Subgroups — C₁₃×#24426 #15710765

Order 3328.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#546	—	2	4	no	—
23	C₁₃×#546	—	2	4	no	—
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	—	2	1	no	—
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#120	—	2	1	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₁₃×#467	—	2	4	no	—
37	C₁₃×#452	—	2	4	no	—
38	C₁₃×#450	—	2	4	no	—
39	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#102	—	2	4	no	—
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#398	—	2	1	no	—
55	C₁₃×#396	—	2	1	no	—
56	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#386	—	2	1	no	—
59	C₁₃×#380	—	2	1	no	—
60	C₁₃×#380	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#336	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₁₃	—	2	1	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	4	1	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	—	2	2	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	2	no	—
80	C₂²×D₄×C₁₃	—	4	1	no	—
81	C₂²×D₄×C₁₃	—	4	1	no	—
82	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	D₄	1	4	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	—	2	1	no	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×Q₁₆	—	2	2	no	—
92	C₂×C₁₃×Q₁₆	—	2	2	no	—
93	C₂×C₁₃×Q₁₆	—	4	1	no	—
94	C₂×C₁₃×SD₁₆	—	2	2	no	—
95	C₂×C₁₃×SD₁₆	—	2	2	no	—
96	C₂×C₁₃×SD₁₆	—	2	2	no	—
97	C₂×C₁₃×SD₁₆	—	2	2	no	—
98	C₂×C₁₃×SD₁₆	—	4	1	no	—
99	C₂×C₁₃×SD₁₆	—	4	1	no	—
100	C₂²×C₈×C₁₃	—	2	2	no	—
101	C₂²×C₈×C₁₃	—	2	2	no	—
102	C₂²×C₈×C₁₃	—	4	1	no	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×#124	—	2	2	no	—
109	C₁₃×#123	—	2	8	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	2	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	4	1	no	—
115	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
116	C₁₃×#121	—	2	8	no	—
117	C₁₃×#121	—	2	2	no	—
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#120	—	2	8	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	2	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	—	2	2	no	—
124	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
148	C₁₃×#107	—	2	2	no	—
149	C₁₃×#103	—	2	2	no	—
150	C₁₃×#103	—	2	2	no	—
151	C₁₃×#103	—	2	2	no	—
152	C₁₃×#103	—	4	1	no	—
153	C₁₃×#102	—	2	2	no	—
154	C₁₃×#102	—	2	2	no	—
155	C₁₃×#102	—	2	2	no	—
156	C₁₃×#102	—	2	2	no	—
157	C₁₃×#102	—	2	2	no	—
158	C₁₃×#102	D₄	1	4	yes	complemented
159	C₁₃×C₂²⋊C₈	—	2	2	no	—
160	C₁₃×C₂²⋊C₈	—	2	2	no	—
161	C₁₃×C₂²⋊C₈	—	4	1	no	—
162	C₁₃×#95	—	2	1	no	—
163	C₁₃×#95	—	2	1	no	—
164	C₁₃×#95	—	2	1	no	—
165	C₁₃×#95	—	2	1	no	—
166	#24426	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	1	no	—
168	C₂⁴×C₁₃	—	2	1	no	—
169	C₂⁴×C₁₃	—	2	4	no	—
170	C₂⁴×C₁₃	—	4	2	no	—
171	C₂⁴×C₁₃	—	4	2	no	—
172	C₂⁴×C₁₃	—	4	2	no	—
173	C₂⁴×C₁₃	—	4	2	no	—
174	C₂⁴×C₁₃	—	8	1	no	—
175	C₂⁴×C₁₃	—	8	1	no	—
176	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₁₃×#41	—	4	4	no	—
179	C₁₃×#41	—	4	4	no	—
180	C₁₃×#41	—	4	4	no	—
181	C₁₃×#41	—	4	4	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	2	4	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	2	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	4	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	1	no	—
207	C₂×D₄×C₁₃	—	2	1	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	2	no	—
213	C₂×D₄×C₁₃	—	4	2	no	—
214	C₂×D₄×C₁₃	—	4	2	no	—
215	C₂×D₄×C₁₃	—	4	2	no	—
216	C₂×D₄×C₁₃	—	8	1	no	—
217	C₂×D₄×C₁₃	—	8	1	no	—
218	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₁₃	#41	1	2	yes	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	4	2	no	—
241	C₂²×C₄×C₁₃	—	4	2	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	8	1	no	—
245	C₂²×C₄×C₁₃	—	8	1	no	—
246	C₂²×C₄×C₁₃	—	8	1	no	—
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×Q₁₆	—	4	4	no	—
255	C₁₃×SD₁₆	—	4	4	no	—
256	C₁₃×SD₁₆	—	4	4	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	4	4	no	—
269	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	4	2	no	—
279	C₁₃×C₄⋊C₄	—	4	2	no	—
280	C₁₃×C₄⋊C₄	—	4	2	no	—
281	C₁₃×C₄⋊C₄	—	8	1	no	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	—	4	2	no	—
292	C₁₃×C₂²⋊C₄	—	4	2	no	—
293	C₁₃×C₂²⋊C₄	—	8	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₂×#546	C₂×C₁₃	1	1	yes	characteristic
297	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
300	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2417	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#1869	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	1	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	2	2	no	—
319	C₂³×C₁₃	—	2	1	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	2	1	no	—
322	C₂³×C₁₃	—	2	1	no	—
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	—	2	1	no	—
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	4	8	no	—
327	C₂³×C₁₃	—	4	1	no	—
328	C₂³×C₁₃	—	4	1	no	—
329	C₂³×C₁₃	—	4	1	no	—
330	C₂³×C₁₃	—	4	1	no	—
331	C₂³×C₁₃	—	4	1	no	—
332	C₂³×C₁₃	—	4	1	no	—
333	C₂³×C₁₃	—	4	1	no	—
334	C₂³×C₁₃	—	4	1	no	—
335	C₂³×C₁₃	—	4	1	no	—
336	C₂³×C₁₃	—	4	1	no	—
337	C₂³×C₁₃	—	4	8	no	—
338	C₂³×C₁₃	—	8	4	no	—
339	C₂³×C₁₃	—	8	4	no	—
340	C₂³×C₁₃	—	8	4	no	—
341	C₂³×C₁₃	—	8	4	no	—
342	C₂³×C₁₃	—	8	4	no	—
343	C₂³×C₁₃	#120	1	2	yes	—
344	C₂³×C₁₃	#135	1	2	yes	—
345	C₂³×C₁₃	#137	1	2	yes	—
346	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₁₃	—	2	2	no	—
348	Q₈×C₁₃	—	2	2	no	—
349	Q₈×C₁₃	—	4	1	no	—
350	Q₈×C₁₃	—	4	1	no	—
351	Q₈×C₁₃	—	4	1	no	—
352	Q₈×C₁₃	—	4	1	no	—
353	Q₈×C₁₃	—	4	1	no	—
354	Q₈×C₁₃	—	4	1	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	—	2	2	no	—
360	D₄×C₁₃	—	4	8	no	—
361	D₄×C₁₃	—	4	8	no	—
362	D₄×C₁₃	—	4	4	no	—
363	D₄×C₁₃	—	4	1	no	—
364	D₄×C₁₃	—	4	1	no	—
365	D₄×C₁₃	—	8	4	no	—
366	D₄×C₁₃	#121	1	4	yes	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	2	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	1	no	—
374	C₂×C₄×C₁₃	—	2	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	4	8	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	1	no	—
403	C₂×C₄×C₁₃	—	4	1	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	8	4	no	—
406	C₂×C₄×C₁₃	—	8	4	no	—
407	C₂×C₄×C₁₃	#120	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
412	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
414	C₈×C₁₃	—	2	2	no	—
415	C₈×C₁₃	—	4	1	no	—
416	C₈×C₁₃	—	4	1	no	—
417	C₈×C₁₃	—	4	1	no	—
418	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
419	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
422	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
423	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
424	#546	—	2	4	no	—
425	#546	—	2	4	no	—
426	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#123	—	2	1	no	—
428	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	C₂×#121	—	2	1	no	—
432	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#120	—	2	1	no	—
434	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
437	C₂²×C₂²⋊C₄	—	2	1	no	—
438	#467	—	2	4	no	—
439	#452	—	2	4	no	—
440	#450	—	2	4	no	—
441	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
442	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	C₂×#102	—	2	4	no	—
447	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	#398	—	2	1	no	—
457	#396	—	2	1	no	—
458	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#386	—	2	1	no	—
461	#380	—	2	1	no	—
462	#380	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#336	C₂²×C₁₃	1	1	yes	characteristic, complemented
467	C₂²×C₁₃	—	2	2	no	—
468	C₂²×C₁₃	—	2	2	no	—
469	C₂²×C₁₃	—	2	2	no	—
470	C₂²×C₁₃	—	2	2	no	—
471	C₂²×C₁₃	—	2	2	no	—
472	C₂²×C₁₃	—	2	2	no	—
473	C₂²×C₁₃	—	2	4	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	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	1	no	—
481	C₂²×C₁₃	—	4	2	no	—
482	C₂²×C₁₃	—	4	1	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	1	no	—
488	C₂²×C₁₃	—	4	1	no	—
489	C₂²×C₁₃	—	4	1	no	—
490	C₂²×C₁₃	—	8	16	no	—
491	C₂²×C₁₃	—	8	1	no	—
492	C₂²×C₁₃	—	8	1	no	—
493	C₂²×C₁₃	—	8	1	no	—
494	C₂²×C₁₃	—	8	1	no	—
495	C₂²×C₁₃	#452	1	4	yes	complemented
496	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
497	C₂²×C₁₃	D₄²	1	1	yes	characteristic
498	C₂²×C₁₃	#546	1	1	yes	characteristic
499	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
500	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
501	C₂²×C₁₃	#576	1	1	yes	characteristic
502	C₂²×C₁₃	#577	1	1	yes	characteristic
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	4	1	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	1	no	—
507	C₄×C₁₃	—	4	1	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	8	1	no	—
511	C₄×C₁₃	—	8	1	no	—
512	C₄×C₁₃	—	8	1	no	—
513	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
514	C₄×C₁₃	#534	1	1	yes	characteristic
515	C₄×C₁₃	D₄²	1	1	yes	characteristic
516	C₄×C₁₃	#546	1	1	yes	characteristic
517	C₂⁵	—	2	1	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	2	2	no	—
522	C₂×#41	—	4	1	no	—
523	C₂×#41	—	4	1	no	—
524	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
526	C₂²×D₄	—	2	2	no	—
527	C₂²×D₄	—	2	2	no	—
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	2	no	—
532	C₂²×D₄	—	4	1	no	—
533	C₂²×D₄	—	4	1	no	—
534	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
535	C₂²×D₄	D₄×C₁₃	1	4	yes	—
536	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂³×C₄	—	2	1	no	—
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×Q₁₆	—	2	2	no	—
544	C₂×Q₁₆	—	2	2	no	—
545	C₂×Q₁₆	—	4	1	no	—
546	C₂×SD₁₆	—	2	2	no	—
547	C₂×SD₁₆	—	2	2	no	—
548	C₂×SD₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	2	2	no	—
550	C₂×SD₁₆	—	4	1	no	—
551	C₂×SD₁₆	—	4	1	no	—
552	C₂²×C₈	—	2	2	no	—
553	C₂²×C₈	—	2	2	no	—
554	C₂²×C₈	—	4	1	no	—
555	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
559	#124	—	2	2	no	—
560	#124	—	2	2	no	—
561	#123	—	2	8	no	—
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	—	4	1	no	—
567	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
568	#121	—	2	8	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	#120	—	2	8	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	4	1	no	—
583	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	—	2	8	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
600	#107	—	2	2	no	—
601	#103	—	2	2	no	—
602	#103	—	2	2	no	—
603	#103	—	2	2	no	—
604	#103	—	4	1	no	—
605	#102	—	2	2	no	—
606	#102	—	2	2	no	—
607	#102	—	2	2	no	—
608	#102	—	2	2	no	—
609	#102	—	2	2	no	—
610	#102	D₄×C₁₃	1	4	yes	complemented
611	C₂²⋊C₈	—	2	2	no	—
612	C₂²⋊C₈	—	2	2	no	—
613	C₂²⋊C₈	—	4	1	no	—
614	#95	—	2	1	no	—
615	#95	—	2	1	no	—
616	#95	—	2	1	no	—
617	#95	—	2	1	no	—
618	C₂×C₁₃	—	2	4	no	—
619	C₂×C₁₃	—	4	4	no	—
620	C₂×C₁₃	—	8	1	no	—
621	C₂×C₁₃	—	8	2	no	—
622	C₂×C₁₃	#2410	1	1	yes	characteristic
623	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
624	C₂×C₁₃	#3012	1	1	yes	characteristic
625	C₂×C₁₃	#3266	1	1	yes	characteristic
626	C₂×C₁₃	#3280	1	1	yes	characteristic
627	C₂×C₁₃	#3296	1	1	yes	characteristic
628	C₂×C₁₃	#3314	1	1	yes	characteristic
629	C₂⁴	—	2	1	no	—
630	C₂⁴	—	2	1	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	2	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	2	no	—
635	C₂⁴	—	4	2	no	—
636	C₂⁴	—	8	1	no	—
637	C₂⁴	—	8	1	no	—
638	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
640	#41	—	4	4	no	—
641	#41	—	4	4	no	—
642	#41	—	4	4	no	—
643	#41	—	4	4	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	1	no	—
655	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
656	C₂×D₄	—	2	8	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	4	4	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	2	no	—
678	C₂×D₄	—	8	1	no	—
679	C₂×D₄	—	8	1	no	—
680	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
683	C₂×D₄	C₁₃×#41	1	2	yes	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	8	1	no	—
707	C₂²×C₄	—	8	1	no	—
708	C₂²×C₄	—	8	1	no	—
709	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
716	Q₁₆	—	4	4	no	—
717	SD₁₆	—	4	4	no	—
718	SD₁₆	—	4	4	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	2	1	no	—
724	C₂×C₈	—	2	1	no	—
725	C₂×C₈	—	2	1	no	—
726	C₂×C₈	—	2	1	no	—
727	C₂×C₈	—	2	1	no	—
728	C₂×C₈	—	2	1	no	—
729	C₂×C₈	—	2	1	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	8	1	no	—
744	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	8	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₁₃	#24426	1	1	yes	characteristic, direct product factor, Sylow
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	4	8	no	—
775	C₂³	—	4	1	no	—
776	C₂³	—	4	1	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	8	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	8	4	no	—
787	C₂³	—	8	4	no	—
788	C₂³	—	8	4	no	—
789	C₂³	—	8	4	no	—
790	C₂³	—	8	4	no	—
791	C₂³	C₁₃×#120	1	2	yes	—
792	C₂³	C₁₃×#135	1	2	yes	—
793	C₂³	C₁₃×#137	1	2	yes	—
794	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	4	1	no	—
798	Q₈	—	4	1	no	—
799	Q₈	—	4	1	no	—
800	Q₈	—	4	1	no	—
801	Q₈	—	4	1	no	—
802	Q₈	—	4	1	no	—
803	D₄	—	2	2	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	1	no	—
812	D₄	—	4	1	no	—
813	D₄	—	8	4	no	—
814	D₄	C₁₃×#121	1	4	yes	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	1	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	8	4	no	—
854	C₂×C₄	—	8	4	no	—
855	C₂×C₄	C₁₃×#120	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
859	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
860	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
862	C₈	—	2	2	no	—
863	C₈	—	4	1	no	—
864	C₈	—	4	1	no	—
865	C₈	—	4	1	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	2	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	16	no	—
890	C₂²	—	8	1	no	—
891	C₂²	—	8	1	no	—
892	C₂²	—	8	1	no	—
893	C₂²	—	8	1	no	—
894	C₂²	C₁₃×#452	1	4	yes	complemented
895	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
896	C₂²	D₄²×C₁₃	1	1	yes	characteristic
897	C₂²	C₁₃×#546	1	1	yes	characteristic
898	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
899	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
900	C₂²	C₁₃×#576	1	1	yes	characteristic
901	C₂²	C₁₃×#577	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	8	1	no	—
910	C₄	—	8	1	no	—
911	C₄	—	8	1	no	—
912	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
913	C₄	C₁₃×#534	1	1	yes	characteristic
914	C₄	D₄²×C₁₃	1	1	yes	characteristic
915	C₄	C₁₃×#546	1	1	yes	characteristic
916	C₂	—	2	4	no	—
917	C₂	—	4	4	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	C₁₃×#2410	1	1	yes	characteristic
921	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
922	C₂	C₁₃×#3012	1	1	yes	characteristic
923	C₂	C₁₃×#3266	1	1	yes	characteristic
924	C₂	C₁₃×#3280	1	1	yes	characteristic
925	C₂	C₁₃×#3296	1	1	yes	characteristic
926	C₂	C₁₃×#3314	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#546	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#467	C₂	semidirect
3. C₂×C₁₃×#452	C₂	semidirect
4. C₂×C₁₃×#450	C₂	semidirect
5. C₂²×C₁₃×#102	C₂	semidirect
6. C₁₃×#2417	C₂	semidirect
7. C₁₃×#2042	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#2015	C₂	semidirect
10. C₁₃×#2000	C₂	semidirect
11. C₁₃×#1877	C₂	semidirect
12. C₁₃×#1872	C₂	semidirect
13. C₁₃×#1869	C₂	semidirect
14. C₁₃×#1862	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
18. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#107	C₂²	semidirect
40. C₂×C₁₃×#103	C₂²	semidirect
41. C₂×C₁₃×#103	C₂²	semidirect
42. C₂×C₁₃×#103	C₂²	semidirect
43. C₂×C₁₃×#103	C₂²	semidirect
52. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
53. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
56. C₁₃×#391	C₂²	semidirect
57. C₁₃×#389	C₂²	semidirect
60. C₁₃×#380	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
63. C₁₃×#336	C₂²	semidirect
64. C₁₃×#336	C₂²	semidirect
158. C₁₃×#102	D₄	semidirect
166. #24426	C₁₃	direct (N × H)
297. C₂×#467	C₂×C₁₃	semidirect
298. C₂×#452	C₂×C₁₃	semidirect
299. C₂×#450	C₂×C₁₃	semidirect
300. C₂²×#102	C₂×C₁₃	semidirect
301. #2417	C₂×C₁₃	semidirect
302. #2042	C₂×C₁₃	semidirect
303. #2033	C₂×C₁₃	semidirect
304. #2015	C₂×C₁₃	semidirect
305. #2000	C₂×C₁₃	semidirect
306. #1877	C₂×C₁₃	semidirect
307. #1872	C₂×C₁₃	semidirect
308. #1869	C₂×C₁₃	semidirect
309. #1862	C₂×C₁₃	semidirect
310. #1788	C₂×C₁₃	semidirect
420. C₂²×Q₁₆	C₂²×C₁₃	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
441. C₂×#107	C₂²×C₁₃	semidirect
442. C₂×#103	C₂²×C₁₃	semidirect
443. C₂×#103	C₂²×C₁₃	semidirect
444. C₂×#103	C₂²×C₁₃	semidirect
445. C₂×#103	C₂²×C₁₃	semidirect
454. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
455. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
458. #391	C₂²×C₁₃	semidirect
459. #389	C₂²×C₁₃	semidirect
462. #380	C₂²×C₁₃	semidirect
463. #340	C₂²×C₁₃	semidirect
464. #340	C₂²×C₁₃	semidirect
465. #336	C₂²×C₁₃	semidirect
466. #336	C₂²×C₁₃	semidirect
495. C₂²×C₁₃	#452	semidirect
610. #102	D₄×C₁₃	semidirect
758. C₁₃	#24426	direct (N × H)
894. C₂²	C₁₃×#452	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#546	2
C₂×C₁₃×#467	2
C₂×C₁₃×#452	2
C₂×C₁₃×#450	2
C₂²×C₁₃×#102	2
C₁₃×#2417	2
C₁₃×#2042	2
C₁₃×#2033	2
C₁₃×#2015	2
C₁₃×#2000	2
C₁₃×#1877	2
C₁₃×#1872	2
C₁₃×#1869	2
C₁₃×#1862	2
C₁₃×#1788	2
#24426	13

Subgroups — C13×#24426 #15710765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24426 #15710765