #62139	C₁₃	direct (N × H)
442. Q₈×#41	C₂×C₁₃	semidirect
443. #3387	C₂×C₁₃	semidirect
444. #3385	C₂×C₁₃	semidirect
445. #3374	C₂×C₁₃	semidirect
446. #3372	C₂×C₁₃	semidirect
447. #3346	C₂×C₁₃	semidirect
448. #3344	C₂×C₁₃	semidirect
449. #3338	C₂×C₁₃	semidirect
450. #3335	C₂×C₁₃	semidirect
451. #3320	C₂×C₁₃	semidirect
452. #3312	C₂×C₁₃	semidirect
453. #3299	C₂×C₁₃	semidirect
454. #3298	C₂×C₁₃	semidirect
455. #3252	C₂×C₁₃	semidirect
456. #3248	C₂×C₁₃	semidirect
457. #3236	C₂×C₁₃	semidirect
458. #3231	C₂×C₁₃	semidirect
459. #3117	C₂×C₁₃	semidirect
460. #3108	C₂×C₁₃	semidirect
461. #3078	C₂×C₁₃	semidirect
462. C₂×#479	C₂×C₁₃	semidirect
463. #2990	C₂×C₁₃	semidirect
983. C₁₃	#62139	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×#3515	2
Q₈×C₁₃×#41	2
C₁₃×#3387	2
C₁₃×#3385	2
C₁₃×#3374	2
C₁₃×#3372	2
C₁₃×#3346	2
C₁₃×#3344	2
C₁₃×#3338	2
C₁₃×#3335	2
C₁₃×#3320	2
C₁₃×#3312	2
C₁₃×#3299	2
C₁₃×#3298	2
C₁₃×#3252	2
C₁₃×#3248	2
C₁₃×#3236	2
C₁₃×#3231	2
C₁₃×#3117	2
C₁₃×#3108	2
C₁₃×#3078	2
C₂×C₁₃×#479	2
C₁₃×#2990	2
#62139	13

Subgroups — C13×#62139 #15748478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62139 #15748478