Subgroups — C₁₃×#60919 #15747258

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3263	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3262	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
19	C₁₃×#542	—	2	2	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#542	C₂²	1	4	yes	—
22	C₁₃×#542	C₂²	1	4	yes	—
23	C₁₃×#542	C₂²	1	2	yes	complemented
24	C₁₃×#542	C₂²	1	2	yes	complemented
25	C₁₃×#541	C₂²	1	2	yes	complemented
26	C₁₃×#540	C₂²	1	2	yes	complemented
27	C₁₃×#539	—	2	1	no	—
28	C₁₃×#539	—	2	1	no	—
29	C₁₃×#538	—	2	1	no	—
30	C₁₃×#538	—	2	1	no	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×#529	—	2	2	no	—
35	C₁₃×#529	—	2	2	no	—
36	C₂×C₁₃×#126	—	2	1	no	—
37	C₂×C₁₃×#124	—	2	1	no	—
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
39	C₁₃×#525	C₂²	1	2	yes	—
40	C₂×C₁₃×#123	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₁₃×#479	C₂²	1	4	yes	complemented
49	C₁₃×#478	C₂²	1	4	yes	complemented
50	C₁₃×#477	C₂²	1	2	yes	complemented
51	C₁₃×#477	C₂²	1	4	yes	complemented
52	C₁₃×#476	C₂²	1	2	yes	complemented
53	C₁₃×#476	C₂²	1	4	yes	complemented
54	C₁₃×#475	C₂²	1	2	yes	complemented
55	C₁₃×#475	C₂²	1	4	yes	complemented
56	C₁₃×#474	C₂²	1	2	yes	complemented
57	C₁₃×#474	C₂²	1	4	yes	complemented
58	C₁₃×#470	C₂²	1	4	yes	complemented
59	C₁₃×#469	C₂²	1	4	yes	—
60	C₁₃×#468	C₂²	1	4	yes	—
61	C₁₃×#468	C₂²	1	4	yes	complemented
62	C₁₃×#467	C₂²	1	4	yes	complemented
63	C₁₃×#466	C₂²	1	4	yes	—
64	C₁₃×#465	C₂²	1	4	yes	—
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#464	C₂²	1	4	yes	complemented
68	C₁₃×#464	C₂²	1	4	yes	complemented
69	C₁₃×#463	C₂²	1	4	yes	complemented
70	C₁₃×#463	C₂²	1	4	yes	complemented
71	C₁₃×#463	C₂²	1	4	yes	complemented
72	C₁₃×#462	C₂²	1	2	yes	complemented
73	C₁₃×#461	C₂²	1	2	yes	complemented
74	C₁₃×#460	C₂²	1	2	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#428	C₂²	1	2	yes	—
77	C₁₃×#428	C₂²	1	2	yes	—
78	C₁₃×#424	C₂²	1	4	yes	complemented
79	C₁₃×#424	C₂²	1	4	yes	complemented
80	C₁₃×#423	C₂²	1	1	yes	characteristic
81	C₁₃×#423	C₂²	1	1	yes	characteristic
82	C₁₃×#423	C₂²	1	2	yes	—
83	C₁₃×#419	C₂²	1	2	yes	—
84	C₁₃×#418	C₂²	1	2	yes	—
85	C₁₃×#417	C₂²	1	2	yes	—
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	—	2	1	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	—	2	1	no	—
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×#137	—	4	4	no	—
95	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	C₂³	1	4	yes	—
100	C₂×C₁₃×M₁₆	—	4	4	no	—
101	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×#127	C₂³	1	1	yes	characteristic
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#126	—	2	2	no	—
114	C₁₃×#126	—	2	2	no	—
115	C₁₃×#126	—	2	2	no	—
116	C₁₃×#126	—	2	2	no	—
117	C₁₃×#125	—	2	2	no	—
118	C₁₃×#125	—	2	2	no	—
119	C₁₃×#125	C₂³	1	2	yes	—
120	C₁₃×#124	—	2	4	no	—
121	C₁₃×#124	—	2	4	no	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#124	C₂³	1	2	yes	—
127	C₁₃×#123	—	2	2	no	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×#123	—	2	2	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	4	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	C₂³	1	4	yes	—
150	C₁₃×#121	C₂³	1	2	yes	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#120	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	C₂³	1	2	yes	—
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₁₃×#117	—	2	2	no	—
174	C₁₃×#117	D₄	1	2	yes	—
175	C₁₃×#117	D₄	1	2	yes	—
176	C₁₃×#117	C₂³	1	2	yes	—
177	C₁₃×#117	C₂³	1	2	yes	—
178	C₁₃×#117	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
183	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
192	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	—	2	1	no	—
194	C₂×C₄²×C₁₃	—	2	2	no	—
195	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
197	C₁₃×#107	C₂³	1	4	yes	—
198	C₁₃×#107	C₂³	1	4	yes	—
199	C₁₃×#106	C₂³	1	4	yes	—
200	C₁₃×#106	C₂³	1	4	yes	—
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
203	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
204	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
205	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
206	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
207	C₁₃×#103	C₂³	1	4	yes	—
208	C₁₃×#103	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#102	C₂³	1	4	yes	—
212	C₁₃×#102	C₂³	1	4	yes	—
213	C₁₃×#102	C₂³	1	4	yes	—
214	C₁₃×#102	C₂³	1	4	yes	—
215	#60919	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂⁴×C₁₃	—	2	1	no	—
217	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₁₃×#41	—	2	4	no	—
219	C₁₃×#41	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	4	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	8	2	no	—
227	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	4	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	2	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	8	2	no	—
239	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	2	no	—
247	C₂²×C₄×C₁₃	—	2	2	no	—
248	C₂²×C₄×C₁₃	—	2	2	no	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	8	2	no	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₁₃×Q₁₆	—	4	4	no	—
261	C₁₃×SD₁₆	—	4	4	no	—
262	C₁₃×SD₁₆	—	4	4	no	—
263	C₁₃×D₈	—	4	4	no	—
264	C₁₃×M₁₆	—	2	4	no	—
265	C₁₃×M₁₆	—	2	4	no	—
266	C₁₃×M₁₆	—	4	4	no	—
267	C₂×C₈×C₁₃	—	4	4	no	—
268	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	2	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
287	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
288	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
289	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
290	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	2	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	4	no	—
301	C₁₃×C₂²⋊C₄	—	2	4	no	—
302	C₁₃×C₂²⋊C₄	—	2	4	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
313	C₄²×C₁₃	—	2	2	no	—
314	C₄²×C₁₃	—	2	2	no	—
315	C₄²×C₁₃	—	2	2	no	—
316	C₄²×C₁₃	—	2	2	no	—
317	C₄²×C₁₃	—	2	2	no	—
318	C₄²×C₁₃	C₂×D₄	1	2	yes	—
319	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₄²×C₁₃	C₂⁴	1	2	yes	—
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3263	C₂×C₁₃	1	4	yes	complemented
327	#3262	C₂×C₁₃	1	4	yes	complemented
328	#3258	C₂×C₁₃	1	4	yes	complemented
329	#3257	C₂×C₁₃	1	4	yes	complemented
330	#3079	C₂×C₁₃	1	2	yes	complemented
331	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#3056	C₂×C₁₃	1	2	yes	complemented
334	#3055	C₂×C₁₃	1	2	yes	complemented
335	#3040	C₂×C₁₃	1	2	yes	complemented
336	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	4	1	no	—
343	C₂³×C₁₃	—	4	1	no	—
344	C₂³×C₁₃	—	4	2	no	—
345	C₂³×C₁₃	—	4	2	no	—
346	C₂³×C₁₃	—	4	2	no	—
347	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
348	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	Q₈×C₁₃	—	2	2	no	—
350	Q₈×C₁₃	—	2	2	no	—
351	Q₈×C₁₃	—	2	2	no	—
352	Q₈×C₁₃	—	2	2	no	—
353	Q₈×C₁₃	—	4	2	no	—
354	Q₈×C₁₃	—	8	1	no	—
355	Q₈×C₁₃	—	8	1	no	—
356	Q₈×C₁₃	—	8	4	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	2	2	no	—
361	D₄×C₁₃	—	4	4	no	—
362	D₄×C₁₃	—	4	2	no	—
363	D₄×C₁₃	—	8	1	no	—
364	D₄×C₁₃	—	8	1	no	—
365	D₄×C₁₃	—	8	2	no	—
366	D₄×C₁₃	—	8	2	no	—
367	D₄×C₁₃	—	8	4	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	2	no	—
383	C₂×C₄×C₁₃	—	4	2	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	4	no	—
386	C₂×C₄×C₁₃	—	8	2	no	—
387	C₂×C₄×C₁₃	—	8	2	no	—
388	C₂×C₄×C₁₃	—	8	2	no	—
389	C₂×C₄×C₁₃	—	8	2	no	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
399	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₁₃	—	2	4	no	—
402	C₈×C₁₃	—	2	4	no	—
403	C₂×#137	C₂²×C₁₃	1	2	yes	—
404	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
405	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
406	#542	—	2	2	no	—
407	#542	—	2	2	no	—
408	#542	C₂²×C₁₃	1	4	yes	—
409	#542	C₂²×C₁₃	1	4	yes	—
410	#542	C₂²×C₁₃	1	2	yes	complemented
411	#542	C₂²×C₁₃	1	2	yes	complemented
412	#541	C₂²×C₁₃	1	2	yes	complemented
413	#540	C₂²×C₁₃	1	2	yes	complemented
414	#539	—	2	1	no	—
415	#539	—	2	1	no	—
416	#538	—	2	1	no	—
417	#538	—	2	1	no	—
418	#533	C₂²×C₁₃	1	1	yes	characteristic
419	#532	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	#529	—	2	2	no	—
422	#529	—	2	2	no	—
423	C₂×#126	—	2	1	no	—
424	C₂×#124	—	2	1	no	—
425	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
426	#525	C₂²×C₁₃	1	2	yes	—
427	C₂×#123	—	2	1	no	—
428	C₂×C₂²⋊Q₈	—	2	1	no	—
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
431	C₄×#41	C₂²×C₁₃	1	2	yes	—
432	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
435	#479	C₂²×C₁₃	1	4	yes	complemented
436	#478	C₂²×C₁₃	1	4	yes	complemented
437	#477	C₂²×C₁₃	1	2	yes	complemented
438	#477	C₂²×C₁₃	1	4	yes	complemented
439	#476	C₂²×C₁₃	1	2	yes	complemented
440	#476	C₂²×C₁₃	1	4	yes	complemented
441	#475	C₂²×C₁₃	1	2	yes	complemented
442	#475	C₂²×C₁₃	1	4	yes	complemented
443	#474	C₂²×C₁₃	1	2	yes	complemented
444	#474	C₂²×C₁₃	1	4	yes	complemented
445	#470	C₂²×C₁₃	1	4	yes	complemented
446	#469	C₂²×C₁₃	1	4	yes	—
447	#468	C₂²×C₁₃	1	4	yes	—
448	#468	C₂²×C₁₃	1	4	yes	complemented
449	#467	C₂²×C₁₃	1	4	yes	complemented
450	#466	C₂²×C₁₃	1	4	yes	—
451	#465	C₂²×C₁₃	1	4	yes	—
452	#465	C₂²×C₁₃	1	4	yes	complemented
453	#464	C₂²×C₁₃	1	4	yes	complemented
454	#464	C₂²×C₁₃	1	4	yes	complemented
455	#464	C₂²×C₁₃	1	4	yes	complemented
456	#463	C₂²×C₁₃	1	4	yes	complemented
457	#463	C₂²×C₁₃	1	4	yes	complemented
458	#463	C₂²×C₁₃	1	4	yes	complemented
459	#462	C₂²×C₁₃	1	2	yes	complemented
460	#461	C₂²×C₁₃	1	2	yes	complemented
461	#460	C₂²×C₁₃	1	2	yes	complemented
462	#459	C₂²×C₁₃	1	2	yes	complemented
463	#428	C₂²×C₁₃	1	2	yes	—
464	#428	C₂²×C₁₃	1	2	yes	—
465	#424	C₂²×C₁₃	1	4	yes	complemented
466	#424	C₂²×C₁₃	1	4	yes	complemented
467	#423	C₂²×C₁₃	1	1	yes	characteristic
468	#423	C₂²×C₁₃	1	1	yes	characteristic
469	#423	C₂²×C₁₃	1	2	yes	—
470	#419	C₂²×C₁₃	1	2	yes	—
471	#418	C₂²×C₁₃	1	2	yes	—
472	#417	C₂²×C₁₃	1	2	yes	—
473	#417	C₂²×C₁₃	1	2	yes	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	2	2	no	—
478	C₂²×C₁₃	—	2	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	8	2	no	—
486	C₂²×C₁₃	—	8	4	no	—
487	C₂²×C₁₃	#537	1	2	yes	—
488	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₁₃	—	2	1	no	—
490	C₄×C₁₃	—	2	1	no	—
491	C₄×C₁₃	—	2	2	no	—
492	C₄×C₁₃	—	2	2	no	—
493	C₄×C₁₃	—	2	1	no	—
494	C₄×C₁₃	—	2	1	no	—
495	C₄×C₁₃	—	2	2	no	—
496	C₄×C₁₃	—	4	2	no	—
497	C₄×C₁₃	—	4	2	no	—
498	C₄×C₁₃	—	4	2	no	—
499	C₄×C₁₃	—	4	2	no	—
500	C₄×C₁₃	—	4	2	no	—
501	C₄×C₁₃	—	4	2	no	—
502	C₄×C₁₃	#537	1	2	yes	—
503	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂×#41	C₂³×C₁₃	1	2	yes	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
512	#137	—	4	4	no	—
513	AGL(1,ℤ/8)	—	4	4	no	—
514	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
517	C₂×D₈	C₂³×C₁₃	1	4	yes	—
518	C₂×M₁₆	—	4	4	no	—
519	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
520	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
521	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
522	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	#127	C₂³×C₁₃	1	1	yes	characteristic
529	#126	—	2	4	no	—
530	#126	—	2	4	no	—
531	#126	—	2	2	no	—
532	#126	—	2	2	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	C₂³×C₁₃	1	2	yes	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	2	no	—
541	#124	—	2	2	no	—
542	#124	—	2	2	no	—
543	#124	C₂³×C₁₃	1	4	yes	—
544	#124	C₂³×C₁₃	1	2	yes	—
545	#123	—	2	2	no	—
546	#123	—	2	2	no	—
547	#123	—	2	2	no	—
548	#123	—	2	4	no	—
549	#123	—	2	4	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	4	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
560	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
561	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
562	#121	—	2	2	no	—
563	#121	—	2	1	no	—
564	#121	—	2	1	no	—
565	#121	—	2	2	no	—
566	#121	—	2	2	no	—
567	#121	C₂³×C₁₃	1	4	yes	—
568	#121	C₂³×C₁₃	1	2	yes	—
569	#121	C₂³×C₁₃	1	2	yes	—
570	#120	—	2	2	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
576	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	C₂³×C₁₃	1	2	yes	—
588	C₄×D₄	C₂³×C₁₃	1	2	yes	—
589	C₄×D₄	C₂³×C₁₃	1	2	yes	—
590	C₄×D₄	C₂³×C₁₃	1	2	yes	—
591	#117	—	2	2	no	—
592	#117	D₄×C₁₃	1	2	yes	—
593	#117	D₄×C₁₃	1	2	yes	—
594	#117	C₂³×C₁₃	1	2	yes	—
595	#117	C₂³×C₁₃	1	2	yes	—
596	#117	C₂³×C₁₃	1	2	yes	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	—	2	2	no	—
613	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	#107	C₂³×C₁₃	1	4	yes	—
616	#107	C₂³×C₁₃	1	4	yes	—
617	#106	C₂³×C₁₃	1	4	yes	—
618	#106	C₂³×C₁₃	1	4	yes	—
619	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
622	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
623	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
624	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
625	#103	C₂³×C₁₃	1	4	yes	—
626	#103	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	4	yes	—
628	#103	C₂³×C₁₃	1	4	yes	—
629	#102	C₂³×C₁₃	1	4	yes	—
630	#102	C₂³×C₁₃	1	4	yes	—
631	#102	C₂³×C₁₃	1	4	yes	—
632	#102	C₂³×C₁₃	1	4	yes	—
633	C₂×C₁₃	—	2	2	no	—
634	C₂×C₁₃	—	4	2	no	—
635	C₂×C₁₃	—	8	2	no	—
636	C₂×C₁₃	—	8	2	no	—
637	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
638	C₂×C₁₃	#3585	1	1	yes	characteristic
639	C₂×C₁₃	#3586	1	1	yes	characteristic
640	C₂⁴	—	2	1	no	—
641	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
642	#41	—	2	4	no	—
643	#41	—	2	4	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	8	2	no	—
651	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
652	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	8	2	no	—
663	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
678	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	Q₁₆	—	4	4	no	—
685	SD₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	D₈	—	4	4	no	—
688	M₁₆	—	2	4	no	—
689	M₁₆	—	2	4	no	—
690	M₁₆	—	4	4	no	—
691	C₂×C₈	—	4	4	no	—
692	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
693	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	C₂×D₄×C₁₃	1	2	yes	—
743	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₄²	C₂⁴×C₁₃	1	2	yes	—
747	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₁₃	#60919	1	1	yes	characteristic, direct product factor, Sylow
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
758	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	8	4	no	—
765	Q₈	—	8	1	no	—
766	Q₈	—	8	1	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	4	no	—
776	D₄	—	8	2	no	—
777	D₄	—	8	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	2	no	—
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₈	—	2	4	no	—
812	C₈	—	2	4	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	8	2	no	—
825	C₂²	—	8	4	no	—
826	C₂²	C₁₃×#537	1	2	yes	—
827	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₁₃×#537	1	2	yes	—
842	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
843	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	4	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
849	C₂	C₁₃×#3585	1	1	yes	characteristic
850	C₂	C₁₃×#3586	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×#3455	C₂	semidirect
2. C₂×C₁₃×#542	C₂	semidirect
3. C₁₃×#3263	C₂	semidirect
4. C₁₃×#3262	C₂	semidirect
5. C₁₃×#3258	C₂	semidirect
6. C₁₃×#3257	C₂	semidirect
7. C₁₃×#3079	C₂	semidirect
8. C₁₃×#3078	C₂	semidirect
9. C₁₃×#3077	C₂	semidirect
10. C₁₃×#3056	C₂	semidirect
11. C₁₃×#3055	C₂	semidirect
12. C₁₃×#3040	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. C₁₃×#2905	C₂	semidirect
23. C₁₃×#542	C₂²	semidirect
24. C₁₃×#542	C₂²	semidirect
25. C₁₃×#541	C₂²	semidirect
26. C₁₃×#540	C₂²	semidirect
48. C₁₃×#479	C₂²	semidirect
49. C₁₃×#478	C₂²	semidirect
50. C₁₃×#477	C₂²	semidirect
51. C₁₃×#477	C₂²	semidirect
52. C₁₃×#476	C₂²	semidirect
53. C₁₃×#476	C₂²	semidirect
54. C₁₃×#475	C₂²	semidirect
55. C₁₃×#475	C₂²	semidirect
56. C₁₃×#474	C₂²	semidirect
57. C₁₃×#474	C₂²	semidirect
58. C₁₃×#470	C₂²	semidirect
61. C₁₃×#468	C₂²	semidirect
62. C₁₃×#467	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
67. C₁₃×#464	C₂²	semidirect
68. C₁₃×#464	C₂²	semidirect
69. C₁₃×#463	C₂²	semidirect
70. C₁₃×#463	C₂²	semidirect
71. C₁₃×#463	C₂²	semidirect
72. C₁₃×#462	C₂²	semidirect
73. C₁₃×#461	C₂²	semidirect
74. C₁₃×#460	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
78. C₁₃×#424	C₂²	semidirect
79. C₁₃×#424	C₂²	semidirect
215. #60919	C₁₃	direct (N × H)
324. #3455	C₂×C₁₃	semidirect
325. C₂×#542	C₂×C₁₃	semidirect
326. #3263	C₂×C₁₃	semidirect
327. #3262	C₂×C₁₃	semidirect
328. #3258	C₂×C₁₃	semidirect
329. #3257	C₂×C₁₃	semidirect
330. #3079	C₂×C₁₃	semidirect
331. #3078	C₂×C₁₃	semidirect
332. #3077	C₂×C₁₃	semidirect
333. #3056	C₂×C₁₃	semidirect
334. #3055	C₂×C₁₃	semidirect
335. #3040	C₂×C₁₃	semidirect
336. #3037	C₂×C₁₃	semidirect
337. #3036	C₂×C₁₃	semidirect
338. #2905	C₂×C₁₃	semidirect
410. #542	C₂²×C₁₃	semidirect
411. #542	C₂²×C₁₃	semidirect
412. #541	C₂²×C₁₃	semidirect
413. #540	C₂²×C₁₃	semidirect
435. #479	C₂²×C₁₃	semidirect
436. #478	C₂²×C₁₃	semidirect
437. #477	C₂²×C₁₃	semidirect
438. #477	C₂²×C₁₃	semidirect
439. #476	C₂²×C₁₃	semidirect
440. #476	C₂²×C₁₃	semidirect
441. #475	C₂²×C₁₃	semidirect
442. #475	C₂²×C₁₃	semidirect
443. #474	C₂²×C₁₃	semidirect
444. #474	C₂²×C₁₃	semidirect
445. #470	C₂²×C₁₃	semidirect
448. #468	C₂²×C₁₃	semidirect
449. #467	C₂²×C₁₃	semidirect
452. #465	C₂²×C₁₃	semidirect
453. #464	C₂²×C₁₃	semidirect
454. #464	C₂²×C₁₃	semidirect
455. #464	C₂²×C₁₃	semidirect
456. #463	C₂²×C₁₃	semidirect
457. #463	C₂²×C₁₃	semidirect
458. #463	C₂²×C₁₃	semidirect
459. #462	C₂²×C₁₃	semidirect
460. #461	C₂²×C₁₃	semidirect
461. #460	C₂²×C₁₃	semidirect
462. #459	C₂²×C₁₃	semidirect
465. #424	C₂²×C₁₃	semidirect
466. #424	C₂²×C₁₃	semidirect
748. C₁₃	#60919	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×#3455	2
C₂×C₁₃×#542	2
C₁₃×#3263	2
C₁₃×#3262	2
C₁₃×#3258	2
C₁₃×#3257	2
C₁₃×#3079	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#3056	2
C₁₃×#3055	2
C₁₃×#3040	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#2905	2
#60919	13

Subgroups — C13×#60919 #15747258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60919 #15747258