Subgroups — C₁₃×#60922 #15747261

Order 3328.

1932 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3259	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3253	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3245	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3081	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×#3062	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3058	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#559	—	2	1	no	—
22	C₁₃×#559	—	2	1	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	complemented
30	C₁₃×#540	—	2	1	no	—
31	C₁₃×#540	C₂²	1	2	yes	complemented
32	C₁₃×#540	C₂²	1	4	yes	complemented
33	C₁₃×#538	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#535	C₂²	1	1	yes	characteristic
36	C₁₃×#535	C₂²	1	1	yes	characteristic
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₁₃×#532	C₂²	1	2	yes	complemented
42	C₁₃×#532	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	1	no	—
45	C₁₃×#529	C₂²	1	2	yes	complemented
46	C₁₃×#525	—	2	2	no	—
47	C₁₃×#518	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×#478	C₂²	1	2	yes	complemented
53	C₁₃×#478	C₂²	1	4	yes	complemented
54	C₁₃×#478	C₂²	1	4	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#476	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	4	yes	complemented
60	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#474	C₂²	1	2	yes	complemented
63	C₁₃×#474	C₂²	1	4	yes	complemented
64	C₁₃×#469	C₂²	1	4	yes	complemented
65	C₁₃×#469	C₂²	1	4	yes	complemented
66	C₁₃×#469	C₂²	1	4	yes	complemented
67	C₁₃×#468	C₂²	1	4	yes	complemented
68	C₁₃×#466	C₂²	1	4	yes	complemented
69	C₁₃×#466	C₂²	1	4	yes	complemented
70	C₁₃×#466	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#463	C₂²	1	4	yes	complemented
73	C₁₃×#463	C₂²	1	4	yes	complemented
74	C₁₃×#460	C₂²	1	2	yes	complemented
75	C₁₃×#460	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	2	yes	—
77	C₁₃×#459	C₂²	1	2	yes	—
78	C₁₃×#459	C₂²	1	4	yes	—
79	C₁₃×#459	C₂²	1	2	yes	complemented
80	C₁₃×#459	C₂²	1	2	yes	complemented
81	C₁₃×#459	C₂²	1	4	yes	complemented
82	C₁₃×#459	C₂²	1	4	yes	complemented
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×#418	C₂²	1	2	yes	—
92	C₁₃×#418	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	—	2	1	no	—
105	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×D₈	—	4	4	no	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₁₃×#131	—	4	4	no	—
112	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
115	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	1	no	—
121	C₁₃×#127	—	2	2	no	—
122	C₁₃×#127	—	2	1	no	—
123	C₁₃×#127	—	2	1	no	—
124	C₁₃×#127	C₂³	1	2	yes	—
125	C₁₃×#127	C₂³	1	2	yes	—
126	C₁₃×#127	C₂³	1	2	yes	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	C₂³	1	2	yes	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	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	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	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	—	2	2	no	—
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	2	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	4	no	—
161	C₁₃×#121	—	2	4	no	—
162	C₁₃×#121	C₂³	1	4	yes	—
163	C₁₃×#121	C₂³	1	4	yes	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	2	no	—
168	C₁₃×#120	—	2	4	no	—
169	C₁₃×#120	—	2	2	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	—	2	1	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	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	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	—	2	2	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₁₃	C₂³	1	4	yes	—
195	C₄×D₄×C₁₃	C₂³	1	4	yes	—
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	C₂³	1	2	yes	—
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	4	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	2	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	2	yes	—
227	C₁₃×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	4	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×#102	C₂³	1	4	yes	—
231	#60922	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₂⁴×C₁₃	—	2	1	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	8	4	no	—
239	C₁₃×#41	—	8	4	no	—
240	C₁₃×#41	—	8	4	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	2	1	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	1	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	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	4	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	8	2	no	—
265	C₂×D₄×C₁₃	—	8	2	no	—
266	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	4	no	—
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	8	2	no	—
280	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₁₃×SD₁₆	—	4	4	no	—
287	C₁₃×D₈	—	4	4	no	—
288	C₁₃×D₈	—	4	4	no	—
289	C₁₃×D₈	—	4	4	no	—
290	C₁₃×M₁₆	—	2	4	no	—
291	C₁₃×M₁₆	—	4	4	no	—
292	C₂×C₈×C₁₃	—	2	4	no	—
293	C₂×C₈×C₁₃	—	4	4	no	—
294	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
295	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	—	2	1	no	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₁₃	C₂×D₄	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₁₃	C₂⁴	1	2	yes	—
346	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
347	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3259	C₂×C₁₃	1	4	yes	complemented
350	#3257	C₂×C₁₃	1	4	yes	complemented
351	#3253	C₂×C₁₃	1	2	yes	complemented
352	#3251	C₂×C₁₃	1	2	yes	complemented
353	#3247	C₂×C₁₃	1	2	yes	complemented
354	#3245	C₂×C₁₃	1	2	yes	complemented
355	#3081	C₂×C₁₃	1	2	yes	complemented
356	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3062	C₂×C₁₃	1	2	yes	complemented
359	#3058	C₂×C₁₃	1	2	yes	complemented
360	#3041	C₂×C₁₃	1	2	yes	complemented
361	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	—	2	4	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	8	1	no	—
370	C₂³×C₁₃	—	8	1	no	—
371	C₂³×C₁₃	—	8	2	no	—
372	C₂³×C₁₃	—	8	2	no	—
373	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	1	no	—
377	Q₈×C₁₃	—	2	1	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	Q₈×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	4	no	—
388	D₄×C₁₃	—	2	1	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	2	no	—
391	D₄×C₁₃	—	4	2	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	—	8	2	no	—
397	D₄×C₁₃	—	8	2	no	—
398	D₄×C₁₃	—	8	2	no	—
399	D₄×C₁₃	—	8	4	no	—
400	D₄×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	—	8	4	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	4	1	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	8	1	no	—
419	C₂×C₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	—	8	4	no	—
421	C₂×C₄×C₁₃	—	8	4	no	—
422	C₂×C₄×C₁₃	—	8	1	no	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
432	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
434	C₈×C₁₃	—	2	2	no	—
435	C₈×C₁₃	—	2	2	no	—
436	C₈×C₁₃	—	2	4	no	—
437	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
438	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
439	C₂×#131	C₂²×C₁₃	1	2	yes	—
440	#559	—	2	1	no	—
441	#559	—	2	1	no	—
442	#550	—	2	1	no	—
443	#550	—	2	1	no	—
444	#546	—	2	2	no	—
445	#546	—	2	2	no	—
446	#544	C₂²×C₁₃	1	1	yes	characteristic
447	#542	—	2	1	no	—
448	#542	C₂²×C₁₃	1	2	yes	complemented
449	#540	—	2	1	no	—
450	#540	C₂²×C₁₃	1	2	yes	complemented
451	#540	C₂²×C₁₃	1	4	yes	complemented
452	#538	—	2	2	no	—
453	#537	C₂²×C₁₃	1	1	yes	characteristic
454	#535	C₂²×C₁₃	1	1	yes	characteristic
455	#535	C₂²×C₁₃	1	1	yes	characteristic
456	#535	C₂²×C₁₃	1	2	yes	—
457	#533	C₂²×C₁₃	1	1	yes	characteristic
458	#532	—	2	1	no	—
459	#532	C₂²×C₁₃	1	2	yes	complemented
460	#532	C₂²×C₁₃	1	2	yes	complemented
461	#532	C₂²×C₁₃	1	2	yes	complemented
462	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
463	#529	—	2	1	no	—
464	#529	C₂²×C₁₃	1	2	yes	complemented
465	#525	—	2	2	no	—
466	#518	C₂²×C₁₃	1	2	yes	—
467	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
468	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
470	#479	C₂²×C₁₃	1	2	yes	complemented
471	#478	C₂²×C₁₃	1	2	yes	complemented
472	#478	C₂²×C₁₃	1	4	yes	complemented
473	#478	C₂²×C₁₃	1	4	yes	complemented
474	#478	C₂²×C₁₃	1	4	yes	complemented
475	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#476	C₂²×C₁₃	1	2	yes	complemented
478	#476	C₂²×C₁₃	1	4	yes	complemented
479	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	#474	C₂²×C₁₃	1	2	yes	complemented
482	#474	C₂²×C₁₃	1	4	yes	complemented
483	#469	C₂²×C₁₃	1	4	yes	complemented
484	#469	C₂²×C₁₃	1	4	yes	complemented
485	#469	C₂²×C₁₃	1	4	yes	complemented
486	#468	C₂²×C₁₃	1	4	yes	complemented
487	#466	C₂²×C₁₃	1	4	yes	complemented
488	#466	C₂²×C₁₃	1	4	yes	complemented
489	#466	C₂²×C₁₃	1	4	yes	complemented
490	#465	C₂²×C₁₃	1	4	yes	complemented
491	#463	C₂²×C₁₃	1	4	yes	complemented
492	#463	C₂²×C₁₃	1	4	yes	complemented
493	#460	C₂²×C₁₃	1	2	yes	complemented
494	#460	C₂²×C₁₃	1	2	yes	complemented
495	#459	C₂²×C₁₃	1	2	yes	—
496	#459	C₂²×C₁₃	1	2	yes	—
497	#459	C₂²×C₁₃	1	4	yes	—
498	#459	C₂²×C₁₃	1	2	yes	complemented
499	#459	C₂²×C₁₃	1	4	yes	complemented
500	#459	C₂²×C₁₃	1	4	yes	complemented
501	#459	C₂²×C₁₃	1	2	yes	complemented
502	#428	C₂²×C₁₃	1	2	yes	—
503	#427	C₂²×C₁₃	1	2	yes	—
504	#424	C₂²×C₁₃	1	2	yes	—
505	#424	C₂²×C₁₃	1	4	yes	complemented
506	#423	C₂²×C₁₃	1	1	yes	characteristic
507	#423	C₂²×C₁₃	1	2	yes	complemented
508	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
509	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
510	#418	C₂²×C₁₃	1	2	yes	—
511	#418	C₂²×C₁₃	1	2	yes	—
512	#416	C₂²×C₁₃	1	2	yes	—
513	C₂×#102	C₂²×C₁₃	1	2	yes	—
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	4	4	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	2	no	—
522	C₂²×C₁₃	—	4	1	no	—
523	C₂²×C₁₃	—	4	2	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	4	2	no	—
526	C₂²×C₁₃	—	4	1	no	—
527	C₂²×C₁₃	—	4	4	no	—
528	C₂²×C₁₃	—	8	4	no	—
529	C₂²×C₁₃	—	16	4	no	—
530	C₂²×C₁₃	#537	1	2	yes	—
531	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
532	C₄×C₁₃	—	2	1	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	1	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	1	no	—
540	C₄×C₁₃	—	4	1	no	—
541	C₄×C₁₃	—	4	2	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₄×C₁₃	#537	1	2	yes	—
545	C₄×C₁₃	#576	1	2	yes	—
546	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	2	no	—
551	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
557	C₂³×C₄	—	2	1	no	—
558	AGL(1,ℤ/8)	—	4	4	no	—
559	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
560	C₂×D₈	—	4	4	no	—
561	C₂×D₈	C₂³×C₁₃	1	4	yes	—
562	C₂×D₈	C₂³×C₁₃	1	4	yes	—
563	C₂×D₈	C₂³×C₁₃	1	4	yes	—
564	#131	—	4	4	no	—
565	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
566	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
568	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
569	C₄⋊Q₈	—	2	1	no	—
570	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	#127	—	2	1	no	—
574	#127	—	2	2	no	—
575	#127	—	2	1	no	—
576	#127	—	2	1	no	—
577	#127	C₂³×C₁₃	1	2	yes	—
578	#127	C₂³×C₁₃	1	2	yes	—
579	#127	C₂³×C₁₃	1	2	yes	—
580	#126	—	2	2	no	—
581	#126	—	2	2	no	—
582	#125	—	2	1	no	—
583	#125	C₂³×C₁₃	1	2	yes	—
584	#125	C₂³×C₁₃	1	2	yes	—
585	#124	—	2	1	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	2	no	—
589	#124	—	2	2	no	—
590	#124	—	2	2	no	—
591	#124	C₂³×C₁₃	1	2	yes	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	4	no	—
614	#121	—	2	4	no	—
615	#121	C₂³×C₁₃	1	2	yes	—
616	#121	C₂³×C₁₃	1	4	yes	—
617	#121	C₂³×C₁₃	1	4	yes	—
618	#121	C₂³×C₁₃	1	2	yes	—
619	#121	C₂³×C₁₃	1	2	yes	—
620	#120	—	2	2	no	—
621	#120	—	2	4	no	—
622	#120	—	2	2	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
626	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
627	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	D₄×C₁₃	1	2	yes	—
640	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
641	C₄×D₄	D₄×C₁₃	1	2	yes	—
642	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₁₃	1	2	yes	—
644	C₄×D₄	C₂³×C₁₃	1	2	yes	—
645	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₄×D₄	C₂³×C₁₃	1	4	yes	—
648	C₄×D₄	C₂³×C₁₃	1	4	yes	—
649	#117	—	2	1	no	—
650	#117	—	2	2	no	—
651	#117	C₂³×C₁₃	1	1	yes	characteristic
652	#117	C₂³×C₁₃	1	2	yes	—
653	#117	C₂³×C₁₃	1	1	yes	characteristic
654	#117	C₂³×C₁₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	4	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
661	#107	C₂³×C₁₃	1	2	yes	—
662	#107	C₂³×C₁₃	1	2	yes	—
663	#107	C₂³×C₁₃	1	4	yes	—
664	#106	C₂³×C₁₃	1	2	yes	—
665	#106	C₂³×C₁₃	1	2	yes	—
666	#106	C₂³×C₁₃	1	4	yes	—
667	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
669	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
671	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
672	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
673	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
674	#103	C₂³×C₁₃	1	2	yes	—
675	#103	C₂³×C₁₃	1	2	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	#102	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	2	yes	—
679	#102	C₂³×C₁₃	1	2	yes	—
680	#102	C₂³×C₁₃	1	4	yes	—
681	#102	C₂³×C₁₃	1	4	yes	—
682	#102	C₂³×C₁₃	1	4	yes	—
683	#102	C₂³×C₁₃	1	4	yes	—
684	C₂×C₁₃	—	2	2	no	—
685	C₂×C₁₃	—	4	2	no	—
686	C₂×C₁₃	—	8	1	no	—
687	C₂×C₁₃	—	8	2	no	—
688	C₂×C₁₃	—	8	4	no	—
689	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
690	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
691	C₂×C₁₃	#3585	1	1	yes	characteristic
692	C₂⁴	—	2	2	no	—
693	C₂⁴	—	2	1	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	2	no	—
697	#41	—	2	2	no	—
698	#41	—	8	4	no	—
699	#41	—	8	4	no	—
700	#41	—	8	4	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	—	8	2	no	—
726	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
729	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	8	2	no	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	SD₁₆	—	4	4	no	—
747	D₈	—	4	4	no	—
748	D₈	—	4	4	no	—
749	D₈	—	4	4	no	—
750	M₁₆	—	2	4	no	—
751	M₁₆	—	4	4	no	—
752	C₂×C₈	—	2	4	no	—
753	C₂×C₈	—	4	4	no	—
754	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
755	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
756	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄²	—	2	1	no	—
797	C₄²	—	2	1	no	—
798	C₄²	—	2	1	no	—
799	C₄²	—	2	2	no	—
800	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₄²	C₂×D₄×C₁₃	1	2	yes	—
802	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
803	C₄²	C₂×D₄×C₁₃	1	2	yes	—
804	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
805	C₄²	C₂⁴×C₁₃	1	2	yes	—
806	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₁₃	#60922	1	1	yes	characteristic, direct product factor, Sylow
808	C₂³	—	2	2	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	—	8	2	no	—
816	C₂³	—	8	2	no	—
817	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	1	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	4	2	no	—
823	Q₈	—	4	2	no	—
824	Q₈	—	8	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	1	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	1	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	—	8	2	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	4	no	—
846	D₄	—	8	4	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	1	no	—
864	C₂×C₄	—	8	4	no	—
865	C₂×C₄	—	8	4	no	—
866	C₂×C₄	—	8	1	no	—
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
876	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
877	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
878	C₈	—	2	2	no	—
879	C₈	—	2	2	no	—
880	C₈	—	2	4	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	4	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	8	4	no	—
896	C₂²	—	16	4	no	—
897	C₂²	C₁₃×#537	1	2	yes	—
898	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
899	C₄	—	2	1	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	1	no	—
911	C₄	C₁₃×#537	1	2	yes	—
912	C₄	C₁₃×#576	1	2	yes	—
913	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
914	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
915	C₂	—	2	2	no	—
916	C₂	—	4	2	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	4	no	—
919	C₂	—	8	1	no	—
920	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
921	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
922	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3460	C₂	semidirect
3. C₁₃×#3259	C₂	semidirect
4. C₁₃×#3257	C₂	semidirect
5. C₁₃×#3253	C₂	semidirect
6. C₁₃×#3251	C₂	semidirect
7. C₁₃×#3247	C₂	semidirect
8. C₁₃×#3245	C₂	semidirect
9. C₁₃×#3081	C₂	semidirect
10. C₁₃×#3077	C₂	semidirect
11. C₁₃×#3076	C₂	semidirect
12. C₁₃×#3062	C₂	semidirect
13. C₁₃×#3058	C₂	semidirect
14. C₁₃×#3041	C₂	semidirect
15. C₁₃×#3038	C₂	semidirect
16. C₂×C₁₃×#459	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
29. C₁₃×#542	C₂²	semidirect
31. C₁₃×#540	C₂²	semidirect
32. C₁₃×#540	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₁₃×#532	C₂²	semidirect
42. C₁₃×#532	C₂²	semidirect
45. C₁₃×#529	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#478	C₂²	semidirect
53. C₁₃×#478	C₂²	semidirect
54. C₁₃×#478	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#477	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#469	C₂²	semidirect
65. C₁₃×#469	C₂²	semidirect
66. C₁₃×#469	C₂²	semidirect
67. C₁₃×#468	C₂²	semidirect
68. C₁₃×#466	C₂²	semidirect
69. C₁₃×#466	C₂²	semidirect
70. C₁₃×#466	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#463	C₂²	semidirect
73. C₁₃×#463	C₂²	semidirect
74. C₁₃×#460	C₂²	semidirect
75. C₁₃×#460	C₂²	semidirect
79. C₁₃×#459	C₂²	semidirect
80. C₁₃×#459	C₂²	semidirect
81. C₁₃×#459	C₂²	semidirect
82. C₁₃×#459	C₂²	semidirect
86. C₁₃×#424	C₂²	semidirect
88. C₁₃×#423	C₂²	semidirect
90. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
231. #60922	C₁₃	direct (N × H)
347. #3508	C₂×C₁₃	semidirect
348. #3460	C₂×C₁₃	semidirect
349. #3259	C₂×C₁₃	semidirect
350. #3257	C₂×C₁₃	semidirect
351. #3253	C₂×C₁₃	semidirect
352. #3251	C₂×C₁₃	semidirect
353. #3247	C₂×C₁₃	semidirect
354. #3245	C₂×C₁₃	semidirect
355. #3081	C₂×C₁₃	semidirect
356. #3077	C₂×C₁₃	semidirect
357. #3076	C₂×C₁₃	semidirect
358. #3062	C₂×C₁₃	semidirect
359. #3058	C₂×C₁₃	semidirect
360. #3041	C₂×C₁₃	semidirect
361. #3038	C₂×C₁₃	semidirect
362. C₂×#459	C₂×C₁₃	semidirect
363. #2906	C₂×C₁₃	semidirect
448. #542	C₂²×C₁₃	semidirect
450. #540	C₂²×C₁₃	semidirect
451. #540	C₂²×C₁₃	semidirect
459. #532	C₂²×C₁₃	semidirect
460. #532	C₂²×C₁₃	semidirect
461. #532	C₂²×C₁₃	semidirect
464. #529	C₂²×C₁₃	semidirect
470. #479	C₂²×C₁₃	semidirect
471. #478	C₂²×C₁₃	semidirect
472. #478	C₂²×C₁₃	semidirect
473. #478	C₂²×C₁₃	semidirect
474. #478	C₂²×C₁₃	semidirect
475. #477	C₂²×C₁₃	semidirect
476. #476	C₂²×C₁₃	semidirect
477. #476	C₂²×C₁₃	semidirect
478. #476	C₂²×C₁₃	semidirect
479. #475	C₂²×C₁₃	semidirect
480. #474	C₂²×C₁₃	semidirect
481. #474	C₂²×C₁₃	semidirect
482. #474	C₂²×C₁₃	semidirect
483. #469	C₂²×C₁₃	semidirect
484. #469	C₂²×C₁₃	semidirect
485. #469	C₂²×C₁₃	semidirect
486. #468	C₂²×C₁₃	semidirect
487. #466	C₂²×C₁₃	semidirect
488. #466	C₂²×C₁₃	semidirect
489. #466	C₂²×C₁₃	semidirect
490. #465	C₂²×C₁₃	semidirect
491. #463	C₂²×C₁₃	semidirect
492. #463	C₂²×C₁₃	semidirect
493. #460	C₂²×C₁₃	semidirect
494. #460	C₂²×C₁₃	semidirect
498. #459	C₂²×C₁₃	semidirect
499. #459	C₂²×C₁₃	semidirect
500. #459	C₂²×C₁₃	semidirect
501. #459	C₂²×C₁₃	semidirect
505. #424	C₂²×C₁₃	semidirect
507. #423	C₂²×C₁₃	semidirect
509. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
807. C₁₃	#60922	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×#3508	2
C₁₃×#3460	2
C₁₃×#3259	2
C₁₃×#3257	2
C₁₃×#3253	2
C₁₃×#3251	2
C₁₃×#3247	2
C₁₃×#3245	2
C₁₃×#3081	2
C₁₃×#3077	2
C₁₃×#3076	2
C₁₃×#3062	2
C₁₃×#3058	2
C₁₃×#3041	2
C₁₃×#3038	2
C₂×C₁₃×#459	2
C₁₃×#2906	2
#60922	13

Subgroups — C13×#60922 #15747261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60922 #15747261