Subgroups — C₁₃×#61160 #15747499

Order 3328.

2172 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3332	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3317	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3309	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3094	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3005	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#553	C₂²	1	2	yes	complemented
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#552	C₂²	1	2	yes	complemented
28	C₁₃×#551	—	2	2	no	—
29	C₁₃×#550	—	2	1	no	—
30	C₁₃×#550	—	2	1	no	—
31	C₁₃×#550	—	2	2	no	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	C₁₃×#550	C₂²	1	4	yes	—
34	C₁₃×#550	C₂²	1	2	yes	—
35	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#546	—	2	1	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#127	—	2	1	no	—
39	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
40	C₁₃×#529	—	2	2	no	—
41	C₁₃×#529	—	2	1	no	—
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×#121	—	2	2	no	—
44	C₂×C₁₃×#121	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	C₂²	1	2	yes	—
51	C₁₃×#490	C₂²	1	4	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#482	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#480	C₂²	1	4	yes	complemented
58	C₁₃×#479	C₂²	1	4	yes	complemented
59	C₁₃×#477	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#469	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#466	C₂²	1	4	yes	complemented
64	C₁₃×#465	C₂²	1	4	yes	complemented
65	C₁₃×#460	C₂²	1	2	yes	complemented
66	C₁₃×#460	C₂²	1	2	yes	complemented
67	C₁₃×#459	C₂²	1	2	yes	complemented
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#452	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#449	C₂²	1	4	yes	complemented
73	C₁₃×#441	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₁₃×#428	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#423	C₂²	1	1	yes	characteristic
83	C₁₃×#419	C₂²	1	2	yes	—
84	C₁₃×#419	C₂²	1	1	yes	characteristic
85	C₁₃×#418	C₂²	1	2	yes	—
86	C₁₃×#418	C₂²	1	2	yes	—
87	C₁₃×#418	C₂²	1	2	yes	—
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#417	C₂²	1	4	yes	complemented
90	C₁₃×#417	C₂²	1	4	yes	complemented
91	C₁₃×#416	C₂²	1	4	yes	complemented
92	C₁₃×#416	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	—
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	2	8	no	—
99	C₂×C₁₃×#41	—	4	4	no	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	C₂³	1	4	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	—	2	2	no	—
111	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
112	C₁₃×#137	—	2	4	no	—
113	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	—	4	4	no	—
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
123	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×#127	—	2	2	no	—
127	C₁₃×#127	—	2	2	no	—
128	C₁₃×#127	—	2	4	no	—
129	C₁₃×#127	—	2	1	no	—
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	C₂³	1	2	yes	—
132	C₁₃×#127	C₂³	1	2	yes	—
133	C₁₃×#126	—	2	2	no	—
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#126	—	2	2	no	—
136	C₁₃×#125	—	2	2	no	—
137	C₁₃×#125	—	2	1	no	—
138	C₁₃×#125	C₂³	1	2	yes	—
139	C₁₃×#124	—	2	1	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	4	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	4	yes	—
162	C₁₃×#121	C₂³	1	4	yes	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	1	no	—
166	C₄×Q₈×C₁₃	—	2	1	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	—	2	1	no	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	4	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₁₃×#117	C₂³	1	2	yes	—
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₁₃×#117	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₁₃	—	2	2	no	—
208	C₂×C₄²×C₁₃	—	2	1	no	—
209	C₂×C₄²×C₁₃	—	2	1	no	—
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	2	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	2	yes	—
227	C₁₃×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	4	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61160	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
236	C₁₃×#41	—	2	8	no	—
237	C₁₃×#41	—	2	8	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	2	2	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₁₃×#41	—	4	4	no	—
242	C₁₃×#41	—	4	8	no	—
243	C₁₃×#41	—	4	8	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₂×Q₈×C₁₃	—	2	1	no	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	2	1	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	#41	1	4	yes	complemented
250	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	4	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	4	no	—
265	C₂×D₄×C₁₃	—	2	4	no	—
266	C₂×D₄×C₁₃	—	4	2	no	—
267	C₂×D₄×C₁₃	—	4	8	no	—
268	C₂×D₄×C₁₃	—	4	4	no	—
269	C₂×D₄×C₁₃	—	8	2	no	—
270	C₂×D₄×C₁₃	—	8	4	no	—
271	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	2	4	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	4	8	no	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₁₃×Q₁₆	—	2	4	no	—
297	C₁₃×SD₁₆	—	2	4	no	—
298	C₁₃×SD₁₆	—	4	4	no	—
299	C₁₃×D₈	—	4	4	no	—
300	C₁₃×M₁₆	—	2	2	no	—
301	C₁₃×M₁₆	—	2	2	no	—
302	C₁₃×M₁₆	—	2	4	no	—
303	C₁₃×M₁₆	—	4	4	no	—
304	C₂×C₈×C₁₃	—	4	4	no	—
305	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
306	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
321	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
327	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₁₃×C₂²⋊C₄	—	2	1	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	4	no	—
336	C₁₃×C₂²⋊C₄	—	2	4	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	no	—
339	C₁₃×C₂²⋊C₄	—	2	1	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₄²×C₁₃	—	2	1	no	—
346	C₄²×C₁₃	—	2	2	no	—
347	C₄²×C₁₃	—	2	1	no	—
348	C₄²×C₁₃	—	2	2	no	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	—	2	1	no	—
351	C₄²×C₁₃	—	2	2	no	—
352	C₄²×C₁₃	—	2	2	no	—
353	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
357	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3333	C₂×C₁₃	1	2	yes	complemented
360	#3332	C₂×C₁₃	1	2	yes	complemented
361	#3317	C₂×C₁₃	1	4	yes	complemented
362	#3309	C₂×C₁₃	1	4	yes	complemented
363	#3305	C₂×C₁₃	1	2	yes	complemented
364	#3304	C₂×C₁₃	1	2	yes	complemented
365	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3094	C₂×C₁₃	1	2	yes	complemented
367	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
368	#3055	C₂×C₁₃	1	2	yes	complemented
369	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3005	C₂×C₁₃	1	2	yes	complemented
371	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
372	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#2896	C₂×C₁₃	1	2	yes	complemented
374	C₂³×C₁₃	—	2	4	no	—
375	C₂³×C₁₃	—	2	1	no	—
376	C₂³×C₁₃	—	2	4	no	—
377	C₂³×C₁₃	—	4	2	no	—
378	C₂³×C₁₃	—	4	2	no	—
379	C₂³×C₁₃	—	4	4	no	—
380	C₂³×C₁₃	—	4	4	no	—
381	C₂³×C₁₃	—	4	4	no	—
382	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	Q₈×C₁₃	—	2	4	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	2	1	no	—
388	Q₈×C₁₃	—	2	1	no	—
389	Q₈×C₁₃	—	4	2	no	—
390	Q₈×C₁₃	—	8	1	no	—
391	Q₈×C₁₃	C₂×#41	1	4	yes	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	2	2	no	—
394	D₄×C₁₃	—	2	1	no	—
395	D₄×C₁₃	—	2	4	no	—
396	D₄×C₁₃	—	2	1	no	—
397	D₄×C₁₃	—	2	4	no	—
398	D₄×C₁₃	—	4	2	no	—
399	D₄×C₁₃	—	4	8	no	—
400	D₄×C₁₃	—	4	8	no	—
401	D₄×C₁₃	—	4	4	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	2	no	—
404	D₄×C₁₃	—	4	4	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	8	2	no	—
407	D₄×C₁₃	—	8	2	no	—
408	D₄×C₁₃	—	8	2	no	—
409	D₄×C₁₃	—	8	4	no	—
410	D₄×C₁₃	—	8	4	no	—
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	4	1	no	—
428	C₂×C₄×C₁₃	—	4	8	no	—
429	C₂×C₄×C₁₃	—	4	8	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	4	4	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	8	1	no	—
435	C₂×C₄×C₁₃	—	8	2	no	—
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
445	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₁₃	—	2	2	no	—
447	C₈×C₁₃	—	2	2	no	—
448	C₈×C₁₃	—	2	4	no	—
449	C₂²×#41	C₂²×C₁₃	1	2	yes	—
450	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
452	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
453	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#553	C₂²×C₁₃	1	2	yes	complemented
457	#552	—	2	1	no	—
458	#552	C₂²×C₁₃	1	2	yes	complemented
459	#551	—	2	2	no	—
460	#550	—	2	1	no	—
461	#550	—	2	1	no	—
462	#550	—	2	2	no	—
463	#550	C₂²×C₁₃	1	2	yes	—
464	#550	C₂²×C₁₃	1	2	yes	—
465	#550	C₂²×C₁₃	1	4	yes	—
466	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	#546	—	2	1	no	—
468	#533	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#127	—	2	1	no	—
470	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
471	#529	—	2	2	no	—
472	#529	—	2	1	no	—
473	#525	C₂²×C₁₃	1	2	yes	—
474	C₂×#121	—	2	2	no	—
475	C₂×#121	C₂²×C₁₃	1	2	yes	—
476	C₄×#41	—	2	1	no	—
477	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×C₄×D₄	—	2	1	no	—
480	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#117	C₂²×C₁₃	1	2	yes	—
482	#490	C₂²×C₁₃	1	4	yes	complemented
483	#486	C₂²×C₁₃	1	2	yes	complemented
484	#486	C₂²×C₁₃	1	2	yes	complemented
485	#482	C₂²×C₁₃	1	4	yes	complemented
486	#482	C₂²×C₁₃	1	4	yes	complemented
487	#481	C₂²×C₁₃	1	4	yes	complemented
488	#480	C₂²×C₁₃	1	4	yes	complemented
489	#479	C₂²×C₁₃	1	4	yes	complemented
490	#477	C₂²×C₁₃	1	2	yes	complemented
491	#475	C₂²×C₁₃	1	2	yes	complemented
492	#469	C₂²×C₁₃	1	4	yes	complemented
493	#468	C₂²×C₁₃	1	4	yes	complemented
494	#466	C₂²×C₁₃	1	4	yes	complemented
495	#465	C₂²×C₁₃	1	4	yes	complemented
496	#460	C₂²×C₁₃	1	2	yes	complemented
497	#460	C₂²×C₁₃	1	2	yes	complemented
498	#459	C₂²×C₁₃	1	2	yes	complemented
499	#459	C₂²×C₁₃	1	2	yes	complemented
500	#452	C₂²×C₁₃	1	4	yes	complemented
501	#452	C₂²×C₁₃	1	4	yes	complemented
502	#449	C₂²×C₁₃	1	4	yes	complemented
503	#449	C₂²×C₁₃	1	4	yes	complemented
504	#441	C₂²×C₁₃	1	2	yes	complemented
505	#440	C₂²×C₁₃	1	2	yes	complemented
506	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
507	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
508	#436	C₂²×C₁₃	1	2	yes	complemented
509	#435	C₂²×C₁₃	1	4	yes	complemented
510	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
511	#428	C₂²×C₁₃	1	2	yes	—
512	#428	C₂²×C₁₃	1	1	yes	characteristic
513	#423	C₂²×C₁₃	1	1	yes	characteristic
514	#419	C₂²×C₁₃	1	2	yes	—
515	#419	C₂²×C₁₃	1	1	yes	characteristic
516	#418	C₂²×C₁₃	1	2	yes	—
517	#418	C₂²×C₁₃	1	2	yes	—
518	#418	C₂²×C₁₃	1	2	yes	—
519	#417	C₂²×C₁₃	1	1	yes	characteristic
520	#417	C₂²×C₁₃	1	4	yes	complemented
521	#417	C₂²×C₁₃	1	4	yes	complemented
522	#416	C₂²×C₁₃	1	4	yes	complemented
523	#416	C₂²×C₁₃	1	4	yes	complemented
524	#407	C₂²×C₁₃	1	2	yes	—
525	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
526	C₂²×C₁₃	—	2	1	no	—
527	C₂²×C₁₃	—	2	1	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	2	2	no	—
530	C₂²×C₁₃	—	2	2	no	—
531	C₂²×C₁₃	—	2	2	no	—
532	C₂²×C₁₃	—	2	2	no	—
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	4	1	no	—
535	C₂²×C₁₃	—	4	4	no	—
536	C₂²×C₁₃	—	4	4	no	—
537	C₂²×C₁₃	—	4	1	no	—
538	C₂²×C₁₃	—	4	1	no	—
539	C₂²×C₁₃	—	4	4	no	—
540	C₂²×C₁₃	—	8	4	no	—
541	C₂²×C₁₃	—	8	8	no	—
542	C₂²×C₁₃	#546	1	2	yes	—
543	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₁₃	—	2	1	no	—
545	C₄×C₁₃	—	2	1	no	—
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	2	2	no	—
548	C₄×C₁₃	—	2	4	no	—
549	C₄×C₁₃	—	2	1	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	1	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	1	no	—
554	C₄×C₁₃	—	4	1	no	—
555	C₄×C₁₃	—	4	2	no	—
556	C₄×C₁₃	#546	1	2	yes	—
557	C₄×C₁₃	#575	1	2	yes	—
558	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
559	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×#41	—	2	1	no	—
561	C₂×#41	—	2	2	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	2	8	no	—
564	C₂×#41	—	4	4	no	—
565	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
566	C₂×#41	C₂³×C₁₃	1	4	yes	—
567	C₂×#41	C₂³×C₁₃	1	4	yes	—
568	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
569	C₂²×D₄	—	2	2	no	—
570	C₂²×D₄	—	2	2	no	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
575	C₂³×C₄	—	2	2	no	—
576	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
577	#137	—	2	4	no	—
578	AGL(1,ℤ/8)	—	4	4	no	—
579	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
582	C₂×D₈	C₂³×C₁₃	1	4	yes	—
583	C₂×M₁₆	—	4	4	no	—
584	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
588	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
589	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	#127	—	2	2	no	—
592	#127	—	2	2	no	—
593	#127	—	2	4	no	—
594	#127	—	2	1	no	—
595	#127	—	2	1	no	—
596	#127	C₂³×C₁₃	1	2	yes	—
597	#127	C₂³×C₁₃	1	2	yes	—
598	#126	—	2	2	no	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	—	2	1	no	—
603	#125	C₂³×C₁₃	1	2	yes	—
604	#124	—	2	1	no	—
605	#124	—	2	2	no	—
606	#123	—	2	2	no	—
607	#123	—	2	2	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	1	no	—
612	C₂²⋊Q₈	—	2	1	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
615	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
616	#121	—	2	2	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	4	no	—
621	#121	—	2	4	no	—
622	#121	—	2	4	no	—
623	#121	—	2	4	no	—
624	#121	C₂³×C₁₃	1	4	yes	—
625	#121	C₂³×C₁₃	1	4	yes	—
626	#121	C₂³×C₁₃	1	2	yes	—
627	#121	C₂³×C₁₃	1	2	yes	—
628	#120	—	2	2	no	—
629	C₄×Q₈	—	2	1	no	—
630	C₄×Q₈	—	2	1	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	—	2	1	no	—
633	C₄×Q₈	—	2	1	no	—
634	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
635	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
636	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
637	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄×D₄	—	2	1	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	1	no	—
642	C₄×D₄	—	2	2	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	4	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
648	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
649	C₄×D₄	D₄×C₁₃	1	2	yes	—
650	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₁₃	1	2	yes	—
654	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	—	2	1	no	—
658	#117	—	2	2	no	—
659	#117	—	2	1	no	—
660	#117	C₂³×C₁₃	1	1	yes	characteristic
661	#117	C₂³×C₁₃	1	2	yes	—
662	#117	C₂³×C₁₃	1	2	yes	—
663	#117	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₂²⋊C₄	—	2	2	no	—
671	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
672	C₂×C₄²	—	2	2	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
676	#107	C₂³×C₁₃	1	2	yes	—
677	#107	C₂³×C₁₃	1	4	yes	—
678	#106	C₂³×C₁₃	1	2	yes	—
679	#106	C₂³×C₁₃	1	4	yes	—
680	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
681	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
682	#103	C₂³×C₁₃	1	2	yes	—
683	#103	C₂³×C₁₃	1	2	yes	—
684	#103	C₂³×C₁₃	1	4	yes	—
685	#103	C₂³×C₁₃	1	4	yes	—
686	#103	C₂³×C₁₃	1	2	yes	—
687	#102	C₂³×C₁₃	1	4	yes	—
688	#102	C₂³×C₁₃	1	4	yes	—
689	#102	C₂³×C₁₃	1	4	yes	—
690	#102	C₂³×C₁₃	1	4	yes	—
691	#102	C₂³×C₁₃	1	2	yes	—
692	#102	C₂³×C₁₃	1	4	yes	—
693	#102	C₂³×C₁₃	1	4	yes	—
694	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
696	#97	C₂³×C₁₃	1	2	yes	—
697	C₄×C₈	C₂³×C₁₃	1	2	yes	—
698	C₂×C₁₃	—	2	2	no	—
699	C₂×C₁₃	—	4	2	no	—
700	C₂×C₁₃	—	4	2	no	—
701	C₂×C₁₃	—	8	1	no	—
702	C₂×C₁₃	—	8	4	no	—
703	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
704	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
705	C₂×C₁₃	#3585	1	1	yes	characteristic
706	C₂⁴	—	2	2	no	—
707	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
708	#41	—	2	8	no	—
709	#41	—	2	8	no	—
710	#41	—	2	2	no	—
711	#41	—	2	2	no	—
712	#41	—	4	4	no	—
713	#41	—	4	4	no	—
714	#41	—	4	8	no	—
715	#41	—	4	8	no	—
716	#41	—	4	4	no	—
717	C₂×Q₈	—	2	1	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	C₁₃×#41	1	4	yes	complemented
722	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
723	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	8	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	8	2	no	—
742	C₂×D₄	—	8	4	no	—
743	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
747	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	4	8	no	—
760	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
762	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	Q₁₆	—	2	4	no	—
769	SD₁₆	—	2	4	no	—
770	SD₁₆	—	4	4	no	—
771	D₈	—	4	4	no	—
772	M₁₆	—	2	2	no	—
773	M₁₆	—	2	2	no	—
774	M₁₆	—	2	4	no	—
775	M₁₆	—	4	4	no	—
776	C₂×C₈	—	4	4	no	—
777	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
778	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
779	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₂²⋊C₄	—	2	1	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
817	C₄²	—	2	1	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	1	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	1	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
826	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
827	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
828	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₁₃	#61160	1	1	yes	characteristic, direct product factor, Sylow
830	C₂³	—	2	4	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	4	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
839	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	1	no	—
844	Q₈	—	2	1	no	—
845	Q₈	—	4	2	no	—
846	Q₈	—	8	1	no	—
847	Q₈	C₂×C₁₃×#41	1	4	yes	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	4	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	4	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	4	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	8	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
900	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
901	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	4	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	4	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	4	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	8	4	no	—
920	C₂²	—	8	8	no	—
921	C₂²	C₁₃×#546	1	2	yes	—
922	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	4	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	1	no	—
935	C₄	C₁₃×#546	1	2	yes	—
936	C₄	C₁₃×#575	1	2	yes	—
937	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
938	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
939	C₂	—	2	2	no	—
940	C₂	—	4	2	no	—
941	C₂	—	4	2	no	—
942	C₂	—	8	4	no	—
943	C₂	—	8	1	no	—
944	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
945	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
946	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×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3475	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3332	C₂	semidirect
5. C₁₃×#3317	C₂	semidirect
6. C₁₃×#3309	C₂	semidirect
7. C₁₃×#3305	C₂	semidirect
8. C₁₃×#3304	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3094	C₂	semidirect
11. C₁₃×#3078	C₂	semidirect
12. C₁₃×#3055	C₂	semidirect
13. C₁₃×#3038	C₂	semidirect
14. C₁₃×#3005	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₁₃×#2896	C₂	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
35. C₁₃×#547	C₂²	semidirect
51. C₁₃×#490	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#482	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#480	C₂²	semidirect
58. C₁₃×#479	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#469	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#466	C₂²	semidirect
64. C₁₃×#465	C₂²	semidirect
65. C₁₃×#460	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#459	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#452	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#449	C₂²	semidirect
73. C₁₃×#441	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×Q₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₁₃×#416	C₂²	semidirect
92. C₁₃×#416	C₂²	semidirect
233. #61160	C₁₃	direct (N × H)
249. C₂×Q₈×C₁₃	#41	semidirect
357. #3475	C₂×C₁₃	semidirect
358. C₂×#550	C₂×C₁₃	semidirect
359. #3333	C₂×C₁₃	semidirect
360. #3332	C₂×C₁₃	semidirect
361. #3317	C₂×C₁₃	semidirect
362. #3309	C₂×C₁₃	semidirect
363. #3305	C₂×C₁₃	semidirect
364. #3304	C₂×C₁₃	semidirect
365. #3138	C₂×C₁₃	semidirect
366. #3094	C₂×C₁₃	semidirect
367. #3078	C₂×C₁₃	semidirect
368. #3055	C₂×C₁₃	semidirect
369. #3038	C₂×C₁₃	semidirect
370. #3005	C₂×C₁₃	semidirect
371. C₄×#137	C₂×C₁₃	semidirect
372. D₄×M₁₆	C₂×C₁₃	semidirect
373. #2896	C₂×C₁₃	semidirect
453. #556	C₂²×C₁₃	semidirect
454. #555	C₂²×C₁₃	semidirect
455. #554	C₂²×C₁₃	semidirect
456. #553	C₂²×C₁₃	semidirect
458. #552	C₂²×C₁₃	semidirect
466. #547	C₂²×C₁₃	semidirect
482. #490	C₂²×C₁₃	semidirect
483. #486	C₂²×C₁₃	semidirect
484. #486	C₂²×C₁₃	semidirect
485. #482	C₂²×C₁₃	semidirect
486. #482	C₂²×C₁₃	semidirect
487. #481	C₂²×C₁₃	semidirect
488. #480	C₂²×C₁₃	semidirect
489. #479	C₂²×C₁₃	semidirect
490. #477	C₂²×C₁₃	semidirect
491. #475	C₂²×C₁₃	semidirect
492. #469	C₂²×C₁₃	semidirect
493. #468	C₂²×C₁₃	semidirect
494. #466	C₂²×C₁₃	semidirect
495. #465	C₂²×C₁₃	semidirect
496. #460	C₂²×C₁₃	semidirect
497. #460	C₂²×C₁₃	semidirect
498. #459	C₂²×C₁₃	semidirect
499. #459	C₂²×C₁₃	semidirect
500. #452	C₂²×C₁₃	semidirect
501. #452	C₂²×C₁₃	semidirect
502. #449	C₂²×C₁₃	semidirect
503. #449	C₂²×C₁₃	semidirect
504. #441	C₂²×C₁₃	semidirect
505. #440	C₂²×C₁₃	semidirect
506. C₄×Q₁₆	C₂²×C₁₃	semidirect
507. C₄×SD₁₆	C₂²×C₁₃	semidirect
508. #436	C₂²×C₁₃	semidirect
509. #435	C₂²×C₁₃	semidirect
510. C₈×D₄	C₂²×C₁₃	semidirect
520. #417	C₂²×C₁₃	semidirect
521. #417	C₂²×C₁₃	semidirect
522. #416	C₂²×C₁₃	semidirect
523. #416	C₂²×C₁₃	semidirect
721. C₂×Q₈	C₁₃×#41	semidirect
829. C₁₃	#61160	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×#3475	2
C₂×C₁₃×#550	2
C₁₃×#3333	2
C₁₃×#3332	2
C₁₃×#3317	2
C₁₃×#3309	2
C₁₃×#3305	2
C₁₃×#3304	2
C₁₃×#3138	2
C₁₃×#3094	2
C₁₃×#3078	2
C₁₃×#3055	2
C₁₃×#3038	2
C₁₃×#3005	2
C₄×C₁₃×#137	2
D₄×C₁₃×M₁₆	2
C₁₃×#2896	2
#61160	13

Subgroups — C13×#61160 #15747499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61160 #15747499