Subgroups — C₁₃×#61581 #15747920

Order 3328.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3323	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3322	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3275	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3273	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3105	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2975	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, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	C₂²	1	2	yes	complemented
23	C₁₃×#552	C₂²	1	2	yes	complemented
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#548	C₂²	1	2	yes	complemented
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	2	no	—
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#546	C₂²	1	4	yes	complemented
30	C₁₃×#546	C₂²	1	2	yes	complemented
31	C₁₃×#539	—	2	1	no	—
32	C₁₃×#538	—	2	1	no	—
33	C₁₃×#534	—	2	1	no	—
34	C₁₃×#529	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#525	C₂²	1	2	yes	—
37	C₂×C₁₃×#123	—	2	1	no	—
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#120	—	2	1	no	—
44	C₁₃×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
48	C₁₃×#495	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#485	C₂²	1	4	yes	complemented
51	C₁₃×#484	C₂²	1	2	yes	complemented
52	C₁₃×#481	C₂²	1	2	yes	complemented
53	C₁₃×#481	C₂²	1	2	yes	complemented
54	C₁₃×#480	C₂²	1	2	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#470	C₂²	1	4	yes	complemented
57	C₁₃×#469	C₂²	1	4	yes	complemented
58	C₁₃×#468	C₂²	1	4	yes	complemented
59	C₁₃×#468	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#452	C₂²	1	4	yes	complemented
64	C₁₃×#452	C₂²	1	4	yes	complemented
65	C₁₃×#451	C₂²	1	2	yes	complemented
66	C₁₃×#450	C₂²	1	2	yes	complemented
67	C₁₃×#450	C₂²	1	4	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#448	C₂²	1	2	yes	complemented
71	C₁₃×#448	C₂²	1	2	yes	complemented
72	C₁₃×#447	C₂²	1	2	yes	—
73	C₁₃×#447	C₂²	1	2	yes	—
74	C₁₃×#447	C₂²	1	4	yes	complemented
75	C₁₃×#447	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
77	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
78	C₁₃×#436	C₂²	1	4	yes	complemented
79	C₁₃×#436	C₂²	1	4	yes	complemented
80	C₁₃×#431	C₂²	1	2	yes	complemented
81	C₁₃×#418	C₂²	1	4	yes	complemented
82	C₁₃×#417	C₂²	1	2	yes	complemented
83	C₁₃×#417	C₂²	1	2	yes	complemented
84	C₁₃×#407	C₂²	1	2	yes	complemented
85	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
87	C₂⁵×C₁₃	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	—	2	1	no	—
90	C₂×C₁₃×#41	—	4	4	no	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
96	C₂²×D₄×C₁₃	—	2	1	no	—
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	2	no	—
101	C₂²×D₄×C₁₃	—	4	4	no	—
102	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
107	C₂³×C₄×C₁₃	—	2	1	no	—
108	C₂³×C₄×C₁₃	—	2	1	no	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#137	—	4	4	no	—
112	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
113	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
118	C₂×C₁₃×D₈	C₂³	1	4	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
122	C₂×C₁₃×M₁₆	C₂³	1	2	yes	complemented
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	C₂³	1	2	yes	complemented
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	4	yes	—
131	C₁₃×#124	C₂³	1	2	yes	complemented
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	2	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	1	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	4	no	—
154	C₁₃×#121	—	2	4	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	complemented
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	4	no	—
163	C₁₃×#120	—	2	4	no	—
164	C₁₃×#120	—	2	2	no	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	D₄	1	2	yes	—
173	C₄×D₄×C₁₃	D₄	1	2	yes	—
174	C₄×D₄×C₁₃	C₂³	1	4	yes	—
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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, complemented
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
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	—	2	1	no	—
192	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	4	yes	complemented
201	C₁₃×#106	C₂³	1	4	yes	complemented
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
203	C₁₃×#103	C₂³	1	4	yes	complemented
204	C₁₃×#103	C₂³	1	4	yes	complemented
205	C₁₃×#103	C₂³	1	4	yes	complemented
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	complemented
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
215	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	complemented
216	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
217	#61581	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	—	2	1	no	—
219	C₂⁴×C₁₃	—	2	1	no	—
220	C₂⁴×C₁₃	—	2	4	no	—
221	C₂⁴×C₁₃	—	2	1	no	—
222	C₂⁴×C₁₃	—	4	4	no	—
223	C₂⁴×C₁₃	—	4	4	no	—
224	C₂⁴×C₁₃	—	8	2	no	—
225	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₁₃×#41	—	2	4	no	—
228	C₁₃×#41	—	2	4	no	—
229	C₁₃×#41	—	4	2	no	—
230	C₁₃×#41	—	4	2	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	4	4	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	8	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	4	4	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	2	no	—
258	C₂×D₄×C₁₃	—	4	8	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	4	4	no	—
261	C₂×D₄×C₁₃	—	4	4	no	—
262	C₂×D₄×C₁₃	—	8	2	no	—
263	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	2	no	—
280	C₂²×C₄×C₁₃	—	4	4	no	—
281	C₂²×C₄×C₁₃	—	8	2	no	—
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₁₃×Q₁₆	—	4	4	no	—
294	C₁₃×SD₁₆	—	2	8	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×SD₁₆	—	4	4	no	—
297	C₁₃×D₈	—	2	8	no	—
298	C₁₃×D₈	—	4	4	no	—
299	C₁₃×M₁₆	—	4	4	no	—
300	C₁₃×M₁₆	—	4	2	no	—
301	C₁₃×M₁₆	—	4	2	no	—
302	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
303	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₁₃×C₂²⋊C₄	—	2	4	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
344	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3323	C₂×C₁₃	1	4	yes	complemented
346	#3322	C₂×C₁₃	1	4	yes	complemented
347	#3275	C₂×C₁₃	1	4	yes	complemented
348	#3273	C₂×C₁₃	1	4	yes	complemented
349	#3211	C₂×C₁₃	1	2	yes	complemented
350	#3196	C₂×C₁₃	1	2	yes	complemented
351	#3193	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3192	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3105	C₂×C₁₃	1	2	yes	complemented
354	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3003	C₂×C₁₃	1	2	yes	complemented
357	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	4	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	4	1	no	—
365	C₂³×C₁₃	—	4	1	no	—
366	C₂³×C₁₃	—	4	1	no	—
367	C₂³×C₁₃	—	4	1	no	—
368	C₂³×C₁₃	—	4	8	no	—
369	C₂³×C₁₃	—	4	2	no	—
370	C₂³×C₁₃	—	4	2	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	4	8	no	—
373	C₂³×C₁₃	—	4	2	no	—
374	C₂³×C₁₃	—	4	2	no	—
375	C₂³×C₁₃	—	4	2	no	—
376	C₂³×C₁₃	—	8	4	no	—
377	C₂³×C₁₃	—	8	1	no	—
378	C₂³×C₁₃	—	8	1	no	—
379	C₂³×C₁₃	—	8	16	no	—
380	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
381	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₁₃	—	2	4	no	—
385	Q₈×C₁₃	—	2	2	no	—
386	Q₈×C₁₃	—	2	2	no	—
387	Q₈×C₁₃	—	4	2	no	—
388	Q₈×C₁₃	—	8	1	no	—
389	D₄×C₁₃	—	2	4	no	—
390	D₄×C₁₃	—	2	2	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	4	no	—
393	D₄×C₁₃	—	4	2	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	8	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	4	no	—
399	D₄×C₁₃	—	4	4	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	8	1	no	—
402	D₄×C₁₃	—	8	2	no	—
403	D₄×C₁₃	—	8	2	no	—
404	D₄×C₁₃	—	8	2	no	—
405	D₄×C₁₃	—	8	2	no	—
406	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	4	1	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	1	no	—
420	C₂×C₄×C₁₃	—	4	1	no	—
421	C₂×C₄×C₁₃	—	4	1	no	—
422	C₂×C₄×C₁₃	—	4	1	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	4	2	no	—
427	C₂×C₄×C₁₃	—	4	2	no	—
428	C₂×C₄×C₁₃	—	8	2	no	—
429	C₂×C₄×C₁₃	—	8	4	no	—
430	C₂×C₄×C₁₃	—	8	2	no	—
431	C₂×C₄×C₁₃	—	8	1	no	—
432	C₂×C₄×C₁₃	—	8	1	no	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
440	C₈×C₁₃	—	2	4	no	—
441	C₈×C₁₃	—	2	4	no	—
442	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
445	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
446	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
447	#553	—	2	2	no	—
448	#553	C₂²×C₁₃	1	2	yes	complemented
449	#552	C₂²×C₁₃	1	2	yes	complemented
450	#551	—	2	2	no	—
451	#548	C₂²×C₁₃	1	2	yes	complemented
452	#546	—	2	2	no	—
453	#546	—	2	2	no	—
454	#546	C₂²×C₁₃	1	4	yes	—
455	#546	C₂²×C₁₃	1	4	yes	complemented
456	#546	C₂²×C₁₃	1	2	yes	complemented
457	#539	—	2	1	no	—
458	#538	—	2	1	no	—
459	#534	—	2	1	no	—
460	#529	C₂²×C₁₃	1	2	yes	complemented
461	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#525	C₂²×C₁₃	1	2	yes	—
463	C₂×#123	—	2	1	no	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	C₂×#121	—	2	1	no	—
467	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	C₂×#120	—	2	1	no	—
470	#518	—	2	1	no	—
471	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	C₂²×C₂²⋊C₄	—	2	1	no	—
474	#495	C₂²×C₁₃	1	4	yes	complemented
475	#488	C₂²×C₁₃	1	4	yes	complemented
476	#485	C₂²×C₁₃	1	4	yes	complemented
477	#484	C₂²×C₁₃	1	2	yes	complemented
478	#481	C₂²×C₁₃	1	2	yes	complemented
479	#481	C₂²×C₁₃	1	2	yes	complemented
480	#480	C₂²×C₁₃	1	2	yes	complemented
481	#478	C₂²×C₁₃	1	4	yes	complemented
482	#470	C₂²×C₁₃	1	4	yes	complemented
483	#469	C₂²×C₁₃	1	4	yes	complemented
484	#468	C₂²×C₁₃	1	4	yes	complemented
485	#468	C₂²×C₁₃	1	4	yes	complemented
486	#464	C₂²×C₁₃	1	4	yes	complemented
487	#463	C₂²×C₁₃	1	4	yes	complemented
488	#463	C₂²×C₁₃	1	4	yes	complemented
489	#452	C₂²×C₁₃	1	4	yes	complemented
490	#452	C₂²×C₁₃	1	4	yes	complemented
491	#451	C₂²×C₁₃	1	2	yes	complemented
492	#450	C₂²×C₁₃	1	2	yes	complemented
493	#450	C₂²×C₁₃	1	2	yes	complemented
494	#450	C₂²×C₁₃	1	4	yes	complemented
495	#449	C₂²×C₁₃	1	4	yes	complemented
496	#448	C₂²×C₁₃	1	2	yes	complemented
497	#448	C₂²×C₁₃	1	2	yes	complemented
498	#447	C₂²×C₁₃	1	2	yes	—
499	#447	C₂²×C₁₃	1	2	yes	—
500	#447	C₂²×C₁₃	1	4	yes	complemented
501	#447	C₂²×C₁₃	1	2	yes	complemented
502	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
503	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
504	#436	C₂²×C₁₃	1	4	yes	complemented
505	#436	C₂²×C₁₃	1	4	yes	complemented
506	#431	C₂²×C₁₃	1	2	yes	complemented
507	#418	C₂²×C₁₃	1	4	yes	complemented
508	#417	C₂²×C₁₃	1	2	yes	complemented
509	#417	C₂²×C₁₃	1	2	yes	complemented
510	#407	C₂²×C₁₃	1	2	yes	complemented
511	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
513	C₂²×C₁₃	—	2	1	no	—
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	1	no	—
517	C₂²×C₁₃	—	2	2	no	—
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	1	no	—
523	C₂²×C₁₃	—	2	1	no	—
524	C₂²×C₁₃	—	2	2	no	—
525	C₂²×C₁₃	—	4	8	no	—
526	C₂²×C₁₃	—	4	4	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	8	2	no	—
536	C₂²×C₁₃	—	8	4	no	—
537	C₂²×C₁₃	—	8	16	no	—
538	C₂²×C₁₃	—	16	2	no	—
539	C₂²×C₁₃	#575	1	2	yes	—
540	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	2	1	no	—
543	C₄×C₁₃	—	2	1	no	—
544	C₄×C₁₃	—	2	1	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	4	2	no	—
548	C₄×C₁₃	—	4	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
553	C₂⁵	—	2	1	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	2	1	no	—
556	C₂×#41	—	4	4	no	—
557	C₂×#41	C₂³×C₁₃	1	2	yes	—
558	C₂×#41	C₂³×C₁₃	1	2	yes	—
559	C₂×#41	C₂³×C₁₃	1	2	yes	—
560	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	2	no	—
567	C₂²×D₄	—	4	4	no	—
568	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
571	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
573	C₂³×C₄	—	2	1	no	—
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
577	#137	—	4	4	no	—
578	AGL(1,ℤ/8)	—	4	4	no	—
579	AGL(1,ℤ/8)	—	4	8	no	—
580	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
581	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
584	C₂×D₈	C₂³×C₁₃	1	4	yes	—
585	C₂×D₈	C₂³×C₁₃	1	4	yes	—
586	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
587	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
588	C₂×M₁₆	C₂³×C₁₃	1	2	yes	complemented
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#125	—	2	2	no	—
593	#125	C₂³×C₁₃	1	2	yes	complemented
594	#124	—	2	2	no	—
595	#124	—	2	2	no	—
596	#124	C₂³×C₁₃	1	4	yes	—
597	#124	C₂³×C₁₃	1	2	yes	complemented
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	#123	—	2	2	no	—
601	#123	—	2	4	no	—
602	#123	—	2	4	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	C₂²⋊Q₈	—	2	1	no	—
606	C₂²⋊Q₈	—	2	2	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
610	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
611	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	4	no	—
620	#121	—	2	4	no	—
621	#121	—	2	2	no	—
622	#121	C₂³×C₁₃	1	2	yes	—
623	#121	C₂³×C₁₃	1	2	yes	—
624	#121	C₂³×C₁₃	1	2	yes	—
625	#121	C₂³×C₁₃	1	2	yes	—
626	#121	C₂³×C₁₃	1	2	yes	complemented
627	#120	—	2	2	no	—
628	#120	—	2	4	no	—
629	#120	—	2	4	no	—
630	#120	—	2	2	no	—
631	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	D₄×C₁₃	1	2	yes	—
639	C₄×D₄	D₄×C₁₃	1	2	yes	—
640	C₄×D₄	C₂³×C₁₃	1	4	yes	—
641	C₄×D₄	C₂³×C₁₃	1	2	yes	—
642	C₄×D₄	C₂³×C₁₃	1	2	yes	—
643	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	4	no	—
661	C₂×C₂²⋊C₄	—	2	4	no	—
662	C₂×C₂²⋊C₄	—	2	2	no	—
663	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
666	#107	C₂³×C₁₃	1	4	yes	complemented
667	#106	C₂³×C₁₃	1	4	yes	complemented
668	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
669	#103	C₂³×C₁₃	1	4	yes	complemented
670	#103	C₂³×C₁₃	1	4	yes	complemented
671	#103	C₂³×C₁₃	1	4	yes	complemented
672	#102	C₂³×C₁₃	1	4	yes	—
673	#102	C₂³×C₁₃	1	4	yes	—
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	4	yes	complemented
677	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
681	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	complemented
682	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
683	C₂×C₁₃	—	2	2	no	—
684	C₂×C₁₃	—	4	2	no	—
685	C₂×C₁₃	—	4	1	no	—
686	C₂×C₁₃	—	4	1	no	—
687	C₂×C₁₃	—	4	4	no	—
688	C₂×C₁₃	—	8	2	no	—
689	C₂×C₁₃	—	8	2	no	—
690	C₂×C₁₃	#3484	1	1	yes	characteristic
691	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
692	C₂×C₁₃	#3585	1	1	yes	characteristic
693	C₂⁴	—	2	1	no	—
694	C₂⁴	—	2	1	no	—
695	C₂⁴	—	2	4	no	—
696	C₂⁴	—	2	1	no	—
697	C₂⁴	—	4	4	no	—
698	C₂⁴	—	4	4	no	—
699	C₂⁴	—	8	2	no	—
700	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
701	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
702	#41	—	2	4	no	—
703	#41	—	2	4	no	—
704	#41	—	4	2	no	—
705	#41	—	4	2	no	—
706	#41	—	4	4	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
714	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	8	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	8	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	8	2	no	—
738	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	4	no	—
756	C₂²×C₄	—	8	2	no	—
757	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	Q₁₆	—	4	4	no	—
769	SD₁₆	—	2	8	no	—
770	SD₁₆	—	4	4	no	—
771	SD₁₆	—	4	4	no	—
772	D₈	—	2	8	no	—
773	D₈	—	4	4	no	—
774	M₁₆	—	4	4	no	—
775	M₁₆	—	4	2	no	—
776	M₁₆	—	4	2	no	—
777	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
778	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	4	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
811	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
812	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	C₂×D₄×C₁₃	1	2	yes	—
817	C₄²	C₂⁴×C₁₃	1	2	yes	—
818	C₁₃	#61581	1	1	yes	characteristic, direct product factor, Sylow
819	C₂³	—	2	4	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	4	1	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	8	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	8	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	8	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	1	no	—
840	C₂³	—	8	16	no	—
841	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	1	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	2	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	1	no	—
893	C₂×C₄	—	8	1	no	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
895	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
901	C₈	—	2	4	no	—
902	C₈	—	2	4	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	8	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	8	2	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	16	2	no	—
929	C₂²	C₁₃×#575	1	2	yes	—
930	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
943	C₂	—	2	2	no	—
944	C₂	—	4	2	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	4	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	C₁₃×#3484	1	1	yes	characteristic
951	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
952	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3505	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3323	C₂	semidirect
4. C₁₃×#3322	C₂	semidirect
5. C₁₃×#3275	C₂	semidirect
6. C₁₃×#3273	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3196	C₂	semidirect
9. C₁₃×#3193	C₂	semidirect
10. C₁₃×#3192	C₂	semidirect
11. C₁₃×#3105	C₂	semidirect
12. C₁₃×#3007	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#3003	C₂	semidirect
15. C₁₃×#2975	C₂	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
25. C₁₃×#548	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
34. C₁₃×#529	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×#121	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃	C₂²	semidirect
48. C₁₃×#495	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#485	C₂²	semidirect
51. C₁₃×#484	C₂²	semidirect
52. C₁₃×#481	C₂²	semidirect
53. C₁₃×#481	C₂²	semidirect
54. C₁₃×#480	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#470	C₂²	semidirect
57. C₁₃×#469	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#468	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#450	C₂²	semidirect
67. C₁₃×#450	C₂²	semidirect
68. C₁₃×#450	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
70. C₁₃×#448	C₂²	semidirect
71. C₁₃×#448	C₂²	semidirect
74. C₁₃×#447	C₂²	semidirect
75. C₁₃×#447	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₄×C₁₃×D₈	C₂²	semidirect
78. C₁₃×#436	C₂²	semidirect
79. C₁₃×#436	C₂²	semidirect
80. C₁₃×#431	C₂²	semidirect
81. C₁₃×#418	C₂²	semidirect
82. C₁₃×#417	C₂²	semidirect
83. C₁₃×#417	C₂²	semidirect
84. C₁₃×#407	C₂²	semidirect
85. C₁₃×#407	C₂²	semidirect
86. C₁₃×#407	C₂²	semidirect
95. C₂²×Q₈×C₁₃	C₂³	semidirect
106. C₂²×D₄×C₁₃	C₂³	semidirect
114. C₂×C₁₃×Q₁₆	C₂³	semidirect
117. C₂×C₁₃×SD₁₆	C₂³	semidirect
121. C₂×C₁₃×M₁₆	C₂³	semidirect
122. C₂×C₁₃×M₁₆	C₂³	semidirect
127. C₁₃×#125	C₂³	semidirect
131. C₁₃×#124	C₂³	semidirect
146. C₁₃×C₂²⋊Q₈	C₂³	semidirect
160. C₁₃×#121	C₂³	semidirect
165. C₄×Q₈×C₁₃	C₂³	semidirect
177. C₄×D₄×C₁₃	C₂³	semidirect
185. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
186. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
200. C₁₃×#107	C₂³	semidirect
201. C₁₃×#106	C₂³	semidirect
202. C₁₃×C₄⋊C₈	C₂³	semidirect
203. C₁₃×#103	C₂³	semidirect
204. C₁₃×#103	C₂³	semidirect
205. C₁₃×#103	C₂³	semidirect
210. C₁₃×#102	C₂³	semidirect
214. C₁₃×C₂²⋊C₈	C₂³	semidirect
215. C₁₃×C₂²⋊C₈	C₂³	semidirect
216. C₄×C₈×C₁₃	C₂³	semidirect
217. #61581	C₁₃	direct (N × H)
343. #3505	C₂×C₁₃	semidirect
344. C₂×#546	C₂×C₁₃	semidirect
345. #3323	C₂×C₁₃	semidirect
346. #3322	C₂×C₁₃	semidirect
347. #3275	C₂×C₁₃	semidirect
348. #3273	C₂×C₁₃	semidirect
349. #3211	C₂×C₁₃	semidirect
350. #3196	C₂×C₁₃	semidirect
351. #3193	C₂×C₁₃	semidirect
352. #3192	C₂×C₁₃	semidirect
353. #3105	C₂×C₁₃	semidirect
354. #3007	C₂×C₁₃	semidirect
355. #3006	C₂×C₁₃	semidirect
356. #3003	C₂×C₁₃	semidirect
357. #2975	C₂×C₁₃	semidirect
443. C₂³×D₄	C₂²×C₁₃	semidirect
444. C₂×#137	C₂²×C₁₃	semidirect
445. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
446. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
448. #553	C₂²×C₁₃	semidirect
449. #552	C₂²×C₁₃	semidirect
451. #548	C₂²×C₁₃	semidirect
455. #546	C₂²×C₁₃	semidirect
456. #546	C₂²×C₁₃	semidirect
460. #529	C₂²×C₁₃	semidirect
461. C₂×#124	C₂²×C₁₃	semidirect
464. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
465. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
468. C₂×#121	C₂²×C₁₃	semidirect
472. C₂×C₄×D₄	C₂²×C₁₃	semidirect
474. #495	C₂²×C₁₃	semidirect
475. #488	C₂²×C₁₃	semidirect
476. #485	C₂²×C₁₃	semidirect
477. #484	C₂²×C₁₃	semidirect
478. #481	C₂²×C₁₃	semidirect
479. #481	C₂²×C₁₃	semidirect
480. #480	C₂²×C₁₃	semidirect
481. #478	C₂²×C₁₃	semidirect
482. #470	C₂²×C₁₃	semidirect
483. #469	C₂²×C₁₃	semidirect
484. #468	C₂²×C₁₃	semidirect
485. #468	C₂²×C₁₃	semidirect
486. #464	C₂²×C₁₃	semidirect
487. #463	C₂²×C₁₃	semidirect
488. #463	C₂²×C₁₃	semidirect
489. #452	C₂²×C₁₃	semidirect
490. #452	C₂²×C₁₃	semidirect
491. #451	C₂²×C₁₃	semidirect
492. #450	C₂²×C₁₃	semidirect
493. #450	C₂²×C₁₃	semidirect
494. #450	C₂²×C₁₃	semidirect
495. #449	C₂²×C₁₃	semidirect
496. #448	C₂²×C₁₃	semidirect
497. #448	C₂²×C₁₃	semidirect
500. #447	C₂²×C₁₃	semidirect
501. #447	C₂²×C₁₃	semidirect
502. C₄×SD₁₆	C₂²×C₁₃	semidirect
503. C₄×D₈	C₂²×C₁₃	semidirect
504. #436	C₂²×C₁₃	semidirect
505. #436	C₂²×C₁₃	semidirect
506. #431	C₂²×C₁₃	semidirect
507. #418	C₂²×C₁₃	semidirect
508. #417	C₂²×C₁₃	semidirect
509. #417	C₂²×C₁₃	semidirect
510. #407	C₂²×C₁₃	semidirect
511. #407	C₂²×C₁₃	semidirect
512. #407	C₂²×C₁₃	semidirect
561. C₂²×Q₈	C₂³×C₁₃	semidirect
572. C₂²×D₄	C₂³×C₁₃	semidirect
580. C₂×Q₁₆	C₂³×C₁₃	semidirect
583. C₂×SD₁₆	C₂³×C₁₃	semidirect
587. C₂×M₁₆	C₂³×C₁₃	semidirect
588. C₂×M₁₆	C₂³×C₁₃	semidirect
593. #125	C₂³×C₁₃	semidirect
597. #124	C₂³×C₁₃	semidirect
612. C₂²⋊Q₈	C₂³×C₁₃	semidirect
626. #121	C₂³×C₁₃	semidirect
631. C₄×Q₈	C₂³×C₁₃	semidirect
643. C₄×D₄	C₂³×C₁₃	semidirect
651. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
652. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
666. #107	C₂³×C₁₃	semidirect
667. #106	C₂³×C₁₃	semidirect
668. C₄⋊C₈	C₂³×C₁₃	semidirect
669. #103	C₂³×C₁₃	semidirect
670. #103	C₂³×C₁₃	semidirect
671. #103	C₂³×C₁₃	semidirect
676. #102	C₂³×C₁₃	semidirect
680. C₂²⋊C₈	C₂³×C₁₃	semidirect
681. C₂²⋊C₈	C₂³×C₁₃	semidirect
682. C₄×C₈	C₂³×C₁₃	semidirect
818. C₁₃	#61581	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×#3505	2
C₂×C₁₃×#546	2
C₁₃×#3323	2
C₁₃×#3322	2
C₁₃×#3275	2
C₁₃×#3273	2
C₁₃×#3211	2
C₁₃×#3196	2
C₁₃×#3193	2
C₁₃×#3192	2
C₁₃×#3105	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#3003	2
C₁₃×#2975	2
#61581	13

Subgroups — C13×#61581 #15747920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61581 #15747920