Subgroups — C₁₃×#61568 #15747907

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3191	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	2	yes	—
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
29	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#554	—	2	1	no	—
31	C₁₃×#552	C₂²	1	2	yes	complemented
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#548	C₂²	1	2	yes	—
37	C₁₃×#548	C₂²	1	2	yes	complemented
38	C₁₃×#547	—	2	1	no	—
39	C₁₃×#547	C₂²	1	1	yes	characteristic
40	C₁₃×#547	C₂²	1	1	yes	characteristic
41	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#546	—	2	1	no	—
43	C₁₃×#546	—	2	2	no	—
44	C₁₃×#546	C₂²	1	2	yes	—
45	D₄²×C₁₃	—	2	1	no	—
46	D₄²×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#542	—	2	1	no	—
48	C₁₃×#539	—	2	2	no	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#532	—	2	1	no	—
51	C₁₃×#532	C₂²	1	1	yes	characteristic
52	C₁₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#525	—	2	2	no	—
54	C₁₃×#525	C₂²	1	2	yes	—
55	C₁₃×#525	C₂²	1	2	yes	complemented
56	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₁₃×#520	—	2	1	no	—
58	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₁₃	—	2	1	no	—
60	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₁₃×#495	C₂²	1	2	yes	complemented
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#488	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#485	C₂²	1	2	yes	complemented
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#480	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#467	C₂²	1	2	yes	complemented
79	C₁₃×#467	C₂²	1	2	yes	complemented
80	C₁₃×#467	C₂²	1	2	yes	complemented
81	C₁₃×#466	C₂²	1	2	yes	complemented
82	C₁₃×#465	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#452	C₂²	1	1	yes	characteristic
97	C₁₃×#452	C₂²	1	2	yes	—
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#452	C₂²	1	2	yes	complemented
100	C₁₃×#452	C₂²	1	2	yes	complemented
101	C₁₃×#452	C₂²	1	2	yes	complemented
102	C₁₃×#452	C₂²	1	2	yes	complemented
103	C₁₃×#452	C₂²	1	2	yes	complemented
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#451	C₂²	1	2	yes	complemented
107	C₁₃×#451	C₂²	1	2	yes	complemented
108	C₁₃×#450	C₂²	1	2	yes	complemented
109	C₁₃×#449	C₂²	1	1	yes	characteristic
110	C₁₃×#449	C₂²	1	2	yes	complemented
111	C₁₃×#449	C₂²	1	2	yes	complemented
112	C₁₃×#448	C₂²	1	2	yes	complemented
113	C₁₃×#448	C₂²	1	2	yes	complemented
114	C₁₃×#447	C₂²	1	2	yes	complemented
115	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
127	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#416	C₂²	1	2	yes	complemented
130	C₁₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
133	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	2	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	4	4	no	—
139	C₂×C₁₃×#41	—	4	4	no	—
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×#41	C₂³	1	2	yes	—
143	C₂×C₁₃×#41	C₂³	1	2	yes	—
144	C₂×C₁₃×#41	C₂³	1	2	yes	—
145	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
146	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₁₃	—	2	2	no	—
148	C₂²×D₄×C₁₃	—	2	1	no	—
149	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
150	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₁₃	—	2	2	no	—
152	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
153	C₁₃×#135	—	4	4	no	—
154	C₁₃×#135	—	4	4	no	—
155	C₂×C₁₃×Q₁₆	—	4	4	no	—
156	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×SD₁₆	—	4	4	no	—
162	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×D₈	C₂³	1	2	yes	—
171	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
172	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
175	C₁₃×C₄⋊Q₈	—	2	1	no	—
176	C₁₃×C₄⋊Q₈	—	2	1	no	—
177	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₁₃×#127	—	2	1	no	—
181	C₁₃×#127	C₂³	1	1	yes	characteristic
182	C₁₃×#126	—	2	2	no	—
183	C₁₃×#126	—	2	2	no	—
184	C₁₃×#126	—	2	1	no	—
185	C₁₃×#125	—	2	2	no	—
186	C₁₃×#125	—	2	1	no	—
187	C₁₃×#125	C₂³	1	1	yes	characteristic
188	C₁₃×#124	—	2	1	no	—
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	C₂³	1	1	yes	characteristic
192	C₁₃×#124	C₂³	1	2	yes	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	1	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	1	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
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	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	—	2	1	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	—	2	1	no	—
221	C₁₃×#121	—	2	1	no	—
222	C₁₃×#121	—	2	1	no	—
223	C₁₃×#121	—	2	2	no	—
224	C₁₃×#121	—	2	2	no	—
225	C₁₃×#121	C₂³	1	2	yes	—
226	C₁₃×#121	C₂³	1	2	yes	—
227	C₁₃×#121	C₂³	1	1	yes	characteristic
228	C₁₃×#121	C₂³	1	2	yes	—
229	C₁₃×#120	—	2	2	no	—
230	C₁₃×#120	—	2	2	no	—
231	C₁₃×#120	—	2	2	no	—
232	C₁₃×#120	—	2	2	no	—
233	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	1	no	—
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	—	2	1	no	—
240	C₄×D₄×C₁₃	—	2	1	no	—
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	2	no	—
245	C₄×D₄×C₁₃	—	2	2	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	1	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	2	no	—
250	C₄×D₄×C₁₃	—	2	2	no	—
251	C₄×D₄×C₁₃	—	2	1	no	—
252	C₄×D₄×C₁₃	—	2	1	no	—
253	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₁₃	D₄	1	2	yes	—
255	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₁₃	C₂³	1	2	yes	—
261	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	—	2	2	no	—
264	C₁₃×#117	—	2	1	no	—
265	C₁₃×#117	—	2	1	no	—
266	C₁₃×#117	C₂³	1	2	yes	—
267	C₁₃×#117	C₂³	1	1	yes	characteristic
268	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
276	C₂×C₄²×C₁₃	—	2	1	no	—
277	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
278	C₁₃×#107	C₂³	1	1	yes	characteristic
279	C₁₃×#107	C₂³	1	2	yes	—
280	C₁₃×#107	C₂³	1	1	yes	characteristic
281	C₁₃×#106	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	1	yes	characteristic
283	C₁₃×#106	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	1	yes	characteristic
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	2	yes	—
305	C₁₃×#102	C₂³	1	2	yes	—
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×#102	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₁₃	C₂³	1	2	yes	—
318	#61568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂⁴×C₁₃	—	2	2	no	—
320	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
321	C₁₃×#41	—	2	2	no	—
322	C₁₃×#41	—	2	2	no	—
323	C₁₃×#41	—	2	4	no	—
324	C₁₃×#41	—	2	4	no	—
325	C₁₃×#41	—	4	2	no	—
326	C₁₃×#41	—	4	2	no	—
327	C₁₃×#41	—	4	2	no	—
328	C₁₃×#41	—	4	2	no	—
329	C₁₃×#41	—	4	8	no	—
330	C₁₃×#41	—	4	2	no	—
331	C₁₃×#41	—	4	2	no	—
332	C₁₃×#41	—	4	8	no	—
333	C₁₃×#41	—	4	4	no	—
334	C₂×Q₈×C₁₃	—	2	1	no	—
335	C₂×Q₈×C₁₃	—	2	2	no	—
336	C₂×Q₈×C₁₃	—	2	2	no	—
337	C₂×Q₈×C₁₃	—	2	4	no	—
338	C₂×Q₈×C₁₃	—	4	2	no	—
339	C₂×Q₈×C₁₃	—	4	2	no	—
340	C₂×Q₈×C₁₃	—	4	2	no	—
341	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
342	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
344	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂×D₄×C₁₃	—	2	1	no	—
346	C₂×D₄×C₁₃	—	2	4	no	—
347	C₂×D₄×C₁₃	—	2	4	no	—
348	C₂×D₄×C₁₃	—	2	1	no	—
349	C₂×D₄×C₁₃	—	2	2	no	—
350	C₂×D₄×C₁₃	—	2	2	no	—
351	C₂×D₄×C₁₃	—	2	2	no	—
352	C₂×D₄×C₁₃	—	2	2	no	—
353	C₂×D₄×C₁₃	—	2	2	no	—
354	C₂×D₄×C₁₃	—	2	2	no	—
355	C₂×D₄×C₁₃	—	2	2	no	—
356	C₂×D₄×C₁₃	—	2	1	no	—
357	C₂×D₄×C₁₃	—	2	2	no	—
358	C₂×D₄×C₁₃	—	2	1	no	—
359	C₂×D₄×C₁₃	—	4	2	no	—
360	C₂×D₄×C₁₃	—	4	8	no	—
361	C₂×D₄×C₁₃	—	4	4	no	—
362	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₁₃	—	2	1	no	—
369	C₂²×C₄×C₁₃	—	2	2	no	—
370	C₂²×C₄×C₁₃	—	2	2	no	—
371	C₂²×C₄×C₁₃	—	2	2	no	—
372	C₂²×C₄×C₁₃	—	2	1	no	—
373	C₂²×C₄×C₁₃	—	2	2	no	—
374	C₂²×C₄×C₁₃	—	2	1	no	—
375	C₂²×C₄×C₁₃	—	2	2	no	—
376	C₂²×C₄×C₁₃	—	2	2	no	—
377	C₂²×C₄×C₁₃	—	2	1	no	—
378	C₂²×C₄×C₁₃	—	2	2	no	—
379	C₂²×C₄×C₁₃	—	4	2	no	—
380	C₂²×C₄×C₁₃	—	4	2	no	—
381	C₂²×C₄×C₁₃	—	4	8	no	—
382	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
385	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
386	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
387	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
390	C₁₃×Q₁₆	—	2	2	no	—
391	C₁₃×Q₁₆	—	2	4	no	—
392	C₁₃×Q₁₆	—	4	2	no	—
393	C₁₃×Q₁₆	—	4	2	no	—
394	C₁₃×Q₁₆	—	4	2	no	—
395	C₁₃×SD₁₆	—	2	2	no	—
396	C₁₃×SD₁₆	—	2	2	no	—
397	C₁₃×SD₁₆	—	2	4	no	—
398	C₁₃×SD₁₆	—	4	2	no	—
399	C₁₃×SD₁₆	—	4	2	no	—
400	C₁₃×SD₁₆	—	4	2	no	—
401	C₁₃×SD₁₆	—	4	2	no	—
402	C₁₃×D₈	—	2	2	no	—
403	C₁₃×D₈	—	4	2	no	—
404	C₂×C₈×C₁₃	—	4	2	no	—
405	C₂×C₈×C₁₃	—	4	2	no	—
406	C₂×C₈×C₁₃	—	4	2	no	—
407	C₂×C₈×C₁₃	—	4	2	no	—
408	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
414	C₁₃×C₄⋊C₄	—	2	1	no	—
415	C₁₃×C₄⋊C₄	—	2	2	no	—
416	C₁₃×C₄⋊C₄	—	2	1	no	—
417	C₁₃×C₄⋊C₄	—	2	2	no	—
418	C₁₃×C₄⋊C₄	—	2	1	no	—
419	C₁₃×C₄⋊C₄	—	2	2	no	—
420	C₁₃×C₄⋊C₄	—	2	2	no	—
421	C₁₃×C₄⋊C₄	—	2	2	no	—
422	C₁₃×C₄⋊C₄	—	2	1	no	—
423	C₁₃×C₄⋊C₄	—	2	1	no	—
424	C₁₃×C₄⋊C₄	—	2	1	no	—
425	C₁₃×C₄⋊C₄	—	2	1	no	—
426	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
431	C₁₃×C₄⋊C₄	—	2	2	no	—
432	C₁₃×C₄⋊C₄	—	2	1	no	—
433	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₁₃×C₂²⋊C₄	—	2	1	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	2	no	—
444	C₁₃×C₂²⋊C₄	—	2	2	no	—
445	C₁₃×C₂²⋊C₄	—	2	2	no	—
446	C₁₃×C₂²⋊C₄	—	2	2	no	—
447	C₁₃×C₂²⋊C₄	—	2	1	no	—
448	C₁₃×C₂²⋊C₄	—	2	2	no	—
449	C₁₃×C₂²⋊C₄	—	2	2	no	—
450	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
461	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₄²×C₁₃	—	2	1	no	—
466	C₄²×C₁₃	—	2	1	no	—
467	C₄²×C₁₃	—	2	1	no	—
468	C₄²×C₁₃	—	2	2	no	—
469	C₄²×C₁₃	—	2	2	no	—
470	C₄²×C₁₃	—	2	1	no	—
471	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
474	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
475	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
476	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
478	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3300	C₂×C₁₃	1	2	yes	complemented
480	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#3296	C₂×C₁₃	1	2	yes	complemented
482	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
483	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
484	#3285	C₂×C₁₃	1	2	yes	complemented
485	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
486	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
487	#3282	C₂×C₁₃	1	2	yes	complemented
488	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
489	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
490	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
491	#3191	C₂×C₁₃	1	2	yes	complemented
492	#3190	C₂×C₁₃	1	2	yes	complemented
493	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
494	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
495	#3002	C₂×C₁₃	1	2	yes	complemented
496	C₂×#452	C₂×C₁₃	1	2	yes	complemented
497	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
498	C₂³×C₁₃	—	2	1	no	—
499	C₂³×C₁₃	—	2	4	no	—
500	C₂³×C₁₃	—	2	1	no	—
501	C₂³×C₁₃	—	2	2	no	—
502	C₂³×C₁₃	—	4	2	no	—
503	C₂³×C₁₃	—	4	2	no	—
504	C₂³×C₁₃	—	4	4	no	—
505	C₂³×C₁₃	—	4	4	no	—
506	C₂³×C₁₃	—	8	2	no	—
507	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
508	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
510	Q₈×C₁₃	—	2	1	no	—
511	Q₈×C₁₃	—	2	1	no	—
512	Q₈×C₁₃	—	2	2	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	—	4	4	no	—
518	Q₈×C₁₃	—	4	2	no	—
519	Q₈×C₁₃	—	8	2	no	—
520	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
521	D₄×C₁₃	—	2	4	no	—
522	D₄×C₁₃	—	2	4	no	—
523	D₄×C₁₃	—	2	2	no	—
524	D₄×C₁₃	—	2	1	no	—
525	D₄×C₁₃	—	2	1	no	—
526	D₄×C₁₃	—	2	1	no	—
527	D₄×C₁₃	—	2	2	no	—
528	D₄×C₁₃	—	2	2	no	—
529	D₄×C₁₃	—	4	4	no	—
530	D₄×C₁₃	—	4	4	no	—
531	D₄×C₁₃	—	4	4	no	—
532	D₄×C₁₃	—	4	2	no	—
533	D₄×C₁₃	—	4	4	no	—
534	D₄×C₁₃	—	4	4	no	—
535	D₄×C₁₃	—	4	4	no	—
536	D₄×C₁₃	—	4	2	no	—
537	D₄×C₁₃	—	8	1	no	—
538	D₄×C₁₃	—	8	2	no	—
539	D₄×C₁₃	—	8	2	no	—
540	D₄×C₁₃	#135	1	4	yes	complemented
541	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
542	C₂×C₄×C₁₃	—	2	4	no	—
543	C₂×C₄×C₁₃	—	2	1	no	—
544	C₂×C₄×C₁₃	—	2	2	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	2	no	—
549	C₂×C₄×C₁₃	—	2	1	no	—
550	C₂×C₄×C₁₃	—	2	1	no	—
551	C₂×C₄×C₁₃	—	2	1	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	2	no	—
557	C₂×C₄×C₁₃	—	2	1	no	—
558	C₂×C₄×C₁₃	—	2	2	no	—
559	C₂×C₄×C₁₃	—	4	2	no	—
560	C₂×C₄×C₁₃	—	4	2	no	—
561	C₂×C₄×C₁₃	—	4	2	no	—
562	C₂×C₄×C₁₃	—	4	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	4	no	—
568	C₂×C₄×C₁₃	—	4	2	no	—
569	C₂×C₄×C₁₃	—	4	2	no	—
570	C₂×C₄×C₁₃	—	8	1	no	—
571	C₂×C₄×C₁₃	—	8	2	no	—
572	C₂×C₄×C₁₃	—	8	2	no	—
573	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
576	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
579	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
581	C₈×C₁₃	—	2	1	no	—
582	C₈×C₁₃	—	2	2	no	—
583	C₈×C₁₃	—	2	1	no	—
584	C₈×C₁₃	—	2	1	no	—
585	C₈×C₁₃	—	2	2	no	—
586	C₈×C₁₃	—	2	1	no	—
587	C₂²×#41	C₂²×C₁₃	1	2	yes	—
588	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
589	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
590	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
591	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
592	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	#554	—	2	1	no	—
594	#552	C₂²×C₁₃	1	2	yes	complemented
595	#551	—	2	2	no	—
596	#550	C₂²×C₁₃	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
599	#548	C₂²×C₁₃	1	2	yes	—
600	#548	C₂²×C₁₃	1	2	yes	complemented
601	#547	—	2	1	no	—
602	#547	C₂²×C₁₃	1	1	yes	characteristic
603	#547	C₂²×C₁₃	1	1	yes	characteristic
604	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#546	—	2	1	no	—
606	#546	—	2	2	no	—
607	#546	C₂²×C₁₃	1	2	yes	—
608	D₄²	—	2	1	no	—
609	D₄²	C₂²×C₁₃	1	1	yes	characteristic
610	#542	—	2	1	no	—
611	#539	—	2	2	no	—
612	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#532	—	2	1	no	—
614	#532	C₂²×C₁₃	1	1	yes	characteristic
615	#529	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#525	—	2	2	no	—
617	#525	C₂²×C₁₃	1	2	yes	—
618	#525	C₂²×C₁₃	1	2	yes	complemented
619	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
620	#520	—	2	1	no	—
621	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
622	C₂×C₄×D₄	—	2	1	no	—
623	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
624	#495	C₂²×C₁₃	1	2	yes	complemented
625	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#488	C₂²×C₁₃	1	2	yes	complemented
628	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
631	#485	C₂²×C₁₃	1	2	yes	complemented
632	#485	C₂²×C₁₃	1	2	yes	complemented
633	#483	C₂²×C₁₃	1	2	yes	complemented
634	#482	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#482	C₂²×C₁₃	1	2	yes	complemented
636	#480	C₂²×C₁₃	1	2	yes	complemented
637	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
639	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
641	#467	C₂²×C₁₃	1	2	yes	complemented
642	#467	C₂²×C₁₃	1	2	yes	complemented
643	#467	C₂²×C₁₃	1	2	yes	complemented
644	#466	C₂²×C₁₃	1	2	yes	complemented
645	#465	C₂²×C₁₃	1	2	yes	complemented
646	#465	C₂²×C₁₃	1	2	yes	complemented
647	#465	C₂²×C₁₃	1	2	yes	complemented
648	#465	C₂²×C₁₃	1	2	yes	complemented
649	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#464	C₂²×C₁₃	1	2	yes	complemented
651	#464	C₂²×C₁₃	1	2	yes	complemented
652	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#452	C₂²×C₁₃	1	1	yes	characteristic
660	#452	C₂²×C₁₃	1	2	yes	—
661	#452	C₂²×C₁₃	1	2	yes	complemented
662	#452	C₂²×C₁₃	1	2	yes	complemented
663	#452	C₂²×C₁₃	1	2	yes	complemented
664	#452	C₂²×C₁₃	1	2	yes	complemented
665	#452	C₂²×C₁₃	1	2	yes	complemented
666	#452	C₂²×C₁₃	1	2	yes	complemented
667	#452	C₂²×C₁₃	1	2	yes	complemented
668	#452	C₂²×C₁₃	1	2	yes	complemented
669	#451	C₂²×C₁₃	1	2	yes	complemented
670	#451	C₂²×C₁₃	1	2	yes	complemented
671	#450	C₂²×C₁₃	1	2	yes	complemented
672	#449	C₂²×C₁₃	1	1	yes	characteristic
673	#449	C₂²×C₁₃	1	2	yes	complemented
674	#449	C₂²×C₁₃	1	2	yes	complemented
675	#448	C₂²×C₁₃	1	2	yes	complemented
676	#448	C₂²×C₁₃	1	2	yes	complemented
677	#447	C₂²×C₁₃	1	2	yes	complemented
678	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
679	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
681	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
683	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
684	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
685	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
686	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
687	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
688	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
689	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
690	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
691	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
692	#416	C₂²×C₁₃	1	2	yes	complemented
693	#416	C₂²×C₁₃	1	2	yes	complemented
694	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
695	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
696	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
697	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
698	C₂²×C₁₃	—	2	2	no	—
699	C₂²×C₁₃	—	2	2	no	—
700	C₂²×C₁₃	—	2	1	no	—
701	C₂²×C₁₃	—	2	2	no	—
702	C₂²×C₁₃	—	2	1	no	—
703	C₂²×C₁₃	—	2	2	no	—
704	C₂²×C₁₃	—	2	2	no	—
705	C₂²×C₁₃	—	2	1	no	—
706	C₂²×C₁₃	—	2	2	no	—
707	C₂²×C₁₃	—	4	1	no	—
708	C₂²×C₁₃	—	4	1	no	—
709	C₂²×C₁₃	—	4	1	no	—
710	C₂²×C₁₃	—	4	2	no	—
711	C₂²×C₁₃	—	4	2	no	—
712	C₂²×C₁₃	—	4	1	no	—
713	C₂²×C₁₃	—	4	1	no	—
714	C₂²×C₁₃	—	4	2	no	—
715	C₂²×C₁₃	—	8	4	no	—
716	C₂²×C₁₃	—	8	8	no	—
717	C₂²×C₁₃	C₂×#135	1	4	yes	—
718	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
719	C₄×C₁₃	—	2	1	no	—
720	C₄×C₁₃	—	2	1	no	—
721	C₄×C₁₃	—	2	1	no	—
722	C₄×C₁₃	—	2	2	no	—
723	C₄×C₁₃	—	2	2	no	—
724	C₄×C₁₃	—	2	2	no	—
725	C₄×C₁₃	—	2	1	no	—
726	C₄×C₁₃	—	4	1	no	—
727	C₄×C₁₃	—	4	1	no	—
728	C₄×C₁₃	—	4	2	no	—
729	C₄×C₁₃	—	4	2	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	C₂×#135	1	2	yes	—
735	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
736	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	—	2	2	no	—
740	C₂×#41	—	4	4	no	—
741	C₂×#41	—	4	4	no	—
742	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×#41	C₂³×C₁₃	1	2	yes	—
744	C₂×#41	C₂³×C₁₃	1	2	yes	—
745	C₂×#41	C₂³×C₁₃	1	2	yes	—
746	C₂×#41	C₂³×C₁₃	1	2	yes	—
747	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
748	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
749	C₂²×D₄	—	2	2	no	—
750	C₂²×D₄	—	2	1	no	—
751	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
752	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
753	C₂³×C₄	—	2	2	no	—
754	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
755	#135	—	4	4	no	—
756	#135	—	4	4	no	—
757	C₂×Q₁₆	—	4	4	no	—
758	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
759	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
760	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
763	C₂×SD₁₆	—	4	4	no	—
764	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
765	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
768	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
769	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
770	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
771	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₂×D₈	C₂³×C₁₃	1	2	yes	—
773	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
774	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
775	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
776	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
777	C₄⋊Q₈	—	2	1	no	—
778	C₄⋊Q₈	—	2	1	no	—
779	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
781	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
782	#127	—	2	1	no	—
783	#127	C₂³×C₁₃	1	1	yes	characteristic
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#126	—	2	1	no	—
787	#125	—	2	2	no	—
788	#125	—	2	1	no	—
789	#125	C₂³×C₁₃	1	1	yes	characteristic
790	#124	—	2	1	no	—
791	#124	—	2	2	no	—
792	#124	—	2	2	no	—
793	#124	C₂³×C₁₃	1	1	yes	characteristic
794	#124	C₂³×C₁₃	1	2	yes	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	1	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
813	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
814	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
815	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
816	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
817	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
818	#121	—	2	2	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	1	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	C₂³×C₁₃	1	2	yes	—
828	#121	C₂³×C₁₃	1	2	yes	—
829	#121	C₂³×C₁₃	1	1	yes	characteristic
830	#121	C₂³×C₁₃	1	2	yes	—
831	#120	—	2	2	no	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	C₄×Q₈	—	2	1	no	—
836	C₄×Q₈	—	2	1	no	—
837	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
838	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
856	C₄×D₄	D₄×C₁₃	1	2	yes	—
857	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₁₃	1	2	yes	—
863	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
864	#117	—	2	1	no	—
865	#117	—	2	2	no	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	C₂³×C₁₃	1	1	yes	characteristic
869	#117	C₂³×C₁₃	1	2	yes	—
870	C₂×C₄⋊C₄	—	2	2	no	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	—	2	1	no	—
873	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
875	C₂×C₂²⋊C₄	—	2	2	no	—
876	C₂×C₂²⋊C₄	—	2	2	no	—
877	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
880	#107	C₂³×C₁₃	1	1	yes	characteristic
881	#107	C₂³×C₁₃	1	2	yes	—
882	#107	C₂³×C₁₃	1	1	yes	characteristic
883	#106	C₂³×C₁₃	1	2	yes	—
884	#106	C₂³×C₁₃	1	1	yes	characteristic
885	#106	C₂³×C₁₃	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
887	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
889	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
890	#103	C₂³×C₁₃	1	1	yes	characteristic
891	#103	C₂³×C₁₃	1	2	yes	—
892	#103	C₂³×C₁₃	1	2	yes	—
893	#103	C₂³×C₁₃	1	2	yes	—
894	#103	C₂³×C₁₃	1	1	yes	characteristic
895	#103	C₂³×C₁₃	1	2	yes	—
896	#103	C₂³×C₁₃	1	2	yes	—
897	#103	C₂³×C₁₃	1	1	yes	characteristic
898	#103	C₂³×C₁₃	1	2	yes	—
899	#103	C₂³×C₁₃	1	2	yes	—
900	#103	C₂³×C₁₃	1	1	yes	characteristic
901	#102	C₂³×C₁₃	1	1	yes	characteristic
902	#102	C₂³×C₁₃	1	2	yes	—
903	#102	C₂³×C₁₃	1	2	yes	—
904	#102	C₂³×C₁₃	1	2	yes	—
905	#102	C₂³×C₁₃	1	1	yes	characteristic
906	#102	C₂³×C₁₃	1	2	yes	—
907	#102	C₂³×C₁₃	1	2	yes	—
908	#102	C₂³×C₁₃	1	1	yes	characteristic
909	#102	C₂³×C₁₃	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
913	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
917	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
918	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
919	C₄×C₈	C₂³×C₁₃	1	2	yes	—
920	C₂×C₁₃	—	2	4	no	—
921	C₂×C₁₃	—	4	2	no	—
922	C₂×C₁₃	—	4	1	no	—
923	C₂×C₁₃	—	4	2	no	—
924	C₂×C₁₃	—	8	1	no	—
925	C₂×C₁₃	—	8	2	no	—
926	C₂×C₁₃	#3484	1	1	yes	characteristic
927	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
928	C₂×C₁₃	#3586	1	1	yes	characteristic
929	C₂⁴	—	2	2	no	—
930	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	4	no	—
934	#41	—	2	4	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	8	no	—
940	#41	—	4	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	4	no	—
948	C₂×Q₈	—	4	2	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	2	no	—
951	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
952	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
954	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	4	no	—
957	C₂×D₄	—	2	4	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	1	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	8	no	—
971	C₂×D₄	—	4	4	no	—
972	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
973	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
974	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
975	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
976	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
977	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	4	2	no	—
990	C₂²×C₄	—	4	2	no	—
991	C₂²×C₄	—	4	8	no	—
992	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
993	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
994	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
995	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
996	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
997	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
999	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1000	Q₁₆	—	2	2	no	—
1001	Q₁₆	—	2	4	no	—
1002	Q₁₆	—	4	2	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	SD₁₆	—	2	2	no	—
1006	SD₁₆	—	2	2	no	—
1007	SD₁₆	—	2	4	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	D₈	—	2	2	no	—
1013	D₈	—	4	2	no	—
1014	C₂×C₈	—	4	2	no	—
1015	C₂×C₈	—	4	2	no	—
1016	C₂×C₈	—	4	2	no	—
1017	C₂×C₈	—	4	2	no	—
1018	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1019	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1021	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1044	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
1045	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1046	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1047	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1072	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1075	C₄²	—	2	1	no	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	2	no	—
1079	C₄²	—	2	2	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1082	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1083	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1085	C₁₃	#61568	1	1	yes	characteristic, direct product factor, Sylow
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	4	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	4	2	no	—
1091	C₂³	—	4	2	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	8	2	no	—
1095	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1096	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1097	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	1	no	—
1100	Q₈	—	2	2	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	2	2	no	—
1105	Q₈	—	4	4	no	—
1106	Q₈	—	4	2	no	—
1107	Q₈	—	8	2	no	—
1108	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
1109	D₄	—	2	4	no	—
1110	D₄	—	2	4	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	4	4	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	8	1	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	C₁₃×#135	1	4	yes	complemented
1129	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1130	C₂×C₄	—	2	4	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	2	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	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	4	2	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	4	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	—	8	1	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
1168	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	8	4	no	—
1193	C₂²	—	8	8	no	—
1194	C₂²	C₂×C₁₃×#135	1	4	yes	—
1195	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1196	C₄	—	2	1	no	—
1197	C₄	—	2	1	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	2	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	C₂×C₁₃×#135	1	2	yes	—
1212	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1214	C₂	—	2	4	no	—
1215	C₂	—	4	1	no	—
1216	C₂	—	4	2	no	—
1217	C₂	—	4	2	no	—
1218	C₂	—	8	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	C₁₃×#3484	1	1	yes	characteristic
1221	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
1222	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×#3520	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3304	C₂	semidirect
4. C₁₃×#3302	C₂	semidirect
5. C₁₃×#3300	C₂	semidirect
6. C₁₃×#3298	C₂	semidirect
7. C₁₃×#3296	C₂	semidirect
8. C₁₃×#3294	C₂	semidirect
9. D₄×C₁₃×Q₁₆	C₂	semidirect
10. C₁₃×#3285	C₂	semidirect
11. C₁₃×#3284	C₂	semidirect
12. C₁₃×#3283	C₂	semidirect
13. C₁₃×#3282	C₂	semidirect
14. D₄×C₁₃×SD₁₆	C₂	semidirect
15. C₁₃×#3212	C₂	semidirect
16. C₁₃×#3210	C₂	semidirect
17. C₁₃×#3191	C₂	semidirect
18. C₁₃×#3190	C₂	semidirect
19. C₁₃×#3107	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3002	C₂	semidirect
22. C₂×C₁₃×#452	C₂	semidirect
23. C₁₃×#2972	C₂	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
27. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
37. C₁₃×#548	C₂²	semidirect
41. C₁₃×#547	C₂²	semidirect
49. C₁₃×#533	C₂²	semidirect
52. C₁₃×#529	C₂²	semidirect
55. C₁₃×#525	C₂²	semidirect
56. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
61. C₁₃×#495	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
64. C₁₃×#488	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#480	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#478	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#474	C₂²	semidirect
78. C₁₃×#467	C₂²	semidirect
79. C₁₃×#467	C₂²	semidirect
80. C₁₃×#467	C₂²	semidirect
81. C₁₃×#466	C₂²	semidirect
82. C₁₃×#465	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#463	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
91. C₁₃×#462	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
93. C₁₃×#461	C₂²	semidirect
94. C₁₃×#460	C₂²	semidirect
95. C₁₃×#459	C₂²	semidirect
98. C₁₃×#452	C₂²	semidirect
99. C₁₃×#452	C₂²	semidirect
100. C₁₃×#452	C₂²	semidirect
101. C₁₃×#452	C₂²	semidirect
102. C₁₃×#452	C₂²	semidirect
103. C₁₃×#452	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#451	C₂²	semidirect
107. C₁₃×#451	C₂²	semidirect
108. C₁₃×#450	C₂²	semidirect
110. C₁₃×#449	C₂²	semidirect
111. C₁₃×#449	C₂²	semidirect
112. C₁₃×#448	C₂²	semidirect
113. C₁₃×#448	C₂²	semidirect
114. C₁₃×#447	C₂²	semidirect
115. C₄×C₁₃×Q₁₆	C₂²	semidirect
116. C₄×C₁₃×Q₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×D₈	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₈×D₄×C₁₃	C₂²	semidirect
126. C₈×D₄×C₁₃	C₂²	semidirect
127. C₁₃×#431	C₂²	semidirect
128. C₁₃×#431	C₂²	semidirect
129. C₁₃×#416	C₂²	semidirect
130. C₁₃×#416	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
318. #61568	C₁₃	direct (N × H)
475. #3520	C₂×C₁₃	semidirect
476. D₄×#41	C₂×C₁₃	semidirect
477. #3304	C₂×C₁₃	semidirect
478. #3302	C₂×C₁₃	semidirect
479. #3300	C₂×C₁₃	semidirect
480. #3298	C₂×C₁₃	semidirect
481. #3296	C₂×C₁₃	semidirect
482. #3294	C₂×C₁₃	semidirect
483. D₄×Q₁₆	C₂×C₁₃	semidirect
484. #3285	C₂×C₁₃	semidirect
485. #3284	C₂×C₁₃	semidirect
486. #3283	C₂×C₁₃	semidirect
487. #3282	C₂×C₁₃	semidirect
488. D₄×SD₁₆	C₂×C₁₃	semidirect
489. #3212	C₂×C₁₃	semidirect
490. #3210	C₂×C₁₃	semidirect
491. #3191	C₂×C₁₃	semidirect
492. #3190	C₂×C₁₃	semidirect
493. #3107	C₂×C₁₃	semidirect
494. #3102	C₂×C₁₃	semidirect
495. #3002	C₂×C₁₃	semidirect
496. C₂×#452	C₂×C₁₃	semidirect
497. #2972	C₂×C₁₃	semidirect
540. D₄×C₁₃	#135	semidirect
588. C₂×#135	C₂²×C₁₃	semidirect
589. C₂×#135	C₂²×C₁₃	semidirect
590. C₂²×Q₁₆	C₂²×C₁₃	semidirect
591. C₂²×SD₁₆	C₂²×C₁₃	semidirect
592. #556	C₂²×C₁₃	semidirect
594. #552	C₂²×C₁₃	semidirect
600. #548	C₂²×C₁₃	semidirect
604. #547	C₂²×C₁₃	semidirect
612. #533	C₂²×C₁₃	semidirect
615. #529	C₂²×C₁₃	semidirect
618. #525	C₂²×C₁₃	semidirect
619. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
624. #495	C₂²×C₁₃	semidirect
625. #494	C₂²×C₁₃	semidirect
626. #492	C₂²×C₁₃	semidirect
627. #488	C₂²×C₁₃	semidirect
628. #487	C₂²×C₁₃	semidirect
629. #486	C₂²×C₁₃	semidirect
630. #485	C₂²×C₁₃	semidirect
631. #485	C₂²×C₁₃	semidirect
632. #485	C₂²×C₁₃	semidirect
633. #483	C₂²×C₁₃	semidirect
634. #482	C₂²×C₁₃	semidirect
635. #482	C₂²×C₁₃	semidirect
636. #480	C₂²×C₁₃	semidirect
637. #479	C₂²×C₁₃	semidirect
638. #478	C₂²×C₁₃	semidirect
639. #475	C₂²×C₁₃	semidirect
640. #474	C₂²×C₁₃	semidirect
641. #467	C₂²×C₁₃	semidirect
642. #467	C₂²×C₁₃	semidirect
643. #467	C₂²×C₁₃	semidirect
644. #466	C₂²×C₁₃	semidirect
645. #465	C₂²×C₁₃	semidirect
646. #465	C₂²×C₁₃	semidirect
647. #465	C₂²×C₁₃	semidirect
648. #465	C₂²×C₁₃	semidirect
649. #464	C₂²×C₁₃	semidirect
650. #464	C₂²×C₁₃	semidirect
651. #464	C₂²×C₁₃	semidirect
652. #463	C₂²×C₁₃	semidirect
653. #462	C₂²×C₁₃	semidirect
654. #462	C₂²×C₁₃	semidirect
655. #461	C₂²×C₁₃	semidirect
656. #461	C₂²×C₁₃	semidirect
657. #460	C₂²×C₁₃	semidirect
658. #459	C₂²×C₁₃	semidirect
661. #452	C₂²×C₁₃	semidirect
662. #452	C₂²×C₁₃	semidirect
663. #452	C₂²×C₁₃	semidirect
664. #452	C₂²×C₁₃	semidirect
665. #452	C₂²×C₁₃	semidirect
666. #452	C₂²×C₁₃	semidirect
667. #452	C₂²×C₁₃	semidirect
668. #452	C₂²×C₁₃	semidirect
669. #451	C₂²×C₁₃	semidirect
670. #451	C₂²×C₁₃	semidirect
671. #450	C₂²×C₁₃	semidirect
673. #449	C₂²×C₁₃	semidirect
674. #449	C₂²×C₁₃	semidirect
675. #448	C₂²×C₁₃	semidirect
676. #448	C₂²×C₁₃	semidirect
677. #447	C₂²×C₁₃	semidirect
678. C₄×Q₁₆	C₂²×C₁₃	semidirect
679. C₄×Q₁₆	C₂²×C₁₃	semidirect
680. C₄×SD₁₆	C₂²×C₁₃	semidirect
681. C₄×SD₁₆	C₂²×C₁₃	semidirect
682. C₄×SD₁₆	C₂²×C₁₃	semidirect
683. C₄×D₈	C₂²×C₁₃	semidirect
686. C₈×D₄	C₂²×C₁₃	semidirect
687. C₈×D₄	C₂²×C₁₃	semidirect
688. C₈×D₄	C₂²×C₁₃	semidirect
689. C₈×D₄	C₂²×C₁₃	semidirect
690. #431	C₂²×C₁₃	semidirect
691. #431	C₂²×C₁₃	semidirect
692. #416	C₂²×C₁₃	semidirect
693. #416	C₂²×C₁₃	semidirect
694. C₂×#103	C₂²×C₁₃	semidirect
695. C₂×#102	C₂²×C₁₃	semidirect
696. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
697. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1085. C₁₃	#61568	direct (N × H)
1128. D₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3520	2
D₄×C₁₃×#41	2
C₁₃×#3304	2
C₁₃×#3302	2
C₁₃×#3300	2
C₁₃×#3298	2
C₁₃×#3296	2
C₁₃×#3294	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3284	2
C₁₃×#3283	2
C₁₃×#3282	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3191	2
C₁₃×#3190	2
C₁₃×#3107	2
C₁₃×#3102	2
C₁₃×#3002	2
C₂×C₁₃×#452	2
C₁₃×#2972	2
#61568	13

Subgroups — C13×#61568 #15747907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61568 #15747907