Subgroups — C₁₃×#60923 #15747262

Order 3328.

1812 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3260	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3254	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#541	C₂²	1	4	yes	complemented
31	C₁₃×#540	—	2	1	no	—
32	C₁₃×#540	C₂²	1	2	yes	—
33	C₁₃×#538	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#535	C₂²	1	1	yes	characteristic
37	C₁₃×#535	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	2	yes	complemented
40	C₁₃×#533	C₂²	1	2	yes	complemented
41	C₁₃×#532	—	2	1	no	—
42	C₁₃×#532	C₂²	1	2	yes	—
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	1	no	—
45	C₁₃×#529	C₂²	1	2	yes	—
46	C₁₃×#525	—	2	2	no	—
47	C₁₃×#519	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#479	C₂²	1	2	yes	complemented
52	C₁₃×#479	C₂²	1	4	yes	complemented
53	C₁₃×#479	C₂²	1	4	yes	complemented
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#478	C₂²	1	2	yes	complemented
56	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#477	C₂²	1	4	yes	complemented
58	C₁₃×#476	C₂²	1	2	yes	—
59	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#475	C₂²	1	4	yes	complemented
62	C₁₃×#474	C₂²	1	2	yes	—
63	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#470	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	—
66	C₁₃×#468	C₂²	1	4	yes	—
67	C₁₃×#468	C₂²	1	4	yes	complemented
68	C₁₃×#467	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	—
70	C₁₃×#465	C₂²	1	4	yes	—
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#464	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	2	yes	complemented
75	C₁₃×#462	C₂²	1	2	yes	complemented
76	C₁₃×#461	C₂²	1	2	yes	—
77	C₁₃×#461	C₂²	1	2	yes	—
78	C₁₃×#461	C₂²	1	4	yes	—
79	C₁₃×#461	C₂²	1	2	yes	complemented
80	C₁₃×#461	C₂²	1	2	yes	complemented
81	C₁₃×#460	C₂²	1	4	yes	—
82	C₁₃×#460	C₂²	1	4	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#427	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₁₃×#424	C₂²	1	4	yes	complemented
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	complemented
89	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₁₃×#419	C₂²	1	2	yes	—
92	C₁₃×#418	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₁₃×#137	—	4	4	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×SD₁₆	—	4	4	no	—
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	C₁₃×#131	—	4	4	no	—
108	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
110	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
112	C₁₃×C₄⋊Q₈	—	2	2	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×#127	—	2	1	no	—
122	C₁₃×#127	C₂³	1	2	yes	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#126	—	2	4	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	—	2	4	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	—	2	2	no	—
132	C₁₃×#125	C₂³	1	2	yes	—
133	C₁₃×#125	C₂³	1	2	yes	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	C₂³	1	2	yes	—
139	C₁₃×#123	—	2	4	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#121	C₂³	1	2	yes	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#120	—	2	2	no	—
165	C₁₃×#120	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	2	no	—
167	C₄×Q₈×C₁₃	—	2	2	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	—	2	1	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	2	no	—
172	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	4	no	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	C₂³	1	2	yes	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	2	yes	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×#106	C₂³	1	2	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	2	yes	—
225	C₁₃×#103	C₂³	1	4	yes	—
226	C₁₃×#103	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×#102	C₂³	1	4	yes	—
231	#60923	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	1	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	8	4	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	8	2	no	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₁₃×Q₁₆	—	4	4	no	—
275	C₁₃×SD₁₆	—	4	4	no	—
276	C₁₃×SD₁₆	—	4	4	no	—
277	C₁₃×SD₁₆	—	4	4	no	—
278	C₁₃×M₁₆	—	2	4	no	—
279	C₁₃×M₁₆	—	4	4	no	—
280	C₂×C₈×C₁₃	—	2	4	no	—
281	C₂×C₈×C₁₃	—	4	4	no	—
282	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
283	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	4	no	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3460	C₂×C₁₃	1	1	yes	characteristic
345	#3260	C₂×C₁₃	1	4	yes	complemented
346	#3258	C₂×C₁₃	1	4	yes	complemented
347	#3254	C₂×C₁₃	1	2	yes	complemented
348	#3252	C₂×C₁₃	1	2	yes	complemented
349	#3248	C₂×C₁₃	1	2	yes	complemented
350	#3246	C₂×C₁₃	1	2	yes	complemented
351	#3082	C₂×C₁₃	1	2	yes	complemented
352	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#3063	C₂×C₁₃	1	2	yes	complemented
355	#3057	C₂×C₁₃	1	2	yes	complemented
356	#3043	C₂×C₁₃	1	2	yes	complemented
357	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	8	1	no	—
364	C₂³×C₁₃	—	8	1	no	—
365	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
366	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	4	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	4	no	—
371	Q₈×C₁₃	—	2	1	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	4	4	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	—	8	2	no	—
376	D₄×C₁₃	—	2	4	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	8	2	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	—	8	2	no	—
387	D₄×C₁₃	—	8	2	no	—
388	D₄×C₁₃	—	8	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	2	no	—
402	C₂×C₄×C₁₃	—	4	4	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	8	1	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	—	8	1	no	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	—	2	2	no	—
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	4	no	—
423	C₂×#137	C₂²×C₁₃	1	2	yes	—
424	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
425	C₂×#131	C₂²×C₁₃	1	2	yes	—
426	#557	—	2	1	no	—
427	#557	—	2	1	no	—
428	#556	—	2	1	no	—
429	#556	—	2	1	no	—
430	#552	—	2	2	no	—
431	#552	—	2	2	no	—
432	#544	C₂²×C₁₃	1	1	yes	characteristic
433	#542	—	2	1	no	—
434	#542	C₂²×C₁₃	1	2	yes	—
435	#541	C₂²×C₁₃	1	4	yes	complemented
436	#540	—	2	1	no	—
437	#540	C₂²×C₁₃	1	2	yes	—
438	#538	—	2	2	no	—
439	#537	C₂²×C₁₃	1	1	yes	characteristic
440	#536	C₂²×C₁₃	1	2	yes	—
441	#535	C₂²×C₁₃	1	1	yes	characteristic
442	#535	C₂²×C₁₃	1	1	yes	characteristic
443	#533	C₂²×C₁₃	1	1	yes	characteristic
444	#533	C₂²×C₁₃	1	2	yes	complemented
445	#533	C₂²×C₁₃	1	2	yes	complemented
446	#532	—	2	1	no	—
447	#532	C₂²×C₁₃	1	2	yes	—
448	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	#529	—	2	1	no	—
450	#529	C₂²×C₁₃	1	2	yes	—
451	#525	—	2	2	no	—
452	#519	C₂²×C₁₃	1	2	yes	—
453	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
454	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
456	#479	C₂²×C₁₃	1	2	yes	complemented
457	#479	C₂²×C₁₃	1	4	yes	complemented
458	#479	C₂²×C₁₃	1	4	yes	complemented
459	#478	C₂²×C₁₃	1	4	yes	—
460	#478	C₂²×C₁₃	1	2	yes	complemented
461	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#477	C₂²×C₁₃	1	4	yes	complemented
463	#476	C₂²×C₁₃	1	2	yes	—
464	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#475	C₂²×C₁₃	1	4	yes	complemented
467	#474	C₂²×C₁₃	1	2	yes	—
468	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#470	C₂²×C₁₃	1	4	yes	complemented
470	#468	C₂²×C₁₃	1	4	yes	—
471	#468	C₂²×C₁₃	1	4	yes	—
472	#468	C₂²×C₁₃	1	4	yes	complemented
473	#467	C₂²×C₁₃	1	4	yes	complemented
474	#465	C₂²×C₁₃	1	4	yes	—
475	#465	C₂²×C₁₃	1	4	yes	—
476	#465	C₂²×C₁₃	1	4	yes	complemented
477	#464	C₂²×C₁₃	1	4	yes	—
478	#464	C₂²×C₁₃	1	4	yes	—
479	#462	C₂²×C₁₃	1	2	yes	complemented
480	#462	C₂²×C₁₃	1	2	yes	complemented
481	#461	C₂²×C₁₃	1	2	yes	—
482	#461	C₂²×C₁₃	1	2	yes	—
483	#461	C₂²×C₁₃	1	4	yes	—
484	#461	C₂²×C₁₃	1	2	yes	complemented
485	#461	C₂²×C₁₃	1	2	yes	complemented
486	#460	C₂²×C₁₃	1	4	yes	—
487	#460	C₂²×C₁₃	1	4	yes	—
488	#428	C₂²×C₁₃	1	2	yes	—
489	#427	C₂²×C₁₃	1	2	yes	—
490	#424	C₂²×C₁₃	1	2	yes	—
491	#424	C₂²×C₁₃	1	4	yes	complemented
492	#423	C₂²×C₁₃	1	1	yes	characteristic
493	#423	C₂²×C₁₃	1	2	yes	complemented
494	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
495	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
496	#419	C₂²×C₁₃	1	2	yes	—
497	#418	C₂²×C₁₃	1	2	yes	—
498	#416	C₂²×C₁₃	1	2	yes	—
499	C₂×#103	C₂²×C₁₃	1	2	yes	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	8	4	no	—
512	C₂²×C₁₃	#537	1	2	yes	—
513	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	4	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	#537	1	2	yes	—
528	C₄×C₁₃	#577	1	2	yes	—
529	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	C₂×#41	—	2	2	no	—
532	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
535	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	—	2	1	no	—
537	#137	—	4	4	no	—
538	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
539	C₂×SD₁₆	—	4	4	no	—
540	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
542	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
543	#131	—	4	4	no	—
544	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
545	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
547	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	#127	—	2	1	no	—
558	#127	C₂³×C₁₃	1	2	yes	—
559	#126	—	2	2	no	—
560	#126	—	2	4	no	—
561	#126	—	2	4	no	—
562	#126	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	—	2	4	no	—
565	#125	—	2	4	no	—
566	#125	—	2	2	no	—
567	#125	—	2	2	no	—
568	#125	C₂³×C₁₃	1	2	yes	—
569	#125	C₂³×C₁₃	1	2	yes	—
570	#124	—	2	1	no	—
571	#124	—	2	2	no	—
572	#124	—	2	2	no	—
573	#124	—	2	2	no	—
574	#124	C₂³×C₁₃	1	2	yes	—
575	#123	—	2	4	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
588	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	1	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₁₃	1	2	yes	—
598	#121	C₂³×C₁₃	1	2	yes	—
599	#121	C₂³×C₁₃	1	2	yes	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
609	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
613	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	D₄×C₁₃	1	2	yes	—
621	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
622	C₄×D₄	D₄×C₁₃	1	2	yes	—
623	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₁₃	1	2	yes	—
625	C₄×D₄	C₂³×C₁₃	1	2	yes	—
626	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	4	no	—
631	#117	—	2	1	no	—
632	#117	—	2	2	no	—
633	#117	C₂³×C₁₃	1	1	yes	characteristic
634	#117	C₂³×C₁₃	1	2	yes	—
635	#117	C₂³×C₁₃	1	1	yes	characteristic
636	#117	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	#107	C₂³×C₁₃	1	2	yes	—
645	#107	C₂³×C₁₃	1	2	yes	—
646	#107	C₂³×C₁₃	1	4	yes	—
647	#106	C₂³×C₁₃	1	2	yes	—
648	#106	C₂³×C₁₃	1	2	yes	—
649	#106	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
651	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
652	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
653	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
654	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
655	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
656	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#103	C₂³×C₁₃	1	2	yes	—
660	#103	C₂³×C₁₃	1	2	yes	—
661	#103	C₂³×C₁₃	1	4	yes	—
662	#103	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	2	yes	—
664	#102	C₂³×C₁₃	1	2	yes	—
665	#102	C₂³×C₁₃	1	4	yes	—
666	#102	C₂³×C₁₃	1	4	yes	—
667	C₂×C₁₃	—	2	2	no	—
668	C₂×C₁₃	—	4	2	no	—
669	C₂×C₁₃	—	8	1	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
672	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
673	C₂×C₁₃	#3586	1	1	yes	characteristic
674	C₂⁴	—	2	1	no	—
675	#41	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	—	8	4	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	8	2	no	—
710	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	Q₁₆	—	4	4	no	—
717	SD₁₆	—	4	4	no	—
718	SD₁₆	—	4	4	no	—
719	SD₁₆	—	4	4	no	—
720	M₁₆	—	2	4	no	—
721	M₁₆	—	4	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	4	4	no	—
724	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
725	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
726	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	4	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	2	yes	—
780	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₄²	C₂⁴×C₁₃	1	2	yes	—
785	C₁₃	#60923	1	1	yes	characteristic, direct product factor, Sylow
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	1	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
792	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	2	4	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	4	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	2	no	—
802	D₄	—	2	4	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	1	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	2	no	—
833	C₂×C₄	—	8	1	no	—
834	C₂×C₄	—	8	1	no	—
835	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
844	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
845	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
846	C₈	—	2	2	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	4	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	8	4	no	—
861	C₂²	C₁₃×#537	1	2	yes	—
862	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
863	C₄	—	2	1	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	4	no	—
876	C₄	C₁₃×#537	1	2	yes	—
877	C₄	C₁₃×#577	1	2	yes	—
878	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
879	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	8	2	no	—
883	C₂	—	8	1	no	—
884	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
885	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
886	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3460	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
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3260	C₂	semidirect
4. C₁₃×#3258	C₂	semidirect
5. C₁₃×#3254	C₂	semidirect
6. C₁₃×#3252	C₂	semidirect
7. C₁₃×#3248	C₂	semidirect
8. C₁₃×#3246	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#3076	C₂	semidirect
12. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3057	C₂	semidirect
14. C₁₃×#3043	C₂	semidirect
15. C₁₃×#3039	C₂	semidirect
16. C₂×C₁₃×#461	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
30. C₁₃×#541	C₂²	semidirect
39. C₁₃×#533	C₂²	semidirect
40. C₁₃×#533	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#479	C₂²	semidirect
53. C₁₃×#479	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#477	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#470	C₂²	semidirect
67. C₁₃×#468	C₂²	semidirect
68. C₁₃×#467	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
74. C₁₃×#462	C₂²	semidirect
75. C₁₃×#462	C₂²	semidirect
79. C₁₃×#461	C₂²	semidirect
80. C₁₃×#461	C₂²	semidirect
86. C₁₃×#424	C₂²	semidirect
88. C₁₃×#423	C₂²	semidirect
90. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
231. #60923	C₁₃	direct (N × H)
343. #3509	C₂×C₁₃	semidirect
345. #3260	C₂×C₁₃	semidirect
346. #3258	C₂×C₁₃	semidirect
347. #3254	C₂×C₁₃	semidirect
348. #3252	C₂×C₁₃	semidirect
349. #3248	C₂×C₁₃	semidirect
350. #3246	C₂×C₁₃	semidirect
351. #3082	C₂×C₁₃	semidirect
352. #3077	C₂×C₁₃	semidirect
353. #3076	C₂×C₁₃	semidirect
354. #3063	C₂×C₁₃	semidirect
355. #3057	C₂×C₁₃	semidirect
356. #3043	C₂×C₁₃	semidirect
357. #3039	C₂×C₁₃	semidirect
358. C₂×#461	C₂×C₁₃	semidirect
359. #2906	C₂×C₁₃	semidirect
435. #541	C₂²×C₁₃	semidirect
444. #533	C₂²×C₁₃	semidirect
445. #533	C₂²×C₁₃	semidirect
456. #479	C₂²×C₁₃	semidirect
457. #479	C₂²×C₁₃	semidirect
458. #479	C₂²×C₁₃	semidirect
460. #478	C₂²×C₁₃	semidirect
461. #477	C₂²×C₁₃	semidirect
462. #477	C₂²×C₁₃	semidirect
464. #476	C₂²×C₁₃	semidirect
465. #475	C₂²×C₁₃	semidirect
466. #475	C₂²×C₁₃	semidirect
468. #474	C₂²×C₁₃	semidirect
469. #470	C₂²×C₁₃	semidirect
472. #468	C₂²×C₁₃	semidirect
473. #467	C₂²×C₁₃	semidirect
476. #465	C₂²×C₁₃	semidirect
479. #462	C₂²×C₁₃	semidirect
480. #462	C₂²×C₁₃	semidirect
484. #461	C₂²×C₁₃	semidirect
485. #461	C₂²×C₁₃	semidirect
491. #424	C₂²×C₁₃	semidirect
493. #423	C₂²×C₁₃	semidirect
495. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
785. C₁₃	#60923	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×#3509	2
C₁₃×#3460	2
C₁₃×#3260	2
C₁₃×#3258	2
C₁₃×#3254	2
C₁₃×#3252	2
C₁₃×#3248	2
C₁₃×#3246	2
C₁₃×#3082	2
C₁₃×#3077	2
C₁₃×#3076	2
C₁₃×#3063	2
C₁₃×#3057	2
C₁₃×#3043	2
C₁₃×#3039	2
C₂×C₁₃×#461	2
C₁₃×#2906	2
#60923	13

Subgroups — C13×#60923 #15747262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60923 #15747262