Subgroups — C₁₃×#60812 #15747151

Order 3328.

2218 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#552	—	2	1	no	—
28	C₁₃×#552	—	2	1	no	—
29	C₁₃×#551	—	2	2	no	—
30	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#542	C₂²	1	2	yes	complemented
32	C₁₃×#541	C₂²	1	2	yes	complemented
33	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#535	—	2	1	no	—
35	C₁₃×#535	—	2	2	no	—
36	C₁₃×#535	—	2	1	no	—
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#535	C₂²	1	4	yes	—
40	C₁₃×#533	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#127	C₂²	1	2	yes	—
42	C₁₃×#529	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#124	C₂²	1	2	yes	—
44	C₁₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#121	—	2	1	no	—
47	C₂×C₁₃×#121	—	2	1	no	—
48	C₂×C₁₃×#120	—	2	2	no	—
49	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	4	yes	complemented
55	C₁₃×#492	C₂²	1	4	yes	complemented
56	C₁₃×#490	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	4	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	complemented
59	C₁₃×#486	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#460	C₂²	1	4	yes	complemented
65	C₁₃×#460	C₂²	1	4	yes	complemented
66	C₁₃×#460	C₂²	1	4	yes	complemented
67	C₁₃×#459	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	4	yes	complemented
69	C₁₃×#452	C₂²	1	2	yes	complemented
70	C₁₃×#451	C₂²	1	2	yes	complemented
71	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#450	C₂²	1	2	yes	—
73	C₁₃×#450	C₂²	1	2	yes	—
74	C₁₃×#450	C₂²	1	2	yes	—
75	C₁₃×#450	C₂²	1	2	yes	complemented
76	C₁₃×#450	C₂²	1	4	yes	complemented
77	C₁₃×#450	C₂²	1	2	yes	complemented
78	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#449	C₂²	1	2	yes	complemented
80	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#447	C₂²	1	2	yes	—
82	C₁₃×#447	C₂²	1	2	yes	complemented
83	C₁₃×#447	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#433	C₂²	1	4	yes	complemented
85	C₁₃×#432	C₂²	1	2	yes	complemented
86	C₁₃×#431	C₂²	1	2	yes	complemented
87	C₁₃×#424	C₂²	1	2	yes	complemented
88	C₁₃×#418	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	complemented
90	C₁₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
92	C₁₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₁₃	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	—	2	2	no	—
109	C₂²×D₄×C₁₃	—	2	2	no	—
110	C₂²×D₄×C₁₃	—	4	4	no	—
111	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₁₃	—	2	1	no	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#137	—	4	4	no	—
118	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
119	C₁₃×#135	—	4	4	no	—
120	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	complemented
122	C₂×C₁₃×SD₁₆	—	4	4	no	—
123	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
129	C₂×C₁₃×D₈	C₂³	1	4	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	complemented
131	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
136	C₁₃×#127	—	2	2	no	—
137	C₁₃×#127	—	2	2	no	—
138	C₁₃×#127	C₂³	1	4	yes	—
139	C₁₃×#127	C₂³	1	4	yes	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#125	—	2	2	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	—	2	1	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	C₂³	1	2	yes	complemented
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	—	2	2	no	—
151	C₁₃×#124	—	2	2	no	—
152	C₁₃×#124	C₂³	1	4	yes	—
153	C₁₃×#124	C₂³	1	4	yes	—
154	C₁₃×#124	C₂³	1	2	yes	complemented
155	C₁₃×#123	—	2	1	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	1	no	—
160	C₁₃×C₂²⋊Q₈	—	2	1	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	1	no	—
163	C₁₃×C₂²⋊Q₈	—	2	1	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	4	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	4	no	—
176	C₁₃×#121	C₂³	1	1	yes	characteristic
177	C₁₃×#121	C₂³	1	1	yes	characteristic
178	C₁₃×#120	—	2	1	no	—
179	C₁₃×#120	—	2	4	no	—
180	C₁₃×#120	—	2	4	no	—
181	C₁₃×#120	—	2	4	no	—
182	C₁₃×#120	—	2	4	no	—
183	C₄×Q₈×C₁₃	—	2	1	no	—
184	C₄×Q₈×C₁₃	—	2	1	no	—
185	C₄×Q₈×C₁₃	—	2	2	no	—
186	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
189	C₄×D₄×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	1	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	D₄	1	1	yes	characteristic
199	C₁₃×#117	D₄	1	2	yes	—
200	C₁₃×#117	D₄	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	1	yes	characteristic
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₁₃×#117	C₂³	1	1	yes	characteristic
204	C₁₃×#117	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
208	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
216	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₁₃×#103	C₂³	1	2	yes	complemented
218	C₁₃×#103	C₂³	1	2	yes	complemented
219	C₁₃×#103	C₂³	1	4	yes	complemented
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	complemented
225	C₁₃×#102	C₂³	1	2	yes	complemented
226	C₁₃×#102	C₂³	1	4	yes	complemented
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×#97	C₂³	1	4	yes	complemented
233	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
234	#60812	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	2	no	—
236	C₂⁴×C₁₃	—	2	1	no	—
237	C₂⁴×C₁₃	—	2	2	no	—
238	C₂⁴×C₁₃	—	2	2	no	—
239	C₂⁴×C₁₃	—	4	4	no	—
240	C₂⁴×C₁₃	—	8	2	no	—
241	C₂⁴×C₁₃	—	8	2	no	—
242	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₁₃×#41	—	2	4	no	—
244	C₁₃×#41	—	2	4	no	—
245	C₁₃×#41	—	2	4	no	—
246	C₁₃×#41	—	4	2	no	—
247	C₁₃×#41	—	4	2	no	—
248	C₁₃×#41	—	4	4	no	—
249	C₁₃×#41	—	4	4	no	—
250	C₂×Q₈×C₁₃	—	2	1	no	—
251	C₂×Q₈×C₁₃	—	2	1	no	—
252	C₂×Q₈×C₁₃	—	2	2	no	—
253	C₂×Q₈×C₁₃	—	2	4	no	—
254	C₂×Q₈×C₁₃	—	4	2	no	—
255	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	1	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	1	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	4	no	—
269	C₂×D₄×C₁₃	—	2	4	no	—
270	C₂×D₄×C₁₃	—	2	4	no	—
271	C₂×D₄×C₁₃	—	2	4	no	—
272	C₂×D₄×C₁₃	—	2	4	no	—
273	C₂×D₄×C₁₃	—	4	4	no	—
274	C₂×D₄×C₁₃	—	4	4	no	—
275	C₂×D₄×C₁₃	—	4	2	no	—
276	C₂×D₄×C₁₃	—	4	4	no	—
277	C₂×D₄×C₁₃	—	4	4	no	—
278	C₂×D₄×C₁₃	—	4	4	no	—
279	C₂×D₄×C₁₃	—	4	4	no	—
280	C₂×D₄×C₁₃	—	8	4	no	—
281	C₂×D₄×C₁₃	—	8	4	no	—
282	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	—	2	4	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	1	no	—
288	C₂²×C₄×C₁₃	—	2	1	no	—
289	C₂²×C₄×C₁₃	—	2	1	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	4	4	no	—
294	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₁₃×Q₁₆	—	4	2	no	—
303	C₁₃×Q₁₆	—	4	4	no	—
304	C₁₃×SD₁₆	—	4	4	no	—
305	C₁₃×SD₁₆	—	4	4	no	—
306	C₁₃×SD₁₆	—	4	4	no	—
307	C₁₃×SD₁₆	—	4	2	no	—
308	C₁₃×SD₁₆	—	4	2	no	—
309	C₁₃×SD₁₆	—	4	4	no	—
310	C₁₃×D₈	—	4	4	no	—
311	C₁₃×D₈	—	4	2	no	—
312	C₁₃×M₁₆	—	2	4	no	—
313	C₂×C₈×C₁₃	—	2	4	no	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	1	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
334	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
335	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
338	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	1	no	—
342	C₁₃×C₂²⋊C₄	—	2	1	no	—
343	C₁₃×C₂²⋊C₄	—	2	1	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	—	2	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	4	no	—
348	C₁₃×C₂²⋊C₄	—	2	1	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	1	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
354	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	2	no	—
360	C₄²×C₁₃	—	2	1	no	—
361	C₄²×C₁₃	C₂×D₄	1	2	yes	—
362	C₄²×C₁₃	C₂×D₄	1	2	yes	—
363	C₄²×C₁₃	C₂⁴	1	2	yes	—
364	C₄²×C₁₃	C₂⁴	1	2	yes	—
365	#3495	C₂×C₁₃	1	1	yes	characteristic, complemented
366	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
367	#3224	C₂×C₁₃	1	4	yes	complemented
368	#3222	C₂×C₁₃	1	4	yes	complemented
369	#3217	C₂×C₁₃	1	2	yes	complemented
370	#3215	C₂×C₁₃	1	2	yes	complemented
371	#3211	C₂×C₁₃	1	2	yes	complemented
372	#3208	C₂×C₁₃	1	2	yes	complemented
373	#3154	C₂×C₁₃	1	2	yes	complemented
374	#3136	C₂×C₁₃	1	2	yes	complemented
375	#3045	C₂×C₁₃	1	2	yes	complemented
376	#3043	C₂×C₁₃	1	2	yes	complemented
377	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#3003	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	2	4	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	4	1	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	4	4	no	—
390	C₂³×C₁₃	—	4	4	no	—
391	C₂³×C₁₃	—	4	2	no	—
392	C₂³×C₁₃	—	4	4	no	—
393	C₂³×C₁₃	—	4	4	no	—
394	C₂³×C₁₃	—	4	2	no	—
395	C₂³×C₁₃	—	4	4	no	—
396	C₂³×C₁₃	—	8	2	no	—
397	C₂³×C₁₃	—	8	2	no	—
398	C₂³×C₁₃	—	8	2	no	—
399	C₂³×C₁₃	—	8	2	no	—
400	C₂³×C₁₃	—	8	16	no	—
401	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₁₃	—	2	4	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	2	2	no	—
408	Q₈×C₁₃	—	4	2	no	—
409	Q₈×C₁₃	—	4	2	no	—
410	Q₈×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	4	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	4	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	4	4	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	4	2	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	4	no	—
421	D₄×C₁₃	—	4	2	no	—
422	D₄×C₁₃	—	4	2	no	—
423	D₄×C₁₃	—	4	4	no	—
424	D₄×C₁₃	—	8	4	no	—
425	D₄×C₁₃	—	8	4	no	—
426	D₄×C₁₃	—	8	4	no	—
427	D₄×C₁₃	—	8	4	no	—
428	D₄×C₁₃	—	8	1	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	4	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	1	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	4	2	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	—	4	2	no	—
444	C₂×C₄×C₁₃	—	4	2	no	—
445	C₂×C₄×C₁₃	—	4	4	no	—
446	C₂×C₄×C₁₃	—	4	2	no	—
447	C₂×C₄×C₁₃	—	8	2	no	—
448	C₂×C₄×C₁₃	—	8	1	no	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
457	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
458	C₈×C₁₃	—	2	2	no	—
459	C₈×C₁₃	—	2	2	no	—
460	C₈×C₁₃	—	2	4	no	—
461	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
462	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
464	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
465	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
466	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
467	#556	—	2	1	no	—
468	#554	—	2	1	no	—
469	#552	—	2	2	no	—
470	#552	—	2	1	no	—
471	#552	—	2	1	no	—
472	#551	—	2	2	no	—
473	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#542	C₂²×C₁₃	1	2	yes	complemented
475	#541	C₂²×C₁₃	1	2	yes	complemented
476	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#535	—	2	1	no	—
478	#535	—	2	2	no	—
479	#535	—	2	1	no	—
480	#535	C₂²×C₁₃	1	2	yes	—
481	#535	C₂²×C₁₃	1	4	yes	—
482	#535	C₂²×C₁₃	1	2	yes	—
483	#533	C₂²×C₁₃	1	2	yes	complemented
484	C₂×#127	C₂²×C₁₃	1	2	yes	—
485	#529	C₂²×C₁₃	1	2	yes	complemented
486	C₂×#124	C₂²×C₁₃	1	2	yes	—
487	#525	C₂²×C₁₃	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×#121	—	2	1	no	—
490	C₂×#121	—	2	1	no	—
491	C₂×#120	—	2	2	no	—
492	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
495	#497	C₂²×C₁₃	1	4	yes	complemented
496	#496	C₂²×C₁₃	1	4	yes	complemented
497	#495	C₂²×C₁₃	1	4	yes	complemented
498	#492	C₂²×C₁₃	1	4	yes	complemented
499	#490	C₂²×C₁₃	1	4	yes	complemented
500	#489	C₂²×C₁₃	1	4	yes	complemented
501	#488	C₂²×C₁₃	1	4	yes	complemented
502	#486	C₂²×C₁₃	1	4	yes	complemented
503	#464	C₂²×C₁₃	1	4	yes	complemented
504	#464	C₂²×C₁₃	1	4	yes	complemented
505	#464	C₂²×C₁₃	1	4	yes	complemented
506	#463	C₂²×C₁₃	1	4	yes	complemented
507	#460	C₂²×C₁₃	1	4	yes	complemented
508	#460	C₂²×C₁₃	1	4	yes	complemented
509	#460	C₂²×C₁₃	1	4	yes	complemented
510	#459	C₂²×C₁₃	1	4	yes	complemented
511	#452	C₂²×C₁₃	1	2	yes	complemented
512	#452	C₂²×C₁₃	1	4	yes	complemented
513	#451	C₂²×C₁₃	1	2	yes	complemented
514	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#450	C₂²×C₁₃	1	2	yes	—
516	#450	C₂²×C₁₃	1	2	yes	—
517	#450	C₂²×C₁₃	1	2	yes	—
518	#450	C₂²×C₁₃	1	2	yes	complemented
519	#450	C₂²×C₁₃	1	4	yes	complemented
520	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#450	C₂²×C₁₃	1	2	yes	complemented
522	#449	C₂²×C₁₃	1	2	yes	complemented
523	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#447	C₂²×C₁₃	1	2	yes	—
525	#447	C₂²×C₁₃	1	2	yes	complemented
526	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#433	C₂²×C₁₃	1	4	yes	complemented
528	#432	C₂²×C₁₃	1	2	yes	complemented
529	#431	C₂²×C₁₃	1	2	yes	complemented
530	#424	C₂²×C₁₃	1	2	yes	complemented
531	#418	C₂²×C₁₃	1	2	yes	complemented
532	#417	C₂²×C₁₃	1	2	yes	complemented
533	#416	C₂²×C₁₃	1	2	yes	complemented
534	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
535	#407	C₂²×C₁₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
537	#405	C₂²×C₁₃	1	2	yes	complemented
538	C₂²×C₁₃	—	2	1	no	—
539	C₂²×C₁₃	—	2	1	no	—
540	C₂²×C₁₃	—	2	1	no	—
541	C₂²×C₁₃	—	2	1	no	—
542	C₂²×C₁₃	—	2	1	no	—
543	C₂²×C₁₃	—	2	1	no	—
544	C₂²×C₁₃	—	2	1	no	—
545	C₂²×C₁₃	—	4	4	no	—
546	C₂²×C₁₃	—	4	1	no	—
547	C₂²×C₁₃	—	4	2	no	—
548	C₂²×C₁₃	—	4	4	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	4	1	no	—
551	C₂²×C₁₃	—	4	4	no	—
552	C₂²×C₁₃	—	4	1	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	4	no	—
555	C₂²×C₁₃	—	8	4	no	—
556	C₂²×C₁₃	—	8	8	no	—
557	C₂²×C₁₃	—	8	8	no	—
558	C₂²×C₁₃	—	8	8	no	—
559	C₂²×C₁₃	#535	1	2	yes	—
560	C₂²×C₁₃	#577	1	2	yes	—
561	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₁₃	—	2	2	no	—
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	1	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	1	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	#535	1	2	yes	—
575	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
576	C₂⁵	—	2	1	no	—
577	C₂×#41	—	2	1	no	—
578	C₂×#41	—	2	1	no	—
579	C₂×#41	—	4	4	no	—
580	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×#41	C₂³×C₁₃	1	2	yes	—
582	C₂×#41	C₂³×C₁₃	1	2	yes	—
583	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	—	2	1	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	—	4	4	no	—
592	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
593	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
594	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
596	C₂³×C₄	—	2	1	no	—
597	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
598	#137	—	4	4	no	—
599	AGL(1,ℤ/8)	—	4	4	no	—
600	#135	—	4	4	no	—
601	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	complemented
602	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
603	C₂×SD₁₆	—	4	4	no	—
604	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
605	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
606	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
607	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
608	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
609	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
610	C₂×D₈	C₂³×C₁₃	1	4	yes	—
611	C₂×D₈	C₂³×C₁₃	1	2	yes	complemented
612	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
613	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
614	C₄⋊Q₈	—	2	1	no	—
615	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
616	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
617	#127	—	2	2	no	—
618	#127	—	2	2	no	—
619	#127	C₂³×C₁₃	1	4	yes	—
620	#127	C₂³×C₁₃	1	4	yes	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	—	2	1	no	—
628	#125	—	2	2	no	—
629	#125	C₂³×C₁₃	1	2	yes	complemented
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	—	2	2	no	—
633	#124	C₂³×C₁₃	1	4	yes	—
634	#124	C₂³×C₁₃	1	4	yes	—
635	#124	C₂³×C₁₃	1	2	yes	complemented
636	#123	—	2	1	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
650	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	4	no	—
655	#121	—	2	2	no	—
656	#121	—	2	4	no	—
657	#121	C₂³×C₁₃	1	1	yes	characteristic
658	#121	C₂³×C₁₃	1	1	yes	characteristic
659	#120	—	2	1	no	—
660	#120	—	2	4	no	—
661	#120	—	2	4	no	—
662	#120	—	2	4	no	—
663	#120	—	2	4	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	2	no	—
667	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
668	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
669	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
675	#117	—	2	2	no	—
676	#117	—	2	1	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	D₄×C₁₃	1	1	yes	characteristic
680	#117	D₄×C₁₃	1	2	yes	—
681	#117	D₄×C₁₃	1	1	yes	characteristic
682	#117	C₂³×C₁₃	1	1	yes	characteristic
683	#117	C₂³×C₁₃	1	1	yes	characteristic
684	#117	C₂³×C₁₃	1	1	yes	characteristic
685	#117	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
697	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
698	#103	C₂³×C₁₃	1	2	yes	complemented
699	#103	C₂³×C₁₃	1	2	yes	complemented
700	#103	C₂³×C₁₃	1	4	yes	complemented
701	#102	C₂³×C₁₃	1	4	yes	—
702	#102	C₂³×C₁₃	1	4	yes	—
703	#102	C₂³×C₁₃	1	4	yes	—
704	#102	C₂³×C₁₃	1	4	yes	—
705	#102	C₂³×C₁₃	1	2	yes	complemented
706	#102	C₂³×C₁₃	1	2	yes	complemented
707	#102	C₂³×C₁₃	1	4	yes	complemented
708	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
710	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
713	#97	C₂³×C₁₃	1	4	yes	complemented
714	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
715	C₂×C₁₃	—	2	2	no	—
716	C₂×C₁₃	—	2	2	no	—
717	C₂×C₁₃	—	4	1	no	—
718	C₂×C₁₃	—	8	1	no	—
719	C₂×C₁₃	—	8	2	no	—
720	C₂×C₁₃	—	8	4	no	—
721	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
722	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
723	C₂×C₁₃	#3585	1	1	yes	characteristic
724	C₂⁴	—	2	2	no	—
725	C₂⁴	—	2	1	no	—
726	C₂⁴	—	2	2	no	—
727	C₂⁴	—	2	2	no	—
728	C₂⁴	—	4	4	no	—
729	C₂⁴	—	8	2	no	—
730	C₂⁴	—	8	2	no	—
731	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
732	#41	—	2	4	no	—
733	#41	—	2	4	no	—
734	#41	—	2	4	no	—
735	#41	—	4	2	no	—
736	#41	—	4	2	no	—
737	#41	—	4	4	no	—
738	#41	—	4	4	no	—
739	C₂×Q₈	—	2	1	no	—
740	C₂×Q₈	—	2	1	no	—
741	C₂×Q₈	—	2	2	no	—
742	C₂×Q₈	—	2	4	no	—
743	C₂×Q₈	—	4	2	no	—
744	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
745	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	1	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	4	4	no	—
763	C₂×D₄	—	4	4	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	4	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	—	4	4	no	—
769	C₂×D₄	—	8	4	no	—
770	C₂×D₄	—	8	4	no	—
771	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
772	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
773	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂²×C₄	—	2	4	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	4	4	no	—
783	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	Q₁₆	—	4	2	no	—
792	Q₁₆	—	4	4	no	—
793	SD₁₆	—	4	4	no	—
794	SD₁₆	—	4	4	no	—
795	SD₁₆	—	4	4	no	—
796	SD₁₆	—	4	2	no	—
797	SD₁₆	—	4	2	no	—
798	SD₁₆	—	4	4	no	—
799	D₈	—	4	4	no	—
800	D₈	—	4	2	no	—
801	M₁₆	—	2	4	no	—
802	C₂×C₈	—	2	4	no	—
803	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
804	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
805	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
821	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
824	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	4	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	1	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	1	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	1	no	—
850	C₄²	C₂×D₄×C₁₃	1	2	yes	—
851	C₄²	C₂×D₄×C₁₃	1	2	yes	—
852	C₄²	C₂⁴×C₁₃	1	2	yes	—
853	C₄²	C₂⁴×C₁₃	1	2	yes	—
854	C₁₃	#60812	1	1	yes	characteristic, direct product factor, Sylow
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	4	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	4	1	no	—
861	C₂³	—	4	2	no	—
862	C₂³	—	4	4	no	—
863	C₂³	—	4	4	no	—
864	C₂³	—	4	2	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	4	4	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	8	2	no	—
870	C₂³	—	8	2	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	2	no	—
873	C₂³	—	8	16	no	—
874	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	Q₈	—	2	4	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	4	2	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	8	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	4	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	4	no	—
897	D₄	—	8	4	no	—
898	D₄	—	8	4	no	—
899	D₄	—	8	4	no	—
900	D₄	—	8	4	no	—
901	D₄	—	8	1	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	1	no	—
922	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
923	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
924	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
929	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
930	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₈	—	2	4	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	4	4	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	8	4	no	—
952	C₂²	—	8	8	no	—
953	C₂²	—	8	8	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₁₃×#535	1	2	yes	—
956	C₂²	C₁₃×#577	1	2	yes	—
957	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	C₁₃×#535	1	2	yes	—
971	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
972	C₂	—	2	2	no	—
973	C₂	—	2	2	no	—
974	C₂	—	4	1	no	—
975	C₂	—	8	4	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	1	no	—
978	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
979	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
980	C₂	C₁₃×#3585	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×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3495	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3222	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3215	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3208	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3043	C₂	semidirect
13. C₁₃×#3007	C₂	semidirect
14. C₁₃×#3003	C₂	semidirect
15. C₁₃×#3002	C₂	semidirect
16. C₂×C₁₃×#450	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#541	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
40. C₁₃×#533	C₂²	semidirect
42. C₁₃×#529	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#519	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#492	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#486	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#460	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#459	C₂²	semidirect
68. C₁₃×#452	C₂²	semidirect
69. C₁₃×#452	C₂²	semidirect
70. C₁₃×#451	C₂²	semidirect
71. C₁₃×#451	C₂²	semidirect
75. C₁₃×#450	C₂²	semidirect
76. C₁₃×#450	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#450	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#448	C₂²	semidirect
82. C₁₃×#447	C₂²	semidirect
83. C₁₃×#447	C₂²	semidirect
84. C₁₃×#433	C₂²	semidirect
85. C₁₃×#432	C₂²	semidirect
86. C₁₃×#431	C₂²	semidirect
87. C₁₃×#424	C₂²	semidirect
88. C₁₃×#418	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#416	C₂²	semidirect
91. C₂×C₁₃×#102	C₂²	semidirect
94. C₁₃×#405	C₂²	semidirect
120. C₂×C₁₃×Q₁₆	C₂³	semidirect
121. C₂×C₁₃×Q₁₆	C₂³	semidirect
126. C₂×C₁₃×SD₁₆	C₂³	semidirect
127. C₂×C₁₃×SD₁₆	C₂³	semidirect
128. C₂×C₁₃×SD₁₆	C₂³	semidirect
130. C₂×C₁₃×D₈	C₂³	semidirect
134. C₁₃×C₄⋊Q₈	C₂³	semidirect
135. C₁₃×C₄⋊Q₈	C₂³	semidirect
148. C₁₃×#125	C₂³	semidirect
154. C₁₃×#124	C₂³	semidirect
186. C₄×Q₈×C₁₃	C₂³	semidirect
187. C₄×Q₈×C₁₃	C₂³	semidirect
188. C₄×Q₈×C₁₃	C₂³	semidirect
193. C₄×D₄×C₁₃	C₂³	semidirect
215. C₁₃×C₄⋊C₈	C₂³	semidirect
216. C₁₃×C₄⋊C₈	C₂³	semidirect
217. C₁₃×#103	C₂³	semidirect
218. C₁₃×#103	C₂³	semidirect
219. C₁₃×#103	C₂³	semidirect
224. C₁₃×#102	C₂³	semidirect
225. C₁₃×#102	C₂³	semidirect
226. C₁₃×#102	C₂³	semidirect
232. C₁₃×#97	C₂³	semidirect
233. C₄×C₈×C₁₃	C₂³	semidirect
234. #60812	C₁₃	direct (N × H)
365. #3495	C₂×C₁₃	semidirect
366. C₂×#535	C₂×C₁₃	semidirect
367. #3224	C₂×C₁₃	semidirect
368. #3222	C₂×C₁₃	semidirect
369. #3217	C₂×C₁₃	semidirect
370. #3215	C₂×C₁₃	semidirect
371. #3211	C₂×C₁₃	semidirect
372. #3208	C₂×C₁₃	semidirect
373. #3154	C₂×C₁₃	semidirect
374. #3136	C₂×C₁₃	semidirect
375. #3045	C₂×C₁₃	semidirect
376. #3043	C₂×C₁₃	semidirect
377. #3007	C₂×C₁₃	semidirect
378. #3003	C₂×C₁₃	semidirect
379. #3002	C₂×C₁₃	semidirect
380. C₂×#450	C₂×C₁₃	semidirect
381. #2924	C₂×C₁₃	semidirect
463. C₂×#137	C₂²×C₁₃	semidirect
464. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
465. C₂×#135	C₂²×C₁₃	semidirect
466. C₂²×SD₁₆	C₂²×C₁₃	semidirect
473. #544	C₂²×C₁₃	semidirect
474. #542	C₂²×C₁₃	semidirect
475. #541	C₂²×C₁₃	semidirect
476. #536	C₂²×C₁₃	semidirect
483. #533	C₂²×C₁₃	semidirect
485. #529	C₂²×C₁₃	semidirect
492. #520	C₂²×C₁₃	semidirect
493. #519	C₂²×C₁₃	semidirect
495. #497	C₂²×C₁₃	semidirect
496. #496	C₂²×C₁₃	semidirect
497. #495	C₂²×C₁₃	semidirect
498. #492	C₂²×C₁₃	semidirect
499. #490	C₂²×C₁₃	semidirect
500. #489	C₂²×C₁₃	semidirect
501. #488	C₂²×C₁₃	semidirect
502. #486	C₂²×C₁₃	semidirect
503. #464	C₂²×C₁₃	semidirect
504. #464	C₂²×C₁₃	semidirect
505. #464	C₂²×C₁₃	semidirect
506. #463	C₂²×C₁₃	semidirect
507. #460	C₂²×C₁₃	semidirect
508. #460	C₂²×C₁₃	semidirect
509. #460	C₂²×C₁₃	semidirect
510. #459	C₂²×C₁₃	semidirect
511. #452	C₂²×C₁₃	semidirect
512. #452	C₂²×C₁₃	semidirect
513. #451	C₂²×C₁₃	semidirect
514. #451	C₂²×C₁₃	semidirect
518. #450	C₂²×C₁₃	semidirect
519. #450	C₂²×C₁₃	semidirect
520. #450	C₂²×C₁₃	semidirect
521. #450	C₂²×C₁₃	semidirect
522. #449	C₂²×C₁₃	semidirect
523. #448	C₂²×C₁₃	semidirect
525. #447	C₂²×C₁₃	semidirect
526. #447	C₂²×C₁₃	semidirect
527. #433	C₂²×C₁₃	semidirect
528. #432	C₂²×C₁₃	semidirect
529. #431	C₂²×C₁₃	semidirect
530. #424	C₂²×C₁₃	semidirect
531. #418	C₂²×C₁₃	semidirect
532. #417	C₂²×C₁₃	semidirect
533. #416	C₂²×C₁₃	semidirect
534. C₂×#102	C₂²×C₁₃	semidirect
537. #405	C₂²×C₁₃	semidirect
601. C₂×Q₁₆	C₂³×C₁₃	semidirect
602. C₂×Q₁₆	C₂³×C₁₃	semidirect
607. C₂×SD₁₆	C₂³×C₁₃	semidirect
608. C₂×SD₁₆	C₂³×C₁₃	semidirect
609. C₂×SD₁₆	C₂³×C₁₃	semidirect
611. C₂×D₈	C₂³×C₁₃	semidirect
615. C₄⋊Q₈	C₂³×C₁₃	semidirect
616. C₄⋊Q₈	C₂³×C₁₃	semidirect
629. #125	C₂³×C₁₃	semidirect
635. #124	C₂³×C₁₃	semidirect
667. C₄×Q₈	C₂³×C₁₃	semidirect
668. C₄×Q₈	C₂³×C₁₃	semidirect
669. C₄×Q₈	C₂³×C₁₃	semidirect
674. C₄×D₄	C₂³×C₁₃	semidirect
696. C₄⋊C₈	C₂³×C₁₃	semidirect
697. C₄⋊C₈	C₂³×C₁₃	semidirect
698. #103	C₂³×C₁₃	semidirect
699. #103	C₂³×C₁₃	semidirect
700. #103	C₂³×C₁₃	semidirect
705. #102	C₂³×C₁₃	semidirect
706. #102	C₂³×C₁₃	semidirect
707. #102	C₂³×C₁₃	semidirect
713. #97	C₂³×C₁₃	semidirect
714. C₄×C₈	C₂³×C₁₃	semidirect
854. C₁₃	#60812	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×#3495	2
C₂×C₁₃×#535	2
C₁₃×#3224	2
C₁₃×#3222	2
C₁₃×#3217	2
C₁₃×#3215	2
C₁₃×#3211	2
C₁₃×#3208	2
C₁₃×#3154	2
C₁₃×#3136	2
C₁₃×#3045	2
C₁₃×#3043	2
C₁₃×#3007	2
C₁₃×#3003	2
C₁₃×#3002	2
C₂×C₁₃×#450	2
C₁₃×#2924	2
#60812	13

Subgroups — C13×#60812 #15747151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60812 #15747151