Subgroups — C₁₃×#61080 #15747419

Order 3328.

2742 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3269	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3268	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3265	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
18	C₁₃×#577	—	2	16	no	—
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
29	C₁₃×#550	—	2	1	no	—
30	C₁₃×#550	C₂²	1	2	yes	complemented
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
33	C₁₃×#548	—	2	2	no	—
34	C₁₃×#548	C₂²	1	4	yes	complemented
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#547	C₂²	1	2	yes	—
37	C₁₃×#546	—	2	2	no	—
38	C₁₃×#546	C₂²	1	4	yes	—
39	D₄²×C₁₃	—	2	1	no	—
40	D₄²×C₁₃	C₂²	1	2	yes	—
41	C₁₃×#537	—	2	2	no	—
42	C₁₃×#537	C₂²	1	2	yes	—
43	C₁₃×#537	C₂²	1	2	yes	complemented
44	C₁₃×#534	—	2	2	no	—
45	C₁₃×#532	—	2	2	no	—
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#532	C₂²	1	1	yes	characteristic
48	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#121	—	2	2	no	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	2	yes	complemented
53	C₁₃×#497	C₂²	1	2	yes	complemented
54	C₁₃×#496	C₂²	1	2	yes	complemented
55	C₁₃×#496	C₂²	1	2	yes	complemented
56	C₁₃×#468	C₂²	1	4	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#467	C₂²	1	4	yes	complemented
59	C₁₃×#466	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#462	C₂²	1	2	yes	complemented
63	C₁₃×#461	C₂²	1	2	yes	complemented
64	C₁₃×#460	C₂²	1	2	yes	complemented
65	C₁₃×#459	C₂²	1	2	yes	complemented
66	C₁₃×#452	C₂²	1	4	yes	complemented
67	C₁₃×#452	C₂²	1	4	yes	complemented
68	C₁₃×#451	C₂²	1	4	yes	complemented
69	C₁₃×#450	C₂²	1	4	yes	complemented
70	C₁₃×#449	C₂²	1	4	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#448	C₂²	1	4	yes	complemented
73	C₁₃×#447	C₂²	1	4	yes	complemented
74	C₁₃×#440	C₂²	1	4	yes	complemented
75	C₁₃×#440	C₂²	1	4	yes	complemented
76	C₁₃×#435	C₂²	1	4	yes	complemented
77	C₁₃×#435	C₂²	1	4	yes	complemented
78	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#417	C₂²	1	2	yes	complemented
81	C₁₃×#417	C₂²	1	2	yes	complemented
82	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
84	C₁₃×#408	C₂²	1	2	yes	complemented
85	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×2₋¹⁺⁴	—	2	8	no	—
87	C₁₃×2₋¹⁺⁴	—	4	4	no	—
88	C₁₃×H(5,𝔽₂)	—	2	8	no	—
89	C₁₃×H(5,𝔽₂)	—	4	4	no	—
90	C₂×C₁₃×#41	—	2	2	no	—
91	C₂×C₁₃×#41	—	2	4	no	—
92	C₂×C₁₃×#41	—	2	2	no	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	4	yes	—
96	C₂×C₁₃×#41	C₂³	1	4	yes	—
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₁₃	—	2	4	no	—
102	C₂²×D₄×C₁₃	—	2	2	no	—
103	C₂²×D₄×C₁₃	—	2	2	no	—
104	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₁₃×#137	—	2	8	no	—
108	C₁₃×#137	—	2	16	no	—
109	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
111	C₁₃×#135	—	2	16	no	—
112	C₁₃×#135	—	2	8	no	—
113	C₁₃×#135	—	4	4	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	—	2	16	no	—
118	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
119	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
126	C₂×C₁₃×D₈	C₂³	1	4	yes	—
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₁₃×#131	—	2	8	no	—
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
134	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×#127	—	2	2	no	—
140	C₁₃×#127	D₄	1	1	yes	characteristic
141	C₁₃×#127	C₂³	1	1	yes	characteristic
142	C₁₃×#127	C₂³	1	1	yes	characteristic
143	C₁₃×#124	—	2	4	no	—
144	C₁₃×#124	D₄	1	2	yes	—
145	C₁₃×#124	C₂³	1	2	yes	—
146	C₁₃×#124	C₂³	1	2	yes	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×#123	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	4	no	—
152	C₁₃×C₂²⋊Q₈	—	2	4	no	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	—	2	1	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	4	no	—
167	C₁₃×#121	—	2	4	no	—
168	C₁₃×#121	D₄	1	2	yes	—
169	C₁₃×#121	D₄	1	2	yes	—
170	C₁₃×#121	C₂³	1	4	yes	—
171	C₁₃×#121	C₂³	1	4	yes	—
172	C₁₃×#120	—	2	4	no	—
173	C₁₃×#120	—	2	4	no	—
174	C₄×Q₈×C₁₃	—	2	1	no	—
175	C₄×Q₈×C₁₃	—	2	1	no	—
176	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	—	2	1	no	—
186	C₄×D₄×C₁₃	—	2	1	no	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₂×C₄²×C₁₃	—	2	1	no	—
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#107	C₂³	1	4	yes	—
200	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₁₃×#97	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	#61080	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂⁴×C₁₃	—	2	1	no	—
214	C₂⁴×C₁₃	—	2	4	no	—
215	C₁₃×#41	—	2	4	no	—
216	C₁₃×#41	—	2	4	no	—
217	C₁₃×#41	—	2	8	no	—
218	C₁₃×#41	—	2	8	no	—
219	C₁₃×#41	—	2	4	no	—
220	C₁₃×#41	—	2	4	no	—
221	C₁₃×#41	—	2	4	no	—
222	C₁₃×#41	—	2	4	no	—
223	C₁₃×#41	—	4	4	no	—
224	C₁₃×#41	—	4	4	no	—
225	C₁₃×#41	—	4	16	no	—
226	C₁₃×#41	—	4	8	no	—
227	C₁₃×#41	—	4	8	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	4	no	—
230	C₂×Q₈×C₁₃	—	2	2	no	—
231	C₂×Q₈×C₁₃	—	2	8	no	—
232	C₂×Q₈×C₁₃	—	4	4	no	—
233	C₂×Q₈×C₁₃	—	4	8	no	—
234	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
236	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₁₃	—	2	8	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	4	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	—	4	8	no	—
255	C₂×D₄×C₁₃	—	4	16	no	—
256	C₂×D₄×C₁₃	—	8	4	no	—
257	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
258	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
260	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	4	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	4	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	8	2	no	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₁₃×Q₁₆	—	2	8	no	—
281	C₁₃×Q₁₆	—	2	4	no	—
282	C₁₃×Q₁₆	—	4	2	no	—
283	C₁₃×SD₁₆	—	2	8	no	—
284	C₁₃×SD₁₆	—	2	8	no	—
285	C₁₃×SD₁₆	—	2	4	no	—
286	C₁₃×SD₁₆	—	2	4	no	—
287	C₁₃×SD₁₆	—	4	2	no	—
288	C₁₃×SD₁₆	—	4	2	no	—
289	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
290	C₁₃×D₈	—	2	8	no	—
291	C₁₃×D₈	—	2	4	no	—
292	C₁₃×D₈	—	4	2	no	—
293	C₁₃×M₁₆	—	2	4	no	—
294	C₁₃×M₁₆	—	2	8	no	—
295	C₂×C₈×C₁₃	—	2	2	no	—
296	C₂×C₈×C₁₃	—	2	8	no	—
297	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
326	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×#577	C₂×C₁₃	1	2	yes	complemented
334	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3269	C₂×C₁₃	1	4	yes	complemented
337	#3268	C₂×C₁₃	1	4	yes	complemented
338	#3266	C₂×C₁₃	1	4	yes	complemented
339	#3265	C₂×C₁₃	1	4	yes	complemented
340	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#3061	C₂×C₁₃	1	2	yes	complemented
342	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3013	C₂×C₁₃	1	2	yes	complemented
345	#3012	C₂×C₁₃	1	2	yes	complemented
346	C₂×#440	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#2932	C₂×C₁₃	1	1	yes	characteristic, complemented
348	C₂³×C₁₃	—	2	2	no	—
349	C₂³×C₁₃	—	2	4	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	4	8	no	—
353	C₂³×C₁₃	—	8	1	no	—
354	C₂³×C₁₃	—	8	1	no	—
355	C₂³×C₁₃	—	8	4	no	—
356	C₂³×C₁₃	—	8	4	no	—
357	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	Q₈×C₁₃	—	2	4	no	—
360	Q₈×C₁₃	—	2	4	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	4	8	no	—
367	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
368	D₄×C₁₃	—	2	8	no	—
369	D₄×C₁₃	—	2	4	no	—
370	D₄×C₁₃	—	2	4	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	2	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	2	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	8	no	—
379	D₄×C₁₃	—	4	8	no	—
380	D₄×C₁₃	—	4	2	no	—
381	D₄×C₁₃	—	4	2	no	—
382	D₄×C₁₃	—	4	8	no	—
383	D₄×C₁₃	—	4	4	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	8	1	no	—
386	D₄×C₁₃	—	8	1	no	—
387	D₄×C₁₃	—	8	4	no	—
388	D₄×C₁₃	—	8	4	no	—
389	D₄×C₁₃	C₂²×D₄	1	4	yes	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	4	no	—
393	C₂×C₄×C₁₃	—	2	4	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	8	no	—
401	C₂×C₄×C₁₃	—	4	8	no	—
402	C₂×C₄×C₁₃	—	4	8	no	—
403	C₂×C₄×C₁₃	—	4	4	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	8	2	no	—
407	C₂×C₄×C₁₃	—	8	1	no	—
408	C₂×C₄×C₁₃	—	8	1	no	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
418	C₈×C₁₃	—	2	4	no	—
419	C₈×C₁₃	—	2	2	no	—
420	C₈×C₁₃	C₂²×D₄	1	4	yes	—
421	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
422	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
423	#577	—	2	16	no	—
424	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
425	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
426	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
427	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
428	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
429	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
430	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
431	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
432	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
433	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
434	#550	—	2	1	no	—
435	#550	C₂²×C₁₃	1	2	yes	complemented
436	D₄×Q₈	—	2	1	no	—
437	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
438	#548	—	2	2	no	—
439	#548	C₂²×C₁₃	1	4	yes	complemented
440	#547	—	2	1	no	—
441	#547	C₂²×C₁₃	1	2	yes	—
442	#546	—	2	2	no	—
443	#546	C₂²×C₁₃	1	4	yes	—
444	D₄²	—	2	1	no	—
445	D₄²	C₂²×C₁₃	1	2	yes	—
446	#537	—	2	2	no	—
447	#537	C₂²×C₁₃	1	2	yes	—
448	#537	C₂²×C₁₃	1	2	yes	complemented
449	#534	—	2	2	no	—
450	#532	—	2	2	no	—
451	#532	C₂²×C₁₃	1	1	yes	characteristic
452	#532	C₂²×C₁₃	1	1	yes	characteristic
453	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	C₂×#121	—	2	2	no	—
455	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
457	#497	C₂²×C₁₃	1	2	yes	complemented
458	#497	C₂²×C₁₃	1	2	yes	complemented
459	#496	C₂²×C₁₃	1	2	yes	complemented
460	#496	C₂²×C₁₃	1	2	yes	complemented
461	#468	C₂²×C₁₃	1	4	yes	complemented
462	#468	C₂²×C₁₃	1	4	yes	complemented
463	#467	C₂²×C₁₃	1	4	yes	complemented
464	#466	C₂²×C₁₃	1	4	yes	complemented
465	#464	C₂²×C₁₃	1	4	yes	complemented
466	#463	C₂²×C₁₃	1	4	yes	complemented
467	#462	C₂²×C₁₃	1	2	yes	complemented
468	#461	C₂²×C₁₃	1	2	yes	complemented
469	#460	C₂²×C₁₃	1	2	yes	complemented
470	#459	C₂²×C₁₃	1	2	yes	complemented
471	#452	C₂²×C₁₃	1	4	yes	complemented
472	#452	C₂²×C₁₃	1	4	yes	complemented
473	#451	C₂²×C₁₃	1	4	yes	complemented
474	#450	C₂²×C₁₃	1	4	yes	complemented
475	#449	C₂²×C₁₃	1	4	yes	complemented
476	#449	C₂²×C₁₃	1	4	yes	complemented
477	#448	C₂²×C₁₃	1	4	yes	complemented
478	#447	C₂²×C₁₃	1	4	yes	complemented
479	#440	C₂²×C₁₃	1	4	yes	complemented
480	#440	C₂²×C₁₃	1	4	yes	complemented
481	#435	C₂²×C₁₃	1	4	yes	complemented
482	#435	C₂²×C₁₃	1	4	yes	complemented
483	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	#417	C₂²×C₁₃	1	2	yes	complemented
486	#417	C₂²×C₁₃	1	2	yes	complemented
487	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
489	#408	C₂²×C₁₃	1	2	yes	complemented
490	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	4	no	—
494	C₂²×C₁₃	—	2	4	no	—
495	C₂²×C₁₃	—	2	4	no	—
496	C₂²×C₁₃	—	2	4	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	8	4	no	—
506	C₂²×C₁₃	—	16	8	no	—
507	C₂²×C₁₃	D₄²	1	2	yes	—
508	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	4	no	—
514	C₄×C₁₃	—	2	4	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	D₄²	1	2	yes	—
520	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
521	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	2₋¹⁺⁴	—	2	8	no	—
523	2₋¹⁺⁴	—	4	4	no	—
524	H(5,𝔽₂)	—	2	8	no	—
525	H(5,𝔽₂)	—	4	4	no	—
526	C₂×#41	—	2	2	no	—
527	C₂×#41	—	2	4	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	C₂³×C₁₃	1	2	yes	—
530	C₂×#41	C₂³×C₁₃	1	2	yes	—
531	C₂×#41	C₂³×C₁₃	1	4	yes	—
532	C₂×#41	C₂³×C₁₃	1	4	yes	—
533	C₂×#41	C₂³×C₁₃	1	2	yes	—
534	C₂²×Q₈	—	2	2	no	—
535	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
536	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×D₄	—	2	4	no	—
538	C₂²×D₄	—	2	2	no	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
541	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	—	2	1	no	—
543	#137	—	2	8	no	—
544	#137	—	2	16	no	—
545	AGL(1,ℤ/8)	—	2	8	no	—
546	AGL(1,ℤ/8)	—	2	16	no	—
547	#135	—	2	16	no	—
548	#135	—	2	8	no	—
549	#135	—	4	4	no	—
550	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
551	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
552	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
553	C₂×SD₁₆	—	2	16	no	—
554	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
555	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
560	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
561	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
562	C₂×D₈	C₂³×C₁₃	1	4	yes	—
563	C₂×D₈	C₂³×C₁₃	1	2	yes	—
564	C₂×D₈	C₂³×C₁₃	1	2	yes	—
565	#131	—	2	8	no	—
566	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
567	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
568	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
569	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
570	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
571	C₄⋊Q₈	—	2	2	no	—
572	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
573	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
575	#127	—	2	2	no	—
576	#127	D₄×C₁₃	1	1	yes	characteristic
577	#127	C₂³×C₁₃	1	1	yes	characteristic
578	#127	C₂³×C₁₃	1	1	yes	characteristic
579	#124	—	2	4	no	—
580	#124	D₄×C₁₃	1	2	yes	—
581	#124	C₂³×C₁₃	1	2	yes	—
582	#124	C₂³×C₁₃	1	2	yes	—
583	#123	—	2	4	no	—
584	#123	—	2	4	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	4	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
590	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
591	#121	—	2	4	no	—
592	#121	—	2	2	no	—
593	#121	—	2	4	no	—
594	#121	—	2	4	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	1	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	4	no	—
603	#121	—	2	4	no	—
604	#121	D₄×C₁₃	1	2	yes	—
605	#121	D₄×C₁₃	1	2	yes	—
606	#121	C₂³×C₁₃	1	4	yes	—
607	#121	C₂³×C₁₃	1	4	yes	—
608	#120	—	2	4	no	—
609	#120	—	2	4	no	—
610	C₄×Q₈	—	2	1	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
613	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	4	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	C₂³×C₁₃	1	2	yes	—
624	C₄×D₄	C₂³×C₁₃	1	2	yes	—
625	C₄×D₄	C₂³×C₁₃	1	2	yes	—
626	C₄×D₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₄²	—	2	1	no	—
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	#107	C₂³×C₁₃	1	4	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	#103	C₂³×C₁₃	1	4	yes	—
639	#103	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	4	yes	—
642	#102	C₂³×C₁₃	1	4	yes	—
643	#102	C₂³×C₁₃	1	4	yes	—
644	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
645	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
646	#97	C₂³×C₁₃	1	2	yes	—
647	#97	C₂³×C₁₃	1	2	yes	—
648	C₂×C₁₃	—	2	2	no	—
649	C₂×C₁₃	—	4	4	no	—
650	C₂×C₁₃	—	4	4	no	—
651	C₂×C₁₃	—	8	2	no	—
652	C₂×C₁₃	—	8	2	no	—
653	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
654	C₂×C₁₃	#3585	1	1	yes	characteristic
655	C₂×C₁₃	#3586	1	1	yes	characteristic
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	4	no	—
658	#41	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	8	no	—
661	#41	—	2	8	no	—
662	#41	—	2	4	no	—
663	#41	—	2	4	no	—
664	#41	—	2	4	no	—
665	#41	—	2	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	16	no	—
669	#41	—	4	8	no	—
670	#41	—	4	8	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	8	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	4	8	no	—
677	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
678	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	complemented
679	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
680	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
682	C₂×D₄	—	2	8	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	4	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	16	no	—
699	C₂×D₄	—	8	4	no	—
700	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
701	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
702	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
703	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
704	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
705	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
706	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
707	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	8	2	no	—
719	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
722	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
723	Q₁₆	—	2	8	no	—
724	Q₁₆	—	2	4	no	—
725	Q₁₆	—	4	2	no	—
726	SD₁₆	—	2	8	no	—
727	SD₁₆	—	2	8	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	4	2	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
733	D₈	—	2	8	no	—
734	D₈	—	2	4	no	—
735	D₈	—	4	2	no	—
736	M₁₆	—	2	4	no	—
737	M₁₆	—	2	8	no	—
738	C₂×C₈	—	2	2	no	—
739	C₂×C₈	—	2	8	no	—
740	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
741	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
742	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
743	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₁₃	#61080	1	1	yes	characteristic, direct product factor, Sylow
777	C₂³	—	2	2	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	4	8	no	—
782	C₂³	—	8	1	no	—
783	C₂³	—	8	1	no	—
784	C₂³	—	8	4	no	—
785	C₂³	—	8	4	no	—
786	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
787	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
788	Q₈	—	2	4	no	—
789	Q₈	—	2	4	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	8	no	—
796	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
797	D₄	—	2	8	no	—
798	D₄	—	2	4	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	4	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	8	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	1	no	—
816	D₄	—	8	4	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₁₃	1	4	yes	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	8	1	no	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
845	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
846	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
847	C₈	—	2	4	no	—
848	C₈	—	2	2	no	—
849	C₈	C₂²×D₄×C₁₃	1	4	yes	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	4	no	—
865	C₂²	—	16	8	no	—
866	C₂²	D₄²×C₁₃	1	2	yes	—
867	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	4	no	—
873	C₄	—	2	4	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	D₄²×C₁₃	1	2	yes	—
879	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
880	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
881	C₂	—	2	2	no	—
882	C₂	—	4	4	no	—
883	C₂	—	4	4	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
887	C₂	C₁₃×#3585	1	1	yes	characteristic
888	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 ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3496	C₂	semidirect
4. C₁₃×#3269	C₂	semidirect
5. C₁₃×#3268	C₂	semidirect
6. C₁₃×#3266	C₂	semidirect
7. C₁₃×#3265	C₂	semidirect
8. C₁₃×#3150	C₂	semidirect
9. C₁₃×#3061	C₂	semidirect
10. C₁₃×#3037	C₂	semidirect
11. C₁₃×#3036	C₂	semidirect
12. C₁₃×#3013	C₂	semidirect
13. C₁₃×#3012	C₂	semidirect
14. C₂×C₁₃×#440	C₂	semidirect
15. C₁₃×#2932	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₁₃×#135	C₂²	semidirect
24. C₂×C₁₃×#135	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
27. C₂²×C₁₃×SD₁₆	C₂²	semidirect
28. C₂×C₁₃×#131	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#548	C₂²	semidirect
43. C₁₃×#537	C₂²	semidirect
48. C₁₃×#532	C₂²	semidirect
50. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
54. C₁₃×#496	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#468	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#466	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#462	C₂²	semidirect
63. C₁₃×#461	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#459	C₂²	semidirect
66. C₁₃×#452	C₂²	semidirect
67. C₁₃×#452	C₂²	semidirect
68. C₁₃×#451	C₂²	semidirect
69. C₁₃×#450	C₂²	semidirect
70. C₁₃×#449	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#448	C₂²	semidirect
73. C₁₃×#447	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₁₃×#440	C₂²	semidirect
76. C₁₃×#435	C₂²	semidirect
77. C₁₃×#435	C₂²	semidirect
78. C₂×C₁₃×#107	C₂²	semidirect
79. C₁₃×#423	C₂²	semidirect
80. C₁₃×#417	C₂²	semidirect
81. C₁₃×#417	C₂²	semidirect
82. C₂×C₁₃×#103	C₂²	semidirect
84. C₁₃×#408	C₂²	semidirect
85. C₂×C₁₃×#97	C₂²	semidirect
118. C₂×C₁₃×SD₁₆	D₄	semidirect
212. #61080	C₁₃	direct (N × H)
235. C₂×Q₈×C₁₃	C₂×D₄	semidirect
289. C₁₃×SD₁₆	C₂×D₄	semidirect
297. C₂×C₈×C₁₃	C₂×D₄	semidirect
333. C₂×#577	C₂×C₁₃	semidirect
334. #3497	C₂×C₁₃	semidirect
335. #3496	C₂×C₁₃	semidirect
336. #3269	C₂×C₁₃	semidirect
337. #3268	C₂×C₁₃	semidirect
338. #3266	C₂×C₁₃	semidirect
339. #3265	C₂×C₁₃	semidirect
340. #3150	C₂×C₁₃	semidirect
341. #3061	C₂×C₁₃	semidirect
342. #3037	C₂×C₁₃	semidirect
343. #3036	C₂×C₁₃	semidirect
344. #3013	C₂×C₁₃	semidirect
345. #3012	C₂×C₁₃	semidirect
346. C₂×#440	C₂×C₁₃	semidirect
347. #2932	C₂×C₁₃	semidirect
421. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
424. C₂×#137	C₂²×C₁₃	semidirect
425. C₂×#137	C₂²×C₁₃	semidirect
427. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
428. C₂×#135	C₂²×C₁₃	semidirect
429. C₂×#135	C₂²×C₁₃	semidirect
430. C₂×#135	C₂²×C₁₃	semidirect
432. C₂²×SD₁₆	C₂²×C₁₃	semidirect
433. C₂×#131	C₂²×C₁₃	semidirect
435. #550	C₂²×C₁₃	semidirect
437. D₄×Q₈	C₂²×C₁₃	semidirect
439. #548	C₂²×C₁₃	semidirect
448. #537	C₂²×C₁₃	semidirect
453. #532	C₂²×C₁₃	semidirect
455. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
457. #497	C₂²×C₁₃	semidirect
458. #497	C₂²×C₁₃	semidirect
459. #496	C₂²×C₁₃	semidirect
460. #496	C₂²×C₁₃	semidirect
461. #468	C₂²×C₁₃	semidirect
462. #468	C₂²×C₁₃	semidirect
463. #467	C₂²×C₁₃	semidirect
464. #466	C₂²×C₁₃	semidirect
465. #464	C₂²×C₁₃	semidirect
466. #463	C₂²×C₁₃	semidirect
467. #462	C₂²×C₁₃	semidirect
468. #461	C₂²×C₁₃	semidirect
469. #460	C₂²×C₁₃	semidirect
470. #459	C₂²×C₁₃	semidirect
471. #452	C₂²×C₁₃	semidirect
472. #452	C₂²×C₁₃	semidirect
473. #451	C₂²×C₁₃	semidirect
474. #450	C₂²×C₁₃	semidirect
475. #449	C₂²×C₁₃	semidirect
476. #449	C₂²×C₁₃	semidirect
477. #448	C₂²×C₁₃	semidirect
478. #447	C₂²×C₁₃	semidirect
479. #440	C₂²×C₁₃	semidirect
480. #440	C₂²×C₁₃	semidirect
481. #435	C₂²×C₁₃	semidirect
482. #435	C₂²×C₁₃	semidirect
483. C₂×#107	C₂²×C₁₃	semidirect
484. #423	C₂²×C₁₃	semidirect
485. #417	C₂²×C₁₃	semidirect
486. #417	C₂²×C₁₃	semidirect
487. C₂×#103	C₂²×C₁₃	semidirect
489. #408	C₂²×C₁₃	semidirect
490. C₂×#97	C₂²×C₁₃	semidirect
554. C₂×SD₁₆	D₄×C₁₃	semidirect
678. C₂×Q₈	C₂×D₄×C₁₃	semidirect
732. SD₁₆	C₂×D₄×C₁₃	semidirect
740. C₂×C₈	C₂×D₄×C₁₃	semidirect
776. C₁₃	#61080	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#577	2
C₁₃×#3497	2
C₁₃×#3496	2
C₁₃×#3269	2
C₁₃×#3268	2
C₁₃×#3266	2
C₁₃×#3265	2
C₁₃×#3150	2
C₁₃×#3061	2
C₁₃×#3037	2
C₁₃×#3036	2
C₁₃×#3013	2
C₁₃×#3012	2
C₂×C₁₃×#440	2
C₁₃×#2932	2
#61080	13

Subgroups — C13×#61080 #15747419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61080 #15747419