Subgroups — C₁₃×#61473 #15747812

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3516	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	2	yes	—
28	C₁₃×#556	—	2	2	no	—
29	C₁₃×#556	C₂²	1	2	yes	—
30	C₁₃×#554	—	2	2	no	—
31	C₁₃×#554	C₂²	1	2	yes	—
32	C₁₃×#553	—	2	2	no	—
33	C₁₃×#553	C₂²	1	2	yes	—
34	C₁₃×#552	—	2	2	no	—
35	C₁₃×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#548	C₂²	1	2	yes	—
38	C₁₃×#548	C₂²	1	2	yes	—
39	C₁₃×#542	—	2	2	no	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#541	—	2	2	no	—
42	C₁₃×#541	C₂²	1	2	yes	—
43	C₁₃×#529	—	2	2	no	—
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#529	C₂²	1	2	yes	—
46	C₁₃×#529	C₂²	1	1	yes	characteristic
47	C₁₃×#520	C₂²	1	2	yes	—
48	C₁₃×#519	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
50	C₁₃×#500	C₂²	1	1	yes	characteristic
51	C₁₃×#499	C₂²	1	1	yes	characteristic
52	C₁₃×#499	C₂²	1	1	yes	characteristic
53	C₁₃×#495	C₂²	1	1	yes	characteristic
54	C₁₃×#495	C₂²	1	1	yes	characteristic
55	C₁₃×#494	C₂²	1	1	yes	characteristic
56	C₁₃×#491	C₂²	1	2	yes	—
57	C₁₃×#489	C₂²	1	2	yes	—
58	C₁₃×#488	C₂²	1	2	yes	—
59	C₁₃×#485	C₂²	1	2	yes	—
60	C₁₃×#484	C₂²	1	2	yes	—
61	C₁₃×#484	C₂²	1	2	yes	—
62	C₁₃×#483	C₂²	1	2	yes	—
63	C₁₃×#482	C₂²	1	2	yes	—
64	C₁₃×#481	C₂²	1	2	yes	—
65	C₁₃×#479	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	2	yes	—
67	C₁₃×#479	C₂²	1	2	yes	—
68	C₁₃×#478	C₂²	1	2	yes	—
69	C₁₃×#477	C₂²	1	2	yes	—
70	C₁₃×#475	C₂²	1	2	yes	—
71	C₁₃×#470	C₂²	1	2	yes	—
72	C₁₃×#468	C₂²	1	2	yes	—
73	C₁₃×#467	C₂²	1	1	yes	characteristic
74	C₁₃×#467	C₂²	1	1	yes	characteristic
75	C₁₃×#467	C₂²	1	1	yes	characteristic
76	C₁₃×#467	C₂²	1	1	yes	characteristic
77	C₁₃×#466	C₂²	1	1	yes	characteristic
78	C₁₃×#466	C₂²	1	1	yes	characteristic
79	C₁₃×#465	C₂²	1	2	yes	—
80	C₁₃×#464	C₂²	1	2	yes	—
81	C₁₃×#464	C₂²	1	2	yes	—
82	C₁₃×#464	C₂²	1	2	yes	—
83	C₁₃×#464	C₂²	1	2	yes	—
84	C₁₃×#462	C₂²	1	2	yes	—
85	C₁₃×#461	C₂²	1	2	yes	—
86	C₁₃×#452	C₂²	1	2	yes	—
87	C₁₃×#452	C₂²	1	2	yes	—
88	C₁₃×#451	C₂²	1	2	yes	—
89	C₁₃×#451	C₂²	1	2	yes	—
90	C₁₃×#448	C₂²	1	2	yes	—
91	C₁₃×#448	C₂²	1	2	yes	—
92	C₁₃×#446	C₂²	1	1	yes	characteristic
93	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
94	C₁₃×#441	C₂²	1	2	yes	—
95	C₁₃×#441	C₂²	1	2	yes	—
96	C₁₃×#441	C₂²	1	2	yes	—
97	C₁₃×#440	C₂²	1	2	yes	—
98	C₁₃×#440	C₂²	1	2	yes	—
99	C₁₃×#440	C₂²	1	2	yes	—
100	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
102	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
104	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
107	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
111	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
113	C₁₃×#436	C₂²	1	1	yes	characteristic
114	C₁₃×#435	C₂²	1	1	yes	characteristic
115	C₁₃×#435	C₂²	1	1	yes	characteristic
116	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
119	C₁₃×#433	C₂²	1	1	yes	characteristic
120	C₁₃×#433	C₂²	1	1	yes	characteristic
121	C₁₃×#432	C₂²	1	1	yes	characteristic
122	C₁₃×#427	C₂²	1	1	yes	characteristic
123	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
124	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
125	C₁₃×#419	C₂²	1	2	yes	—
126	C₁₃×#417	C₂²	1	2	yes	—
127	C₂×C₁₃×#103	C₂²	1	2	yes	—
128	C₁₃×#405	C₂²	1	1	yes	characteristic
129	C₁₃×#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#41	C₂³	1	2	yes	—
132	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×#135	—	2	4	no	—
135	C₂×C₁₃×Q₁₆	—	2	4	no	—
136	C₂×C₁₃×Q₁₆	—	2	4	no	—
137	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊Q₈	—	2	2	no	—
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₁₃×#126	—	2	2	no	—
158	C₁₃×#126	—	2	2	no	—
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	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	D₄	1	1	yes	characteristic
166	C₁₃×#126	D₄	1	1	yes	characteristic
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	D₄	1	1	yes	characteristic
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#125	C₂³	1	2	yes	—
176	C₁₃×#124	—	2	2	no	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
187	C₁₃×#123	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	D₄	1	1	yes	characteristic
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	—	2	2	no	—
208	C₄×Q₈×C₁₃	—	2	2	no	—
209	C₄×Q₈×C₁₃	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	2	no	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₁₃	—	2	2	no	—
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	2	no	—
229	C₄×D₄×C₁₃	C₂³	1	2	yes	—
230	C₄×D₄×C₁₃	C₂³	1	2	yes	—
231	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
234	C₁₃×#117	—	2	2	no	—
235	C₁₃×#117	—	2	2	no	—
236	C₁₃×#117	—	2	2	no	—
237	C₁₃×#117	—	2	2	no	—
238	C₁₃×#117	—	2	2	no	—
239	C₁₃×#117	—	2	2	no	—
240	C₁₃×#117	C₂³	1	2	yes	—
241	C₁₃×#117	C₂³	1	1	yes	characteristic
242	C₁₃×#117	C₂³	1	1	yes	characteristic
243	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₄²×C₁₃	—	2	2	no	—
248	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
249	C₁₃×#107	C₂³	1	1	yes	characteristic
250	C₁₃×#107	C₂³	1	1	yes	characteristic
251	C₁₃×#107	C₂³	1	1	yes	characteristic
252	C₁₃×#107	C₂³	1	2	yes	—
253	C₁₃×#107	C₂³	1	2	yes	—
254	C₁₃×#107	C₂³	1	1	yes	characteristic
255	C₁₃×#107	C₂³	1	2	yes	—
256	C₁₃×#106	C₂³	1	2	yes	—
257	C₁₃×#106	C₂³	1	2	yes	—
258	C₁₃×#106	C₂³	1	2	yes	—
259	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₁₃×#103	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#103	C₂³	1	2	yes	—
269	C₁₃×#103	C₂³	1	2	yes	—
270	C₁₃×#103	C₂³	1	2	yes	—
271	C₁₃×#103	C₂³	1	2	yes	—
272	C₁₃×#103	C₂³	1	2	yes	—
273	C₁₃×#103	C₂³	1	2	yes	—
274	C₁₃×#103	C₂³	1	2	yes	—
275	C₁₃×#103	C₂³	1	2	yes	—
276	C₁₃×#103	C₂³	1	2	yes	—
277	C₁₃×#102	C₂³	1	2	yes	—
278	C₁₃×#102	C₂³	1	2	yes	—
279	C₁₃×#102	C₂³	1	2	yes	—
280	C₁₃×#102	C₂³	1	2	yes	—
281	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#97	C₂³	1	1	yes	characteristic
288	C₁₃×#97	C₂³	1	1	yes	characteristic
289	C₁₃×#97	C₂³	1	1	yes	characteristic
290	C₁₃×#97	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
297	#61473	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₁₃×#41	—	2	4	no	—
299	C₁₃×#41	—	4	2	no	—
300	C₂×Q₈×C₁₃	—	2	2	no	—
301	C₂×Q₈×C₁₃	—	2	2	no	—
302	C₂×Q₈×C₁₃	—	2	2	no	—
303	C₂×Q₈×C₁₃	—	2	4	no	—
304	C₂×Q₈×C₁₃	—	2	4	no	—
305	C₂×Q₈×C₁₃	—	4	2	no	—
306	C₂×Q₈×C₁₃	—	4	2	no	—
307	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
310	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×D₄×C₁₃	—	2	2	no	—
312	C₂×D₄×C₁₃	—	2	2	no	—
313	C₂×D₄×C₁₃	—	2	2	no	—
314	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	—	2	2	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	—	2	2	no	—
324	C₂²×C₄×C₁₃	—	2	2	no	—
325	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₁₃×Q₁₆	—	2	4	no	—
331	C₁₃×Q₁₆	—	2	4	no	—
332	C₁₃×Q₁₆	—	2	2	no	—
333	C₁₃×Q₁₆	—	2	2	no	—
334	C₁₃×Q₁₆	—	4	2	no	—
335	C₁₃×Q₁₆	#41	1	4	yes	—
336	C₁₃×SD₁₆	—	2	4	no	—
337	C₁₃×SD₁₆	—	4	2	no	—
338	C₁₃×SD₁₆	—	4	2	no	—
339	C₁₃×D₈	—	2	2	no	—
340	C₁₃×M₁₆	—	4	1	no	—
341	C₁₃×M₁₆	—	4	1	no	—
342	C₂×C₈×C₁₃	—	2	2	no	—
343	C₂×C₈×C₁₃	—	2	2	no	—
344	C₂×C₈×C₁₃	—	2	2	no	—
345	C₂×C₈×C₁₃	—	4	1	no	—
346	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	2	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	2	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
376	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
377	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
383	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
386	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
387	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
388	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
389	C₁₃×C₂²⋊C₄	—	2	2	no	—
390	C₁₃×C₂²⋊C₄	—	2	2	no	—
391	C₁₃×C₂²⋊C₄	—	2	2	no	—
392	C₁₃×C₂²⋊C₄	—	2	2	no	—
393	C₁₃×C₂²⋊C₄	—	2	2	no	—
394	C₁₃×C₂²⋊C₄	—	2	2	no	—
395	C₁₃×C₂²⋊C₄	—	2	2	no	—
396	C₁₃×C₂²⋊C₄	—	2	2	no	—
397	C₁₃×C₂²⋊C₄	—	2	2	no	—
398	C₁₃×C₂²⋊C₄	—	2	2	no	—
399	C₁₃×C₂²⋊C₄	—	2	2	no	—
400	C₁₃×C₂²⋊C₄	—	2	2	no	—
401	C₁₃×C₂²⋊C₄	—	2	2	no	—
402	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₄²×C₁₃	—	2	2	no	—
413	C₄²×C₁₃	—	2	2	no	—
414	C₄²×C₁₃	—	2	2	no	—
415	C₄²×C₁₃	—	2	2	no	—
416	C₄²×C₁₃	—	2	2	no	—
417	C₄²×C₁₃	—	2	2	no	—
418	C₄²×C₁₃	—	2	2	no	—
419	C₄²×C₁₃	—	2	2	no	—
420	C₄²×C₁₃	—	2	2	no	—
421	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
423	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
424	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
425	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
426	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
427	#3516	C₂×C₁₃	1	2	yes	complemented
428	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
429	#3383	C₂×C₁₃	1	1	yes	characteristic, complemented
430	#3377	C₂×C₁₃	1	2	yes	complemented
431	#3339	C₂×C₁₃	1	1	yes	characteristic, complemented
432	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
433	#3336	C₂×C₁₃	1	1	yes	characteristic, complemented
434	#3327	C₂×C₁₃	1	2	yes	complemented
435	#3320	C₂×C₁₃	1	2	yes	complemented
436	#3316	C₂×C₁₃	1	2	yes	complemented
437	D₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
438	#3285	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#3285	C₂×C₁₃	1	1	yes	characteristic, complemented
440	#3177	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#3175	C₂×C₁₃	1	1	yes	characteristic, complemented
442	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
443	#3121	C₂×C₁₃	1	2	yes	complemented
444	#3120	C₂×C₁₃	1	2	yes	complemented
445	#3117	C₂×C₁₃	1	2	yes	complemented
446	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#2951	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
449	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
450	C₂³×C₁₃	—	2	2	no	—
451	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₁₃	—	2	2	no	—
455	Q₈×C₁₃	—	2	2	no	—
456	Q₈×C₁₃	—	2	2	no	—
457	Q₈×C₁₃	—	2	2	no	—
458	Q₈×C₁₃	—	2	2	no	—
459	Q₈×C₁₃	—	4	1	no	—
460	Q₈×C₁₃	—	4	4	no	—
461	Q₈×C₁₃	—	4	4	no	—
462	Q₈×C₁₃	—	8	2	no	—
463	Q₈×C₁₃	C₂×#41	1	4	yes	—
464	D₄×C₁₃	—	2	2	no	—
465	D₄×C₁₃	—	2	2	no	—
466	D₄×C₁₃	—	2	2	no	—
467	D₄×C₁₃	—	2	2	no	—
468	D₄×C₁₃	—	4	1	no	—
469	D₄×C₁₃	—	4	4	no	—
470	D₄×C₁₃	—	4	4	no	—
471	D₄×C₁₃	—	8	2	no	—
472	C₂×C₄×C₁₃	—	2	2	no	—
473	C₂×C₄×C₁₃	—	2	2	no	—
474	C₂×C₄×C₁₃	—	2	1	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	1	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	2	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	2	2	no	—
484	C₂×C₄×C₁₃	—	2	2	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	4	1	no	—
487	C₂×C₄×C₁₃	—	4	4	no	—
488	C₂×C₄×C₁₃	—	4	4	no	—
489	C₂×C₄×C₁₃	—	4	4	no	—
490	C₂×C₄×C₁₃	—	8	2	no	—
491	C₂×C₄×C₁₃	—	8	2	no	—
492	C₂×C₄×C₁₃	—	8	2	no	—
493	C₂×C₄×C₁₃	—	8	2	no	—
494	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
506	C₈×C₁₃	—	2	1	no	—
507	C₈×C₁₃	—	2	1	no	—
508	C₈×C₁₃	—	2	1	no	—
509	C₈×C₁₃	—	2	1	no	—
510	C₈×C₁₃	—	2	1	no	—
511	C₈×C₁₃	—	2	1	no	—
512	C₈×C₁₃	—	2	1	no	—
513	C₈×C₁₃	C₂×#41	1	2	yes	—
514	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
515	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
516	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
517	#557	C₂²×C₁₃	1	2	yes	—
518	#556	—	2	2	no	—
519	#556	C₂²×C₁₃	1	2	yes	—
520	#554	—	2	2	no	—
521	#554	C₂²×C₁₃	1	2	yes	—
522	#553	—	2	2	no	—
523	#553	C₂²×C₁₃	1	2	yes	—
524	#552	—	2	2	no	—
525	#552	C₂²×C₁₃	1	2	yes	—
526	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
527	#548	C₂²×C₁₃	1	2	yes	—
528	#548	C₂²×C₁₃	1	2	yes	—
529	#542	—	2	2	no	—
530	#542	C₂²×C₁₃	1	2	yes	—
531	#541	—	2	2	no	—
532	#541	C₂²×C₁₃	1	2	yes	—
533	#529	—	2	2	no	—
534	#529	—	2	2	no	—
535	#529	C₂²×C₁₃	1	2	yes	—
536	#529	C₂²×C₁₃	1	1	yes	characteristic
537	#520	C₂²×C₁₃	1	2	yes	—
538	#519	C₂²×C₁₃	1	2	yes	—
539	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
540	#500	C₂²×C₁₃	1	1	yes	characteristic
541	#499	C₂²×C₁₃	1	1	yes	characteristic
542	#499	C₂²×C₁₃	1	1	yes	characteristic
543	#495	C₂²×C₁₃	1	1	yes	characteristic
544	#495	C₂²×C₁₃	1	1	yes	characteristic
545	#494	C₂²×C₁₃	1	1	yes	characteristic
546	#491	C₂²×C₁₃	1	2	yes	—
547	#489	C₂²×C₁₃	1	2	yes	—
548	#488	C₂²×C₁₃	1	2	yes	—
549	#485	C₂²×C₁₃	1	2	yes	—
550	#484	C₂²×C₁₃	1	2	yes	—
551	#484	C₂²×C₁₃	1	2	yes	—
552	#483	C₂²×C₁₃	1	2	yes	—
553	#482	C₂²×C₁₃	1	2	yes	—
554	#481	C₂²×C₁₃	1	2	yes	—
555	#479	C₂²×C₁₃	1	2	yes	—
556	#479	C₂²×C₁₃	1	2	yes	—
557	#479	C₂²×C₁₃	1	2	yes	—
558	#478	C₂²×C₁₃	1	2	yes	—
559	#477	C₂²×C₁₃	1	2	yes	—
560	#475	C₂²×C₁₃	1	2	yes	—
561	#470	C₂²×C₁₃	1	2	yes	—
562	#468	C₂²×C₁₃	1	2	yes	—
563	#467	C₂²×C₁₃	1	1	yes	characteristic
564	#467	C₂²×C₁₃	1	1	yes	characteristic
565	#467	C₂²×C₁₃	1	1	yes	characteristic
566	#467	C₂²×C₁₃	1	1	yes	characteristic
567	#466	C₂²×C₁₃	1	1	yes	characteristic
568	#466	C₂²×C₁₃	1	1	yes	characteristic
569	#465	C₂²×C₁₃	1	2	yes	—
570	#464	C₂²×C₁₃	1	2	yes	—
571	#464	C₂²×C₁₃	1	2	yes	—
572	#464	C₂²×C₁₃	1	2	yes	—
573	#464	C₂²×C₁₃	1	2	yes	—
574	#462	C₂²×C₁₃	1	2	yes	—
575	#461	C₂²×C₁₃	1	2	yes	—
576	#452	C₂²×C₁₃	1	2	yes	—
577	#452	C₂²×C₁₃	1	2	yes	—
578	#451	C₂²×C₁₃	1	2	yes	—
579	#451	C₂²×C₁₃	1	2	yes	—
580	#448	C₂²×C₁₃	1	2	yes	—
581	#448	C₂²×C₁₃	1	2	yes	—
582	#446	C₂²×C₁₃	1	1	yes	characteristic
583	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
584	#441	C₂²×C₁₃	1	2	yes	—
585	#441	C₂²×C₁₃	1	2	yes	—
586	#441	C₂²×C₁₃	1	2	yes	—
587	#440	C₂²×C₁₃	1	2	yes	—
588	#440	C₂²×C₁₃	1	2	yes	—
589	#440	C₂²×C₁₃	1	2	yes	—
590	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
591	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
592	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
593	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
594	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
595	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
596	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
597	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
598	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
599	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
600	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
601	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
602	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
603	#436	C₂²×C₁₃	1	1	yes	characteristic
604	#435	C₂²×C₁₃	1	1	yes	characteristic
605	#435	C₂²×C₁₃	1	1	yes	characteristic
606	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
607	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
608	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
609	#433	C₂²×C₁₃	1	1	yes	characteristic
610	#433	C₂²×C₁₃	1	1	yes	characteristic
611	#432	C₂²×C₁₃	1	1	yes	characteristic
612	#427	C₂²×C₁₃	1	1	yes	characteristic
613	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
614	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
615	#419	C₂²×C₁₃	1	2	yes	—
616	#417	C₂²×C₁₃	1	2	yes	—
617	C₂×#103	C₂²×C₁₃	1	2	yes	—
618	#405	C₂²×C₁₃	1	1	yes	characteristic
619	#405	C₂²×C₁₃	1	1	yes	characteristic
620	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
621	C₂²×C₁₃	—	2	1	no	—
622	C₂²×C₁₃	—	2	1	no	—
623	C₂²×C₁₃	—	2	1	no	—
624	C₂²×C₁₃	—	2	1	no	—
625	C₂²×C₁₃	—	2	1	no	—
626	C₂²×C₁₃	—	2	1	no	—
627	C₂²×C₁₃	—	2	1	no	—
628	C₂²×C₁₃	—	2	1	no	—
629	C₂²×C₁₃	—	4	2	no	—
630	C₂²×C₁₃	—	4	2	no	—
631	C₂²×C₁₃	—	4	2	no	—
632	C₂²×C₁₃	#578	1	2	yes	—
633	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₁₃	—	2	1	no	—
635	C₄×C₁₃	—	2	1	no	—
636	C₄×C₁₃	—	2	1	no	—
637	C₄×C₁₃	—	2	1	no	—
638	C₄×C₁₃	—	2	1	no	—
639	C₄×C₁₃	—	2	1	no	—
640	C₄×C₁₃	—	2	1	no	—
641	C₄×C₁₃	—	2	4	no	—
642	C₄×C₁₃	—	2	1	no	—
643	C₄×C₁₃	—	2	1	no	—
644	C₄×C₁₃	—	2	1	no	—
645	C₄×C₁₃	—	2	1	no	—
646	C₄×C₁₃	—	4	2	no	—
647	C₄×C₁₃	—	4	2	no	—
648	C₄×C₁₃	—	4	2	no	—
649	C₄×C₁₃	—	4	2	no	—
650	C₄×C₁₃	—	4	2	no	—
651	C₄×C₁₃	—	4	2	no	—
652	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
653	C₄×C₁₃	#585	1	1	yes	characteristic
654	C₂×#41	C₂³×C₁₃	1	2	yes	—
655	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
657	#135	—	2	4	no	—
658	C₂×Q₁₆	—	2	4	no	—
659	C₂×Q₁₆	—	2	4	no	—
660	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
661	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
662	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
664	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
665	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
666	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
667	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
668	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
669	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
672	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
673	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
679	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
680	#126	—	2	2	no	—
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#126	D₄×C₁₃	1	1	yes	characteristic
689	#126	D₄×C₁₃	1	1	yes	characteristic
690	#125	—	2	2	no	—
691	#125	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	D₄×C₁₃	1	1	yes	characteristic
697	#125	C₂³×C₁₃	1	2	yes	—
698	#125	C₂³×C₁₃	1	2	yes	—
699	#124	—	2	2	no	—
700	#124	—	2	2	no	—
701	#124	—	2	2	no	—
702	#124	D₄×C₁₃	1	1	yes	characteristic
703	#124	C₂³×C₁₃	1	2	yes	—
704	#124	C₂³×C₁₃	1	2	yes	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	D₄×C₁₃	1	1	yes	characteristic
710	#123	D₄×C₁₃	1	1	yes	characteristic
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	2	no	—
716	C₂²⋊Q₈	—	2	2	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
720	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
721	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
722	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
723	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	D₄×C₁₃	1	1	yes	characteristic
728	#121	C₂³×C₁₃	1	2	yes	—
729	#121	C₂³×C₁₃	1	2	yes	—
730	C₄×Q₈	—	2	2	no	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	2	no	—
735	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
736	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
737	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
738	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
739	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
740	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
741	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
742	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
743	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	2	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	2	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	C₂³×C₁₃	1	2	yes	—
753	C₄×D₄	C₂³×C₁₃	1	2	yes	—
754	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
755	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
756	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
757	#117	—	2	2	no	—
758	#117	—	2	2	no	—
759	#117	—	2	2	no	—
760	#117	—	2	2	no	—
761	#117	—	2	2	no	—
762	#117	—	2	2	no	—
763	#117	C₂³×C₁₃	1	2	yes	—
764	#117	C₂³×C₁₃	1	1	yes	characteristic
765	#117	C₂³×C₁₃	1	1	yes	characteristic
766	C₂×C₄⋊C₄	—	2	2	no	—
767	C₂×C₄⋊C₄	—	2	2	no	—
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
770	C₂×C₄²	—	2	2	no	—
771	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
772	#107	C₂³×C₁₃	1	1	yes	characteristic
773	#107	C₂³×C₁₃	1	1	yes	characteristic
774	#107	C₂³×C₁₃	1	1	yes	characteristic
775	#107	C₂³×C₁₃	1	2	yes	—
776	#107	C₂³×C₁₃	1	2	yes	—
777	#107	C₂³×C₁₃	1	1	yes	characteristic
778	#107	C₂³×C₁₃	1	2	yes	—
779	#106	C₂³×C₁₃	1	2	yes	—
780	#106	C₂³×C₁₃	1	2	yes	—
781	#106	C₂³×C₁₃	1	2	yes	—
782	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
785	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
788	#103	C₂³×C₁₃	1	2	yes	—
789	#103	C₂³×C₁₃	1	2	yes	—
790	#103	C₂³×C₁₃	1	2	yes	—
791	#103	C₂³×C₁₃	1	2	yes	—
792	#103	C₂³×C₁₃	1	2	yes	—
793	#103	C₂³×C₁₃	1	2	yes	—
794	#103	C₂³×C₁₃	1	2	yes	—
795	#103	C₂³×C₁₃	1	2	yes	—
796	#103	C₂³×C₁₃	1	2	yes	—
797	#103	C₂³×C₁₃	1	2	yes	—
798	#103	C₂³×C₁₃	1	2	yes	—
799	#103	C₂³×C₁₃	1	2	yes	—
800	#102	C₂³×C₁₃	1	2	yes	—
801	#102	C₂³×C₁₃	1	2	yes	—
802	#102	C₂³×C₁₃	1	2	yes	—
803	#102	C₂³×C₁₃	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
805	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
806	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
810	#97	C₂³×C₁₃	1	1	yes	characteristic
811	#97	C₂³×C₁₃	1	1	yes	characteristic
812	#97	C₂³×C₁₃	1	1	yes	characteristic
813	#97	C₂³×C₁₃	1	1	yes	characteristic
814	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
816	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
817	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
818	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
819	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
820	C₂×C₁₃	—	2	2	no	—
821	C₂×C₁₃	—	4	1	no	—
822	C₂×C₁₃	—	4	1	no	—
823	C₂×C₁₃	—	8	2	no	—
824	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
825	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
826	C₂×C₁₃	#3584	1	1	yes	characteristic
827	#41	—	2	4	no	—
828	#41	—	4	2	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	—	2	4	no	—
833	C₂×Q₈	—	2	4	no	—
834	C₂×Q₈	—	4	2	no	—
835	C₂×Q₈	—	4	2	no	—
836	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
837	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
838	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
839	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
844	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
845	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
859	Q₁₆	—	2	4	no	—
860	Q₁₆	—	2	4	no	—
861	Q₁₆	—	2	2	no	—
862	Q₁₆	—	2	2	no	—
863	Q₁₆	—	4	2	no	—
864	Q₁₆	C₁₃×#41	1	4	yes	—
865	SD₁₆	—	2	4	no	—
866	SD₁₆	—	4	2	no	—
867	SD₁₆	—	4	2	no	—
868	D₈	—	2	2	no	—
869	M₁₆	—	4	1	no	—
870	M₁₆	—	4	1	no	—
871	C₂×C₈	—	2	2	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	2	no	—
874	C₂×C₈	—	4	1	no	—
875	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
876	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
905	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
907	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
908	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
909	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
910	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
914	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
915	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
916	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
917	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
932	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
933	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
934	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
935	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
936	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
937	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
938	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
940	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
951	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
952	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
953	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
954	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
956	C₁₃	#61473	1	1	yes	characteristic, direct product factor, Sylow
957	C₂³	—	2	2	no	—
958	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
959	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
960	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
961	Q₈	—	2	2	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	2	no	—
966	Q₈	—	4	1	no	—
967	Q₈	—	4	4	no	—
968	Q₈	—	4	4	no	—
969	Q₈	—	8	2	no	—
970	Q₈	C₂×C₁₃×#41	1	4	yes	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	2	no	—
974	D₄	—	2	2	no	—
975	D₄	—	4	1	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	8	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	4	1	no	—
994	C₂×C₄	—	4	4	no	—
995	C₂×C₄	—	4	4	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	—	8	2	no	—
998	C₂×C₄	—	8	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	2	no	—
1001	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1005	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1008	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1009	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1010	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1011	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1012	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1013	C₈	—	2	1	no	—
1014	C₈	—	2	1	no	—
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	C₂×C₁₃×#41	1	2	yes	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	C₁₃×#578	1	2	yes	—
1033	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	4	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1053	C₄	C₁₃×#585	1	1	yes	characteristic
1054	C₂	—	2	2	no	—
1055	C₂	—	4	1	no	—
1056	C₂	—	4	1	no	—
1057	C₂	—	8	2	no	—
1058	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1059	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1060	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3516	C₂	semidirect
2. C₁₃×#3393	C₂	semidirect
3. C₁₃×#3383	C₂	semidirect
4. C₁₃×#3377	C₂	semidirect
5. C₁₃×#3339	C₂	semidirect
6. C₁₃×#3338	C₂	semidirect
7. C₁₃×#3336	C₂	semidirect
8. C₁₃×#3327	C₂	semidirect
9. C₁₃×#3320	C₂	semidirect
10. C₁₃×#3316	C₂	semidirect
11. D₄×C₁₃×Q₁₆	C₂	semidirect
12. C₁₃×#3285	C₂	semidirect
13. C₁₃×#3285	C₂	semidirect
14. C₁₃×#3177	C₂	semidirect
15. C₁₃×#3175	C₂	semidirect
16. C₁₃×#3168	C₂	semidirect
17. C₁₃×#3121	C₂	semidirect
18. C₁₃×#3120	C₂	semidirect
19. C₁₃×#3117	C₂	semidirect
20. C₁₃×#2966	C₂	semidirect
21. C₁₃×#2951	C₂	semidirect
22. C₁₃×#2950	C₂	semidirect
23. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
297. #61473	C₁₃	direct (N × H)
427. #3516	C₂×C₁₃	semidirect
428. #3393	C₂×C₁₃	semidirect
429. #3383	C₂×C₁₃	semidirect
430. #3377	C₂×C₁₃	semidirect
431. #3339	C₂×C₁₃	semidirect
432. #3338	C₂×C₁₃	semidirect
433. #3336	C₂×C₁₃	semidirect
434. #3327	C₂×C₁₃	semidirect
435. #3320	C₂×C₁₃	semidirect
436. #3316	C₂×C₁₃	semidirect
437. D₄×Q₁₆	C₂×C₁₃	semidirect
438. #3285	C₂×C₁₃	semidirect
439. #3285	C₂×C₁₃	semidirect
440. #3177	C₂×C₁₃	semidirect
441. #3175	C₂×C₁₃	semidirect
442. #3168	C₂×C₁₃	semidirect
443. #3121	C₂×C₁₃	semidirect
444. #3120	C₂×C₁₃	semidirect
445. #3117	C₂×C₁₃	semidirect
446. #2966	C₂×C₁₃	semidirect
447. #2951	C₂×C₁₃	semidirect
448. #2950	C₂×C₁₃	semidirect
449. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
956. C₁₃	#61473	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×#3516	2
C₁₃×#3393	2
C₁₃×#3383	2
C₁₃×#3377	2
C₁₃×#3339	2
C₁₃×#3338	2
C₁₃×#3336	2
C₁₃×#3327	2
C₁₃×#3320	2
C₁₃×#3316	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3285	2
C₁₃×#3177	2
C₁₃×#3175	2
C₁₃×#3168	2
C₁₃×#3121	2
C₁₃×#3120	2
C₁₃×#3117	2
C₁₃×#2966	2
C₁₃×#2951	2
C₁₃×#2950	2
C₂×C₄×C₁₃×Q₁₆	2
#61473	13

Subgroups — C13×#61473 #15747812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61473 #15747812