Subgroups — C₁₃×#61176 #15747515

Order 3328.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3328	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3326	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	2	yes	—
33	C₁₃×#555	—	2	1	no	—
34	C₁₃×#555	C₂²	1	2	yes	—
35	C₁₃×#553	—	2	1	no	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#552	—	2	1	no	—
38	C₁₃×#552	C₂²	1	2	yes	—
39	D₄×Q₈×C₁₃	—	2	1	no	—
40	D₄×Q₈×C₁₃	—	2	1	no	—
41	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
42	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
43	C₁₃×#548	—	2	1	no	—
44	C₁₃×#548	—	2	1	no	—
45	C₁₃×#548	C₂²	1	2	yes	—
46	C₁₃×#548	C₂²	1	2	yes	—
47	C₁₃×#544	C₂²	1	1	yes	characteristic
48	C₁₃×#538	—	2	2	no	—
49	C₁₃×#537	C₂²	1	1	yes	characteristic
50	C₁₃×#536	—	2	2	no	—
51	C₁₃×#536	C₂²	1	1	yes	characteristic
52	C₁₃×#536	C₂²	1	1	yes	characteristic
53	C₁₃×#529	—	2	2	no	—
54	C₁₃×#525	—	2	2	no	—
55	C₁₃×#525	C₂²	1	1	yes	characteristic
56	C₁₃×#525	C₂²	1	1	yes	characteristic
57	C₁₃×#525	C₂²	1	1	yes	characteristic
58	C₁₃×#520	C₂²	1	1	yes	characteristic
59	C₁₃×#520	C₂²	1	1	yes	characteristic
60	C₁₃×#519	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
62	C₁₃×#491	C₂²	1	2	yes	complemented
63	C₁₃×#489	C₂²	1	2	yes	complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	2	yes	complemented
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#484	C₂²	1	2	yes	complemented
71	C₁₃×#483	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	2	yes	—
73	C₁₃×#482	C₂²	1	2	yes	—
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#479	C₂²	1	2	yes	complemented
76	C₁₃×#477	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#470	C₂²	1	1	yes	characteristic
79	C₁₃×#470	C₂²	1	1	yes	characteristic
80	C₁₃×#470	C₂²	1	2	yes	complemented
81	C₁₃×#469	C₂²	1	1	yes	characteristic
82	C₁₃×#469	C₂²	1	1	yes	characteristic
83	C₁₃×#468	C₂²	1	1	yes	characteristic
84	C₁₃×#468	C₂²	1	1	yes	characteristic
85	C₁₃×#468	C₂²	1	1	yes	characteristic
86	C₁₃×#468	C₂²	1	1	yes	characteristic
87	C₁₃×#468	C₂²	1	2	yes	complemented
88	C₁₃×#467	C₂²	1	2	yes	complemented
89	C₁₃×#465	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#462	C₂²	1	2	yes	complemented
93	C₁₃×#461	C₂²	1	2	yes	complemented
94	C₁₃×#452	C₂²	1	2	yes	complemented
95	C₁₃×#451	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	2	yes	—
97	C₁₃×#451	C₂²	1	2	yes	complemented
98	C₁₃×#449	C₂²	1	2	yes	complemented
99	C₁₃×#448	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	2	yes	—
101	C₁₃×#448	C₂²	1	2	yes	complemented
102	C₁₃×#441	C₂²	1	2	yes	complemented
103	C₁₃×#440	C₂²	1	2	yes	complemented
104	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
106	C₁₃×#436	C₂²	1	2	yes	—
107	C₁₃×#436	C₂²	1	2	yes	—
108	C₁₃×#435	C₂²	1	2	yes	—
109	C₁₃×#435	C₂²	1	2	yes	—
110	C₁₃×#428	C₂²	1	1	yes	characteristic
111	C₁₃×#428	C₂²	1	1	yes	characteristic
112	C₁₃×#427	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	1	yes	characteristic
114	C₁₃×#419	C₂²	1	2	yes	—
115	C₁₃×#419	C₂²	1	2	yes	—
116	C₁₃×#419	C₂²	1	2	yes	—
117	C₁₃×#419	C₂²	1	2	yes	—
118	C₁₃×#419	C₂²	1	1	yes	characteristic
119	C₁₃×#419	C₂²	1	1	yes	characteristic
120	C₁₃×#419	C₂²	1	2	yes	complemented
121	C₁₃×#417	C₂²	1	1	yes	characteristic
122	C₁₃×#417	C₂²	1	1	yes	characteristic
123	C₁₃×#417	C₂²	1	2	yes	complemented
124	C₁₃×#416	C₂²	1	1	yes	characteristic
125	C₁₃×#416	C₂²	1	1	yes	characteristic
126	C₁₃×#416	C₂²	1	2	yes	complemented
127	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
128	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
129	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₁₃×#408	C₂²	1	1	yes	characteristic
133	C₁₃×#407	C₂²	1	1	yes	characteristic
134	C₁₃×#405	C₂²	1	1	yes	characteristic
135	C₁₃×2₋¹⁺⁴	—	2	4	no	—
136	C₁₃×2₋¹⁺⁴	—	4	2	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₁₃	—	2	1	no	—
144	C₂²×Q₈×C₁₃	—	2	1	no	—
145	C₂²×Q₈×C₁₃	—	2	1	no	—
146	C₂²×Q₈×C₁₃	—	2	1	no	—
147	C₂²×Q₈×C₁₃	—	2	4	no	—
148	C₂²×Q₈×C₁₃	—	4	2	no	—
149	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₁₃	—	2	1	no	—
155	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#137	—	2	4	no	—
157	C₁₃×#137	—	4	2	no	—
158	C₁₃×#135	—	4	2	no	—
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
166	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
167	C₁₃×#131	—	4	2	no	—
168	C₂×C₁₃×M₁₆	—	4	2	no	—
169	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
172	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
179	C₁₃×C₄⋊Q₈	—	2	1	no	—
180	C₁₃×C₄⋊Q₈	—	2	2	no	—
181	C₁₃×C₄⋊Q₈	—	2	2	no	—
182	C₁₃×C₄⋊Q₈	—	2	1	no	—
183	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
184	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₁₃×#126	—	2	2	no	—
186	C₁₃×#126	—	2	2	no	—
187	C₁₃×#126	—	2	2	no	—
188	C₁₃×#126	—	2	2	no	—
189	C₁₃×#125	—	2	2	no	—
190	C₁₃×#125	—	2	1	no	—
191	C₁₃×#125	C₂³	1	2	yes	—
192	C₁₃×#124	—	2	1	no	—
193	C₁₃×#124	—	2	2	no	—
194	C₁₃×#124	—	2	2	no	—
195	C₁₃×#124	—	2	2	no	—
196	C₁₃×#124	—	2	2	no	—
197	C₁₃×#124	—	2	2	no	—
198	C₁₃×#124	C₂³	1	2	yes	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	1	no	—
202	C₁₃×#123	—	2	1	no	—
203	C₁₃×#123	—	2	2	no	—
204	C₁₃×#123	—	2	2	no	—
205	C₁₃×#123	D₄	1	2	yes	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	2	no	—
209	C₁₃×C₂²⋊Q₈	—	2	1	no	—
210	C₁₃×C₂²⋊Q₈	—	2	1	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	—	2	2	no	—
216	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₁₃×#121	—	2	2	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	2	no	—
228	C₁₃×#121	—	2	1	no	—
229	C₁₃×#121	—	2	2	no	—
230	C₁₃×#121	—	2	2	no	—
231	C₁₃×#121	D₄	1	1	yes	characteristic
232	C₁₃×#121	D₄	1	1	yes	characteristic
233	C₁₃×#121	C₂³	1	1	yes	characteristic
234	C₁₃×#121	C₂³	1	1	yes	characteristic
235	C₁₃×#121	C₂³	1	2	yes	—
236	C₁₃×#121	C₂³	1	1	yes	characteristic
237	C₁₃×#121	C₂³	1	1	yes	characteristic
238	C₁₃×#120	—	2	1	no	—
239	C₁₃×#120	—	2	1	no	—
240	C₁₃×#120	D₄	1	2	yes	—
241	C₄×Q₈×C₁₃	—	2	1	no	—
242	C₄×Q₈×C₁₃	—	2	1	no	—
243	C₄×Q₈×C₁₃	—	2	1	no	—
244	C₄×Q₈×C₁₃	—	2	2	no	—
245	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
248	C₄×D₄×C₁₃	—	2	2	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	—	2	2	no	—
251	C₄×D₄×C₁₃	—	2	2	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	—	2	1	no	—
254	C₄×D₄×C₁₃	—	2	1	no	—
255	C₄×D₄×C₁₃	—	2	1	no	—
256	C₄×D₄×C₁₃	—	2	2	no	—
257	C₄×D₄×C₁₃	—	2	2	no	—
258	C₄×D₄×C₁₃	—	2	2	no	—
259	C₄×D₄×C₁₃	—	2	2	no	—
260	C₄×D₄×C₁₃	C₂³	1	2	yes	—
261	C₄×D₄×C₁₃	C₂³	1	2	yes	—
262	C₄×D₄×C₁₃	C₂³	1	2	yes	—
263	C₁₃×#117	—	2	1	no	—
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	—	2	1	no	—
266	C₁₃×#117	—	2	2	no	—
267	C₁₃×#117	—	2	2	no	—
268	C₁₃×#117	—	2	2	no	—
269	C₁₃×#117	C₂³	1	1	yes	characteristic
270	C₁₃×#117	C₂³	1	1	yes	characteristic
271	C₁₃×#117	C₂³	1	2	yes	—
272	C₁₃×#117	C₂³	1	2	yes	—
273	C₁₃×#117	C₂³	1	2	yes	—
274	C₁₃×#117	C₂³	1	1	yes	characteristic
275	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
277	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
279	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₄²×C₁₃	—	2	1	no	—
281	C₁₃×#107	C₂³	1	1	yes	characteristic
282	C₁₃×#107	C₂³	1	1	yes	characteristic
283	C₁₃×#107	C₂³	1	2	yes	—
284	C₁₃×#107	C₂³	1	2	yes	—
285	C₁₃×#106	C₂³	1	1	yes	characteristic
286	C₁₃×#106	C₂³	1	1	yes	characteristic
287	C₁₃×#106	C₂³	1	2	yes	—
288	C₁₃×#106	C₂³	1	2	yes	—
289	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#103	C₂³	1	1	yes	characteristic
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#103	C₂³	1	2	yes	—
302	C₁₃×#103	C₂³	1	1	yes	characteristic
303	C₁₃×#103	C₂³	1	1	yes	characteristic
304	C₁₃×#103	C₂³	1	1	yes	characteristic
305	C₁₃×#103	C₂³	1	2	yes	—
306	C₁₃×#103	C₂³	1	2	yes	—
307	C₁₃×#103	C₂³	1	2	yes	—
308	C₁₃×#103	C₂³	1	2	yes	—
309	C₁₃×#102	C₂³	1	1	yes	characteristic
310	C₁₃×#102	C₂³	1	1	yes	characteristic
311	C₁₃×#102	C₂³	1	1	yes	characteristic
312	C₁₃×#102	C₂³	1	1	yes	characteristic
313	C₁₃×#102	C₂³	1	2	yes	—
314	C₁₃×#102	C₂³	1	2	yes	—
315	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₁₃×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₁₃	C₂³	1	2	yes	—
321	#61176	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₁₃×#41	—	2	2	no	—
324	C₁₃×#41	—	2	2	no	—
325	C₁₃×#41	—	2	4	no	—
326	C₁₃×#41	—	2	2	no	—
327	C₁₃×#41	—	2	2	no	—
328	C₁₃×#41	—	2	2	no	—
329	C₁₃×#41	—	2	2	no	—
330	C₁₃×#41	—	4	2	no	—
331	C₁₃×#41	—	4	8	no	—
332	C₁₃×#41	—	4	4	no	—
333	C₂×Q₈×C₁₃	—	2	1	no	—
334	C₂×Q₈×C₁₃	—	2	2	no	—
335	C₂×Q₈×C₁₃	—	2	2	no	—
336	C₂×Q₈×C₁₃	—	2	1	no	—
337	C₂×Q₈×C₁₃	—	2	2	no	—
338	C₂×Q₈×C₁₃	—	2	2	no	—
339	C₂×Q₈×C₁₃	—	2	2	no	—
340	C₂×Q₈×C₁₃	—	2	4	no	—
341	C₂×Q₈×C₁₃	—	2	4	no	—
342	C₂×Q₈×C₁₃	—	2	4	no	—
343	C₂×Q₈×C₁₃	—	2	2	no	—
344	C₂×Q₈×C₁₃	—	2	2	no	—
345	C₂×Q₈×C₁₃	—	4	4	no	—
346	C₂×Q₈×C₁₃	—	4	2	no	—
347	C₂×Q₈×C₁₃	—	4	2	no	—
348	C₂×Q₈×C₁₃	—	4	2	no	—
349	C₂×Q₈×C₁₃	—	4	4	no	—
350	C₂×Q₈×C₁₃	—	4	4	no	—
351	C₂×Q₈×C₁₃	—	4	4	no	—
352	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₁₃	#41	1	4	yes	—
354	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
358	C₂×D₄×C₁₃	—	2	1	no	—
359	C₂×D₄×C₁₃	—	2	1	no	—
360	C₂×D₄×C₁₃	—	2	1	no	—
361	C₂×D₄×C₁₃	—	2	1	no	—
362	C₂×D₄×C₁₃	—	2	2	no	—
363	C₂×D₄×C₁₃	—	2	1	no	—
364	C₂×D₄×C₁₃	—	2	1	no	—
365	C₂×D₄×C₁₃	—	2	2	no	—
366	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
368	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₁₃	—	2	1	no	—
373	C₂²×C₄×C₁₃	—	2	2	no	—
374	C₂²×C₄×C₁₃	—	2	2	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	2	no	—
378	C₂²×C₄×C₁₃	—	2	1	no	—
379	C₂²×C₄×C₁₃	—	2	1	no	—
380	C₂²×C₄×C₁₃	—	2	1	no	—
381	C₂²×C₄×C₁₃	—	2	2	no	—
382	C₂²×C₄×C₁₃	—	2	1	no	—
383	C₂²×C₄×C₁₃	—	2	2	no	—
384	C₂²×C₄×C₁₃	—	2	1	no	—
385	C₂²×C₄×C₁₃	—	2	2	no	—
386	C₂²×C₄×C₁₃	—	4	4	no	—
387	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
394	C₁₃×Q₁₆	—	2	4	no	—
395	C₁₃×Q₁₆	—	4	1	no	—
396	C₁₃×Q₁₆	—	4	2	no	—
397	C₁₃×SD₁₆	—	2	4	no	—
398	C₁₃×SD₁₆	—	4	1	no	—
399	C₁₃×SD₁₆	—	4	1	no	—
400	C₁₃×SD₁₆	—	4	2	no	—
401	C₁₃×D₈	—	4	1	no	—
402	C₁₃×M₁₆	—	2	2	no	—
403	C₁₃×M₁₆	—	2	2	no	—
404	C₁₃×M₁₆	—	4	1	no	—
405	C₁₃×M₁₆	—	4	1	no	—
406	C₁₃×M₁₆	—	4	1	no	—
407	C₁₃×M₁₆	—	4	1	no	—
408	C₁₃×M₁₆	—	4	2	no	—
409	C₂×C₈×C₁₃	—	2	2	no	—
410	C₂×C₈×C₁₃	—	2	2	no	—
411	C₂×C₈×C₁₃	—	4	2	no	—
412	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
414	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
416	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
418	C₁₃×C₄⋊C₄	—	2	1	no	—
419	C₁₃×C₄⋊C₄	—	2	2	no	—
420	C₁₃×C₄⋊C₄	—	2	1	no	—
421	C₁₃×C₄⋊C₄	—	2	2	no	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	2	no	—
424	C₁₃×C₄⋊C₄	—	2	2	no	—
425	C₁₃×C₄⋊C₄	—	2	2	no	—
426	C₁₃×C₄⋊C₄	—	2	2	no	—
427	C₁₃×C₄⋊C₄	—	2	1	no	—
428	C₁₃×C₄⋊C₄	—	2	2	no	—
429	C₁₃×C₄⋊C₄	—	2	2	no	—
430	C₁₃×C₄⋊C₄	—	2	2	no	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	—	2	1	no	—
434	C₁₃×C₄⋊C₄	—	2	2	no	—
435	C₁₃×C₄⋊C₄	—	2	2	no	—
436	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
439	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
440	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
441	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
442	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	2	no	—
448	C₁₃×C₂²⋊C₄	—	2	1	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	1	no	—
451	C₁₃×C₂²⋊C₄	—	2	2	no	—
452	C₁₃×C₂²⋊C₄	—	2	1	no	—
453	C₁₃×C₂²⋊C₄	—	2	1	no	—
454	C₁₃×C₂²⋊C₄	—	2	1	no	—
455	C₁₃×C₂²⋊C₄	—	2	1	no	—
456	C₁₃×C₂²⋊C₄	—	2	2	no	—
457	C₁₃×C₂²⋊C₄	—	2	2	no	—
458	C₁₃×C₂²⋊C₄	—	2	1	no	—
459	C₁₃×C₂²⋊C₄	—	2	2	no	—
460	C₁₃×C₂²⋊C₄	—	2	2	no	—
461	C₁₃×C₂²⋊C₄	—	2	1	no	—
462	C₁₃×C₂²⋊C₄	—	2	2	no	—
463	C₁₃×C₂²⋊C₄	—	2	2	no	—
464	C₁₃×C₂²⋊C₄	—	2	1	no	—
465	C₁₃×C₂²⋊C₄	—	2	1	no	—
466	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
469	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
470	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
471	C₄²×C₁₃	—	2	2	no	—
472	C₄²×C₁₃	—	2	2	no	—
473	C₄²×C₁₃	—	2	2	no	—
474	C₄²×C₁₃	—	2	2	no	—
475	C₄²×C₁₃	—	2	2	no	—
476	C₄²×C₁₃	—	2	2	no	—
477	C₄²×C₁₃	—	2	1	no	—
478	C₄²×C₁₃	—	2	1	no	—
479	C₄²×C₁₃	C₂⁴	1	2	yes	—
480	#3493	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3486	C₂×C₁₃	1	1	yes	characteristic, complemented
482	#3329	C₂×C₁₃	1	2	yes	complemented
483	#3328	C₂×C₁₃	1	2	yes	complemented
484	#3327	C₂×C₁₃	1	2	yes	complemented
485	#3326	C₂×C₁₃	1	2	yes	complemented
486	#3321	C₂×C₁₃	1	2	yes	complemented
487	#3320	C₂×C₁₃	1	2	yes	complemented
488	#3313	C₂×C₁₃	1	2	yes	complemented
489	#3312	C₂×C₁₃	1	2	yes	complemented
490	#3137	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3097	C₂×C₁₃	1	1	yes	characteristic, complemented
492	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
493	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3063	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
496	#3046	C₂×C₁₃	1	1	yes	characteristic, complemented
497	#3013	C₂×C₁₃	1	1	yes	characteristic, complemented
498	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
499	#2947	C₂×C₁₃	1	1	yes	characteristic, complemented
500	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
501	#2898	C₂×C₁₃	1	1	yes	characteristic, complemented
502	C₂×#419	C₂×C₁₃	1	1	yes	characteristic, complemented
503	C₂³×C₁₃	—	2	2	no	—
504	C₂³×C₁₃	—	2	1	no	—
505	C₂³×C₁₃	—	2	1	no	—
506	C₂³×C₁₃	—	4	1	no	—
507	C₂³×C₁₃	—	4	1	no	—
508	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
511	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₁₃	—	2	4	no	—
513	Q₈×C₁₃	—	2	2	no	—
514	Q₈×C₁₃	—	2	2	no	—
515	Q₈×C₁₃	—	2	1	no	—
516	Q₈×C₁₃	—	2	2	no	—
517	Q₈×C₁₃	—	2	1	no	—
518	Q₈×C₁₃	—	2	1	no	—
519	Q₈×C₁₃	—	2	2	no	—
520	Q₈×C₁₃	—	2	1	no	—
521	Q₈×C₁₃	—	4	4	no	—
522	Q₈×C₁₃	—	4	4	no	—
523	Q₈×C₁₃	—	4	4	no	—
524	Q₈×C₁₃	—	4	2	no	—
525	Q₈×C₁₃	—	8	2	no	—
526	Q₈×C₁₃	C₂×#41	1	4	yes	—
527	D₄×C₁₃	—	2	4	no	—
528	D₄×C₁₃	—	2	2	no	—
529	D₄×C₁₃	—	2	1	no	—
530	D₄×C₁₃	—	2	1	no	—
531	D₄×C₁₃	—	2	1	no	—
532	D₄×C₁₃	—	2	1	no	—
533	D₄×C₁₃	—	4	2	no	—
534	D₄×C₁₃	—	4	2	no	—
535	D₄×C₁₃	—	4	4	no	—
536	D₄×C₁₃	—	4	2	no	—
537	D₄×C₁₃	—	4	2	no	—
538	D₄×C₁₃	—	4	2	no	—
539	D₄×C₁₃	—	4	2	no	—
540	D₄×C₁₃	—	8	1	no	—
541	D₄×C₁₃	—	8	2	no	—
542	D₄×C₁₃	—	8	1	no	—
543	C₂×C₄×C₁₃	—	2	2	no	—
544	C₂×C₄×C₁₃	—	2	4	no	—
545	C₂×C₄×C₁₃	—	2	2	no	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	2	no	—
548	C₂×C₄×C₁₃	—	2	1	no	—
549	C₂×C₄×C₁₃	—	2	1	no	—
550	C₂×C₄×C₁₃	—	2	2	no	—
551	C₂×C₄×C₁₃	—	2	2	no	—
552	C₂×C₄×C₁₃	—	2	1	no	—
553	C₂×C₄×C₁₃	—	2	1	no	—
554	C₂×C₄×C₁₃	—	2	2	no	—
555	C₂×C₄×C₁₃	—	2	1	no	—
556	C₂×C₄×C₁₃	—	2	1	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	1	no	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	1	no	—
561	C₂×C₄×C₁₃	—	2	2	no	—
562	C₂×C₄×C₁₃	—	2	1	no	—
563	C₂×C₄×C₁₃	—	4	4	no	—
564	C₂×C₄×C₁₃	—	4	4	no	—
565	C₂×C₄×C₁₃	—	4	4	no	—
566	C₂×C₄×C₁₃	—	4	4	no	—
567	C₂×C₄×C₁₃	—	4	2	no	—
568	C₂×C₄×C₁₃	—	4	2	no	—
569	C₂×C₄×C₁₃	—	4	2	no	—
570	C₂×C₄×C₁₃	—	8	2	no	—
571	C₂×C₄×C₁₃	—	8	1	no	—
572	C₂×C₄×C₁₃	—	8	2	no	—
573	C₂×C₄×C₁₃	—	8	1	no	—
574	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
575	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
578	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
581	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
582	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
583	C₈×C₁₃	—	2	2	no	—
584	C₈×C₁₃	—	2	1	no	—
585	C₈×C₁₃	—	2	1	no	—
586	C₈×C₁₃	—	2	1	no	—
587	C₈×C₁₃	—	2	1	no	—
588	C₈×C₁₃	—	2	2	no	—
589	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
590	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
591	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
592	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
593	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
594	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
595	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
596	#556	—	2	1	no	—
597	#556	C₂²×C₁₃	1	2	yes	—
598	#555	—	2	1	no	—
599	#555	C₂²×C₁₃	1	2	yes	—
600	#553	—	2	1	no	—
601	#553	C₂²×C₁₃	1	2	yes	—
602	#552	—	2	1	no	—
603	#552	C₂²×C₁₃	1	2	yes	—
604	D₄×Q₈	—	2	1	no	—
605	D₄×Q₈	—	2	1	no	—
606	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
607	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
608	#548	—	2	1	no	—
609	#548	—	2	1	no	—
610	#548	C₂²×C₁₃	1	2	yes	—
611	#548	C₂²×C₁₃	1	2	yes	—
612	#544	C₂²×C₁₃	1	1	yes	characteristic
613	#538	—	2	2	no	—
614	#537	C₂²×C₁₃	1	1	yes	characteristic
615	#536	—	2	2	no	—
616	#536	C₂²×C₁₃	1	1	yes	characteristic
617	#536	C₂²×C₁₃	1	1	yes	characteristic
618	#529	—	2	2	no	—
619	#525	—	2	2	no	—
620	#525	C₂²×C₁₃	1	1	yes	characteristic
621	#525	C₂²×C₁₃	1	1	yes	characteristic
622	#525	C₂²×C₁₃	1	1	yes	characteristic
623	#520	C₂²×C₁₃	1	1	yes	characteristic
624	#520	C₂²×C₁₃	1	1	yes	characteristic
625	#519	C₂²×C₁₃	1	1	yes	characteristic
626	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
627	#491	C₂²×C₁₃	1	2	yes	complemented
628	#489	C₂²×C₁₃	1	2	yes	complemented
629	#488	C₂²×C₁₃	1	2	yes	complemented
630	#487	C₂²×C₁₃	1	2	yes	complemented
631	#485	C₂²×C₁₃	1	2	yes	—
632	#485	C₂²×C₁₃	1	2	yes	—
633	#485	C₂²×C₁₃	1	2	yes	complemented
634	#485	C₂²×C₁₃	1	2	yes	complemented
635	#484	C₂²×C₁₃	1	2	yes	complemented
636	#483	C₂²×C₁₃	1	2	yes	complemented
637	#482	C₂²×C₁₃	1	2	yes	—
638	#482	C₂²×C₁₃	1	2	yes	—
639	#479	C₂²×C₁₃	1	2	yes	complemented
640	#479	C₂²×C₁₃	1	2	yes	complemented
641	#477	C₂²×C₁₃	1	2	yes	complemented
642	#475	C₂²×C₁₃	1	2	yes	complemented
643	#470	C₂²×C₁₃	1	1	yes	characteristic
644	#470	C₂²×C₁₃	1	1	yes	characteristic
645	#470	C₂²×C₁₃	1	2	yes	complemented
646	#469	C₂²×C₁₃	1	1	yes	characteristic
647	#469	C₂²×C₁₃	1	1	yes	characteristic
648	#468	C₂²×C₁₃	1	1	yes	characteristic
649	#468	C₂²×C₁₃	1	1	yes	characteristic
650	#468	C₂²×C₁₃	1	1	yes	characteristic
651	#468	C₂²×C₁₃	1	1	yes	characteristic
652	#468	C₂²×C₁₃	1	2	yes	complemented
653	#467	C₂²×C₁₃	1	2	yes	complemented
654	#465	C₂²×C₁₃	1	2	yes	complemented
655	#464	C₂²×C₁₃	1	2	yes	complemented
656	#463	C₂²×C₁₃	1	2	yes	complemented
657	#462	C₂²×C₁₃	1	2	yes	complemented
658	#461	C₂²×C₁₃	1	2	yes	complemented
659	#452	C₂²×C₁₃	1	2	yes	complemented
660	#451	C₂²×C₁₃	1	2	yes	—
661	#451	C₂²×C₁₃	1	2	yes	—
662	#451	C₂²×C₁₃	1	2	yes	complemented
663	#449	C₂²×C₁₃	1	2	yes	complemented
664	#448	C₂²×C₁₃	1	2	yes	—
665	#448	C₂²×C₁₃	1	2	yes	—
666	#448	C₂²×C₁₃	1	2	yes	complemented
667	#441	C₂²×C₁₃	1	2	yes	complemented
668	#440	C₂²×C₁₃	1	2	yes	complemented
669	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
670	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
671	#436	C₂²×C₁₃	1	2	yes	—
672	#436	C₂²×C₁₃	1	2	yes	—
673	#435	C₂²×C₁₃	1	2	yes	—
674	#435	C₂²×C₁₃	1	2	yes	—
675	#428	C₂²×C₁₃	1	1	yes	characteristic
676	#428	C₂²×C₁₃	1	1	yes	characteristic
677	#427	C₂²×C₁₃	1	1	yes	characteristic
678	#424	C₂²×C₁₃	1	1	yes	characteristic
679	#419	C₂²×C₁₃	1	2	yes	—
680	#419	C₂²×C₁₃	1	2	yes	—
681	#419	C₂²×C₁₃	1	1	yes	characteristic
682	#419	C₂²×C₁₃	1	1	yes	characteristic
683	#419	C₂²×C₁₃	1	2	yes	—
684	#419	C₂²×C₁₃	1	2	yes	—
685	#419	C₂²×C₁₃	1	2	yes	complemented
686	#417	C₂²×C₁₃	1	1	yes	characteristic
687	#417	C₂²×C₁₃	1	1	yes	characteristic
688	#417	C₂²×C₁₃	1	2	yes	complemented
689	#416	C₂²×C₁₃	1	1	yes	characteristic
690	#416	C₂²×C₁₃	1	1	yes	characteristic
691	#416	C₂²×C₁₃	1	2	yes	complemented
692	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
693	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
694	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
695	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
696	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
697	#408	C₂²×C₁₃	1	1	yes	characteristic
698	#407	C₂²×C₁₃	1	1	yes	characteristic
699	#405	C₂²×C₁₃	1	1	yes	characteristic
700	C₂²×C₁₃	—	2	1	no	—
701	C₂²×C₁₃	—	2	1	no	—
702	C₂²×C₁₃	—	2	2	no	—
703	C₂²×C₁₃	—	2	1	no	—
704	C₂²×C₁₃	—	2	1	no	—
705	C₂²×C₁₃	—	2	2	no	—
706	C₂²×C₁₃	—	2	1	no	—
707	C₂²×C₁₃	—	2	1	no	—
708	C₂²×C₁₃	—	2	1	no	—
709	C₂²×C₁₃	—	2	1	no	—
710	C₂²×C₁₃	—	2	2	no	—
711	C₂²×C₁₃	—	4	4	no	—
712	C₂²×C₁₃	—	4	1	no	—
713	C₂²×C₁₃	—	4	1	no	—
714	C₂²×C₁₃	—	4	1	no	—
715	C₂²×C₁₃	—	4	1	no	—
716	C₂²×C₁₃	—	4	1	no	—
717	C₂²×C₁₃	—	4	1	no	—
718	C₂²×C₁₃	#546	1	2	yes	—
719	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
720	C₄×C₁₃	—	2	2	no	—
721	C₄×C₁₃	—	2	2	no	—
722	C₄×C₁₃	—	2	1	no	—
723	C₄×C₁₃	—	2	1	no	—
724	C₄×C₁₃	—	2	4	no	—
725	C₄×C₁₃	—	2	2	no	—
726	C₄×C₁₃	—	4	2	no	—
727	C₄×C₁₃	—	4	1	no	—
728	C₄×C₁₃	—	4	2	no	—
729	C₄×C₁₃	—	4	1	no	—
730	C₄×C₁₃	—	4	1	no	—
731	C₄×C₁₃	—	4	1	no	—
732	C₄×C₁₃	—	4	1	no	—
733	C₄×C₁₃	—	4	2	no	—
734	C₄×C₁₃	—	4	1	no	—
735	C₄×C₁₃	#546	1	2	yes	—
736	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
737	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
738	2₋¹⁺⁴	—	2	4	no	—
739	2₋¹⁺⁴	—	4	2	no	—
740	C₂×#41	—	2	2	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
744	C₂×#41	C₂³×C₁₃	1	2	yes	—
745	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
746	C₂²×Q₈	—	2	1	no	—
747	C₂²×Q₈	—	2	1	no	—
748	C₂²×Q₈	—	2	1	no	—
749	C₂²×Q₈	—	2	1	no	—
750	C₂²×Q₈	—	2	4	no	—
751	C₂²×Q₈	—	4	2	no	—
752	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
753	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
754	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
755	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
756	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₂³×C₄	—	2	1	no	—
758	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
759	#137	—	2	4	no	—
760	#137	—	4	2	no	—
761	#135	—	4	2	no	—
762	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
764	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
768	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
769	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
770	#131	—	4	2	no	—
771	C₂×M₁₆	—	4	2	no	—
772	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
773	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
774	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
775	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
777	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
779	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
781	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	2	no	—
784	C₄⋊Q₈	—	2	2	no	—
785	C₄⋊Q₈	—	2	1	no	—
786	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
787	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
788	#126	—	2	2	no	—
789	#126	—	2	2	no	—
790	#126	—	2	2	no	—
791	#126	—	2	2	no	—
792	#125	—	2	2	no	—
793	#125	—	2	1	no	—
794	#125	C₂³×C₁₃	1	2	yes	—
795	#124	—	2	1	no	—
796	#124	—	2	2	no	—
797	#124	—	2	2	no	—
798	#124	—	2	2	no	—
799	#124	—	2	2	no	—
800	#124	—	2	2	no	—
801	#124	C₂³×C₁₃	1	2	yes	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	1	no	—
805	#123	—	2	1	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	D₄×C₁₃	1	2	yes	—
809	C₂²⋊Q₈	—	2	1	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	1	no	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
820	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
825	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	D₄×C₁₃	1	1	yes	characteristic
835	#121	D₄×C₁₃	1	1	yes	characteristic
836	#121	C₂³×C₁₃	1	1	yes	characteristic
837	#121	C₂³×C₁₃	1	1	yes	characteristic
838	#121	C₂³×C₁₃	1	1	yes	characteristic
839	#121	C₂³×C₁₃	1	1	yes	characteristic
840	#121	C₂³×C₁₃	1	2	yes	—
841	#120	—	2	1	no	—
842	#120	—	2	1	no	—
843	#120	D₄×C₁₃	1	2	yes	—
844	C₄×Q₈	—	2	1	no	—
845	C₄×Q₈	—	2	1	no	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	—	2	2	no	—
848	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
849	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
850	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	C₂³×C₁₃	1	2	yes	—
864	C₄×D₄	C₂³×C₁₃	1	2	yes	—
865	C₄×D₄	C₂³×C₁₃	1	2	yes	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	—	2	1	no	—
869	#117	—	2	2	no	—
870	#117	—	2	2	no	—
871	#117	—	2	2	no	—
872	#117	C₂³×C₁₃	1	2	yes	—
873	#117	C₂³×C₁₃	1	2	yes	—
874	#117	C₂³×C₁₃	1	1	yes	characteristic
875	#117	C₂³×C₁₃	1	1	yes	characteristic
876	#117	C₂³×C₁₃	1	2	yes	—
877	#117	C₂³×C₁₃	1	1	yes	characteristic
878	C₂×C₄⋊C₄	—	2	1	no	—
879	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
882	C₂×C₂²⋊C₄	—	2	1	no	—
883	C₂×C₄²	—	2	1	no	—
884	#107	C₂³×C₁₃	1	1	yes	characteristic
885	#107	C₂³×C₁₃	1	1	yes	characteristic
886	#107	C₂³×C₁₃	1	2	yes	—
887	#107	C₂³×C₁₃	1	2	yes	—
888	#106	C₂³×C₁₃	1	1	yes	characteristic
889	#106	C₂³×C₁₃	1	1	yes	characteristic
890	#106	C₂³×C₁₃	1	2	yes	—
891	#106	C₂³×C₁₃	1	2	yes	—
892	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
893	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
894	#103	C₂³×C₁₃	1	2	yes	—
895	#103	C₂³×C₁₃	1	2	yes	—
896	#103	C₂³×C₁₃	1	2	yes	—
897	#103	C₂³×C₁₃	1	2	yes	—
898	#103	C₂³×C₁₃	1	2	yes	—
899	#103	C₂³×C₁₃	1	2	yes	—
900	#103	C₂³×C₁₃	1	2	yes	—
901	#103	C₂³×C₁₃	1	2	yes	—
902	#103	C₂³×C₁₃	1	1	yes	characteristic
903	#103	C₂³×C₁₃	1	2	yes	—
904	#103	C₂³×C₁₃	1	2	yes	—
905	#103	C₂³×C₁₃	1	1	yes	characteristic
906	#103	C₂³×C₁₃	1	1	yes	characteristic
907	#103	C₂³×C₁₃	1	1	yes	characteristic
908	#103	C₂³×C₁₃	1	2	yes	—
909	#103	C₂³×C₁₃	1	2	yes	—
910	#103	C₂³×C₁₃	1	2	yes	—
911	#103	C₂³×C₁₃	1	2	yes	—
912	#102	C₂³×C₁₃	1	1	yes	characteristic
913	#102	C₂³×C₁₃	1	1	yes	characteristic
914	#102	C₂³×C₁₃	1	1	yes	characteristic
915	#102	C₂³×C₁₃	1	1	yes	characteristic
916	#102	C₂³×C₁₃	1	2	yes	—
917	#102	C₂³×C₁₃	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
919	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
920	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
922	#97	C₂³×C₁₃	1	2	yes	—
923	C₄×C₈	C₂³×C₁₃	1	2	yes	—
924	C₂×C₁₃	—	2	2	no	—
925	C₂×C₁₃	—	4	2	no	—
926	C₂×C₁₃	—	4	1	no	—
927	C₂×C₁₃	—	4	1	no	—
928	C₂×C₁₃	—	8	1	no	—
929	C₂×C₁₃	—	8	1	no	—
930	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
931	C₂×C₁₃	#3586	1	1	yes	characteristic
932	C₂×C₁₃	#3586	1	1	yes	characteristic
933	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	4	no	—
937	#41	—	2	2	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	4	2	no	—
942	#41	—	4	8	no	—
943	#41	—	4	4	no	—
944	C₂×Q₈	—	2	1	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	1	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	2	no	—
951	C₂×Q₈	—	2	4	no	—
952	C₂×Q₈	—	2	4	no	—
953	C₂×Q₈	—	2	4	no	—
954	C₂×Q₈	—	2	2	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	4	4	no	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	4	2	no	—
959	C₂×Q₈	—	4	2	no	—
960	C₂×Q₈	—	4	4	no	—
961	C₂×Q₈	—	4	4	no	—
962	C₂×Q₈	—	4	4	no	—
963	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
964	C₂×Q₈	C₁₃×#41	1	4	yes	—
965	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
966	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
967	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
968	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
969	C₂×D₄	—	2	1	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
978	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
979	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
980	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
981	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
982	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	4	4	no	—
998	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1002	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1003	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1005	Q₁₆	—	2	4	no	—
1006	Q₁₆	—	4	1	no	—
1007	Q₁₆	—	4	2	no	—
1008	SD₁₆	—	2	4	no	—
1009	SD₁₆	—	4	1	no	—
1010	SD₁₆	—	4	1	no	—
1011	SD₁₆	—	4	2	no	—
1012	D₈	—	4	1	no	—
1013	M₁₆	—	2	2	no	—
1014	M₁₆	—	2	2	no	—
1015	M₁₆	—	4	1	no	—
1016	M₁₆	—	4	1	no	—
1017	M₁₆	—	4	1	no	—
1018	M₁₆	—	4	1	no	—
1019	M₁₆	—	4	2	no	—
1020	C₂×C₈	—	2	2	no	—
1021	C₂×C₈	—	2	2	no	—
1022	C₂×C₈	—	4	2	no	—
1023	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1048	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1050	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1054	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1055	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1078	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1080	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	—	2	2	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	C₂⁴×C₁₃	1	2	yes	—
1091	C₁₃	#61176	1	1	yes	characteristic, direct product factor, Sylow
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	4	1	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1098	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1099	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1100	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	Q₈	—	2	4	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	1	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	4	4	no	—
1111	Q₈	—	4	4	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	2	no	—
1114	Q₈	—	8	2	no	—
1115	Q₈	C₂×C₁₃×#41	1	4	yes	—
1116	D₄	—	2	4	no	—
1117	D₄	—	2	2	no	—
1118	D₄	—	2	1	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	1	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	4	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	4	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	4	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1164	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1169	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
1170	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1171	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1172	C₈	—	2	2	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	4	4	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	C₁₃×#546	1	2	yes	—
1197	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	4	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	4	2	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	1	no	—
1213	C₄	C₁₃×#546	1	2	yes	—
1214	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1215	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1216	C₂	—	2	2	no	—
1217	C₂	—	4	1	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	8	1	no	—
1222	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
1223	C₂	C₁₃×#3586	1	1	yes	characteristic
1224	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 ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3493	C₂	semidirect
2. C₁₃×#3486	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3328	C₂	semidirect
5. C₁₃×#3327	C₂	semidirect
6. C₁₃×#3326	C₂	semidirect
7. C₁₃×#3321	C₂	semidirect
8. C₁₃×#3320	C₂	semidirect
9. C₁₃×#3313	C₂	semidirect
10. C₁₃×#3312	C₂	semidirect
11. C₁₃×#3137	C₂	semidirect
12. C₁₃×#3097	C₂	semidirect
13. C₁₃×#3093	C₂	semidirect
14. C₁₃×#3082	C₂	semidirect
15. C₁₃×#3063	C₂	semidirect
16. C₁₃×#3054	C₂	semidirect
17. C₁₃×#3046	C₂	semidirect
18. C₁₃×#3013	C₂	semidirect
19. C₁₃×#3004	C₂	semidirect
20. C₁₃×#2947	C₂	semidirect
21. C₁₃×#2930	C₂	semidirect
22. C₁₃×#2898	C₂	semidirect
23. C₂×C₁₃×#419	C₂	semidirect
62. C₁₃×#491	C₂²	semidirect
63. C₁₃×#489	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#484	C₂²	semidirect
71. C₁₃×#483	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#479	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
80. C₁₃×#470	C₂²	semidirect
87. C₁₃×#468	C₂²	semidirect
88. C₁₃×#467	C₂²	semidirect
89. C₁₃×#465	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
94. C₁₃×#452	C₂²	semidirect
97. C₁₃×#451	C₂²	semidirect
98. C₁₃×#449	C₂²	semidirect
101. C₁₃×#448	C₂²	semidirect
102. C₁₃×#441	C₂²	semidirect
103. C₁₃×#440	C₂²	semidirect
104. C₄×C₁₃×Q₁₆	C₂²	semidirect
105. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₁₃×#419	C₂²	semidirect
123. C₁₃×#417	C₂²	semidirect
126. C₁₃×#416	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
321. #61176	C₁₃	direct (N × H)
480. #3493	C₂×C₁₃	semidirect
481. #3486	C₂×C₁₃	semidirect
482. #3329	C₂×C₁₃	semidirect
483. #3328	C₂×C₁₃	semidirect
484. #3327	C₂×C₁₃	semidirect
485. #3326	C₂×C₁₃	semidirect
486. #3321	C₂×C₁₃	semidirect
487. #3320	C₂×C₁₃	semidirect
488. #3313	C₂×C₁₃	semidirect
489. #3312	C₂×C₁₃	semidirect
490. #3137	C₂×C₁₃	semidirect
491. #3097	C₂×C₁₃	semidirect
492. #3093	C₂×C₁₃	semidirect
493. #3082	C₂×C₁₃	semidirect
494. #3063	C₂×C₁₃	semidirect
495. #3054	C₂×C₁₃	semidirect
496. #3046	C₂×C₁₃	semidirect
497. #3013	C₂×C₁₃	semidirect
498. #3004	C₂×C₁₃	semidirect
499. #2947	C₂×C₁₃	semidirect
500. #2930	C₂×C₁₃	semidirect
501. #2898	C₂×C₁₃	semidirect
502. C₂×#419	C₂×C₁₃	semidirect
627. #491	C₂²×C₁₃	semidirect
628. #489	C₂²×C₁₃	semidirect
629. #488	C₂²×C₁₃	semidirect
630. #487	C₂²×C₁₃	semidirect
633. #485	C₂²×C₁₃	semidirect
634. #485	C₂²×C₁₃	semidirect
635. #484	C₂²×C₁₃	semidirect
636. #483	C₂²×C₁₃	semidirect
639. #479	C₂²×C₁₃	semidirect
640. #479	C₂²×C₁₃	semidirect
641. #477	C₂²×C₁₃	semidirect
642. #475	C₂²×C₁₃	semidirect
645. #470	C₂²×C₁₃	semidirect
652. #468	C₂²×C₁₃	semidirect
653. #467	C₂²×C₁₃	semidirect
654. #465	C₂²×C₁₃	semidirect
655. #464	C₂²×C₁₃	semidirect
656. #463	C₂²×C₁₃	semidirect
657. #462	C₂²×C₁₃	semidirect
658. #461	C₂²×C₁₃	semidirect
659. #452	C₂²×C₁₃	semidirect
662. #451	C₂²×C₁₃	semidirect
663. #449	C₂²×C₁₃	semidirect
666. #448	C₂²×C₁₃	semidirect
667. #441	C₂²×C₁₃	semidirect
668. #440	C₂²×C₁₃	semidirect
669. C₄×Q₁₆	C₂²×C₁₃	semidirect
670. C₄×SD₁₆	C₂²×C₁₃	semidirect
685. #419	C₂²×C₁₃	semidirect
688. #417	C₂²×C₁₃	semidirect
691. #416	C₂²×C₁₃	semidirect
696. C₂×#103	C₂²×C₁₃	semidirect
1091. C₁₃	#61176	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×#3493	2
C₁₃×#3486	2
C₁₃×#3329	2
C₁₃×#3328	2
C₁₃×#3327	2
C₁₃×#3326	2
C₁₃×#3321	2
C₁₃×#3320	2
C₁₃×#3313	2
C₁₃×#3312	2
C₁₃×#3137	2
C₁₃×#3097	2
C₁₃×#3093	2
C₁₃×#3082	2
C₁₃×#3063	2
C₁₃×#3054	2
C₁₃×#3046	2
C₁₃×#3013	2
C₁₃×#3004	2
C₁₃×#2947	2
C₁₃×#2930	2
C₁₃×#2898	2
C₂×C₁₃×#419	2
#61176	13

Subgroups — C13×#61176 #15747515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61176 #15747515