Subgroups — C₁₃×#61064 #15747403

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3489	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3276	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3275	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3270	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3267	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	—
18	C₁₃×#578	—	2	8	no	—
19	C₁₃×#575	—	2	8	no	—
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×#137	C₂²	1	2	yes	—
22	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₂×C₁₃×#135	C₂²	1	2	yes	—
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
31	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
36	C₁₃×#548	C₂²	1	4	yes	—
37	C₁₃×#547	—	2	4	no	—
38	C₁₃×#547	C₂²	1	4	yes	—
39	C₁₃×#546	—	2	4	no	—
40	C₁₃×#546	C₂²	1	4	yes	complemented
41	C₁₃×#537	—	2	2	no	—
42	C₁₃×#537	C₂²	1	2	yes	complemented
43	C₁₃×#536	—	2	2	no	—
44	C₁₃×#536	C₂²	1	2	yes	complemented
45	C₁₃×#525	—	2	2	no	—
46	C₁₃×#525	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₁₃×#520	C₂²	1	2	yes	complemented
50	C₁₃×#497	C₂²	1	4	yes	complemented
51	C₁₃×#495	C₂²	1	2	yes	complemented
52	C₁₃×#494	C₂²	1	2	yes	complemented
53	C₁₃×#470	C₂²	1	4	yes	complemented
54	C₁₃×#470	C₂²	1	4	yes	complemented
55	C₁₃×#470	C₂²	1	2	yes	complemented
56	C₁₃×#469	C₂²	1	2	yes	complemented
57	C₁₃×#465	C₂²	1	4	yes	complemented
58	C₁₃×#464	C₂²	1	4	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#462	C₂²	1	4	yes	complemented
61	C₁₃×#461	C₂²	1	4	yes	complemented
62	C₁₃×#452	C₂²	1	4	yes	—
63	C₁₃×#452	C₂²	1	4	yes	—
64	C₁₃×#452	C₂²	1	4	yes	complemented
65	C₁₃×#451	C₂²	1	4	yes	complemented
66	C₁₃×#451	C₂²	1	4	yes	complemented
67	C₁₃×#450	C₂²	1	4	yes	complemented
68	C₁₃×#449	C₂²	1	4	yes	complemented
69	C₁₃×#448	C₂²	1	4	yes	complemented
70	C₁₃×#442	C₂²	1	2	yes	complemented
71	C₁₃×#441	C₂²	1	2	yes	complemented
72	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
73	C₁₃×#436	C₂²	1	4	yes	complemented
74	C₁₃×#435	C₂²	1	4	yes	complemented
75	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#417	C₂²	1	2	yes	complemented
78	C₁₃×#417	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
80	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#407	C₂²	1	1	yes	characteristic
82	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×2₋¹⁺⁴	—	2	8	no	—
84	C₁₃×2₋¹⁺⁴	—	4	4	no	—
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	—	2	4	no	—
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	2	2	no	—
89	C₂×C₁₃×#41	—	2	8	no	—
90	C₂×C₁₃×#41	—	4	4	no	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	4	yes	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	2	yes	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₁₃	—	2	2	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	—	2	2	no	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#137	—	2	8	no	—
106	C₁₃×#137	—	2	8	no	—
107	C₁₃×#137	—	2	8	no	—
108	C₁₃×#137	—	2	16	no	—
109	C₁₃×#137	—	4	4	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
112	C₁₃×#135	—	2	8	no	—
113	C₁₃×#135	—	2	8	no	—
114	C₁₃×#135	—	2	4	no	—
115	C₁₃×#135	D₄	1	8	yes	complemented
116	C₂×C₁₃×Q₁₆	—	2	8	no	—
117	C₂×C₁₃×Q₁₆	—	2	4	no	—
118	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×D₈	C₂³	1	2	yes	—
132	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
134	C₁₃×#131	—	2	4	no	—
135	C₂×C₁₃×M₁₆	—	2	4	no	—
136	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
141	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	—	2	4	no	—
145	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×#124	—	2	4	no	—
147	C₁₃×#124	C₂³	1	4	yes	—
148	C₁₃×#123	—	2	4	no	—
149	C₁₃×#123	—	2	4	no	—
150	C₁₃×#123	—	2	4	no	—
151	C₁₃×#123	—	2	4	no	—
152	C₁₃×#123	D₄	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	—	2	2	no	—
157	C₁₃×C₂²⋊Q₈	—	2	4	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	4	no	—
160	C₁₃×C₂²⋊Q₈	—	2	4	no	—
161	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	4	no	—
167	C₁₃×#121	—	2	4	no	—
168	C₁₃×#121	—	2	4	no	—
169	C₁₃×#121	—	2	4	no	—
170	C₁₃×#121	D₄	1	2	yes	—
171	C₁₃×#121	C₂³	1	4	yes	—
172	C₁₃×#120	—	2	4	no	—
173	C₁₃×#120	D₄	1	2	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
175	C₄×D₄×C₁₃	—	2	4	no	—
176	C₄×D₄×C₁₃	—	2	4	no	—
177	C₄×D₄×C₁₃	—	2	4	no	—
178	C₄×D₄×C₁₃	C₂³	1	4	yes	—
179	C₄×D₄×C₁₃	C₂³	1	4	yes	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×#106	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#103	C₂³	1	4	yes	—
193	C₁₃×#103	C₂³	1	4	yes	—
194	C₁₃×#103	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×#102	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₁₃×#97	C₂³	1	2	yes	—
200	C₄×C₈×C₁₃	C₂³	1	2	yes	—
201	#61064	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₃	—	2	2	no	—
203	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₁₃×#41	—	2	2	no	—
205	C₁₃×#41	—	2	4	no	—
206	C₁₃×#41	—	2	2	no	—
207	C₁₃×#41	—	2	4	no	—
208	C₁₃×#41	—	2	8	no	—
209	C₁₃×#41	—	2	4	no	—
210	C₁₃×#41	—	2	4	no	—
211	C₁₃×#41	—	2	4	no	—
212	C₁₃×#41	—	4	8	no	—
213	C₁₃×#41	—	4	2	no	—
214	C₁₃×#41	—	4	2	no	—
215	C₁₃×#41	—	4	4	no	—
216	C₁₃×#41	—	4	8	no	—
217	C₁₃×#41	—	4	8	no	—
218	C₁₃×#41	—	4	16	no	—
219	C₁₃×#41	C₂×D₄	1	8	yes	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	2	2	no	—
223	C₂×Q₈×C₁₃	—	2	8	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	2	4	no	—
226	C₂×Q₈×C₁₃	—	2	4	no	—
227	C₂×Q₈×C₁₃	—	4	2	no	—
228	C₂×Q₈×C₁₃	—	4	4	no	—
229	C₂×Q₈×C₁₃	—	4	8	no	—
230	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	2	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	4	2	no	—
243	C₂×D₄×C₁₃	—	4	8	no	—
244	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₃	—	2	2	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	2	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	4	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	4	no	—
261	C₂²×C₄×C₁₃	—	4	8	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₁₃×Q₁₆	—	2	8	no	—
268	C₁₃×Q₁₆	—	2	4	no	—
269	C₁₃×Q₁₆	—	2	4	no	—
270	C₁₃×Q₁₆	—	2	4	no	—
271	C₁₃×Q₁₆	—	2	2	no	—
272	C₁₃×Q₁₆	—	4	4	no	—
273	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
274	C₁₃×SD₁₆	—	2	4	no	—
275	C₁₃×SD₁₆	—	2	4	no	—
276	C₁₃×SD₁₆	—	2	8	no	—
277	C₁₃×SD₁₆	—	2	4	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
280	C₁₃×D₈	—	2	4	no	—
281	C₁₃×D₈	—	2	2	no	—
282	C₁₃×D₈	C₂×D₄	1	4	yes	—
283	C₁₃×M₁₆	—	2	2	no	—
284	C₁₃×M₁₆	—	2	2	no	—
285	C₁₃×M₁₆	—	2	4	no	—
286	C₁₃×M₁₆	—	2	4	no	—
287	C₁₃×M₁₆	—	2	4	no	—
288	C₂×C₈×C₁₃	—	2	2	no	—
289	C₂×C₈×C₁₃	—	2	4	no	—
290	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
291	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
314	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
316	C₄²×C₁₃	—	2	4	no	—
317	C₄²×C₁₃	C₂⁴	1	2	yes	—
318	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂×#575	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#3489	C₂×C₁₃	1	2	yes	complemented
321	#3276	C₂×C₁₃	1	4	yes	complemented
322	#3275	C₂×C₁₃	1	4	yes	complemented
323	#3270	C₂×C₁₃	1	4	yes	complemented
324	#3267	C₂×C₁₃	1	4	yes	complemented
325	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
327	C₂×#470	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3046	C₂×C₁₃	1	2	yes	complemented
329	#3013	C₂×C₁₃	1	2	yes	complemented
330	#3007	C₂×C₁₃	1	2	yes	complemented
331	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
333	C₂³×C₁₃	—	2	2	no	—
334	C₂³×C₁₃	—	2	2	no	—
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	4	2	no	—
337	C₂³×C₁₃	—	4	4	no	—
338	C₂³×C₁₃	—	4	4	no	—
339	C₂³×C₁₃	—	8	2	no	—
340	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
341	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
342	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	2	2	no	—
346	Q₈×C₁₃	—	2	4	no	—
347	Q₈×C₁₃	—	2	4	no	—
348	Q₈×C₁₃	—	2	2	no	—
349	Q₈×C₁₃	—	4	8	no	—
350	Q₈×C₁₃	—	4	4	no	—
351	Q₈×C₁₃	—	4	4	no	—
352	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
353	D₄×C₁₃	—	2	8	no	—
354	D₄×C₁₃	—	2	4	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	4	4	no	—
360	D₄×C₁₃	—	4	4	no	—
361	D₄×C₁₃	—	4	4	no	—
362	D₄×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	4	8	no	—
364	D₄×C₁₃	—	4	4	no	—
365	D₄×C₁₃	—	8	4	no	—
366	D₄×C₁₃	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	4	no	—
370	C₂×C₄×C₁₃	—	2	8	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	4	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	4	4	no	—
379	C₂×C₄×C₁₃	—	4	4	no	—
380	C₂×C₄×C₁₃	—	4	4	no	—
381	C₂×C₄×C₁₃	—	4	8	no	—
382	C₂×C₄×C₁₃	—	4	8	no	—
383	C₂×C₄×C₁₃	—	4	4	no	—
384	C₂×C₄×C₁₃	—	4	4	no	—
385	C₂×C₄×C₁₃	—	8	4	no	—
386	C₂×C₄×C₁₃	—	8	2	no	—
387	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
393	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
394	C₈×C₁₃	—	2	2	no	—
395	C₈×C₁₃	—	2	2	no	—
396	C₈×C₁₃	—	2	2	no	—
397	C₈×C₁₃	C₂²×D₄	1	2	yes	—
398	C₈×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
400	C₂²×#41	C₂²×C₁₃	1	2	yes	—
401	#578	—	2	8	no	—
402	#575	—	2	8	no	—
403	C₂×#137	C₂²×C₁₃	1	2	yes	—
404	C₂×#137	C₂²×C₁₃	1	2	yes	—
405	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
406	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
407	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
408	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
409	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
410	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#135	C₂²×C₁₃	1	2	yes	—
412	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
414	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
416	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
418	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
419	#548	C₂²×C₁₃	1	4	yes	—
420	#547	—	2	4	no	—
421	#547	C₂²×C₁₃	1	4	yes	—
422	#546	—	2	4	no	—
423	#546	C₂²×C₁₃	1	4	yes	complemented
424	#537	—	2	2	no	—
425	#537	C₂²×C₁₃	1	2	yes	complemented
426	#536	—	2	2	no	—
427	#536	C₂²×C₁₃	1	2	yes	complemented
428	#525	—	2	2	no	—
429	#525	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	—	2	2	no	—
431	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
432	#520	C₂²×C₁₃	1	2	yes	complemented
433	#497	C₂²×C₁₃	1	4	yes	complemented
434	#495	C₂²×C₁₃	1	2	yes	complemented
435	#494	C₂²×C₁₃	1	2	yes	complemented
436	#470	C₂²×C₁₃	1	4	yes	complemented
437	#470	C₂²×C₁₃	1	4	yes	complemented
438	#470	C₂²×C₁₃	1	2	yes	complemented
439	#469	C₂²×C₁₃	1	2	yes	complemented
440	#465	C₂²×C₁₃	1	4	yes	complemented
441	#464	C₂²×C₁₃	1	4	yes	complemented
442	#463	C₂²×C₁₃	1	4	yes	complemented
443	#462	C₂²×C₁₃	1	4	yes	complemented
444	#461	C₂²×C₁₃	1	4	yes	complemented
445	#452	C₂²×C₁₃	1	4	yes	—
446	#452	C₂²×C₁₃	1	4	yes	—
447	#452	C₂²×C₁₃	1	4	yes	complemented
448	#451	C₂²×C₁₃	1	4	yes	complemented
449	#451	C₂²×C₁₃	1	4	yes	complemented
450	#450	C₂²×C₁₃	1	4	yes	complemented
451	#449	C₂²×C₁₃	1	4	yes	complemented
452	#448	C₂²×C₁₃	1	4	yes	complemented
453	#442	C₂²×C₁₃	1	2	yes	complemented
454	#441	C₂²×C₁₃	1	2	yes	complemented
455	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
456	#436	C₂²×C₁₃	1	4	yes	complemented
457	#435	C₂²×C₁₃	1	4	yes	complemented
458	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#417	C₂²×C₁₃	1	2	yes	complemented
461	#417	C₂²×C₁₃	1	2	yes	complemented
462	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
463	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	#407	C₂²×C₁₃	1	1	yes	characteristic
465	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	C₂²×C₁₃	—	2	2	no	—
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	4	no	—
469	C₂²×C₁₃	—	2	2	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	4	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	4	2	no	—
478	C₂²×C₁₃	—	8	2	no	—
479	C₂²×C₁₃	—	8	8	no	—
480	C₂²×C₁₃	D₄²	1	2	yes	—
481	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
482	C₄×C₁₃	—	2	4	no	—
483	C₄×C₁₃	—	2	2	no	—
484	C₄×C₁₃	—	2	4	no	—
485	C₄×C₁₃	—	2	2	no	—
486	C₄×C₁₃	—	4	4	no	—
487	C₄×C₁₃	—	4	2	no	—
488	C₄×C₁₃	—	4	4	no	—
489	C₄×C₁₃	D₄²	1	2	yes	—
490	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
492	2₋¹⁺⁴	—	2	8	no	—
493	2₋¹⁺⁴	—	4	4	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	4	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	8	no	—
499	C₂×#41	—	4	4	no	—
500	C₂×#41	C₂³×C₁₃	1	2	yes	—
501	C₂×#41	C₂³×C₁₃	1	4	yes	—
502	C₂×#41	C₂³×C₁₃	1	2	yes	—
503	C₂×#41	C₂³×C₁₃	1	2	yes	—
504	C₂×#41	C₂³×C₁₃	1	2	yes	—
505	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
508	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
509	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
512	C₂³×C₄	—	2	2	no	—
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	#137	—	2	8	no	—
515	#137	—	2	8	no	—
516	#137	—	2	8	no	—
517	#137	—	2	16	no	—
518	#137	—	4	4	no	—
519	AGL(1,ℤ/8)	—	2	8	no	—
520	AGL(1,ℤ/8)	—	2	8	no	—
521	#135	—	2	8	no	—
522	#135	—	2	8	no	—
523	#135	—	2	4	no	—
524	#135	D₄×C₁₃	1	8	yes	complemented
525	C₂×Q₁₆	—	2	8	no	—
526	C₂×Q₁₆	—	2	4	no	—
527	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
528	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
530	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
533	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
540	C₂×D₈	C₂³×C₁₃	1	2	yes	—
541	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
543	#131	—	2	4	no	—
544	C₂×M₁₆	—	2	4	no	—
545	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
547	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
549	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
552	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₄⋊Q₈	—	2	4	no	—
554	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
555	#124	—	2	4	no	—
556	#124	C₂³×C₁₃	1	4	yes	—
557	#123	—	2	4	no	—
558	#123	—	2	4	no	—
559	#123	—	2	4	no	—
560	#123	—	2	4	no	—
561	#123	D₄×C₁₃	1	2	yes	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
574	#121	—	2	2	no	—
575	#121	—	2	4	no	—
576	#121	—	2	4	no	—
577	#121	—	2	4	no	—
578	#121	—	2	4	no	—
579	#121	D₄×C₁₃	1	2	yes	—
580	#121	C₂³×C₁₃	1	4	yes	—
581	#120	—	2	4	no	—
582	#120	D₄×C₁₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	4	no	—
587	C₄×D₄	C₂³×C₁₃	1	4	yes	—
588	C₄×D₄	C₂³×C₁₃	1	4	yes	—
589	#117	—	2	2	no	—
590	#117	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	4	no	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
595	C₂×C₂²⋊C₄	—	2	2	no	—
596	C₂×C₂²⋊C₄	—	2	4	no	—
597	#106	C₂³×C₁₃	1	2	yes	—
598	#106	C₂³×C₁₃	1	2	yes	—
599	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
600	#103	C₂³×C₁₃	1	4	yes	—
601	#103	C₂³×C₁₃	1	4	yes	—
602	#103	C₂³×C₁₃	1	4	yes	—
603	#103	C₂³×C₁₃	1	4	yes	—
604	#102	C₂³×C₁₃	1	4	yes	—
605	#102	C₂³×C₁₃	1	4	yes	—
606	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
608	#97	C₂³×C₁₃	1	2	yes	—
609	C₄×C₈	C₂³×C₁₃	1	2	yes	—
610	C₂×C₁₃	—	2	2	no	—
611	C₂×C₁₃	—	4	2	no	—
612	C₂×C₁₃	—	4	2	no	—
613	C₂×C₁₃	—	4	4	no	—
614	C₂×C₁₃	—	8	2	no	—
615	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
616	C₂×C₁₃	#3586	1	2	yes	—
617	C₂⁴	—	2	2	no	—
618	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
619	#41	—	2	2	no	—
620	#41	—	2	4	no	—
621	#41	—	2	2	no	—
622	#41	—	2	4	no	—
623	#41	—	2	8	no	—
624	#41	—	2	4	no	—
625	#41	—	2	4	no	—
626	#41	—	2	4	no	—
627	#41	—	4	8	no	—
628	#41	—	4	2	no	—
629	#41	—	4	2	no	—
630	#41	—	4	4	no	—
631	#41	—	4	8	no	—
632	#41	—	4	8	no	—
633	#41	—	4	16	no	—
634	#41	C₂×D₄×C₁₃	1	8	yes	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	4	no	—
637	C₂×Q₈	—	2	2	no	—
638	C₂×Q₈	—	2	8	no	—
639	C₂×Q₈	—	2	4	no	—
640	C₂×Q₈	—	2	4	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	4	2	no	—
643	C₂×Q₈	—	4	4	no	—
644	C₂×Q₈	—	4	8	no	—
645	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
647	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	8	no	—
659	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
662	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
663	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	4	8	no	—
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	Q₁₆	—	2	8	no	—
683	Q₁₆	—	2	4	no	—
684	Q₁₆	—	2	4	no	—
685	Q₁₆	—	2	4	no	—
686	Q₁₆	—	2	2	no	—
687	Q₁₆	—	4	4	no	—
688	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
689	SD₁₆	—	2	4	no	—
690	SD₁₆	—	2	4	no	—
691	SD₁₆	—	2	8	no	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
695	D₈	—	2	4	no	—
696	D₈	—	2	2	no	—
697	D₈	C₂×D₄×C₁₃	1	4	yes	—
698	M₁₆	—	2	2	no	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	2	4	no	—
701	M₁₆	—	2	4	no	—
702	M₁₆	—	2	4	no	—
703	C₂×C₈	—	2	2	no	—
704	C₂×C₈	—	2	4	no	—
705	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
720	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
729	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
730	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
731	C₄²	—	2	4	no	—
732	C₄²	C₂⁴×C₁₃	1	2	yes	—
733	C₁₃	#61064	1	1	yes	characteristic, direct product factor, Sylow
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	8	2	no	—
741	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
742	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
743	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	2	2	no	—
746	Q₈	—	2	2	no	—
747	Q₈	—	2	4	no	—
748	Q₈	—	2	4	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	4	8	no	—
751	Q₈	—	4	4	no	—
752	Q₈	—	4	4	no	—
753	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
754	D₄	—	2	8	no	—
755	D₄	—	2	4	no	—
756	D₄	—	2	2	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	4	no	—
762	D₄	—	4	4	no	—
763	D₄	—	4	4	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	4	no	—
766	D₄	—	8	4	no	—
767	D₄	C₂²×D₄×C₁₃	1	4	yes	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	8	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	—	8	2	no	—
788	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
789	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
790	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
791	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
793	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
794	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
795	C₈	—	2	2	no	—
796	C₈	—	2	2	no	—
797	C₈	—	2	2	no	—
798	C₈	C₂²×D₄×C₁₃	1	2	yes	—
799	C₈	C₂²×D₄×C₁₃	1	2	yes	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	8	2	no	—
813	C₂²	—	8	8	no	—
814	C₂²	D₄²×C₁₃	1	2	yes	—
815	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
816	C₄	—	2	4	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	4	no	—
819	C₄	—	2	2	no	—
820	C₄	—	4	4	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	4	no	—
823	C₄	D₄²×C₁₃	1	2	yes	—
824	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
825	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	—	2	2	no	—
827	C₂	—	4	2	no	—
828	C₂	—	4	2	no	—
829	C₂	—	4	4	no	—
830	C₂	—	8	2	no	—
831	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
832	C₂	C₁₃×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂×C₁₃×#575	C₂	semidirect
3. C₁₃×#3489	C₂	semidirect
4. C₁₃×#3276	C₂	semidirect
5. C₁₃×#3275	C₂	semidirect
6. C₁₃×#3270	C₂	semidirect
7. C₁₃×#3267	C₂	semidirect
8. C₁₃×#3156	C₂	semidirect
9. C₁₃×#3060	C₂	semidirect
10. C₂×C₁₃×#470	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3013	C₂	semidirect
13. C₁₃×#3007	C₂	semidirect
14. C₁₃×#2952	C₂	semidirect
15. C₁₃×#2930	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₁₃×#137	C₂²	semidirect
23. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
30. C₂×C₁₃×#135	C₂²	semidirect
31. C₂²×C₁₃×Q₁₆	C₂²	semidirect
32. C₂²×C₁₃×Q₁₆	C₂²	semidirect
33. C₂×C₁₃×#131	C₂²	semidirect
35. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
42. C₁₃×#537	C₂²	semidirect
44. C₁₃×#536	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
51. C₁₃×#495	C₂²	semidirect
52. C₁₃×#494	C₂²	semidirect
53. C₁₃×#470	C₂²	semidirect
54. C₁₃×#470	C₂²	semidirect
55. C₁₃×#470	C₂²	semidirect
56. C₁₃×#469	C₂²	semidirect
57. C₁₃×#465	C₂²	semidirect
58. C₁₃×#464	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#462	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#451	C₂²	semidirect
67. C₁₃×#450	C₂²	semidirect
68. C₁₃×#449	C₂²	semidirect
69. C₁₃×#448	C₂²	semidirect
70. C₁₃×#442	C₂²	semidirect
71. C₁₃×#441	C₂²	semidirect
72. C₄×C₁₃×SD₁₆	C₂²	semidirect
73. C₁₃×#436	C₂²	semidirect
74. C₁₃×#435	C₂²	semidirect
75. C₂×C₁₃×#106	C₂²	semidirect
76. C₁₃×#424	C₂²	semidirect
77. C₁₃×#417	C₂²	semidirect
78. C₁₃×#417	C₂²	semidirect
79. C₂×C₁₃×#103	C₂²	semidirect
80. C₁₃×#408	C₂²	semidirect
82. C₁₃×#405	C₂²	semidirect
115. C₁₃×#135	D₄	semidirect
201. #61064	C₁₃	direct (N × H)
318. C₂×#578	C₂×C₁₃	semidirect
319. C₂×#575	C₂×C₁₃	semidirect
320. #3489	C₂×C₁₃	semidirect
321. #3276	C₂×C₁₃	semidirect
322. #3275	C₂×C₁₃	semidirect
323. #3270	C₂×C₁₃	semidirect
324. #3267	C₂×C₁₃	semidirect
325. #3156	C₂×C₁₃	semidirect
326. #3060	C₂×C₁₃	semidirect
327. C₂×#470	C₂×C₁₃	semidirect
328. #3046	C₂×C₁₃	semidirect
329. #3013	C₂×C₁₃	semidirect
330. #3007	C₂×C₁₃	semidirect
331. #2952	C₂×C₁₃	semidirect
332. #2930	C₂×C₁₃	semidirect
399. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
405. C₂×#137	C₂²×C₁₃	semidirect
406. C₂×#137	C₂²×C₁₃	semidirect
407. C₂×#137	C₂²×C₁₃	semidirect
413. C₂×#135	C₂²×C₁₃	semidirect
414. C₂²×Q₁₆	C₂²×C₁₃	semidirect
415. C₂²×Q₁₆	C₂²×C₁₃	semidirect
416. C₂×#131	C₂²×C₁₃	semidirect
418. D₄×Q₈	C₂²×C₁₃	semidirect
423. #546	C₂²×C₁₃	semidirect
425. #537	C₂²×C₁₃	semidirect
427. #536	C₂²×C₁₃	semidirect
432. #520	C₂²×C₁₃	semidirect
433. #497	C₂²×C₁₃	semidirect
434. #495	C₂²×C₁₃	semidirect
435. #494	C₂²×C₁₃	semidirect
436. #470	C₂²×C₁₃	semidirect
437. #470	C₂²×C₁₃	semidirect
438. #470	C₂²×C₁₃	semidirect
439. #469	C₂²×C₁₃	semidirect
440. #465	C₂²×C₁₃	semidirect
441. #464	C₂²×C₁₃	semidirect
442. #463	C₂²×C₁₃	semidirect
443. #462	C₂²×C₁₃	semidirect
444. #461	C₂²×C₁₃	semidirect
447. #452	C₂²×C₁₃	semidirect
448. #451	C₂²×C₁₃	semidirect
449. #451	C₂²×C₁₃	semidirect
450. #450	C₂²×C₁₃	semidirect
451. #449	C₂²×C₁₃	semidirect
452. #448	C₂²×C₁₃	semidirect
453. #442	C₂²×C₁₃	semidirect
454. #441	C₂²×C₁₃	semidirect
455. C₄×SD₁₆	C₂²×C₁₃	semidirect
456. #436	C₂²×C₁₃	semidirect
457. #435	C₂²×C₁₃	semidirect
458. C₂×#106	C₂²×C₁₃	semidirect
459. #424	C₂²×C₁₃	semidirect
460. #417	C₂²×C₁₃	semidirect
461. #417	C₂²×C₁₃	semidirect
462. C₂×#103	C₂²×C₁₃	semidirect
463. #408	C₂²×C₁₃	semidirect
465. #405	C₂²×C₁₃	semidirect
524. #135	D₄×C₁₃	semidirect
733. C₁₃	#61064	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×#578	2
C₂×C₁₃×#575	2
C₁₃×#3489	2
C₁₃×#3276	2
C₁₃×#3275	2
C₁₃×#3270	2
C₁₃×#3267	2
C₁₃×#3156	2
C₁₃×#3060	2
C₂×C₁₃×#470	2
C₁₃×#3046	2
C₁₃×#3013	2
C₁₃×#3007	2
C₁₃×#2952	2
C₁₃×#2930	2
#61064	13

Subgroups — C13×#61064 #15747403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61064 #15747403