Subgroups — C₁₃×#61702 #15748041

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3337	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3191	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3091	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#482	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#555	C₂²	1	1	yes	characteristic
26	C₁₃×#555	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#554	C₂²	1	1	yes	characteristic
28	C₁₃×#554	C₂²	1	1	yes	characteristic
29	C₁₃×#553	—	2	1	no	—
30	C₁₃×#553	C₂²	1	2	yes	—
31	C₁₃×#553	C₂²	1	2	yes	complemented
32	C₁₃×#552	—	2	1	no	—
33	C₁₃×#552	C₂²	1	2	yes	complemented
34	C₁₃×#551	—	2	2	no	—
35	C₁₃×#550	C₂²	1	1	yes	characteristic
36	C₁₃×#547	C₂²	1	1	yes	characteristic
37	C₁₃×#546	—	2	1	no	—
38	C₁₃×#546	—	2	2	no	—
39	C₁₃×#546	C₂²	1	2	yes	—
40	D₄²×C₁₃	—	2	1	no	—
41	D₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#540	—	2	1	no	—
43	C₁₃×#538	—	2	2	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₁₃×#529	—	2	2	no	—
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	C₂²	1	1	yes	characteristic
49	C₁₃×#525	C₂²	1	2	yes	—
50	C₁₃×#525	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#121	C₂²	1	2	yes	—
52	C₁₃×#518	—	2	1	no	—
53	C₄×C₁₃×#41	—	2	1	no	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
57	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#499	C₂²	1	2	yes	complemented
59	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#488	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#485	C₂²	1	2	yes	complemented
64	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#485	C₂²	1	2	yes	complemented
66	C₁₃×#484	C₂²	1	2	yes	complemented
67	C₁₃×#484	C₂²	1	2	yes	complemented
68	C₁₃×#483	C₂²	1	2	yes	complemented
69	C₁₃×#482	C₂²	1	1	yes	characteristic
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#482	C₂²	1	2	yes	complemented
72	C₁₃×#482	C₂²	1	2	yes	complemented
73	C₁₃×#482	C₂²	1	2	yes	complemented
74	C₁₃×#482	C₂²	1	2	yes	complemented
75	C₁₃×#482	C₂²	1	2	yes	complemented
76	C₁₃×#482	C₂²	1	2	yes	complemented
77	C₁₃×#482	C₂²	1	2	yes	complemented
78	C₁₃×#482	C₂²	1	2	yes	complemented
79	C₁₃×#481	C₂²	1	2	yes	complemented
80	C₁₃×#481	C₂²	1	2	yes	complemented
81	C₁₃×#480	C₂²	1	2	yes	complemented
82	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#478	C₂²	1	2	yes	complemented
84	C₁₃×#478	C₂²	1	2	yes	complemented
85	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
86	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
87	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#467	C₂²	1	2	yes	complemented
93	C₁₃×#466	C₂²	1	2	yes	complemented
94	C₁₃×#466	C₂²	1	2	yes	complemented
95	C₁₃×#466	C₂²	1	2	yes	complemented
96	C₁₃×#465	C₂²	1	2	yes	complemented
97	C₁₃×#465	C₂²	1	2	yes	complemented
98	C₁₃×#465	C₂²	1	2	yes	complemented
99	C₁₃×#465	C₂²	1	2	yes	complemented
100	C₁₃×#464	C₂²	1	1	yes	characteristic, complemented
101	C₁₃×#463	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#450	C₂²	1	2	yes	complemented
107	C₁₃×#449	C₂²	1	1	yes	characteristic
108	C₁₃×#449	C₂²	1	2	yes	complemented
109	C₁₃×#449	C₂²	1	2	yes	complemented
110	C₁₃×#447	C₂²	1	2	yes	complemented
111	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
117	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
119	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
120	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
121	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
124	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#427	C₂²	1	2	yes	complemented
126	C₁₃×#427	C₂²	1	2	yes	complemented
127	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
129	C₁₃×#416	C₂²	1	2	yes	complemented
130	C₁₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₁₃×#102	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	1	no	—
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₁₃	—	2	2	no	—
140	C₂²×D₄×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×D₈	C₂³	1	2	yes	—
150	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×#127	—	2	1	no	—
158	C₁₃×#127	C₂³	1	1	yes	characteristic
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	1	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	1	no	—
167	C₁₃×#125	C₂³	1	2	yes	—
168	C₁₃×#125	C₂³	1	1	yes	characteristic
169	C₁₃×#124	—	2	1	no	—
170	C₁₃×#124	—	2	2	no	—
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	—	2	1	no	—
173	C₁₃×#124	C₂³	1	1	yes	characteristic
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	—	2	1	no	—
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	1	no	—
183	C₁₃×C₂²⋊Q₈	—	2	1	no	—
184	C₁₃×C₂²⋊Q₈	—	2	1	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	1	no	—
193	C₁₃×#121	—	2	2	no	—
194	C₁₃×#121	—	2	1	no	—
195	C₁₃×#121	—	2	2	no	—
196	C₁₃×#121	—	2	2	no	—
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	C₂³	1	2	yes	—
202	C₁₃×#121	C₂³	1	1	yes	characteristic
203	C₁₃×#121	C₂³	1	2	yes	—
204	C₁₃×#121	C₂³	1	2	yes	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#120	—	2	2	no	—
209	C₁₃×#120	—	2	2	no	—
210	C₁₃×#120	—	2	2	no	—
211	C₁₃×#120	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
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×D₄×C₁₃	—	2	1	no	—
219	C₄×D₄×C₁₃	—	2	1	no	—
220	C₄×D₄×C₁₃	—	2	2	no	—
221	C₄×D₄×C₁₃	—	2	1	no	—
222	C₄×D₄×C₁₃	—	2	1	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	1	no	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
232	C₄×D₄×C₁₃	D₄	1	2	yes	—
233	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
234	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₁₃×#117	—	2	2	no	—
242	C₁₃×#117	—	2	2	no	—
243	C₁₃×#117	—	2	1	no	—
244	C₁₃×#117	—	2	1	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	C₂³	1	2	yes	—
249	C₁₃×#117	C₂³	1	2	yes	—
250	C₁₃×#117	C₂³	1	2	yes	—
251	C₁₃×#117	C₂³	1	1	yes	characteristic
252	C₁₃×#117	C₂³	1	2	yes	—
253	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
261	C₂×C₄²×C₁₃	—	2	2	no	—
262	C₂×C₄²×C₁₃	—	2	1	no	—
263	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	1	yes	characteristic
265	C₁₃×#107	C₂³	1	2	yes	—
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×#103	C₂³	1	1	yes	characteristic
283	C₁₃×#103	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#102	C₂³	1	1	yes	characteristic
290	C₁₃×#102	C₂³	1	1	yes	characteristic
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
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	#61702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂⁴×C₁₃	—	2	2	no	—
314	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
315	C₁₃×#41	—	4	1	no	—
316	C₁₃×#41	—	4	1	no	—
317	C₁₃×#41	—	4	2	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₁₃×#41	—	4	4	no	—
320	C₁₃×#41	—	8	2	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₁₃	—	2	4	no	—
327	C₂×D₄×C₁₃	—	2	2	no	—
328	C₂×D₄×C₁₃	—	2	1	no	—
329	C₂×D₄×C₁₃	—	2	2	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	1	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	1	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	4	2	no	—
340	C₂×D₄×C₁₃	—	4	2	no	—
341	C₂×D₄×C₁₃	—	4	4	no	—
342	C₂×D₄×C₁₃	—	8	4	no	—
343	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
348	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	1	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	2	no	—
359	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
368	C₁₃×Q₁₆	—	4	1	no	—
369	C₁₃×SD₁₆	—	4	1	no	—
370	C₁₃×SD₁₆	—	4	1	no	—
371	C₁₃×SD₁₆	—	4	2	no	—
372	C₁₃×D₈	—	4	2	no	—
373	C₁₃×D₈	—	4	1	no	—
374	C₂×C₈×C₁₃	—	4	2	no	—
375	C₂×C₈×C₁₃	—	4	2	no	—
376	C₂×C₈×C₁₃	—	4	2	no	—
377	C₂×C₈×C₁₃	—	4	2	no	—
378	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	1	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	1	no	—
440	C₄²×C₁₃	—	2	2	no	—
441	C₄²×C₁₃	—	2	2	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
448	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
449	#3519	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3475	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3341	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3339	C₂×C₁₃	1	2	yes	complemented
454	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3337	C₂×C₁₃	1	2	yes	complemented
456	#3335	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3297	C₂×C₁₃	1	2	yes	complemented
460	#3296	C₂×C₁₃	1	2	yes	complemented
461	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3294	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3233	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3191	C₂×C₁₃	1	2	yes	complemented
466	#3188	C₂×C₁₃	1	2	yes	complemented
467	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3091	C₂×C₁₃	1	2	yes	complemented
470	C₂×#482	C₂×C₁₃	1	2	yes	complemented
471	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
472	C₂³×C₁₃	—	2	4	no	—
473	C₂³×C₁₃	—	2	1	no	—
474	C₂³×C₁₃	—	2	1	no	—
475	C₂³×C₁₃	—	2	2	no	—
476	C₂³×C₁₃	—	4	2	no	—
477	C₂³×C₁₃	—	4	2	no	—
478	C₂³×C₁₃	—	4	4	no	—
479	C₂³×C₁₃	—	8	2	no	—
480	C₂³×C₁₃	—	8	2	no	—
481	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
482	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
484	Q₈×C₁₃	—	2	1	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	1	no	—
487	Q₈×C₁₃	—	2	1	no	—
488	Q₈×C₁₃	—	4	2	no	—
489	Q₈×C₁₃	—	8	1	no	—
490	Q₈×C₁₃	—	8	1	no	—
491	D₄×C₁₃	—	2	4	no	—
492	D₄×C₁₃	—	2	2	no	—
493	D₄×C₁₃	—	2	1	no	—
494	D₄×C₁₃	—	2	1	no	—
495	D₄×C₁₃	—	2	1	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	1	no	—
498	D₄×C₁₃	—	2	2	no	—
499	D₄×C₁₃	—	4	2	no	—
500	D₄×C₁₃	—	4	4	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	4	4	no	—
504	D₄×C₁₃	—	4	2	no	—
505	D₄×C₁₃	—	8	2	no	—
506	D₄×C₁₃	—	8	1	no	—
507	D₄×C₁₃	—	8	2	no	—
508	D₄×C₁₃	—	8	2	no	—
509	D₄×C₁₃	—	8	2	no	—
510	D₄×C₁₃	—	8	2	no	—
511	D₄×C₁₃	#135	1	4	yes	—
512	C₂×C₄×C₁₃	—	2	2	no	—
513	C₂×C₄×C₁₃	—	2	2	no	—
514	C₂×C₄×C₁₃	—	2	2	no	—
515	C₂×C₄×C₁₃	—	2	2	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	1	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	2	2	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	2	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	4	2	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	4	2	no	—
531	C₂×C₄×C₁₃	—	4	1	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	4	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	8	1	no	—
537	C₂×C₄×C₁₃	—	8	2	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
549	C₈×C₁₃	—	2	2	no	—
550	C₈×C₁₃	—	2	1	no	—
551	C₈×C₁₃	—	2	1	no	—
552	C₈×C₁₃	—	2	2	no	—
553	C₈×C₁₃	—	2	1	no	—
554	C₈×C₁₃	—	2	1	no	—
555	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
556	#555	C₂²×C₁₃	1	1	yes	characteristic
557	#555	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	#554	C₂²×C₁₃	1	1	yes	characteristic
559	#554	C₂²×C₁₃	1	1	yes	characteristic
560	#553	—	2	1	no	—
561	#553	C₂²×C₁₃	1	2	yes	—
562	#553	C₂²×C₁₃	1	2	yes	complemented
563	#552	—	2	1	no	—
564	#552	C₂²×C₁₃	1	2	yes	complemented
565	#551	—	2	2	no	—
566	#550	C₂²×C₁₃	1	1	yes	characteristic
567	#547	C₂²×C₁₃	1	1	yes	characteristic
568	#546	—	2	1	no	—
569	#546	—	2	2	no	—
570	#546	C₂²×C₁₃	1	2	yes	—
571	D₄²	—	2	1	no	—
572	D₄²	C₂²×C₁₃	1	1	yes	characteristic
573	#540	—	2	1	no	—
574	#538	—	2	2	no	—
575	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	#532	C₂²×C₁₃	1	1	yes	characteristic
577	#529	—	2	2	no	—
578	#529	—	2	1	no	—
579	#529	C₂²×C₁₃	1	1	yes	characteristic
580	#525	C₂²×C₁₃	1	2	yes	—
581	#525	C₂²×C₁₃	1	2	yes	complemented
582	C₂×#121	C₂²×C₁₃	1	2	yes	—
583	#518	—	2	1	no	—
584	C₄×#41	—	2	1	no	—
585	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
586	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
587	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
588	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#499	C₂²×C₁₃	1	2	yes	complemented
590	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#488	C₂²×C₁₃	1	2	yes	complemented
592	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#485	C₂²×C₁₃	1	2	yes	complemented
595	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#485	C₂²×C₁₃	1	2	yes	complemented
597	#484	C₂²×C₁₃	1	2	yes	complemented
598	#484	C₂²×C₁₃	1	2	yes	complemented
599	#483	C₂²×C₁₃	1	2	yes	complemented
600	#482	C₂²×C₁₃	1	1	yes	characteristic
601	#482	C₂²×C₁₃	1	2	yes	—
602	#482	C₂²×C₁₃	1	2	yes	complemented
603	#482	C₂²×C₁₃	1	2	yes	complemented
604	#482	C₂²×C₁₃	1	2	yes	complemented
605	#482	C₂²×C₁₃	1	2	yes	complemented
606	#482	C₂²×C₁₃	1	2	yes	complemented
607	#482	C₂²×C₁₃	1	2	yes	complemented
608	#482	C₂²×C₁₃	1	2	yes	complemented
609	#482	C₂²×C₁₃	1	2	yes	complemented
610	#481	C₂²×C₁₃	1	2	yes	complemented
611	#481	C₂²×C₁₃	1	2	yes	complemented
612	#480	C₂²×C₁₃	1	2	yes	complemented
613	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
614	#478	C₂²×C₁₃	1	2	yes	complemented
615	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
616	#478	C₂²×C₁₃	1	2	yes	complemented
617	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
618	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
619	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
621	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
623	#467	C₂²×C₁₃	1	2	yes	complemented
624	#466	C₂²×C₁₃	1	2	yes	complemented
625	#466	C₂²×C₁₃	1	2	yes	complemented
626	#466	C₂²×C₁₃	1	2	yes	complemented
627	#465	C₂²×C₁₃	1	2	yes	complemented
628	#465	C₂²×C₁₃	1	2	yes	complemented
629	#465	C₂²×C₁₃	1	2	yes	complemented
630	#465	C₂²×C₁₃	1	2	yes	complemented
631	#464	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#463	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#452	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#452	C₂²×C₁₃	1	2	yes	complemented
637	#450	C₂²×C₁₃	1	2	yes	complemented
638	#449	C₂²×C₁₃	1	1	yes	characteristic
639	#449	C₂²×C₁₃	1	2	yes	complemented
640	#449	C₂²×C₁₃	1	2	yes	complemented
641	#447	C₂²×C₁₃	1	2	yes	complemented
642	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
643	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
644	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
646	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
647	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
649	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
650	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
651	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
652	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
654	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#427	C₂²×C₁₃	1	2	yes	complemented
657	#427	C₂²×C₁₃	1	2	yes	complemented
658	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
659	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
660	#416	C₂²×C₁₃	1	2	yes	complemented
661	#416	C₂²×C₁₃	1	2	yes	complemented
662	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
663	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
664	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
665	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
666	C₂²×C₁₃	—	2	2	no	—
667	C₂²×C₁₃	—	2	2	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	1	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	4	2	no	—
675	C₂²×C₁₃	—	4	1	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	2	no	—
679	C₂²×C₁₃	—	4	1	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	2	no	—
683	C₂²×C₁₃	—	8	4	no	—
684	C₂²×C₁₃	—	16	4	no	—
685	C₂²×C₁₃	C₂×#135	1	4	yes	—
686	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	1	no	—
689	C₄×C₁₃	—	2	1	no	—
690	C₄×C₁₃	—	2	2	no	—
691	C₄×C₁₃	—	2	2	no	—
692	C₄×C₁₃	—	2	1	no	—
693	C₄×C₁₃	—	4	1	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	2	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	2	no	—
702	C₄×C₁₃	C₂×#135	1	2	yes	—
703	C₄×C₁₃	#585	1	1	yes	characteristic
704	C₄×C₁₃	#585	1	1	yes	characteristic
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	1	no	—
707	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×#41	C₂³×C₁₃	1	2	yes	—
709	C₂²×D₄	—	2	2	no	—
710	C₂²×D₄	—	2	1	no	—
711	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
712	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
713	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×D₈	C₂³×C₁₃	1	2	yes	—
720	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
721	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
723	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
727	#127	—	2	1	no	—
728	#127	C₂³×C₁₃	1	1	yes	characteristic
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	—	2	2	no	—
733	#126	—	2	1	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	C₂³×C₁₃	1	1	yes	characteristic
738	#125	C₂³×C₁₃	1	2	yes	—
739	#124	—	2	1	no	—
740	#124	—	2	2	no	—
741	#124	—	2	2	no	—
742	#124	—	2	1	no	—
743	#124	C₂³×C₁₃	1	1	yes	characteristic
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	1	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	C₂³×C₁₃	1	1	yes	characteristic
772	#121	C₂³×C₁₃	1	2	yes	—
773	#121	C₂³×C₁₃	1	2	yes	—
774	#121	C₂³×C₁₃	1	2	yes	—
775	#121	C₂³×C₁₃	1	2	yes	—
776	#121	C₂³×C₁₃	1	2	yes	—
777	#121	C₂³×C₁₃	1	2	yes	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
802	C₄×D₄	D₄×C₁₃	1	2	yes	—
803	C₄×D₄	D₄×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	1	yes	characteristic
809	C₄×D₄	C₂³×C₁₃	1	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	C₂³×C₁₃	1	1	yes	characteristic
819	#117	C₂³×C₁₃	1	2	yes	—
820	#117	C₂³×C₁₃	1	2	yes	—
821	#117	C₂³×C₁₃	1	2	yes	—
822	#117	C₂³×C₁₃	1	2	yes	—
823	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
825	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₂²⋊C₄	—	2	2	no	—
830	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
831	C₂×C₄²	—	2	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
834	#107	C₂³×C₁₃	1	1	yes	characteristic
835	#107	C₂³×C₁₃	1	2	yes	—
836	#107	C₂³×C₁₃	1	2	yes	—
837	#107	C₂³×C₁₃	1	2	yes	—
838	#107	C₂³×C₁₃	1	1	yes	characteristic
839	#107	C₂³×C₁₃	1	2	yes	—
840	#107	C₂³×C₁₃	1	2	yes	—
841	#106	C₂³×C₁₃	1	1	yes	characteristic
842	#106	C₂³×C₁₃	1	2	yes	—
843	#106	C₂³×C₁₃	1	2	yes	—
844	#106	C₂³×C₁₃	1	2	yes	—
845	#106	C₂³×C₁₃	1	1	yes	characteristic
846	#106	C₂³×C₁₃	1	2	yes	—
847	#106	C₂³×C₁₃	1	2	yes	—
848	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
851	C₄⋊C₈	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	1	yes	characteristic
858	#103	C₂³×C₁₃	1	1	yes	characteristic
859	#102	C₂³×C₁₃	1	1	yes	characteristic
860	#102	C₂³×C₁₃	1	1	yes	characteristic
861	#102	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	2	yes	—
863	#102	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	1	yes	characteristic
871	#102	C₂³×C₁₃	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
879	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₁₃	1	2	yes	—
882	C₂×C₁₃	—	2	4	no	—
883	C₂×C₁₃	—	4	2	no	—
884	C₂×C₁₃	—	4	1	no	—
885	C₂×C₁₃	—	8	1	no	—
886	C₂×C₁₃	—	8	2	no	—
887	C₂×C₁₃	—	8	1	no	—
888	C₂×C₁₃	#3485	1	1	yes	characteristic
889	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
890	C₂×C₁₃	#3585	1	1	yes	characteristic
891	C₂⁴	—	2	2	no	—
892	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
893	#41	—	4	1	no	—
894	#41	—	4	1	no	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	4	no	—
898	#41	—	8	2	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	4	no	—
920	C₂×D₄	—	8	4	no	—
921	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
922	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
923	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
926	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
946	Q₁₆	—	4	1	no	—
947	SD₁₆	—	4	1	no	—
948	SD₁₆	—	4	1	no	—
949	SD₁₆	—	4	2	no	—
950	D₈	—	4	2	no	—
951	D₈	—	4	1	no	—
952	C₂×C₈	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	—	4	2	no	—
956	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
960	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	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	—	2	1	no	—
979	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	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	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1024	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1027	C₁₃	#61702	1	1	yes	characteristic, direct product factor, Sylow
1028	C₂³	—	2	4	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	2	no	—
1032	C₂³	—	4	2	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	8	2	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1038	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1039	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	4	2	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	8	1	no	—
1047	D₄	—	2	4	no	—
1048	D₄	—	2	2	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	4	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	C₁₃×#135	1	4	yes	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	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	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1104	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1105	C₈	—	2	2	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₂×C₁₃×#135	1	4	yes	—
1131	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	C₂×C₁₃×#135	1	2	yes	—
1148	C₄	C₁₃×#585	1	1	yes	characteristic
1149	C₄	C₁₃×#585	1	1	yes	characteristic
1150	C₂	—	2	4	no	—
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₁₃×#3485	1	1	yes	characteristic
1157	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
1158	C₂	C₁₃×#3585	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×#3519	C₂	semidirect
2. C₁₃×#3475	C₂	semidirect
3. C₁₃×#3341	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#3339	C₂	semidirect
6. C₁₃×#3338	C₂	semidirect
7. C₁₃×#3337	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3305	C₂	semidirect
10. C₁₃×#3304	C₂	semidirect
11. C₁₃×#3297	C₂	semidirect
12. C₁₃×#3296	C₂	semidirect
13. C₁₃×#3295	C₂	semidirect
14. C₁₃×#3294	C₂	semidirect
15. C₁₃×#3233	C₂	semidirect
16. C₁₃×#3228	C₂	semidirect
17. C₁₃×#3191	C₂	semidirect
18. C₁₃×#3188	C₂	semidirect
19. C₁₃×#3106	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3091	C₂	semidirect
22. C₂×C₁₃×#482	C₂	semidirect
23. C₁₃×#2972	C₂	semidirect
24. C₁₃×#556	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
31. C₁₃×#553	C₂²	semidirect
33. C₁₃×#552	C₂²	semidirect
44. C₁₃×#533	C₂²	semidirect
50. C₁₃×#525	C₂²	semidirect
54. C₄×C₁₃×#41	C₂²	semidirect
56. C₂×C₁₃×#117	C₂²	semidirect
57. C₁₃×#500	C₂²	semidirect
58. C₁₃×#499	C₂²	semidirect
59. C₁₃×#498	C₂²	semidirect
60. C₁₃×#488	C₂²	semidirect
61. C₁₃×#486	C₂²	semidirect
62. C₁₃×#486	C₂²	semidirect
63. C₁₃×#485	C₂²	semidirect
64. C₁₃×#485	C₂²	semidirect
65. C₁₃×#485	C₂²	semidirect
66. C₁₃×#484	C₂²	semidirect
67. C₁₃×#484	C₂²	semidirect
68. C₁₃×#483	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#482	C₂²	semidirect
73. C₁₃×#482	C₂²	semidirect
74. C₁₃×#482	C₂²	semidirect
75. C₁₃×#482	C₂²	semidirect
76. C₁₃×#482	C₂²	semidirect
77. C₁₃×#482	C₂²	semidirect
78. C₁₃×#482	C₂²	semidirect
79. C₁₃×#481	C₂²	semidirect
80. C₁₃×#481	C₂²	semidirect
81. C₁₃×#480	C₂²	semidirect
82. C₁₃×#479	C₂²	semidirect
83. C₁₃×#478	C₂²	semidirect
84. C₁₃×#478	C₂²	semidirect
85. C₁₃×#478	C₂²	semidirect
86. C₁₃×#477	C₂²	semidirect
87. C₁₃×#477	C₂²	semidirect
88. C₁₃×#476	C₂²	semidirect
89. C₁₃×#476	C₂²	semidirect
90. C₁₃×#475	C₂²	semidirect
91. C₁₃×#474	C₂²	semidirect
92. C₁₃×#467	C₂²	semidirect
93. C₁₃×#466	C₂²	semidirect
94. C₁₃×#466	C₂²	semidirect
95. C₁₃×#466	C₂²	semidirect
96. C₁₃×#465	C₂²	semidirect
97. C₁₃×#465	C₂²	semidirect
98. C₁₃×#465	C₂²	semidirect
99. C₁₃×#465	C₂²	semidirect
100. C₁₃×#464	C₂²	semidirect
101. C₁₃×#463	C₂²	semidirect
102. C₁₃×#460	C₂²	semidirect
103. C₁₃×#459	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#450	C₂²	semidirect
108. C₁₃×#449	C₂²	semidirect
109. C₁₃×#449	C₂²	semidirect
110. C₁₃×#447	C₂²	semidirect
111. C₄×C₁₃×Q₁₆	C₂²	semidirect
112. C₄×C₁₃×SD₁₆	C₂²	semidirect
113. C₄×C₁₃×SD₁₆	C₂²	semidirect
114. C₄×C₁₃×SD₁₆	C₂²	semidirect
115. C₄×C₁₃×D₈	C₂²	semidirect
116. C₄×C₁₃×D₈	C₂²	semidirect
119. C₈×D₄×C₁₃	C₂²	semidirect
120. C₈×D₄×C₁₃	C₂²	semidirect
121. C₈×D₄×C₁₃	C₂²	semidirect
122. C₈×D₄×C₁₃	C₂²	semidirect
123. C₁₃×#431	C₂²	semidirect
124. C₁₃×#431	C₂²	semidirect
125. C₁₃×#427	C₂²	semidirect
126. C₁₃×#427	C₂²	semidirect
127. C₂×C₁₃×#107	C₂²	semidirect
128. C₂×C₁₃×#106	C₂²	semidirect
129. C₁₃×#416	C₂²	semidirect
130. C₁₃×#416	C₂²	semidirect
131. C₂×C₁₃×#102	C₂²	semidirect
132. C₂×C₁₃×#102	C₂²	semidirect
133. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
312. #61702	C₁₃	direct (N × H)
449. #3519	C₂×C₁₃	semidirect
450. #3475	C₂×C₁₃	semidirect
451. #3341	C₂×C₁₃	semidirect
452. #3340	C₂×C₁₃	semidirect
453. #3339	C₂×C₁₃	semidirect
454. #3338	C₂×C₁₃	semidirect
455. #3337	C₂×C₁₃	semidirect
456. #3335	C₂×C₁₃	semidirect
457. #3305	C₂×C₁₃	semidirect
458. #3304	C₂×C₁₃	semidirect
459. #3297	C₂×C₁₃	semidirect
460. #3296	C₂×C₁₃	semidirect
461. #3295	C₂×C₁₃	semidirect
462. #3294	C₂×C₁₃	semidirect
463. #3233	C₂×C₁₃	semidirect
464. #3228	C₂×C₁₃	semidirect
465. #3191	C₂×C₁₃	semidirect
466. #3188	C₂×C₁₃	semidirect
467. #3106	C₂×C₁₃	semidirect
468. #3102	C₂×C₁₃	semidirect
469. #3091	C₂×C₁₃	semidirect
470. C₂×#482	C₂×C₁₃	semidirect
471. #2972	C₂×C₁₃	semidirect
555. #556	C₂²×C₁₃	semidirect
557. #555	C₂²×C₁₃	semidirect
562. #553	C₂²×C₁₃	semidirect
564. #552	C₂²×C₁₃	semidirect
575. #533	C₂²×C₁₃	semidirect
581. #525	C₂²×C₁₃	semidirect
585. C₄×#41	C₂²×C₁₃	semidirect
587. C₂×#117	C₂²×C₁₃	semidirect
588. #500	C₂²×C₁₃	semidirect
589. #499	C₂²×C₁₃	semidirect
590. #498	C₂²×C₁₃	semidirect
591. #488	C₂²×C₁₃	semidirect
592. #486	C₂²×C₁₃	semidirect
593. #486	C₂²×C₁₃	semidirect
594. #485	C₂²×C₁₃	semidirect
595. #485	C₂²×C₁₃	semidirect
596. #485	C₂²×C₁₃	semidirect
597. #484	C₂²×C₁₃	semidirect
598. #484	C₂²×C₁₃	semidirect
599. #483	C₂²×C₁₃	semidirect
602. #482	C₂²×C₁₃	semidirect
603. #482	C₂²×C₁₃	semidirect
604. #482	C₂²×C₁₃	semidirect
605. #482	C₂²×C₁₃	semidirect
606. #482	C₂²×C₁₃	semidirect
607. #482	C₂²×C₁₃	semidirect
608. #482	C₂²×C₁₃	semidirect
609. #482	C₂²×C₁₃	semidirect
610. #481	C₂²×C₁₃	semidirect
611. #481	C₂²×C₁₃	semidirect
612. #480	C₂²×C₁₃	semidirect
613. #479	C₂²×C₁₃	semidirect
614. #478	C₂²×C₁₃	semidirect
615. #478	C₂²×C₁₃	semidirect
616. #478	C₂²×C₁₃	semidirect
617. #477	C₂²×C₁₃	semidirect
618. #477	C₂²×C₁₃	semidirect
619. #476	C₂²×C₁₃	semidirect
620. #476	C₂²×C₁₃	semidirect
621. #475	C₂²×C₁₃	semidirect
622. #474	C₂²×C₁₃	semidirect
623. #467	C₂²×C₁₃	semidirect
624. #466	C₂²×C₁₃	semidirect
625. #466	C₂²×C₁₃	semidirect
626. #466	C₂²×C₁₃	semidirect
627. #465	C₂²×C₁₃	semidirect
628. #465	C₂²×C₁₃	semidirect
629. #465	C₂²×C₁₃	semidirect
630. #465	C₂²×C₁₃	semidirect
631. #464	C₂²×C₁₃	semidirect
632. #463	C₂²×C₁₃	semidirect
633. #460	C₂²×C₁₃	semidirect
634. #459	C₂²×C₁₃	semidirect
635. #452	C₂²×C₁₃	semidirect
636. #452	C₂²×C₁₃	semidirect
637. #450	C₂²×C₁₃	semidirect
639. #449	C₂²×C₁₃	semidirect
640. #449	C₂²×C₁₃	semidirect
641. #447	C₂²×C₁₃	semidirect
642. C₄×Q₁₆	C₂²×C₁₃	semidirect
643. C₄×SD₁₆	C₂²×C₁₃	semidirect
644. C₄×SD₁₆	C₂²×C₁₃	semidirect
645. C₄×SD₁₆	C₂²×C₁₃	semidirect
646. C₄×D₈	C₂²×C₁₃	semidirect
647. C₄×D₈	C₂²×C₁₃	semidirect
650. C₈×D₄	C₂²×C₁₃	semidirect
651. C₈×D₄	C₂²×C₁₃	semidirect
652. C₈×D₄	C₂²×C₁₃	semidirect
653. C₈×D₄	C₂²×C₁₃	semidirect
654. #431	C₂²×C₁₃	semidirect
655. #431	C₂²×C₁₃	semidirect
656. #427	C₂²×C₁₃	semidirect
657. #427	C₂²×C₁₃	semidirect
658. C₂×#107	C₂²×C₁₃	semidirect
659. C₂×#106	C₂²×C₁₃	semidirect
660. #416	C₂²×C₁₃	semidirect
661. #416	C₂²×C₁₃	semidirect
662. C₂×#102	C₂²×C₁₃	semidirect
663. C₂×#102	C₂²×C₁₃	semidirect
664. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
665. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
1027. C₁₃	#61702	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×#3519	2
C₁₃×#3475	2
C₁₃×#3341	2
C₁₃×#3340	2
C₁₃×#3339	2
C₁₃×#3338	2
C₁₃×#3337	2
C₁₃×#3335	2
C₁₃×#3305	2
C₁₃×#3304	2
C₁₃×#3297	2
C₁₃×#3296	2
C₁₃×#3295	2
C₁₃×#3294	2
C₁₃×#3233	2
C₁₃×#3228	2
C₁₃×#3191	2
C₁₃×#3188	2
C₁₃×#3106	2
C₁₃×#3102	2
C₁₃×#3091	2
C₂×C₁₃×#482	2
C₁₃×#2972	2
#61702	13

Subgroups — C13×#61702 #15748041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61702 #15748041