Subgroups — C₁₃×#61575 #15747914

Order 3328.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 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×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3315	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3307	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3269	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3267	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3114	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×#3002	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#135	C₂²	1	4	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×#547	—	2	2	no	—
27	C₁₃×#547	—	2	2	no	—
28	C₁₃×#547	C₂²	1	4	yes	—
29	C₁₃×#547	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	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#529	C₂²	1	2	yes	—
36	C₁₃×#525	C₂²	1	2	yes	—
37	C₂×C₁₃×#123	—	2	1	no	—
38	C₂×C₁₃×#123	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#121	—	2	1	no	—
43	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	—	2	1	no	—
48	C₁₃×#497	C₂²	1	4	yes	complemented
49	C₁₃×#491	C₂²	1	4	yes	complemented
50	C₁₃×#485	C₂²	1	4	yes	complemented
51	C₁₃×#484	C₂²	1	2	yes	complemented
52	C₁₃×#483	C₂²	1	2	yes	complemented
53	C₁₃×#483	C₂²	1	2	yes	complemented
54	C₁₃×#480	C₂²	1	2	yes	—
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#470	C₂²	1	4	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#467	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#463	C₂²	1	4	yes	complemented
61	C₁₃×#462	C₂²	1	4	yes	complemented
62	C₁₃×#461	C₂²	1	4	yes	complemented
63	C₁₃×#452	C₂²	1	4	yes	complemented
64	C₁₃×#452	C₂²	1	4	yes	complemented
65	C₁₃×#452	C₂²	1	4	yes	complemented
66	C₁₃×#451	C₂²	1	2	yes	complemented
67	C₁₃×#451	C₂²	1	2	yes	complemented
68	C₁₃×#451	C₂²	1	2	yes	complemented
69	C₁₃×#450	C₂²	1	2	yes	complemented
70	C₁₃×#450	C₂²	1	2	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#449	C₂²	1	4	yes	complemented
73	C₁₃×#448	C₂²	1	2	yes	—
74	C₁₃×#448	C₂²	1	2	yes	—
75	C₁₃×#447	C₂²	1	2	yes	—
76	C₁₃×#442	C₂²	1	4	yes	complemented
77	C₁₃×#440	C₂²	1	4	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₁₃×#435	C₂²	1	4	yes	complemented
80	C₁₃×#432	C₂²	1	2	yes	complemented
81	C₁₃×#417	C₂²	1	2	yes	complemented
82	C₁₃×#417	C₂²	1	2	yes	complemented
83	C₁₃×#416	C₂²	1	4	yes	complemented
84	C₁₃×#407	C₂²	1	1	yes	characteristic
85	C₁₃×#407	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	—	4	4	no	—
91	C₂×C₁₃×#41	—	4	4	no	—
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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	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	1	yes	characteristic
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₂³×C₄×C₁₃	—	2	1	no	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#137	—	4	4	no	—
111	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
112	C₁₃×#135	—	4	8	no	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	4	yes	—
119	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	2	yes	—
131	C₁₃×#123	—	2	2	no	—
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	4	no	—
138	C₁₃×#123	—	2	4	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
152	C₁₃×#121	—	2	4	no	—
153	C₁₃×#121	—	2	4	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	—	2	2	no	—
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	D₄	1	2	yes	—
172	C₄×D₄×C₁₃	D₄	1	2	yes	—
173	C₄×D₄×C₁₃	C₂³	1	4	yes	—
174	C₄×D₄×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₁₃×#117	—	2	2	no	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	C₂³	1	2	yes	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	1	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	—
201	C₁₃×#106	C₂³	1	4	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	4	yes	—
207	C₁₃×#103	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	—
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	—
215	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
216	C₁₃×#97	C₂³	1	4	yes	—
217	#61575	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	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₁₃×#41	—	2	8	no	—
223	C₁₃×#41	—	2	4	no	—
224	C₁₃×#41	—	2	4	no	—
225	C₁₃×#41	—	4	4	no	—
226	C₁₃×#41	—	4	2	no	—
227	C₁₃×#41	—	4	2	no	—
228	C₁₃×#41	—	4	4	no	—
229	C₁₃×#41	—	4	4	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	4	8	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	4	2	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×Q₈×C₁₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₃	—	2	4	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	4	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	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	—	4	4	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	2	no	—
274	C₂²×C₄×C₁₃	—	4	4	no	—
275	C₂²×C₄×C₁₃	—	4	4	no	—
276	C₂²×C₄×C₁₃	—	4	4	no	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₁₃×Q₁₆	—	4	4	no	—
289	C₁₃×Q₁₆	—	4	4	no	—
290	C₁₃×SD₁₆	—	2	8	no	—
291	C₁₃×SD₁₆	—	4	4	no	—
292	C₁₃×SD₁₆	—	4	4	no	—
293	C₁₃×D₈	—	2	8	no	—
294	C₁₃×M₁₆	—	4	2	no	—
295	C₁₃×M₁₆	—	4	2	no	—
296	C₂×C₈×C₁₃	—	4	4	no	—
297	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	4	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	2	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	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	4	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	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	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3315	C₂×C₁₃	1	4	yes	complemented
343	#3307	C₂×C₁₃	1	4	yes	complemented
344	#3269	C₂×C₁₃	1	4	yes	complemented
345	#3267	C₂×C₁₃	1	4	yes	complemented
346	#3218	C₂×C₁₃	1	2	yes	complemented
347	#3195	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3193	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3190	C₂×C₁₃	1	2	yes	complemented
350	#3114	C₂×C₁₃	1	2	yes	complemented
351	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3002	C₂×C₁₃	1	2	yes	complemented
354	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	4	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	2	2	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	4	1	no	—
361	C₂³×C₁₃	—	4	1	no	—
362	C₂³×C₁₃	—	4	1	no	—
363	C₂³×C₁₃	—	4	1	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	2	no	—
366	C₂³×C₁₃	—	4	2	no	—
367	C₂³×C₁₃	—	8	1	no	—
368	C₂³×C₁₃	—	8	1	no	—
369	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₁₃	—	2	4	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	4	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	4	2	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	2	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	4	8	no	—
387	D₄×C₁₃	—	4	4	no	—
388	D₄×C₁₃	—	4	4	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	8	1	no	—
391	D₄×C₁₃	—	8	2	no	—
392	D₄×C₁₃	—	8	2	no	—
393	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	4	1	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	2	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	1	no	—
410	C₂×C₄×C₁₃	—	4	1	no	—
411	C₂×C₄×C₁₃	—	4	8	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	4	no	—
414	C₂×C₄×C₁₃	—	4	8	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	2	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	—	8	1	no	—
422	C₂×C₄×C₁₃	—	8	1	no	—
423	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
430	C₈×C₁₃	—	2	4	no	—
431	C₈×C₁₃	—	2	4	no	—
432	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
433	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
435	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
436	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
437	#553	—	2	2	no	—
438	#553	C₂²×C₁₃	1	2	yes	complemented
439	#552	C₂²×C₁₃	1	2	yes	complemented
440	#551	—	2	2	no	—
441	#548	C₂²×C₁₃	1	2	yes	complemented
442	#547	—	2	2	no	—
443	#547	—	2	2	no	—
444	#547	C₂²×C₁₃	1	4	yes	—
445	#547	C₂²×C₁₃	1	4	yes	complemented
446	#546	C₂²×C₁₃	1	2	yes	complemented
447	#539	—	2	1	no	—
448	#538	—	2	1	no	—
449	#534	—	2	1	no	—
450	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#529	C₂²×C₁₃	1	2	yes	—
452	#525	C₂²×C₁₃	1	2	yes	—
453	C₂×#123	—	2	1	no	—
454	C₂×#123	—	2	1	no	—
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×#121	—	2	1	no	—
459	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
460	#518	—	2	1	no	—
461	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂²×C₄⋊C₄	—	2	1	no	—
464	#497	C₂²×C₁₃	1	4	yes	complemented
465	#491	C₂²×C₁₃	1	4	yes	complemented
466	#485	C₂²×C₁₃	1	4	yes	complemented
467	#484	C₂²×C₁₃	1	2	yes	complemented
468	#483	C₂²×C₁₃	1	2	yes	complemented
469	#483	C₂²×C₁₃	1	2	yes	complemented
470	#480	C₂²×C₁₃	1	2	yes	—
471	#478	C₂²×C₁₃	1	4	yes	complemented
472	#470	C₂²×C₁₃	1	4	yes	complemented
473	#468	C₂²×C₁₃	1	4	yes	complemented
474	#467	C₂²×C₁₃	1	4	yes	complemented
475	#465	C₂²×C₁₃	1	4	yes	complemented
476	#463	C₂²×C₁₃	1	4	yes	complemented
477	#462	C₂²×C₁₃	1	4	yes	complemented
478	#461	C₂²×C₁₃	1	4	yes	complemented
479	#452	C₂²×C₁₃	1	4	yes	complemented
480	#452	C₂²×C₁₃	1	4	yes	complemented
481	#452	C₂²×C₁₃	1	4	yes	complemented
482	#451	C₂²×C₁₃	1	2	yes	complemented
483	#451	C₂²×C₁₃	1	2	yes	complemented
484	#451	C₂²×C₁₃	1	2	yes	complemented
485	#450	C₂²×C₁₃	1	2	yes	complemented
486	#450	C₂²×C₁₃	1	2	yes	complemented
487	#449	C₂²×C₁₃	1	4	yes	complemented
488	#449	C₂²×C₁₃	1	4	yes	complemented
489	#448	C₂²×C₁₃	1	2	yes	—
490	#448	C₂²×C₁₃	1	2	yes	—
491	#447	C₂²×C₁₃	1	2	yes	—
492	#442	C₂²×C₁₃	1	4	yes	complemented
493	#440	C₂²×C₁₃	1	4	yes	complemented
494	#435	C₂²×C₁₃	1	4	yes	complemented
495	#435	C₂²×C₁₃	1	4	yes	complemented
496	#432	C₂²×C₁₃	1	2	yes	complemented
497	#417	C₂²×C₁₃	1	2	yes	complemented
498	#417	C₂²×C₁₃	1	2	yes	complemented
499	#416	C₂²×C₁₃	1	4	yes	complemented
500	#407	C₂²×C₁₃	1	1	yes	characteristic
501	#407	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	2	2	no	—
510	C₂²×C₁₃	—	2	1	no	—
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	1	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	4	8	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	2	no	—
521	C₂²×C₁₃	—	8	2	no	—
522	C₂²×C₁₃	—	8	2	no	—
523	C₂²×C₁₃	—	16	2	no	—
524	C₂²×C₁₃	#575	1	2	yes	—
525	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
526	C₄×C₁₃	—	2	2	no	—
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	2	no	—
542	C₂×#41	—	4	4	no	—
543	C₂×#41	—	4	4	no	—
544	C₂×#41	C₂³×C₁₃	1	2	yes	—
545	C₂×#41	C₂³×C₁₃	1	4	yes	—
546	C₂×#41	C₂³×C₁₃	1	2	yes	—
547	C₂×#41	C₂³×C₁₃	1	2	yes	—
548	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	1	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	#137	—	4	4	no	—
563	AGL(1,ℤ/8)	—	4	4	no	—
564	#135	—	4	8	no	—
565	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
568	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
569	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
570	C₂×D₈	C₂³×C₁₃	1	4	yes	—
571	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
572	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
573	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
574	C₄⋊Q₈	—	2	2	no	—
575	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	C₂³×C₁₃	1	2	yes	—
581	#124	—	2	2	no	—
582	#124	C₂³×C₁₃	1	2	yes	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	4	no	—
588	#123	—	2	4	no	—
589	#123	—	2	4	no	—
590	#123	—	2	4	no	—
591	#123	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
604	#121	—	2	4	no	—
605	#121	—	2	4	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#121	—	2	2	no	—
611	#121	C₂³×C₁₃	1	2	yes	—
612	#121	C₂³×C₁₃	1	2	yes	—
613	#121	C₂³×C₁₃	1	2	yes	—
614	#120	—	2	2	no	—
615	#120	—	2	2	no	—
616	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	D₄×C₁₃	1	2	yes	—
624	C₄×D₄	D₄×C₁₃	1	2	yes	—
625	C₄×D₄	C₂³×C₁₃	1	4	yes	—
626	C₄×D₄	C₂³×C₁₃	1	2	yes	—
627	C₄×D₄	C₂³×C₁₃	1	2	yes	—
628	C₄×D₄	C₂³×C₁₃	1	2	yes	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	4	no	—
638	C₂×C₄⋊C₄	—	2	4	no	—
639	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
652	#107	C₂³×C₁₃	1	4	yes	—
653	#106	C₂³×C₁₃	1	4	yes	—
654	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	4	yes	—
663	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
668	#97	C₂³×C₁₃	1	4	yes	—
669	C₂×C₁₃	—	2	2	no	—
670	C₂×C₁₃	—	4	1	no	—
671	C₂×C₁₃	—	4	2	no	—
672	C₂×C₁₃	—	4	1	no	—
673	C₂×C₁₃	—	4	4	no	—
674	C₂×C₁₃	—	8	2	no	—
675	C₂×C₁₃	#3484	1	1	yes	characteristic
676	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
677	C₂×C₁₃	#3586	1	1	yes	characteristic
678	C₂⁴	—	2	1	no	—
679	C₂⁴	—	2	1	no	—
680	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
682	#41	—	2	8	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	4	4	no	—
686	#41	—	4	2	no	—
687	#41	—	4	2	no	—
688	#41	—	4	4	no	—
689	#41	—	4	4	no	—
690	#41	—	4	4	no	—
691	#41	—	4	8	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	4	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
717	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
719	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	4	no	—
735	C₂²×C₄	—	4	4	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
748	Q₁₆	—	4	4	no	—
749	Q₁₆	—	4	4	no	—
750	SD₁₆	—	2	8	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	D₈	—	2	8	no	—
754	M₁₆	—	4	2	no	—
755	M₁₆	—	4	2	no	—
756	C₂×C₈	—	4	4	no	—
757	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
758	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
793	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	C₂×D₄×C₁₃	1	2	yes	—
799	C₄²	C₂⁴×C₁₃	1	2	yes	—
800	C₁₃	#61575	1	1	yes	characteristic, direct product factor, Sylow
801	C₂³	—	2	4	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
816	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	4	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	4	2	no	—
824	Q₈	—	4	2	no	—
825	Q₈	—	8	1	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	4	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	4	no	—
835	D₄	—	4	4	no	—
836	D₄	—	8	1	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
876	C₈	—	2	4	no	—
877	C₈	—	2	4	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	1	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	4	8	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	2	no	—
898	C₂²	—	16	2	no	—
899	C₂²	C₁₃×#575	1	2	yes	—
900	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
914	C₂	—	2	2	no	—
915	C₂	—	4	1	no	—
916	C₂	—	4	1	no	—
917	C₂	—	4	2	no	—
918	C₂	—	4	4	no	—
919	C₂	—	8	2	no	—
920	C₂	C₁₃×#3484	1	1	yes	characteristic
921	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
922	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×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×#547	C₂	semidirect
3. C₁₃×#3315	C₂	semidirect
4. C₁₃×#3307	C₂	semidirect
5. C₁₃×#3269	C₂	semidirect
6. C₁₃×#3267	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3195	C₂	semidirect
9. C₁₃×#3193	C₂	semidirect
10. C₁₃×#3190	C₂	semidirect
11. C₁₃×#3114	C₂	semidirect
12. C₁₃×#3007	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#3002	C₂	semidirect
15. C₁₃×#2973	C₂	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×#135	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
25. C₁₃×#548	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
34. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃	C₂²	semidirect
48. C₁₃×#497	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#485	C₂²	semidirect
51. C₁₃×#484	C₂²	semidirect
52. C₁₃×#483	C₂²	semidirect
53. C₁₃×#483	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#470	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#463	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
62. C₁₃×#461	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#452	C₂²	semidirect
66. C₁₃×#451	C₂²	semidirect
67. C₁₃×#451	C₂²	semidirect
68. C₁₃×#451	C₂²	semidirect
69. C₁₃×#450	C₂²	semidirect
70. C₁₃×#450	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#449	C₂²	semidirect
76. C₁₃×#442	C₂²	semidirect
77. C₁₃×#440	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₁₃×#435	C₂²	semidirect
80. C₁₃×#432	C₂²	semidirect
81. C₁₃×#417	C₂²	semidirect
82. C₁₃×#417	C₂²	semidirect
83. C₁₃×#416	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
217. #61575	C₁₃	direct (N × H)
340. #3505	C₂×C₁₃	semidirect
341. C₂×#547	C₂×C₁₃	semidirect
342. #3315	C₂×C₁₃	semidirect
343. #3307	C₂×C₁₃	semidirect
344. #3269	C₂×C₁₃	semidirect
345. #3267	C₂×C₁₃	semidirect
346. #3218	C₂×C₁₃	semidirect
347. #3195	C₂×C₁₃	semidirect
348. #3193	C₂×C₁₃	semidirect
349. #3190	C₂×C₁₃	semidirect
350. #3114	C₂×C₁₃	semidirect
351. #3007	C₂×C₁₃	semidirect
352. #3006	C₂×C₁₃	semidirect
353. #3002	C₂×C₁₃	semidirect
354. #2973	C₂×C₁₃	semidirect
433. C₂²×#41	C₂²×C₁₃	semidirect
434. C₂×#137	C₂²×C₁₃	semidirect
435. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
436. C₂×#135	C₂²×C₁₃	semidirect
438. #553	C₂²×C₁₃	semidirect
439. #552	C₂²×C₁₃	semidirect
441. #548	C₂²×C₁₃	semidirect
445. #547	C₂²×C₁₃	semidirect
446. #546	C₂²×C₁₃	semidirect
450. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
457. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
462. C₂×C₄×D₄	C₂²×C₁₃	semidirect
464. #497	C₂²×C₁₃	semidirect
465. #491	C₂²×C₁₃	semidirect
466. #485	C₂²×C₁₃	semidirect
467. #484	C₂²×C₁₃	semidirect
468. #483	C₂²×C₁₃	semidirect
469. #483	C₂²×C₁₃	semidirect
471. #478	C₂²×C₁₃	semidirect
472. #470	C₂²×C₁₃	semidirect
473. #468	C₂²×C₁₃	semidirect
474. #467	C₂²×C₁₃	semidirect
475. #465	C₂²×C₁₃	semidirect
476. #463	C₂²×C₁₃	semidirect
477. #462	C₂²×C₁₃	semidirect
478. #461	C₂²×C₁₃	semidirect
479. #452	C₂²×C₁₃	semidirect
480. #452	C₂²×C₁₃	semidirect
481. #452	C₂²×C₁₃	semidirect
482. #451	C₂²×C₁₃	semidirect
483. #451	C₂²×C₁₃	semidirect
484. #451	C₂²×C₁₃	semidirect
485. #450	C₂²×C₁₃	semidirect
486. #450	C₂²×C₁₃	semidirect
487. #449	C₂²×C₁₃	semidirect
488. #449	C₂²×C₁₃	semidirect
492. #442	C₂²×C₁₃	semidirect
493. #440	C₂²×C₁₃	semidirect
494. #435	C₂²×C₁₃	semidirect
495. #435	C₂²×C₁₃	semidirect
496. #432	C₂²×C₁₃	semidirect
497. #417	C₂²×C₁₃	semidirect
498. #417	C₂²×C₁₃	semidirect
499. #416	C₂²×C₁₃	semidirect
502. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
800. C₁₃	#61575	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×#547	2
C₁₃×#3315	2
C₁₃×#3307	2
C₁₃×#3269	2
C₁₃×#3267	2
C₁₃×#3218	2
C₁₃×#3195	2
C₁₃×#3193	2
C₁₃×#3190	2
C₁₃×#3114	2
C₁₃×#3007	2
C₁₃×#3006	2
C₁₃×#3002	2
C₁₃×#2973	2
#61575	13

Subgroups — C13×#61575 #15747914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61575 #15747914