Subgroups — C₁₃×#61061 #15747400

Order 3328.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3278	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3277	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#578	—	2	8	no	—
25	C₂×C₁₃×#137	—	2	8	no	—
26	C₂×C₁₃×#137	C₂²	1	4	yes	—
27	C₂×C₁₃×#137	C₂²	1	4	yes	—
28	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
33	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
36	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
39	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
43	C₁₃×#550	—	2	2	no	—
44	C₁₃×#550	C₂²	1	4	yes	—
45	D₄×Q₈×C₁₃	—	2	2	no	—
46	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
47	C₁₃×#548	—	2	2	no	—
48	C₁₃×#548	—	2	2	no	—
49	C₁₃×#548	C₂²	1	4	yes	—
50	C₁₃×#548	C₂²	1	4	yes	complemented
51	C₁₃×#536	—	2	2	no	—
52	C₁₃×#536	C₂²	1	1	yes	characteristic
53	C₁₃×#536	C₂²	1	1	yes	characteristic
54	C₁₃×#535	—	2	2	no	—
55	C₁₃×#535	C₂²	1	1	yes	characteristic
56	C₁₃×#535	C₂²	1	1	yes	characteristic
57	C₁₃×#525	—	2	2	no	—
58	C₁₃×#525	—	2	2	no	—
59	C₁₃×#525	C₂²	1	1	yes	characteristic
60	C₁₃×#525	C₂²	1	1	yes	characteristic
61	C₁₃×#525	C₂²	1	1	yes	characteristic
62	C₁₃×#519	C₂²	1	1	yes	characteristic
63	C₁₃×#519	C₂²	1	1	yes	characteristic
64	C₁₃×#497	C₂²	1	2	yes	complemented
65	C₁₃×#496	C₂²	1	2	yes	complemented
66	C₁₃×#495	C₂²	1	2	yes	complemented
67	C₁₃×#492	C₂²	1	2	yes	complemented
68	C₁₃×#470	C₂²	1	2	yes	complemented
69	C₁₃×#469	C₂²	1	2	yes	complemented
70	C₁₃×#468	C₂²	1	2	yes	complemented
71	C₁₃×#468	C₂²	1	4	yes	complemented
72	C₁₃×#468	C₂²	1	2	yes	complemented
73	C₁₃×#465	C₂²	1	4	yes	complemented
74	C₁₃×#464	C₂²	1	4	yes	complemented
75	C₁₃×#464	C₂²	1	4	yes	complemented
76	C₁₃×#462	C₂²	1	4	yes	complemented
77	C₁₃×#460	C₂²	1	4	yes	complemented
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#452	C₂²	1	4	yes	complemented
80	C₁₃×#451	C₂²	1	4	yes	complemented
81	C₁₃×#451	C₂²	1	4	yes	complemented
82	C₁₃×#449	C₂²	1	4	yes	—
83	C₁₃×#449	C₂²	1	4	yes	complemented
84	C₁₃×#448	C₂²	1	4	yes	complemented
85	C₁₃×#448	C₂²	1	4	yes	complemented
86	C₁₃×#441	C₂²	1	4	yes	complemented
87	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
88	C₁₃×#436	C₂²	1	4	yes	complemented
89	C₁₃×#435	C₂²	1	4	yes	complemented
90	C₁₃×#427	C₂²	1	1	yes	characteristic
91	C₁₃×#424	C₂²	1	1	yes	characteristic
92	C₁₃×#419	C₂²	1	1	yes	characteristic
93	C₁₃×#419	C₂²	1	1	yes	characteristic
94	C₁₃×#419	C₂²	1	1	yes	characteristic
95	C₁₃×#418	C₂²	1	1	yes	characteristic
96	C₁₃×#416	C₂²	1	1	yes	characteristic
97	C₁₃×#416	C₂²	1	1	yes	characteristic
98	C₁₃×#408	C₂²	1	1	yes	characteristic
99	C₁₃×#407	C₂²	1	1	yes	characteristic
100	C₁₃×#405	C₂²	1	1	yes	characteristic
101	C₁₃×2₋¹⁺⁴	—	2	4	no	—
102	C₁₃×2₋¹⁺⁴	—	2	4	no	—
103	C₁₃×2₋¹⁺⁴	—	4	2	no	—
104	C₁₃×2₋¹⁺⁴	—	4	2	no	—
105	C₂×C₁₃×#41	—	2	2	no	—
106	C₂×C₁₃×#41	—	2	2	no	—
107	C₂×C₁₃×#41	—	2	1	no	—
108	C₂×C₁₃×#41	—	2	1	no	—
109	C₂×C₁₃×#41	—	2	2	no	—
110	C₂×C₁₃×#41	—	2	4	no	—
111	C₂×C₁₃×#41	—	4	2	no	—
112	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×#41	C₂³	1	4	yes	—
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂×C₁₃×#41	C₂³	1	2	yes	—
117	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
118	C₂²×Q₈×C₁₃	—	2	1	no	—
119	C₂²×Q₈×C₁₃	—	2	1	no	—
120	C₂²×Q₈×C₁₃	—	2	1	no	—
121	C₂²×Q₈×C₁₃	—	2	2	no	—
122	C₂²×Q₈×C₁₃	—	2	4	no	—
123	C₂²×Q₈×C₁₃	—	4	2	no	—
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
127	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
128	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃	—	2	1	no	—
131	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃	—	2	1	no	—
133	C₂³×C₄×C₁₃	—	2	1	no	—
134	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×#137	—	2	4	no	—
136	C₁₃×#137	—	2	4	no	—
137	C₁₃×#137	—	2	16	no	—
138	C₁₃×#137	—	2	16	no	—
139	C₁₃×#137	—	2	8	no	—
140	C₁₃×#137	—	2	8	no	—
141	C₁₃×#137	—	4	2	no	—
142	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
143	C₁₃×#135	—	2	8	no	—
144	C₁₃×#135	—	2	4	no	—
145	C₂×C₁₃×Q₁₆	—	2	4	no	—
146	C₂×C₁₃×Q₁₆	—	2	8	no	—
147	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
148	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
150	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
155	C₂×C₁₃×SD₁₆	—	2	4	no	—
156	C₂×C₁₃×SD₁₆	—	2	4	no	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
159	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×D₈	C₂³	1	2	yes	—
168	C₁₃×#131	—	2	4	no	—
169	C₂×C₁₃×M₁₆	—	2	4	no	—
170	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
173	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
174	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
175	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
177	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊Q₈	—	2	1	no	—
179	C₁₃×C₄⋊Q₈	—	2	4	no	—
180	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₁₃×#127	—	2	4	no	—
182	C₁₃×#127	—	2	1	no	—
183	C₁₃×#127	C₂³	1	2	yes	—
184	C₁₃×#124	—	2	1	no	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#124	—	2	4	no	—
187	C₁₃×#124	—	2	4	no	—
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	1	no	—
192	C₁₃×#123	—	2	1	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	D₄	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	—	2	4	no	—
196	C₁₃×C₂²⋊Q₈	—	2	4	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	4	no	—
199	C₁₃×C₂²⋊Q₈	—	2	4	no	—
200	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×#121	—	2	4	no	—
205	C₁₃×#121	—	2	4	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	4	no	—
208	C₁₃×#121	—	2	4	no	—
209	C₁₃×#121	D₄	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	4	yes	—
212	C₁₃×#121	C₂³	1	2	yes	—
213	C₁₃×#120	—	2	1	no	—
214	C₁₃×#120	—	2	1	no	—
215	C₁₃×#120	—	2	2	no	—
216	C₁₃×#120	—	2	2	no	—
217	C₁₃×#120	D₄	1	2	yes	—
218	C₄×Q₈×C₁₃	—	2	2	no	—
219	C₄×Q₈×C₁₃	—	2	2	no	—
220	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
222	C₄×D₄×C₁₃	—	2	4	no	—
223	C₄×D₄×C₁₃	—	2	2	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	4	no	—
226	C₄×D₄×C₁₃	—	2	4	no	—
227	C₄×D₄×C₁₃	—	2	4	no	—
228	C₄×D₄×C₁₃	C₂³	1	4	yes	—
229	C₁₃×#117	—	2	2	no	—
230	C₁₃×#117	—	2	2	no	—
231	C₁₃×#117	C₂³	1	1	yes	characteristic
232	C₁₃×#117	C₂³	1	1	yes	characteristic
233	C₁₃×#117	C₂³	1	1	yes	characteristic
234	C₁₃×#107	C₂³	1	2	yes	—
235	C₁₃×#106	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
237	C₁₃×#103	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	4	yes	—
240	C₁₃×#103	C₂³	1	4	yes	—
241	C₁₃×#103	C₂³	1	4	yes	—
242	C₁₃×#102	C₂³	1	2	yes	—
243	C₁₃×#102	C₂³	1	2	yes	—
244	C₁₃×#102	C₂³	1	4	yes	—
245	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
246	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₁₃×#97	C₂³	1	2	yes	—
248	C₄×C₈×C₁₃	C₂³	1	2	yes	—
249	#61061	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂⁴×C₁₃	—	2	1	no	—
251	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₁₃×#41	—	2	2	no	—
253	C₁₃×#41	—	2	2	no	—
254	C₁₃×#41	—	2	4	no	—
255	C₁₃×#41	—	2	4	no	—
256	C₁₃×#41	—	2	8	no	—
257	C₁₃×#41	—	2	2	no	—
258	C₁₃×#41	—	2	2	no	—
259	C₁₃×#41	—	2	2	no	—
260	C₁₃×#41	—	2	2	no	—
261	C₁₃×#41	—	4	4	no	—
262	C₁₃×#41	—	4	2	no	—
263	C₁₃×#41	—	4	2	no	—
264	C₁₃×#41	—	4	8	no	—
265	C₁₃×#41	—	4	8	no	—
266	C₁₃×#41	—	4	8	no	—
267	C₁₃×#41	—	4	4	no	—
268	C₁₃×#41	—	4	4	no	—
269	C₂×Q₈×C₁₃	—	2	1	no	—
270	C₂×Q₈×C₁₃	—	2	1	no	—
271	C₂×Q₈×C₁₃	—	2	2	no	—
272	C₂×Q₈×C₁₃	—	2	4	no	—
273	C₂×Q₈×C₁₃	—	2	1	no	—
274	C₂×Q₈×C₁₃	—	2	2	no	—
275	C₂×Q₈×C₁₃	—	2	2	no	—
276	C₂×Q₈×C₁₃	—	2	2	no	—
277	C₂×Q₈×C₁₃	—	2	4	no	—
278	C₂×Q₈×C₁₃	—	2	4	no	—
279	C₂×Q₈×C₁₃	—	2	8	no	—
280	C₂×Q₈×C₁₃	—	2	2	no	—
281	C₂×Q₈×C₁₃	—	2	2	no	—
282	C₂×Q₈×C₁₃	—	4	4	no	—
283	C₂×Q₈×C₁₃	—	4	4	no	—
284	C₂×Q₈×C₁₃	—	4	2	no	—
285	C₂×Q₈×C₁₃	—	4	2	no	—
286	C₂×Q₈×C₁₃	—	4	8	no	—
287	C₂×Q₈×C₁₃	—	4	4	no	—
288	C₂×Q₈×C₁₃	—	4	4	no	—
289	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
290	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
291	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
296	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	1	no	—
299	C₂×D₄×C₁₃	—	2	1	no	—
300	C₂×D₄×C₁₃	—	2	2	no	—
301	C₂×D₄×C₁₃	—	2	4	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	4	no	—
304	C₂×D₄×C₁₃	—	2	2	no	—
305	C₂×D₄×C₁₃	—	2	2	no	—
306	C₂×D₄×C₁₃	—	2	1	no	—
307	C₂×D₄×C₁₃	—	2	4	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	4	4	no	—
310	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
315	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	—	2	1	no	—
317	C₂²×C₄×C₁₃	—	2	1	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	—	2	2	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	4	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	—	2	1	no	—
324	C₂²×C₄×C₁₃	—	2	2	no	—
325	C₂²×C₄×C₁₃	—	2	1	no	—
326	C₂²×C₄×C₁₃	—	2	4	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	1	no	—
329	C₂²×C₄×C₁₃	—	4	4	no	—
330	C₂²×C₄×C₁₃	—	4	4	no	—
331	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
332	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₁₃×Q₁₆	—	2	8	no	—
337	C₁₃×Q₁₆	—	2	4	no	—
338	C₁₃×Q₁₆	—	2	4	no	—
339	C₁₃×Q₁₆	—	2	2	no	—
340	C₁₃×Q₁₆	—	4	2	no	—
341	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
342	C₁₃×Q₁₆	C₂×D₄	1	8	yes	—
343	C₁₃×SD₁₆	—	2	8	no	—
344	C₁₃×SD₁₆	—	2	4	no	—
345	C₁₃×SD₁₆	—	2	4	no	—
346	C₁₃×SD₁₆	—	2	4	no	—
347	C₁₃×SD₁₆	—	2	4	no	—
348	C₁₃×SD₁₆	—	2	2	no	—
349	C₁₃×SD₁₆	—	2	2	no	—
350	C₁₃×SD₁₆	—	4	2	no	—
351	C₁₃×SD₁₆	—	4	2	no	—
352	C₁₃×D₈	—	2	2	no	—
353	C₁₃×D₈	—	4	2	no	—
354	C₁₃×M₁₆	—	2	2	no	—
355	C₁₃×M₁₆	—	2	2	no	—
356	C₁₃×M₁₆	—	2	4	no	—
357	C₁₃×M₁₆	—	2	4	no	—
358	C₁₃×M₁₆	—	2	4	no	—
359	C₂×C₈×C₁₃	—	2	2	no	—
360	C₂×C₈×C₁₃	—	2	4	no	—
361	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
362	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	—	2	4	no	—
368	C₁₃×C₄⋊C₄	—	2	4	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	4	no	—
371	C₁₃×C₄⋊C₄	—	2	4	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
374	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
377	C₁₃×C₂²⋊C₄	—	2	1	no	—
378	C₁₃×C₂²⋊C₄	—	2	1	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	no	—
381	C₁₃×C₂²⋊C₄	—	2	4	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	4	no	—
384	C₁₃×C₂²⋊C₄	—	2	4	no	—
385	C₁₃×C₂²⋊C₄	—	2	4	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
389	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
390	C₄²×C₁₃	—	2	4	no	—
391	C₄²×C₁₃	—	2	4	no	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	—	2	1	no	—
394	C₄²×C₁₃	C₂⁴	1	2	yes	—
395	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂²×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3487	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#3486	C₂×C₁₃	1	1	yes	characteristic, complemented
399	#3278	C₂×C₁₃	1	4	yes	complemented
400	#3277	C₂×C₁₃	1	4	yes	complemented
401	#3271	C₂×C₁₃	1	4	yes	complemented
402	#3270	C₂×C₁₃	1	4	yes	complemented
403	#3154	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3057	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
406	#3044	C₂×C₁₃	1	1	yes	characteristic, complemented
407	#3043	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3011	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3010	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#3005	C₂×C₁₃	1	1	yes	characteristic, complemented
411	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
412	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
413	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
414	C₂³×C₁₃	—	2	2	no	—
415	C₂³×C₁₃	—	2	1	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	1	no	—
418	C₂³×C₁₃	—	4	2	no	—
419	C₂³×C₁₃	—	4	2	no	—
420	C₂³×C₁₃	—	8	2	no	—
421	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
423	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	Q₈×C₁₃	—	2	4	no	—
425	Q₈×C₁₃	—	2	4	no	—
426	Q₈×C₁₃	—	2	2	no	—
427	Q₈×C₁₃	—	2	2	no	—
428	Q₈×C₁₃	—	2	2	no	—
429	Q₈×C₁₃	—	2	2	no	—
430	Q₈×C₁₃	—	2	1	no	—
431	Q₈×C₁₃	—	2	1	no	—
432	Q₈×C₁₃	—	2	1	no	—
433	Q₈×C₁₃	—	2	2	no	—
434	Q₈×C₁₃	—	2	1	no	—
435	Q₈×C₁₃	—	4	8	no	—
436	Q₈×C₁₃	—	4	4	no	—
437	Q₈×C₁₃	—	4	4	no	—
438	Q₈×C₁₃	—	4	2	no	—
439	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
440	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
441	D₄×C₁₃	—	2	4	no	—
442	D₄×C₁₃	—	2	2	no	—
443	D₄×C₁₃	—	2	1	no	—
444	D₄×C₁₃	—	2	1	no	—
445	D₄×C₁₃	—	2	2	no	—
446	D₄×C₁₃	—	2	1	no	—
447	D₄×C₁₃	—	2	2	no	—
448	D₄×C₁₃	—	2	1	no	—
449	D₄×C₁₃	—	4	4	no	—
450	D₄×C₁₃	—	4	8	no	—
451	D₄×C₁₃	—	4	4	no	—
452	D₄×C₁₃	—	4	4	no	—
453	D₄×C₁₃	—	4	4	no	—
454	D₄×C₁₃	—	4	2	no	—
455	D₄×C₁₃	—	4	2	no	—
456	D₄×C₁₃	—	4	2	no	—
457	D₄×C₁₃	—	8	4	no	—
458	D₄×C₁₃	—	8	4	no	—
459	D₄×C₁₃	—	8	2	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	4	no	—
462	C₂×C₄×C₁₃	—	2	4	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	4	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	2	no	—
469	C₂×C₄×C₁₃	—	2	2	no	—
470	C₂×C₄×C₁₃	—	2	2	no	—
471	C₂×C₄×C₁₃	—	2	2	no	—
472	C₂×C₄×C₁₃	—	2	1	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	1	no	—
475	C₂×C₄×C₁₃	—	4	8	no	—
476	C₂×C₄×C₁₃	—	4	4	no	—
477	C₂×C₄×C₁₃	—	4	4	no	—
478	C₂×C₄×C₁₃	—	4	8	no	—
479	C₂×C₄×C₁₃	—	4	4	no	—
480	C₂×C₄×C₁₃	—	4	4	no	—
481	C₂×C₄×C₁₃	—	4	2	no	—
482	C₂×C₄×C₁₃	—	4	2	no	—
483	C₂×C₄×C₁₃	—	4	2	no	—
484	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
485	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
491	C₈×C₁₃	—	2	2	no	—
492	C₈×C₁₃	—	2	2	no	—
493	C₈×C₁₃	—	2	2	no	—
494	C₈×C₁₃	C₂²×D₄	1	2	yes	—
495	C₈×C₁₃	C₂²×D₄	1	2	yes	—
496	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
498	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
499	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
500	#578	—	2	8	no	—
501	C₂×#137	—	2	8	no	—
502	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
504	C₂×#137	C₂²×C₁₃	1	4	yes	—
505	C₂×#137	C₂²×C₁₃	1	4	yes	—
506	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
507	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
508	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
509	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
510	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
511	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
512	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
513	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
514	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
515	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
516	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
517	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
518	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
519	#550	—	2	2	no	—
520	#550	C₂²×C₁₃	1	4	yes	—
521	D₄×Q₈	—	2	2	no	—
522	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
523	#548	—	2	2	no	—
524	#548	—	2	2	no	—
525	#548	C₂²×C₁₃	1	4	yes	—
526	#548	C₂²×C₁₃	1	4	yes	complemented
527	#536	—	2	2	no	—
528	#536	C₂²×C₁₃	1	1	yes	characteristic
529	#536	C₂²×C₁₃	1	1	yes	characteristic
530	#535	—	2	2	no	—
531	#535	C₂²×C₁₃	1	1	yes	characteristic
532	#535	C₂²×C₁₃	1	1	yes	characteristic
533	#525	—	2	2	no	—
534	#525	—	2	2	no	—
535	#525	C₂²×C₁₃	1	1	yes	characteristic
536	#525	C₂²×C₁₃	1	1	yes	characteristic
537	#525	C₂²×C₁₃	1	1	yes	characteristic
538	#519	C₂²×C₁₃	1	1	yes	characteristic
539	#519	C₂²×C₁₃	1	1	yes	characteristic
540	#497	C₂²×C₁₃	1	2	yes	complemented
541	#496	C₂²×C₁₃	1	2	yes	complemented
542	#495	C₂²×C₁₃	1	2	yes	complemented
543	#492	C₂²×C₁₃	1	2	yes	complemented
544	#470	C₂²×C₁₃	1	2	yes	complemented
545	#469	C₂²×C₁₃	1	2	yes	complemented
546	#468	C₂²×C₁₃	1	2	yes	complemented
547	#468	C₂²×C₁₃	1	4	yes	complemented
548	#468	C₂²×C₁₃	1	2	yes	complemented
549	#465	C₂²×C₁₃	1	4	yes	complemented
550	#464	C₂²×C₁₃	1	4	yes	complemented
551	#464	C₂²×C₁₃	1	4	yes	complemented
552	#462	C₂²×C₁₃	1	4	yes	complemented
553	#460	C₂²×C₁₃	1	4	yes	complemented
554	#452	C₂²×C₁₃	1	4	yes	—
555	#452	C₂²×C₁₃	1	4	yes	complemented
556	#451	C₂²×C₁₃	1	4	yes	complemented
557	#451	C₂²×C₁₃	1	4	yes	complemented
558	#449	C₂²×C₁₃	1	4	yes	—
559	#449	C₂²×C₁₃	1	4	yes	complemented
560	#448	C₂²×C₁₃	1	4	yes	complemented
561	#448	C₂²×C₁₃	1	4	yes	complemented
562	#441	C₂²×C₁₃	1	4	yes	complemented
563	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
564	#436	C₂²×C₁₃	1	4	yes	complemented
565	#435	C₂²×C₁₃	1	4	yes	complemented
566	#427	C₂²×C₁₃	1	1	yes	characteristic
567	#424	C₂²×C₁₃	1	1	yes	characteristic
568	#419	C₂²×C₁₃	1	1	yes	characteristic
569	#419	C₂²×C₁₃	1	1	yes	characteristic
570	#419	C₂²×C₁₃	1	1	yes	characteristic
571	#418	C₂²×C₁₃	1	1	yes	characteristic
572	#416	C₂²×C₁₃	1	1	yes	characteristic
573	#416	C₂²×C₁₃	1	1	yes	characteristic
574	#408	C₂²×C₁₃	1	1	yes	characteristic
575	#407	C₂²×C₁₃	1	1	yes	characteristic
576	#405	C₂²×C₁₃	1	1	yes	characteristic
577	C₂²×C₁₃	—	2	2	no	—
578	C₂²×C₁₃	—	2	2	no	—
579	C₂²×C₁₃	—	2	4	no	—
580	C₂²×C₁₃	—	2	2	no	—
581	C₂²×C₁₃	—	2	2	no	—
582	C₂²×C₁₃	—	2	2	no	—
583	C₂²×C₁₃	—	4	4	no	—
584	C₂²×C₁₃	—	4	2	no	—
585	C₂²×C₁₃	—	4	2	no	—
586	C₂²×C₁₃	—	4	4	no	—
587	C₂²×C₁₃	—	4	1	no	—
588	C₂²×C₁₃	—	4	1	no	—
589	C₂²×C₁₃	—	4	2	no	—
590	C₂²×C₁₃	—	8	4	no	—
591	C₂²×C₁₃	D₄²	1	2	yes	—
592	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
593	C₄×C₁₃	—	2	4	no	—
594	C₄×C₁₃	—	2	2	no	—
595	C₄×C₁₃	—	2	4	no	—
596	C₄×C₁₃	—	2	4	no	—
597	C₄×C₁₃	—	2	2	no	—
598	C₄×C₁₃	—	4	2	no	—
599	C₄×C₁₃	—	4	2	no	—
600	C₄×C₁₃	—	4	1	no	—
601	C₄×C₁₃	—	4	1	no	—
602	C₄×C₁₃	—	4	2	no	—
603	C₄×C₁₃	D₄²	1	2	yes	—
604	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
605	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	2₋¹⁺⁴	—	2	4	no	—
607	2₋¹⁺⁴	—	2	4	no	—
608	2₋¹⁺⁴	—	4	2	no	—
609	2₋¹⁺⁴	—	4	2	no	—
610	C₂×#41	—	2	2	no	—
611	C₂×#41	—	2	2	no	—
612	C₂×#41	—	2	1	no	—
613	C₂×#41	—	2	1	no	—
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	4	no	—
616	C₂×#41	—	4	2	no	—
617	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×#41	C₂³×C₁₃	1	4	yes	—
620	C₂×#41	C₂³×C₁₃	1	2	yes	—
621	C₂×#41	C₂³×C₁₃	1	2	yes	—
622	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×Q₈	—	2	1	no	—
624	C₂²×Q₈	—	2	1	no	—
625	C₂²×Q₈	—	2	1	no	—
626	C₂²×Q₈	—	2	2	no	—
627	C₂²×Q₈	—	2	4	no	—
628	C₂²×Q₈	—	4	2	no	—
629	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
631	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
632	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
633	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
634	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₂²×D₄	—	2	1	no	—
636	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
637	C₂³×C₄	—	2	1	no	—
638	C₂³×C₄	—	2	1	no	—
639	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
640	#137	—	2	4	no	—
641	#137	—	2	4	no	—
642	#137	—	2	16	no	—
643	#137	—	2	16	no	—
644	#137	—	2	8	no	—
645	#137	—	2	8	no	—
646	#137	—	4	2	no	—
647	AGL(1,ℤ/8)	—	4	2	no	—
648	#135	—	2	8	no	—
649	#135	—	2	4	no	—
650	C₂×Q₁₆	—	2	4	no	—
651	C₂×Q₁₆	—	2	8	no	—
652	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
653	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
654	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
658	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
659	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
660	C₂×SD₁₆	—	2	4	no	—
661	C₂×SD₁₆	—	2	4	no	—
662	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
663	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
664	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
667	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
670	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
671	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×D₈	C₂³×C₁₃	1	2	yes	—
673	#131	—	2	4	no	—
674	C₂×M₁₆	—	2	4	no	—
675	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
676	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
677	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
679	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
680	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
682	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	—	2	4	no	—
685	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
686	#127	—	2	4	no	—
687	#127	—	2	1	no	—
688	#127	C₂³×C₁₃	1	2	yes	—
689	#124	—	2	1	no	—
690	#124	—	2	1	no	—
691	#124	—	2	4	no	—
692	#124	—	2	4	no	—
693	#124	C₂³×C₁₃	1	2	yes	—
694	#124	C₂³×C₁₃	1	2	yes	—
695	#123	—	2	2	no	—
696	#123	—	2	1	no	—
697	#123	—	2	1	no	—
698	#123	—	2	2	no	—
699	#123	D₄×C₁₃	1	2	yes	—
700	C₂²⋊Q₈	—	2	4	no	—
701	C₂²⋊Q₈	—	2	4	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	4	no	—
704	C₂²⋊Q₈	—	2	4	no	—
705	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
706	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
709	#121	—	2	4	no	—
710	#121	—	2	4	no	—
711	#121	—	2	2	no	—
712	#121	—	2	4	no	—
713	#121	—	2	4	no	—
714	#121	D₄×C₁₃	1	2	yes	—
715	#121	C₂³×C₁₃	1	2	yes	—
716	#121	C₂³×C₁₃	1	2	yes	—
717	#121	C₂³×C₁₃	1	4	yes	—
718	#120	—	2	1	no	—
719	#120	—	2	1	no	—
720	#120	—	2	2	no	—
721	#120	—	2	2	no	—
722	#120	D₄×C₁₃	1	2	yes	—
723	C₄×Q₈	—	2	2	no	—
724	C₄×Q₈	—	2	2	no	—
725	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
726	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
727	C₄×D₄	—	2	4	no	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	4	no	—
731	C₄×D₄	—	2	4	no	—
732	C₄×D₄	—	2	4	no	—
733	C₄×D₄	C₂³×C₁₃	1	4	yes	—
734	#117	—	2	2	no	—
735	#117	—	2	2	no	—
736	#117	C₂³×C₁₃	1	1	yes	characteristic
737	#117	C₂³×C₁₃	1	1	yes	characteristic
738	#117	C₂³×C₁₃	1	1	yes	characteristic
739	#107	C₂³×C₁₃	1	2	yes	—
740	#106	C₂³×C₁₃	1	2	yes	—
741	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
742	#103	C₂³×C₁₃	1	2	yes	—
743	#103	C₂³×C₁₃	1	2	yes	—
744	#103	C₂³×C₁₃	1	4	yes	—
745	#103	C₂³×C₁₃	1	4	yes	—
746	#103	C₂³×C₁₃	1	4	yes	—
747	#102	C₂³×C₁₃	1	2	yes	—
748	#102	C₂³×C₁₃	1	2	yes	—
749	#102	C₂³×C₁₃	1	4	yes	—
750	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
751	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
752	#97	C₂³×C₁₃	1	2	yes	—
753	C₄×C₈	C₂³×C₁₃	1	2	yes	—
754	C₂×C₁₃	—	2	2	no	—
755	C₂×C₁₃	—	4	2	no	—
756	C₂×C₁₃	—	4	2	no	—
757	C₂×C₁₃	—	8	1	no	—
758	C₂×C₁₃	—	8	1	no	—
759	C₂×C₁₃	—	8	2	no	—
760	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
761	C₂×C₁₃	#3586	1	2	yes	—
762	C₂⁴	—	2	1	no	—
763	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
764	#41	—	2	2	no	—
765	#41	—	2	2	no	—
766	#41	—	2	4	no	—
767	#41	—	2	4	no	—
768	#41	—	2	8	no	—
769	#41	—	2	2	no	—
770	#41	—	2	2	no	—
771	#41	—	2	2	no	—
772	#41	—	2	2	no	—
773	#41	—	4	4	no	—
774	#41	—	4	2	no	—
775	#41	—	4	2	no	—
776	#41	—	4	8	no	—
777	#41	—	4	8	no	—
778	#41	—	4	8	no	—
779	#41	—	4	4	no	—
780	#41	—	4	4	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	4	no	—
790	C₂×Q₈	—	2	4	no	—
791	C₂×Q₈	—	2	8	no	—
792	C₂×Q₈	—	2	2	no	—
793	C₂×Q₈	—	2	2	no	—
794	C₂×Q₈	—	4	4	no	—
795	C₂×Q₈	—	4	4	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	4	2	no	—
798	C₂×Q₈	—	4	8	no	—
799	C₂×Q₈	—	4	4	no	—
800	C₂×Q₈	—	4	4	no	—
801	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
802	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
803	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
807	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
808	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	4	4	no	—
822	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
823	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
824	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
825	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
826	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
827	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	4	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	4	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
848	Q₁₆	—	2	8	no	—
849	Q₁₆	—	2	4	no	—
850	Q₁₆	—	2	4	no	—
851	Q₁₆	—	2	2	no	—
852	Q₁₆	—	4	2	no	—
853	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
854	Q₁₆	C₂×D₄×C₁₃	1	8	yes	—
855	SD₁₆	—	2	8	no	—
856	SD₁₆	—	2	4	no	—
857	SD₁₆	—	2	4	no	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	2	2	no	—
861	SD₁₆	—	2	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	D₈	—	2	2	no	—
865	D₈	—	4	2	no	—
866	M₁₆	—	2	2	no	—
867	M₁₆	—	2	2	no	—
868	M₁₆	—	2	4	no	—
869	M₁₆	—	2	4	no	—
870	M₁₆	—	2	4	no	—
871	C₂×C₈	—	2	2	no	—
872	C₂×C₈	—	2	4	no	—
873	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
874	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
875	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
876	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
877	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₄⋊C₄	—	2	4	no	—
880	C₄⋊C₄	—	2	4	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	2	4	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
886	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
887	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
900	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
901	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
902	C₄²	—	2	4	no	—
903	C₄²	—	2	4	no	—
904	C₄²	—	2	1	no	—
905	C₄²	—	2	1	no	—
906	C₄²	C₂⁴×C₁₃	1	2	yes	—
907	C₁₃	#61061	1	1	yes	characteristic, direct product factor, Sylow
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	2	no	—
915	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
916	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
917	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
918	Q₈	—	2	4	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	2	2	no	—
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	1	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	1	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	1	no	—
929	Q₈	—	4	8	no	—
930	Q₈	—	4	4	no	—
931	Q₈	—	4	4	no	—
932	Q₈	—	4	2	no	—
933	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
934	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
935	D₄	—	2	4	no	—
936	D₄	—	2	2	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	1	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	1	no	—
943	D₄	—	4	4	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	4	no	—
952	D₄	—	8	4	no	—
953	D₄	—	8	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	4	no	—
956	C₂×C₄	—	2	4	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	8	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	2	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
979	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
983	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
984	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	C₂²×D₄×C₁₃	1	2	yes	—
989	C₈	C₂²×D₄×C₁₃	1	2	yes	—
990	C₂²	—	2	2	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	4	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	4	4	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	4	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	D₄²×C₁₃	1	2	yes	—
1005	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1006	C₄	—	2	4	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	4	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	2	no	—
1016	C₄	D₄²×C₁₃	1	2	yes	—
1017	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
1018	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1019	C₂	—	2	2	no	—
1020	C₂	—	4	2	no	—
1021	C₂	—	4	2	no	—
1022	C₂	—	8	2	no	—
1023	C₂	—	8	1	no	—
1024	C₂	—	8	1	no	—
1025	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
1026	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂²×C₁₃×#137	C₂	semidirect
3. C₁₃×#3487	C₂	semidirect
4. C₁₃×#3486	C₂	semidirect
5. C₁₃×#3278	C₂	semidirect
6. C₁₃×#3277	C₂	semidirect
7. C₁₃×#3271	C₂	semidirect
8. C₁₃×#3270	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3057	C₂	semidirect
11. C₁₃×#3054	C₂	semidirect
12. C₁₃×#3044	C₂	semidirect
13. C₁₃×#3043	C₂	semidirect
14. C₁₃×#3011	C₂	semidirect
15. C₁₃×#3010	C₂	semidirect
16. C₁₃×#3005	C₂	semidirect
17. C₁₃×#3004	C₂	semidirect
18. C₁₃×#2950	C₂	semidirect
19. C₁₃×#2930	C₂	semidirect
31. C₂×C₁₃×#137	C₂²	semidirect
32. C₂×C₁₃×#137	C₂²	semidirect
35. C₂×C₁₃×#135	C₂²	semidirect
38. C₂²×C₁₃×Q₁₆	C₂²	semidirect
46. D₄×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#548	C₂²	semidirect
64. C₁₃×#497	C₂²	semidirect
65. C₁₃×#496	C₂²	semidirect
66. C₁₃×#495	C₂²	semidirect
67. C₁₃×#492	C₂²	semidirect
68. C₁₃×#470	C₂²	semidirect
69. C₁₃×#469	C₂²	semidirect
70. C₁₃×#468	C₂²	semidirect
71. C₁₃×#468	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#465	C₂²	semidirect
74. C₁₃×#464	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#462	C₂²	semidirect
77. C₁₃×#460	C₂²	semidirect
79. C₁₃×#452	C₂²	semidirect
80. C₁₃×#451	C₂²	semidirect
81. C₁₃×#451	C₂²	semidirect
83. C₁₃×#449	C₂²	semidirect
84. C₁₃×#448	C₂²	semidirect
85. C₁₃×#448	C₂²	semidirect
86. C₁₃×#441	C₂²	semidirect
87. C₄×C₁₃×Q₁₆	C₂²	semidirect
88. C₁₃×#436	C₂²	semidirect
89. C₁₃×#435	C₂²	semidirect
147. C₂×C₁₃×Q₁₆	D₄	semidirect
249. #61061	C₁₃	direct (N × H)
395. C₂×#578	C₂×C₁₃	semidirect
396. C₂²×#137	C₂×C₁₃	semidirect
397. #3487	C₂×C₁₃	semidirect
398. #3486	C₂×C₁₃	semidirect
399. #3278	C₂×C₁₃	semidirect
400. #3277	C₂×C₁₃	semidirect
401. #3271	C₂×C₁₃	semidirect
402. #3270	C₂×C₁₃	semidirect
403. #3154	C₂×C₁₃	semidirect
404. #3057	C₂×C₁₃	semidirect
405. #3054	C₂×C₁₃	semidirect
406. #3044	C₂×C₁₃	semidirect
407. #3043	C₂×C₁₃	semidirect
408. #3011	C₂×C₁₃	semidirect
409. #3010	C₂×C₁₃	semidirect
410. #3005	C₂×C₁₃	semidirect
411. #3004	C₂×C₁₃	semidirect
412. #2950	C₂×C₁₃	semidirect
413. #2930	C₂×C₁₃	semidirect
507. C₂×#137	C₂²×C₁₃	semidirect
508. C₂×#137	C₂²×C₁₃	semidirect
511. C₂×#135	C₂²×C₁₃	semidirect
514. C₂²×Q₁₆	C₂²×C₁₃	semidirect
522. D₄×Q₈	C₂²×C₁₃	semidirect
526. #548	C₂²×C₁₃	semidirect
540. #497	C₂²×C₁₃	semidirect
541. #496	C₂²×C₁₃	semidirect
542. #495	C₂²×C₁₃	semidirect
543. #492	C₂²×C₁₃	semidirect
544. #470	C₂²×C₁₃	semidirect
545. #469	C₂²×C₁₃	semidirect
546. #468	C₂²×C₁₃	semidirect
547. #468	C₂²×C₁₃	semidirect
548. #468	C₂²×C₁₃	semidirect
549. #465	C₂²×C₁₃	semidirect
550. #464	C₂²×C₁₃	semidirect
551. #464	C₂²×C₁₃	semidirect
552. #462	C₂²×C₁₃	semidirect
553. #460	C₂²×C₁₃	semidirect
555. #452	C₂²×C₁₃	semidirect
556. #451	C₂²×C₁₃	semidirect
557. #451	C₂²×C₁₃	semidirect
559. #449	C₂²×C₁₃	semidirect
560. #448	C₂²×C₁₃	semidirect
561. #448	C₂²×C₁₃	semidirect
562. #441	C₂²×C₁₃	semidirect
563. C₄×Q₁₆	C₂²×C₁₃	semidirect
564. #436	C₂²×C₁₃	semidirect
565. #435	C₂²×C₁₃	semidirect
652. C₂×Q₁₆	D₄×C₁₃	semidirect
907. C₁₃	#61061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#578	2
C₂²×C₁₃×#137	2
C₁₃×#3487	2
C₁₃×#3486	2
C₁₃×#3278	2
C₁₃×#3277	2
C₁₃×#3271	2
C₁₃×#3270	2
C₁₃×#3154	2
C₁₃×#3057	2
C₁₃×#3054	2
C₁₃×#3044	2
C₁₃×#3043	2
C₁₃×#3011	2
C₁₃×#3010	2
C₁₃×#3005	2
C₁₃×#3004	2
C₁₃×#2950	2
C₁₃×#2930	2
#61061	13

Subgroups — C13×#61061 #15747400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61061 #15747400