Subgroups — C₁₃×#61428 #15747767

Order 3328.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3337	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3300	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#135	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#135	C₂²	1	2	yes	—
25	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
26	C₁₃×#559	—	2	1	no	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	—	2	1	no	—
30	C₁₃×#556	C₂²	1	1	yes	characteristic
31	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#555	C₂²	1	1	yes	characteristic
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#553	—	2	2	no	—
36	C₁₃×#553	C₂²	1	2	yes	—
37	C₁₃×#552	—	2	1	no	—
38	C₁₃×#552	C₂²	1	2	yes	—
39	C₁₃×#551	—	2	2	no	—
40	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#548	C₂²	1	2	yes	—
42	C₁₃×#547	C₂²	1	1	yes	characteristic
43	C₁₃×#546	C₂²	1	2	yes	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#532	—	2	1	no	—
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	—	2	2	no	—
48	C₁₃×#529	—	2	2	no	—
49	C₁₃×#529	C₂²	1	2	yes	—
50	C₁₃×#529	C₂²	1	2	yes	complemented
51	C₁₃×#525	—	2	1	no	—
52	C₄×C₁₃×#41	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	2	yes	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#117	—	2	1	no	—
59	C₁₃×#499	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#495	C₂²	1	2	yes	—
62	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	—
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	2	yes	complemented
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	2	yes	—
76	C₁₃×#478	C₂²	1	2	yes	complemented
77	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#474	C₂²	1	1	yes	characteristic
80	C₁₃×#474	C₂²	1	1	yes	characteristic
81	C₁₃×#467	C₂²	1	2	yes	complemented
82	C₁₃×#466	C₂²	1	2	yes	—
83	C₁₃×#465	C₂²	1	2	yes	—
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#463	C₂²	1	2	yes	—
91	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#459	C₂²	1	1	yes	characteristic
94	C₁₃×#459	C₂²	1	1	yes	characteristic
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	complemented
97	C₁₃×#451	C₂²	1	2	yes	—
98	C₁₃×#449	C₂²	1	2	yes	—
99	C₁₃×#449	C₂²	1	2	yes	—
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
107	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×D₈	C₂²	1	2	yes	—
119	C₄×C₁₃×D₈	C₂²	1	2	yes	—
120	C₄×C₁₃×D₈	C₂²	1	2	yes	—
121	C₈×D₄×C₁₃	C₂²	1	2	yes	—
122	C₈×D₄×C₁₃	C₂²	1	2	yes	—
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#431	C₂²	1	1	yes	characteristic
126	C₁₃×#431	C₂²	1	2	yes	complemented
127	C₁₃×#427	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
129	C₁₃×#416	C₂²	1	2	yes	—
130	C₁₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
132	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
133	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	—	2	1	no	—
142	C₁₃×#135	—	2	8	no	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	—	2	4	no	—
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×D₈	C₂³	1	2	yes	—
153	C₂×C₁₃×D₈	C₂³	1	2	yes	—
154	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
158	C₁₃×C₄⋊Q₈	—	2	1	no	—
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×#127	—	2	1	no	—
163	C₁₃×#127	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	1	no	—
173	C₁₃×#125	C₂³	1	2	yes	—
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#124	—	2	1	no	—
176	C₁₃×#124	—	2	1	no	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	C₂³	1	2	yes	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	1	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	1	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	1	no	—
198	C₁₃×#121	—	2	1	no	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	C₂³	1	2	yes	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#120	—	2	2	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₁₃	—	2	2	no	—
223	C₄×D₄×C₁₃	—	2	2	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	2	no	—
226	C₄×D₄×C₁₃	—	2	2	no	—
227	C₄×D₄×C₁₃	—	2	2	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	D₄	1	2	yes	—
236	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	—	2	1	no	—
249	C₁₃×#117	—	2	2	no	—
250	C₁₃×#117	—	2	2	no	—
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	2	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	D₄	1	1	yes	characteristic
255	C₁₃×#117	D₄	1	2	yes	—
256	C₁₃×#117	C₂³	1	2	yes	—
257	C₁₃×#117	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	—	2	1	no	—
266	C₂×C₄²×C₁₃	—	2	2	no	—
267	C₂×C₄²×C₁₃	—	2	2	no	—
268	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
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	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	1	yes	characteristic
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
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	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	C₄×C₈×C₁₃	C₂³	1	2	yes	—
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61428	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	2	4	no	—
318	C₁₃×#41	—	2	4	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	4	4	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	4	1	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	4	1	no	—
341	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₁₃	—	2	1	no	—
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	1	no	—
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	2	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	2	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	—	4	4	no	—
359	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
365	C₁₃×Q₁₆	—	2	4	no	—
366	C₁₃×Q₁₆	—	4	2	no	—
367	C₁₃×SD₁₆	—	2	2	no	—
368	C₁₃×SD₁₆	—	2	2	no	—
369	C₁₃×SD₁₆	—	2	2	no	—
370	C₁₃×SD₁₆	—	2	4	no	—
371	C₁₃×SD₁₆	—	4	2	no	—
372	C₁₃×SD₁₆	#41	1	4	yes	complemented
373	C₁₃×D₈	—	2	4	no	—
374	C₁₃×D₈	—	4	2	no	—
375	C₂×C₈×C₁₃	—	2	2	no	—
376	C₂×C₈×C₁₃	—	2	4	no	—
377	C₂×C₈×C₁₃	—	4	2	no	—
378	C₂×C₈×C₁₃	—	4	1	no	—
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
383	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	2	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	1	no	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	2	no	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	1	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	C₂×D₄	1	2	yes	—
447	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₁₃	C₂×D₄	1	2	yes	—
449	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₁₃	C₂⁴	1	2	yes	—
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3337	C₂×C₁₃	1	2	yes	complemented
461	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3300	C₂×C₁₃	1	2	yes	complemented
464	#3297	C₂×C₁₃	1	2	yes	complemented
465	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3282	C₂×C₁₃	1	2	yes	complemented
467	#3168	C₂×C₁₃	1	2	yes	complemented
468	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3102	C₂×C₁₃	1	2	yes	complemented
471	#3102	C₂×C₁₃	1	2	yes	complemented
472	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
473	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
474	C₄×#135	C₂×C₁₃	1	2	yes	complemented
475	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	2	1	no	—
478	C₂³×C₁₃	—	2	2	no	—
479	C₂³×C₁₃	—	4	2	no	—
480	C₂³×C₁₃	—	4	2	no	—
481	C₂³×C₁₃	—	8	1	no	—
482	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
483	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₁₃	—	2	2	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	1	no	—
487	Q₈×C₁₃	—	2	2	no	—
488	Q₈×C₁₃	—	2	2	no	—
489	Q₈×C₁₃	—	2	1	no	—
490	Q₈×C₁₃	—	4	2	no	—
491	Q₈×C₁₃	—	4	2	no	—
492	Q₈×C₁₃	—	8	1	no	—
493	Q₈×C₁₃	C₂×#41	1	2	yes	—
494	D₄×C₁₃	—	2	4	no	—
495	D₄×C₁₃	—	2	2	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	1	no	—
498	D₄×C₁₃	—	2	1	no	—
499	D₄×C₁₃	—	2	1	no	—
500	D₄×C₁₃	—	2	2	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	4	4	no	—
504	D₄×C₁₃	—	4	4	no	—
505	D₄×C₁₃	—	4	2	no	—
506	D₄×C₁₃	—	8	1	no	—
507	D₄×C₁₃	—	8	2	no	—
508	D₄×C₁₃	—	8	2	no	—
509	D₄×C₁₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	4	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	2	no	—
514	C₂×C₄×C₁₃	—	2	1	no	—
515	C₂×C₄×C₁₃	—	2	2	no	—
516	C₂×C₄×C₁₃	—	2	1	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	2	no	—
520	C₂×C₄×C₁₃	—	2	2	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	4	2	no	—
525	C₂×C₄×C₁₃	—	4	1	no	—
526	C₂×C₄×C₁₃	—	4	4	no	—
527	C₂×C₄×C₁₃	—	4	2	no	—
528	C₂×C₄×C₁₃	—	4	4	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	4	2	no	—
531	C₂×C₄×C₁₃	—	4	2	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	4	4	no	—
535	C₂×C₄×C₁₃	—	8	2	no	—
536	C₂×C₄×C₁₃	—	8	2	no	—
537	C₂×C₄×C₁₃	—	8	1	no	—
538	C₂×C₄×C₁₃	#135	1	4	yes	complemented
539	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
548	C₈×C₁₃	—	2	2	no	—
549	C₈×C₁₃	—	2	1	no	—
550	C₈×C₁₃	—	2	1	no	—
551	C₈×C₁₃	—	2	2	no	—
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	C₂×#41	1	2	yes	—
554	C₂×#135	C₂²×C₁₃	1	2	yes	—
555	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
556	#559	—	2	1	no	—
557	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#556	—	2	1	no	—
560	#556	C₂²×C₁₃	1	1	yes	characteristic
561	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	#555	C₂²×C₁₃	1	1	yes	characteristic
563	#554	C₂²×C₁₃	1	1	yes	characteristic
564	#553	—	2	1	no	—
565	#553	—	2	2	no	—
566	#553	C₂²×C₁₃	1	2	yes	—
567	#552	—	2	1	no	—
568	#552	C₂²×C₁₃	1	2	yes	—
569	#551	—	2	2	no	—
570	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
571	#548	C₂²×C₁₃	1	2	yes	—
572	#547	C₂²×C₁₃	1	1	yes	characteristic
573	#546	C₂²×C₁₃	1	2	yes	—
574	#533	C₂²×C₁₃	1	1	yes	characteristic
575	#532	—	2	1	no	—
576	#532	C₂²×C₁₃	1	1	yes	characteristic
577	#529	—	2	2	no	—
578	#529	—	2	2	no	—
579	#529	C₂²×C₁₃	1	2	yes	—
580	#529	C₂²×C₁₃	1	2	yes	complemented
581	#525	—	2	1	no	—
582	C₄×#41	—	2	1	no	—
583	C₄×#41	C₂²×C₁₃	1	2	yes	—
584	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
585	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
586	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
587	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
588	C₂×#117	—	2	1	no	—
589	#499	C₂²×C₁₃	1	2	yes	complemented
590	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#495	C₂²×C₁₃	1	2	yes	—
592	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	#488	C₂²×C₁₃	1	2	yes	—
594	#488	C₂²×C₁₃	1	2	yes	complemented
595	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
597	#485	C₂²×C₁₃	1	2	yes	complemented
598	#485	C₂²×C₁₃	1	2	yes	complemented
599	#484	C₂²×C₁₃	1	2	yes	—
600	#482	C₂²×C₁₃	1	2	yes	—
601	#482	C₂²×C₁₃	1	2	yes	complemented
602	#480	C₂²×C₁₃	1	2	yes	—
603	#479	C₂²×C₁₃	1	2	yes	complemented
604	#479	C₂²×C₁₃	1	2	yes	complemented
605	#478	C₂²×C₁₃	1	2	yes	—
606	#478	C₂²×C₁₃	1	2	yes	complemented
607	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
609	#474	C₂²×C₁₃	1	1	yes	characteristic
610	#474	C₂²×C₁₃	1	1	yes	characteristic
611	#467	C₂²×C₁₃	1	2	yes	complemented
612	#466	C₂²×C₁₃	1	2	yes	—
613	#465	C₂²×C₁₃	1	2	yes	—
614	#465	C₂²×C₁₃	1	2	yes	—
615	#465	C₂²×C₁₃	1	2	yes	—
616	#465	C₂²×C₁₃	1	2	yes	complemented
617	#464	C₂²×C₁₃	1	2	yes	—
618	#464	C₂²×C₁₃	1	2	yes	complemented
619	#463	C₂²×C₁₃	1	2	yes	—
620	#463	C₂²×C₁₃	1	2	yes	—
621	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#459	C₂²×C₁₃	1	1	yes	characteristic
624	#459	C₂²×C₁₃	1	1	yes	characteristic
625	#452	C₂²×C₁₃	1	2	yes	—
626	#452	C₂²×C₁₃	1	2	yes	complemented
627	#451	C₂²×C₁₃	1	2	yes	—
628	#449	C₂²×C₁₃	1	2	yes	—
629	#449	C₂²×C₁₃	1	2	yes	—
630	#447	C₂²×C₁₃	1	2	yes	—
631	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
634	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
635	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
636	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
637	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
639	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
640	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
641	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
642	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
643	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
644	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
645	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
646	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
647	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
648	C₄×D₈	C₂²×C₁₃	1	2	yes	—
649	C₄×D₈	C₂²×C₁₃	1	2	yes	—
650	C₄×D₈	C₂²×C₁₃	1	2	yes	—
651	C₈×D₄	C₂²×C₁₃	1	2	yes	—
652	C₈×D₄	C₂²×C₁₃	1	2	yes	—
653	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#431	C₂²×C₁₃	1	1	yes	characteristic
656	#431	C₂²×C₁₃	1	2	yes	complemented
657	#427	C₂²×C₁₃	1	2	yes	complemented
658	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
659	#416	C₂²×C₁₃	1	2	yes	—
660	#416	C₂²×C₁₃	1	2	yes	complemented
661	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
662	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
663	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
664	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
665	C₂²×C₁₃	—	2	1	no	—
666	C₂²×C₁₃	—	2	1	no	—
667	C₂²×C₁₃	—	2	2	no	—
668	C₂²×C₁₃	—	2	2	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	2	2	no	—
671	C₂²×C₁₃	—	4	1	no	—
672	C₂²×C₁₃	—	4	1	no	—
673	C₂²×C₁₃	—	4	2	no	—
674	C₂²×C₁₃	—	4	1	no	—
675	C₂²×C₁₃	—	4	2	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	2	no	—
679	C₂²×C₁₃	—	8	4	no	—
680	C₂²×C₁₃	C₂×#135	1	2	yes	—
681	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
682	C₄×C₁₃	—	2	1	no	—
683	C₄×C₁₃	—	2	2	no	—
684	C₄×C₁₃	—	2	1	no	—
685	C₄×C₁₃	—	2	2	no	—
686	C₄×C₁₃	—	2	1	no	—
687	C₄×C₁₃	—	2	2	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	4	1	no	—
690	C₄×C₁₃	—	4	1	no	—
691	C₄×C₁₃	—	4	2	no	—
692	C₄×C₁₃	—	4	2	no	—
693	C₄×C₁₃	—	4	1	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	C₂×#135	1	2	yes	—
698	C₄×C₁₃	C₂×#135	1	2	yes	—
699	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
700	C₄×C₁₃	#585	1	1	yes	characteristic
701	C₂×#41	—	2	1	no	—
702	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
703	C₂×#41	C₂³×C₁₃	1	2	yes	—
704	C₂×#41	C₂³×C₁₃	1	2	yes	—
705	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
707	C₂³×C₄	—	2	1	no	—
708	#135	—	2	8	no	—
709	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
711	C₂×SD₁₆	—	2	4	no	—
712	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×D₈	C₂³×C₁₃	1	2	yes	—
719	C₂×D₈	C₂³×C₁₃	1	2	yes	—
720	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
727	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
728	#127	—	2	1	no	—
729	#127	C₂³×C₁₃	1	1	yes	characteristic
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	C₂³×C₁₃	1	2	yes	—
740	#125	C₂³×C₁₃	1	2	yes	—
741	#124	—	2	1	no	—
742	#124	—	2	1	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	C₂³×C₁₃	1	2	yes	—
747	#124	C₂³×C₁₃	1	2	yes	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	C₂³×C₁₃	1	2	yes	—
771	#121	C₂³×C₁₃	1	2	yes	—
772	#121	C₂³×C₁₃	1	2	yes	—
773	#120	—	2	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	D₄×C₁₃	1	2	yes	—
802	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₁₃	1	2	yes	—
808	C₄×D₄	C₂³×C₁₃	1	2	yes	—
809	C₄×D₄	C₂³×C₁₃	1	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	2	yes	—
811	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	—	2	2	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	D₄×C₁₃	1	1	yes	characteristic
821	#117	D₄×C₁₃	1	2	yes	—
822	#117	C₂³×C₁₃	1	2	yes	—
823	#117	C₂³×C₁₃	1	2	yes	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	—	2	1	no	—
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
829	C₂×C₂²⋊C₄	—	2	1	no	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	2	2	no	—
833	C₂×C₄²	—	2	2	no	—
834	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
835	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
836	#107	C₂³×C₁₃	1	2	yes	—
837	#107	C₂³×C₁₃	1	2	yes	—
838	#107	C₂³×C₁₃	1	2	yes	—
839	#107	C₂³×C₁₃	1	2	yes	—
840	#106	C₂³×C₁₃	1	1	yes	characteristic
841	#106	C₂³×C₁₃	1	1	yes	characteristic
842	#106	C₂³×C₁₃	1	1	yes	characteristic
843	#106	C₂³×C₁₃	1	1	yes	characteristic
844	#106	C₂³×C₁₃	1	2	yes	—
845	#106	C₂³×C₁₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
849	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
850	#103	C₂³×C₁₃	1	1	yes	characteristic
851	#103	C₂³×C₁₃	1	1	yes	characteristic
852	#103	C₂³×C₁₃	1	1	yes	characteristic
853	#103	C₂³×C₁₃	1	1	yes	characteristic
854	#103	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	2	yes	—
856	#103	C₂³×C₁₃	1	2	yes	—
857	#103	C₂³×C₁₃	1	2	yes	—
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#102	C₂³×C₁₃	1	1	yes	characteristic
861	#102	C₂³×C₁₃	1	1	yes	characteristic
862	#102	C₂³×C₁₃	1	1	yes	characteristic
863	#102	C₂³×C₁₃	1	1	yes	characteristic
864	#102	C₂³×C₁₃	1	2	yes	—
865	#102	C₂³×C₁₃	1	2	yes	—
866	#102	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	2	yes	—
868	#102	C₂³×C₁₃	1	2	yes	—
869	#102	C₂³×C₁₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
873	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₁₃	1	2	yes	—
878	C₄×C₈	C₂³×C₁₃	1	2	yes	—
879	C₄×C₈	C₂³×C₁₃	1	2	yes	—
880	C₂×C₁₃	—	2	2	no	—
881	C₂×C₁₃	—	4	2	no	—
882	C₂×C₁₃	—	4	2	no	—
883	C₂×C₁₃	—	8	2	no	—
884	C₂×C₁₃	—	8	1	no	—
885	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
886	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
887	C₂×C₁₃	#3584	1	1	yes	characteristic
888	C₂⁴	—	2	1	no	—
889	#41	—	2	4	no	—
890	#41	—	2	4	no	—
891	#41	—	2	4	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	4	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	4	1	no	—
900	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	4	1	no	—
914	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
918	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	4	4	no	—
932	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
933	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
935	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
938	Q₁₆	—	2	4	no	—
939	Q₁₆	—	4	2	no	—
940	SD₁₆	—	2	2	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	2	2	no	—
943	SD₁₆	—	2	4	no	—
944	SD₁₆	—	4	2	no	—
945	SD₁₆	C₁₃×#41	1	4	yes	complemented
946	D₈	—	2	4	no	—
947	D₈	—	4	2	no	—
948	C₂×C₈	—	2	2	no	—
949	C₂×C₈	—	2	4	no	—
950	C₂×C₈	—	4	2	no	—
951	C₂×C₈	—	4	1	no	—
952	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
956	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
957	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
981	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1020	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1021	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1022	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₁₃	1	2	yes	—
1025	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1026	C₁₃	#61428	1	1	yes	characteristic, direct product factor, Sylow
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	4	2	no	—
1031	C₂³	—	4	2	no	—
1032	C₂³	—	8	1	no	—
1033	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1034	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	C₂×C₁₃×#41	1	2	yes	—
1045	D₄	—	2	4	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	C₂×C₁₃×#41	1	2	yes	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	4	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	C₁₃×#135	1	4	yes	complemented
1090	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1098	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	2	no	—
1103	C₈	—	2	1	no	—
1104	C₈	C₂×C₁₃×#41	1	2	yes	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	8	4	no	—
1120	C₂²	C₂×C₁₃×#135	1	2	yes	—
1121	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	C₂×C₁₃×#135	1	2	yes	—
1138	C₄	C₂×C₁₃×#135	1	2	yes	—
1139	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1140	C₄	C₁₃×#585	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	2	no	—
1146	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1147	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
1148	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3480	C₂	semidirect
2. C₁₃×#3475	C₂	semidirect
3. C₁₃×#3394	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. C₁₃×#3364	C₂	semidirect
6. C₁₃×#3361	C₂	semidirect
7. C₁₃×#3340	C₂	semidirect
8. C₁₃×#3337	C₂	semidirect
9. C₁₃×#3305	C₂	semidirect
10. C₁₃×#3302	C₂	semidirect
11. C₁₃×#3300	C₂	semidirect
12. C₁₃×#3297	C₂	semidirect
13. C₁₃×#3284	C₂	semidirect
14. C₁₃×#3282	C₂	semidirect
15. C₁₃×#3168	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3104	C₂	semidirect
18. C₁₃×#3102	C₂	semidirect
19. C₁₃×#3102	C₂	semidirect
20. C₁₃×#3100	C₂	semidirect
21. C₈×C₁₃×#41	C₂	semidirect
22. C₄×C₁₃×#135	C₂	semidirect
23. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
27. C₁₃×#559	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
40. C₁₃×#550	C₂²	semidirect
50. C₁₃×#529	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
59. C₁₃×#499	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
62. 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
71. C₁₃×#482	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
76. C₁₃×#478	C₂²	semidirect
77. C₁₃×#477	C₂²	semidirect
78. C₁₃×#477	C₂²	semidirect
81. C₁₃×#467	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
91. C₁₃×#462	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
96. C₁₃×#452	C₂²	semidirect
101. C₈×Q₈×C₁₃	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
103. C₄×C₁₃×Q₁₆	C₂²	semidirect
104. C₄×C₁₃×Q₁₆	C₂²	semidirect
105. C₄×C₁₃×Q₁₆	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
126. C₁₃×#431	C₂²	semidirect
127. C₁₃×#427	C₂²	semidirect
130. C₁₃×#416	C₂²	semidirect
134. C₂×C₄×C₈×C₁₃	C₂²	semidirect
314. #61428	C₁₃	direct (N × H)
372. C₁₃×SD₁₆	#41	semidirect
453. #3480	C₂×C₁₃	semidirect
454. #3475	C₂×C₁₃	semidirect
455. #3394	C₂×C₁₃	semidirect
456. #3381	C₂×C₁₃	semidirect
457. #3364	C₂×C₁₃	semidirect
458. #3361	C₂×C₁₃	semidirect
459. #3340	C₂×C₁₃	semidirect
460. #3337	C₂×C₁₃	semidirect
461. #3305	C₂×C₁₃	semidirect
462. #3302	C₂×C₁₃	semidirect
463. #3300	C₂×C₁₃	semidirect
464. #3297	C₂×C₁₃	semidirect
465. #3284	C₂×C₁₃	semidirect
466. #3282	C₂×C₁₃	semidirect
467. #3168	C₂×C₁₃	semidirect
468. #3167	C₂×C₁₃	semidirect
469. #3104	C₂×C₁₃	semidirect
470. #3102	C₂×C₁₃	semidirect
471. #3102	C₂×C₁₃	semidirect
472. #3100	C₂×C₁₃	semidirect
473. C₈×#41	C₂×C₁₃	semidirect
474. C₄×#135	C₂×C₁₃	semidirect
475. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
538. C₂×C₄×C₁₃	#135	semidirect
557. #559	C₂²×C₁₃	semidirect
558. #557	C₂²×C₁₃	semidirect
561. #556	C₂²×C₁₃	semidirect
570. #550	C₂²×C₁₃	semidirect
580. #529	C₂²×C₁₃	semidirect
585. C₄×#41	C₂²×C₁₃	semidirect
589. #499	C₂²×C₁₃	semidirect
590. #498	C₂²×C₁₃	semidirect
592. #492	C₂²×C₁₃	semidirect
594. #488	C₂²×C₁₃	semidirect
595. #487	C₂²×C₁₃	semidirect
596. #486	C₂²×C₁₃	semidirect
597. #485	C₂²×C₁₃	semidirect
598. #485	C₂²×C₁₃	semidirect
601. #482	C₂²×C₁₃	semidirect
603. #479	C₂²×C₁₃	semidirect
604. #479	C₂²×C₁₃	semidirect
606. #478	C₂²×C₁₃	semidirect
607. #477	C₂²×C₁₃	semidirect
608. #477	C₂²×C₁₃	semidirect
611. #467	C₂²×C₁₃	semidirect
616. #465	C₂²×C₁₃	semidirect
618. #464	C₂²×C₁₃	semidirect
621. #462	C₂²×C₁₃	semidirect
622. #462	C₂²×C₁₃	semidirect
626. #452	C₂²×C₁₃	semidirect
631. C₈×Q₈	C₂²×C₁₃	semidirect
632. C₈×Q₈	C₂²×C₁₃	semidirect
633. C₄×Q₁₆	C₂²×C₁₃	semidirect
634. C₄×Q₁₆	C₂²×C₁₃	semidirect
635. C₄×Q₁₆	C₂²×C₁₃	semidirect
645. C₄×SD₁₆	C₂²×C₁₃	semidirect
646. C₄×SD₁₆	C₂²×C₁₃	semidirect
647. C₄×SD₁₆	C₂²×C₁₃	semidirect
653. C₈×D₄	C₂²×C₁₃	semidirect
654. C₈×D₄	C₂²×C₁₃	semidirect
656. #431	C₂²×C₁₃	semidirect
657. #427	C₂²×C₁₃	semidirect
660. #416	C₂²×C₁₃	semidirect
664. C₂×C₄×C₈	C₂²×C₁₃	semidirect
945. SD₁₆	C₁₃×#41	semidirect
1026. C₁₃	#61428	direct (N × H)
1089. C₂×C₄	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×#3480	2
C₁₃×#3475	2
C₁₃×#3394	2
C₁₃×#3381	2
C₁₃×#3364	2
C₁₃×#3361	2
C₁₃×#3340	2
C₁₃×#3337	2
C₁₃×#3305	2
C₁₃×#3302	2
C₁₃×#3300	2
C₁₃×#3297	2
C₁₃×#3284	2
C₁₃×#3282	2
C₁₃×#3168	2
C₁₃×#3167	2
C₁₃×#3104	2
C₁₃×#3102	2
C₁₃×#3100	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×SD₁₆	2
#61428	13

Subgroups — C13×#61428 #15747767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61428 #15747767