Subgroups — C₁₃×#62021 #15748360

Order 3328.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3298	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3263	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₁₃×#563	—	2	1	no	—
25	C₁₃×#562	—	2	1	no	—
26	C₁₃×#559	—	2	1	no	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
28	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	C₂²	1	2	yes	—
30	C₁₃×#554	—	2	1	no	—
31	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#551	—	2	2	no	—
33	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
34	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	C₁₃×#548	C₂²	1	2	yes	—
36	C₁₃×#548	C₂²	1	2	yes	—
37	C₁₃×#547	—	2	2	no	—
38	C₁₃×#547	C₂²	1	2	yes	—
39	C₁₃×#546	C₂²	1	2	yes	—
40	C₁₃×#543	—	2	1	no	—
41	C₁₃×#542	—	2	2	no	—
42	C₁₃×#542	—	2	2	no	—
43	C₁₃×#542	C₂²	1	2	yes	—
44	C₁₃×#542	C₂²	1	2	yes	complemented
45	C₁₃×#538	—	2	1	no	—
46	C₁₃×#536	C₂²	1	2	yes	—
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#532	—	2	1	no	—
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	1	no	—
51	C₁₃×#529	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
53	C₁₃×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#497	C₂²	1	2	yes	complemented
56	C₁₃×#496	C₂²	1	2	yes	—
57	C₁₃×#495	C₂²	1	2	yes	—
58	C₁₃×#489	C₂²	1	2	yes	—
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#487	C₂²	1	2	yes	complemented
61	C₁₃×#483	C₂²	1	2	yes	—
62	C₁₃×#483	C₂²	1	2	yes	complemented
63	C₁₃×#481	C₂²	1	2	yes	—
64	C₁₃×#476	C₂²	1	2	yes	—
65	C₁₃×#476	C₂²	1	2	yes	complemented
66	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#475	C₂²	1	2	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#470	C₂²	1	2	yes	complemented
71	C₁₃×#469	C₂²	1	2	yes	—
72	C₁₃×#465	C₂²	1	2	yes	—
73	C₁₃×#465	C₂²	1	2	yes	—
74	C₁₃×#465	C₂²	1	2	yes	—
75	C₁₃×#465	C₂²	1	2	yes	complemented
76	C₁₃×#464	C₂²	1	2	yes	—
77	C₁₃×#464	C₂²	1	2	yes	—
78	C₁₃×#464	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	—
80	C₁₃×#464	C₂²	1	2	yes	—
81	C₁₃×#464	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	—
83	C₁₃×#463	C₂²	1	2	yes	—
84	C₁₃×#463	C₂²	1	2	yes	—
85	C₁₃×#463	C₂²	1	2	yes	—
86	C₁₃×#462	C₂²	1	2	yes	complemented
87	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#461	C₂²	1	2	yes	complemented
90	C₁₃×#461	C₂²	1	2	yes	complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#452	C₂²	1	2	yes	—
93	C₁₃×#452	C₂²	1	2	yes	complemented
94	C₁₃×#451	C₂²	1	2	yes	—
95	C₁₃×#451	C₂²	1	2	yes	complemented
96	C₁₃×#449	C₂²	1	2	yes	—
97	C₁₃×#449	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	2	yes	—
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#447	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#442	C₂²	1	2	yes	—
103	C₁₃×#441	C₂²	1	2	yes	complemented
104	C₁₃×#441	C₂²	1	2	yes	complemented
105	C₁₃×#441	C₂²	1	2	yes	complemented
106	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
107	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
108	C₁₃×#435	C₂²	1	2	yes	—
109	C₁₃×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₁₃	C₂²	1	2	yes	—
111	C₁₃×#433	C₂²	1	2	yes	complemented
112	C₁₃×#432	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₁₃×#417	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
117	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
118	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	2	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂×C₁₃×#41	C₂³	1	2	yes	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×#137	—	4	4	no	—
128	C₁₃×#135	—	4	4	no	—
129	C₂×C₁₃×Q₁₆	—	4	2	no	—
130	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×SD₁₆	—	4	2	no	—
135	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
136	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
137	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×D₈	C₂³	1	2	yes	—
142	C₂×C₁₃×D₈	C₂³	1	2	yes	—
143	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
144	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
147	C₁₃×C₄⋊Q₈	—	2	1	no	—
148	C₁₃×C₄⋊Q₈	—	2	2	no	—
149	C₁₃×C₄⋊Q₈	—	2	2	no	—
150	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×#127	—	2	1	no	—
156	C₁₃×#127	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
162	C₁₃×#125	—	2	1	no	—
163	C₁₃×#125	—	2	1	no	—
164	C₁₃×#125	D₄	1	1	yes	characteristic
165	C₁₃×#124	—	2	1	no	—
166	C₁₃×#124	—	2	2	no	—
167	C₁₃×#124	—	2	2	no	—
168	C₁₃×#124	—	2	2	no	—
169	C₁₃×#124	—	2	2	no	—
170	C₁₃×#124	—	2	1	no	—
171	C₁₃×#124	—	2	1	no	—
172	C₁₃×#124	—	2	1	no	—
173	C₁₃×#124	D₄	1	1	yes	characteristic
174	C₁₃×#124	C₂³	1	2	yes	—
175	C₁₃×#124	C₂³	1	2	yes	—
176	C₁₃×#124	C₂³	1	2	yes	—
177	C₁₃×#124	C₂³	1	2	yes	—
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×#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	2	yes	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	D₄	1	1	yes	characteristic
209	C₁₃×#121	C₂³	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₁₃×#120	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₁₃	—	2	1	no	—
226	C₄×D₄×C₁₃	—	2	2	no	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	C₂³	1	2	yes	—
235	C₄×D₄×C₁₃	C₂³	1	2	yes	—
236	C₄×D₄×C₁₃	C₂³	1	2	yes	—
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₁₃×#117	—	2	1	no	—
240	C₁₃×#117	—	2	2	no	—
241	C₁₃×#117	—	2	2	no	—
242	C₁₃×#117	C₂³	1	2	yes	—
243	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²×C₁₃	—	2	1	no	—
251	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
252	C₁₃×#106	C₂³	1	2	yes	—
253	C₁₃×#106	C₂³	1	2	yes	—
254	C₁₃×#106	C₂³	1	2	yes	—
255	C₁₃×#106	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×#102	C₂³	1	2	yes	—
275	C₁₃×#102	C₂³	1	2	yes	—
276	C₁₃×#102	C₂³	1	2	yes	—
277	C₁₃×#102	C₂³	1	2	yes	—
278	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₁₃×#97	C₂³	1	2	yes	—
282	C₁₃×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₁₃	C₂³	1	2	yes	—
284	#62021	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂⁴×C₁₃	—	2	1	no	—
286	C₁₃×#41	—	2	4	no	—
287	C₁₃×#41	—	4	2	no	—
288	C₁₃×#41	—	4	2	no	—
289	C₁₃×#41	—	4	2	no	—
290	C₁₃×#41	—	8	2	no	—
291	C₁₃×#41	—	8	4	no	—
292	C₂×Q₈×C₁₃	—	2	1	no	—
293	C₂×Q₈×C₁₃	—	2	1	no	—
294	C₂×Q₈×C₁₃	—	2	2	no	—
295	C₂×Q₈×C₁₃	—	2	1	no	—
296	C₂×Q₈×C₁₃	—	2	2	no	—
297	C₂×Q₈×C₁₃	—	2	1	no	—
298	C₂×Q₈×C₁₃	—	2	2	no	—
299	C₂×Q₈×C₁₃	—	4	1	no	—
300	C₂×Q₈×C₁₃	—	4	1	no	—
301	C₂×Q₈×C₁₃	—	4	2	no	—
302	C₂×Q₈×C₁₃	—	4	1	no	—
303	C₂×Q₈×C₁₃	—	4	2	no	—
304	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
306	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂×D₄×C₁₃	—	2	2	no	—
310	C₂×D₄×C₁₃	—	2	2	no	—
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	—	2	1	no	—
315	C₂×D₄×C₁₃	—	2	1	no	—
316	C₂×D₄×C₁₃	—	2	1	no	—
317	C₂×D₄×C₁₃	—	4	1	no	—
318	C₂×D₄×C₁₃	—	4	1	no	—
319	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
322	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₁₃	—	2	1	no	—
324	C₂²×C₄×C₁₃	—	2	1	no	—
325	C₂²×C₄×C₁₃	—	2	1	no	—
326	C₂²×C₄×C₁₃	—	2	2	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	2	no	—
329	C₂²×C₄×C₁₃	—	2	2	no	—
330	C₂²×C₄×C₁₃	—	2	2	no	—
331	C₂²×C₄×C₁₃	—	2	2	no	—
332	C₂²×C₄×C₁₃	—	2	2	no	—
333	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
337	C₁₃×Q₁₆	—	2	4	no	—
338	C₁₃×Q₁₆	—	2	4	no	—
339	C₁₃×Q₁₆	—	4	2	no	—
340	C₁₃×Q₁₆	—	4	2	no	—
341	C₁₃×SD₁₆	—	2	4	no	—
342	C₁₃×SD₁₆	—	4	2	no	—
343	C₁₃×SD₁₆	—	4	2	no	—
344	C₁₃×SD₁₆	—	4	2	no	—
345	C₁₃×SD₁₆	—	4	2	no	—
346	C₁₃×SD₁₆	—	4	2	no	—
347	C₁₃×D₈	—	4	2	no	—
348	C₁₃×D₈	—	4	2	no	—
349	C₁₃×M₁₆	—	4	2	no	—
350	C₂×C₈×C₁₃	—	4	1	no	—
351	C₂×C₈×C₁₃	—	4	1	no	—
352	C₂×C₈×C₁₃	—	4	2	no	—
353	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	1	no	—
361	C₁₃×C₄⋊C₄	—	2	1	no	—
362	C₁₃×C₄⋊C₄	—	2	1	no	—
363	C₁₃×C₄⋊C₄	—	2	1	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	1	no	—
366	C₁₃×C₄⋊C₄	—	2	1	no	—
367	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
377	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
378	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
382	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
383	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
384	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
403	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
405	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
406	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
407	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
408	C₄²×C₁₃	—	2	1	no	—
409	C₄²×C₁₃	—	2	1	no	—
410	C₄²×C₁₃	—	2	1	no	—
411	C₄²×C₁₃	—	2	1	no	—
412	C₄²×C₁₃	—	2	2	no	—
413	C₄²×C₁₃	—	2	2	no	—
414	C₄²×C₁₃	—	2	2	no	—
415	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₁₃	C₂⁴	1	2	yes	—
418	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
419	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
420	#3561	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#3401	C₂×C₁₃	1	2	yes	complemented
423	#3369	C₂×C₁₃	1	2	yes	complemented
424	#3316	C₂×C₁₃	1	2	yes	complemented
425	#3306	C₂×C₁₃	1	2	yes	complemented
426	#3298	C₂×C₁₃	1	2	yes	complemented
427	#3282	C₂×C₁₃	1	2	yes	complemented
428	#3271	C₂×C₁₃	1	2	yes	complemented
429	#3270	C₂×C₁₃	1	2	yes	complemented
430	#3263	C₂×C₁₃	1	2	yes	complemented
431	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
432	#3225	C₂×C₁₃	1	2	yes	complemented
433	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
434	#3125	C₂×C₁₃	1	2	yes	complemented
435	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
436	#3046	C₂×C₁₃	1	2	yes	complemented
437	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
438	#2992	C₂×C₁₃	1	1	yes	characteristic, complemented
439	C₂³×C₁₃	—	2	2	no	—
440	C₂³×C₁₃	—	2	2	no	—
441	C₂³×C₁₃	—	4	2	no	—
442	C₂³×C₁₃	—	8	1	no	—
443	C₂³×C₁₃	—	8	1	no	—
444	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₁₃	—	2	1	no	—
447	Q₈×C₁₃	—	2	2	no	—
448	Q₈×C₁₃	—	2	1	no	—
449	Q₈×C₁₃	—	2	2	no	—
450	Q₈×C₁₃	—	2	2	no	—
451	Q₈×C₁₃	—	2	1	no	—
452	Q₈×C₁₃	—	2	2	no	—
453	Q₈×C₁₃	—	4	1	no	—
454	Q₈×C₁₃	—	4	2	no	—
455	Q₈×C₁₃	—	8	1	no	—
456	Q₈×C₁₃	—	8	2	no	—
457	Q₈×C₁₃	—	8	1	no	—
458	Q₈×C₁₃	—	8	1	no	—
459	Q₈×C₁₃	—	8	2	no	—
460	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
461	D₄×C₁₃	—	2	4	no	—
462	D₄×C₁₃	—	2	2	no	—
463	D₄×C₁₃	—	2	2	no	—
464	D₄×C₁₃	—	2	2	no	—
465	D₄×C₁₃	—	2	2	no	—
466	D₄×C₁₃	—	4	1	no	—
467	D₄×C₁₃	—	4	4	no	—
468	D₄×C₁₃	—	4	2	no	—
469	D₄×C₁₃	—	4	4	no	—
470	D₄×C₁₃	—	8	1	no	—
471	D₄×C₁₃	—	8	1	no	—
472	D₄×C₁₃	—	8	2	no	—
473	D₄×C₁₃	—	8	2	no	—
474	D₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	—	2	2	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	2	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	1	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	2	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	4	1	no	—
489	C₂×C₄×C₁₃	—	4	4	no	—
490	C₂×C₄×C₁₃	—	4	2	no	—
491	C₂×C₄×C₁₃	—	4	2	no	—
492	C₂×C₄×C₁₃	—	8	2	no	—
493	C₂×C₄×C₁₃	—	8	2	no	—
494	C₂×C₄×C₁₃	—	8	2	no	—
495	C₂×C₄×C₁₃	—	8	2	no	—
496	C₂×C₄×C₁₃	—	8	2	no	—
497	C₂×C₄×C₁₃	—	8	1	no	—
498	C₂×C₄×C₁₃	—	8	2	no	—
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	2	yes	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
508	C₈×C₁₃	—	2	2	no	—
509	C₈×C₁₃	—	2	2	no	—
510	C₈×C₁₃	—	2	2	no	—
511	C₈×C₁₃	—	2	2	no	—
512	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
513	C₂×#135	C₂²×C₁₃	1	2	yes	—
514	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
515	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
516	#563	—	2	1	no	—
517	#562	—	2	1	no	—
518	#559	—	2	1	no	—
519	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#556	C₂²×C₁₃	1	2	yes	—
522	#554	—	2	1	no	—
523	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#551	—	2	2	no	—
525	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
527	#548	C₂²×C₁₃	1	2	yes	—
528	#548	C₂²×C₁₃	1	2	yes	—
529	#547	—	2	2	no	—
530	#547	C₂²×C₁₃	1	2	yes	—
531	#546	C₂²×C₁₃	1	2	yes	—
532	#543	—	2	1	no	—
533	#542	—	2	2	no	—
534	#542	—	2	2	no	—
535	#542	C₂²×C₁₃	1	2	yes	—
536	#542	C₂²×C₁₃	1	2	yes	complemented
537	#538	—	2	1	no	—
538	#536	C₂²×C₁₃	1	2	yes	—
539	#533	C₂²×C₁₃	1	1	yes	characteristic
540	#532	—	2	1	no	—
541	#532	C₂²×C₁₃	1	1	yes	characteristic
542	#529	—	2	1	no	—
543	#529	C₂²×C₁₃	1	1	yes	characteristic
544	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
545	#520	C₂²×C₁₃	1	2	yes	complemented
546	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
547	#497	C₂²×C₁₃	1	2	yes	complemented
548	#496	C₂²×C₁₃	1	2	yes	—
549	#495	C₂²×C₁₃	1	2	yes	—
550	#489	C₂²×C₁₃	1	2	yes	—
551	#489	C₂²×C₁₃	1	2	yes	—
552	#487	C₂²×C₁₃	1	2	yes	complemented
553	#483	C₂²×C₁₃	1	2	yes	—
554	#483	C₂²×C₁₃	1	2	yes	complemented
555	#481	C₂²×C₁₃	1	2	yes	—
556	#476	C₂²×C₁₃	1	2	yes	—
557	#476	C₂²×C₁₃	1	2	yes	complemented
558	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
559	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#475	C₂²×C₁₃	1	2	yes	complemented
561	#475	C₂²×C₁₃	1	2	yes	complemented
562	#470	C₂²×C₁₃	1	2	yes	complemented
563	#469	C₂²×C₁₃	1	2	yes	—
564	#465	C₂²×C₁₃	1	2	yes	—
565	#465	C₂²×C₁₃	1	2	yes	—
566	#465	C₂²×C₁₃	1	2	yes	—
567	#465	C₂²×C₁₃	1	2	yes	complemented
568	#464	C₂²×C₁₃	1	2	yes	—
569	#464	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	complemented
574	#463	C₂²×C₁₃	1	2	yes	—
575	#463	C₂²×C₁₃	1	2	yes	—
576	#463	C₂²×C₁₃	1	2	yes	—
577	#463	C₂²×C₁₃	1	2	yes	—
578	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
579	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
580	#462	C₂²×C₁₃	1	2	yes	complemented
581	#461	C₂²×C₁₃	1	2	yes	complemented
582	#461	C₂²×C₁₃	1	2	yes	complemented
583	#460	C₂²×C₁₃	1	2	yes	complemented
584	#452	C₂²×C₁₃	1	2	yes	—
585	#452	C₂²×C₁₃	1	2	yes	complemented
586	#451	C₂²×C₁₃	1	2	yes	—
587	#451	C₂²×C₁₃	1	2	yes	complemented
588	#449	C₂²×C₁₃	1	2	yes	—
589	#449	C₂²×C₁₃	1	2	yes	—
590	#448	C₂²×C₁₃	1	2	yes	—
591	#448	C₂²×C₁₃	1	2	yes	complemented
592	#447	C₂²×C₁₃	1	2	yes	—
593	#446	C₂²×C₁₃	1	2	yes	complemented
594	#442	C₂²×C₁₃	1	2	yes	—
595	#441	C₂²×C₁₃	1	2	yes	complemented
596	#441	C₂²×C₁₃	1	2	yes	complemented
597	#441	C₂²×C₁₃	1	2	yes	complemented
598	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
599	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
600	#435	C₂²×C₁₃	1	2	yes	—
601	#435	C₂²×C₁₃	1	2	yes	complemented
602	C₈×D₄	C₂²×C₁₃	1	2	yes	—
603	#433	C₂²×C₁₃	1	2	yes	complemented
604	#432	C₂²×C₁₃	1	1	yes	characteristic
605	#424	C₂²×C₁₃	1	2	yes	complemented
606	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
607	#417	C₂²×C₁₃	1	2	yes	—
608	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
609	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
610	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
611	C₂²×C₁₃	—	2	1	no	—
612	C₂²×C₁₃	—	2	1	no	—
613	C₂²×C₁₃	—	2	2	no	—
614	C₂²×C₁₃	—	2	2	no	—
615	C₂²×C₁₃	—	2	2	no	—
616	C₂²×C₁₃	—	4	2	no	—
617	C₂²×C₁₃	—	4	2	no	—
618	C₂²×C₁₃	—	4	2	no	—
619	C₂²×C₁₃	—	4	2	no	—
620	C₂²×C₁₃	—	4	2	no	—
621	C₂²×C₁₃	—	4	2	no	—
622	C₂²×C₁₃	—	16	2	no	—
623	C₂²×C₁₃	#577	1	2	yes	—
624	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
625	C₄×C₁₃	—	2	1	no	—
626	C₄×C₁₃	—	2	1	no	—
627	C₄×C₁₃	—	2	2	no	—
628	C₄×C₁₃	—	2	2	no	—
629	C₄×C₁₃	—	2	1	no	—
630	C₄×C₁₃	—	2	2	no	—
631	C₄×C₁₃	—	2	1	no	—
632	C₄×C₁₃	—	2	1	no	—
633	C₄×C₁₃	—	2	2	no	—
634	C₄×C₁₃	—	4	2	no	—
635	C₄×C₁₃	—	4	1	no	—
636	C₄×C₁₃	—	4	2	no	—
637	C₄×C₁₃	—	4	2	no	—
638	C₄×C₁₃	—	4	1	no	—
639	C₄×C₁₃	—	4	1	no	—
640	C₄×C₁₃	—	4	2	no	—
641	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
642	C₄×C₁₃	#585	1	1	yes	characteristic
643	C₂×#41	—	2	2	no	—
644	C₂×#41	—	2	1	no	—
645	C₂×#41	C₂³×C₁₃	1	2	yes	—
646	C₂×#41	C₂³×C₁₃	1	2	yes	—
647	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
649	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
650	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
651	#137	—	4	4	no	—
652	#135	—	4	4	no	—
653	C₂×Q₁₆	—	4	2	no	—
654	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
658	C₂×SD₁₆	—	4	2	no	—
659	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
663	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
664	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
665	C₂×D₈	C₂³×C₁₃	1	2	yes	—
666	C₂×D₈	C₂³×C₁₃	1	2	yes	—
667	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
668	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
669	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
670	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
671	C₄⋊Q₈	—	2	1	no	—
672	C₄⋊Q₈	—	2	2	no	—
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
675	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
676	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
677	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
679	#127	—	2	1	no	—
680	#127	C₂³×C₁₃	1	1	yes	characteristic
681	#126	—	2	2	no	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	D₄×C₁₃	1	2	yes	—
686	#125	—	2	1	no	—
687	#125	—	2	1	no	—
688	#125	D₄×C₁₃	1	1	yes	characteristic
689	#124	—	2	1	no	—
690	#124	—	2	2	no	—
691	#124	—	2	2	no	—
692	#124	—	2	2	no	—
693	#124	—	2	2	no	—
694	#124	—	2	1	no	—
695	#124	—	2	1	no	—
696	#124	—	2	1	no	—
697	#124	D₄×C₁₃	1	1	yes	characteristic
698	#124	C₂³×C₁₃	1	2	yes	—
699	#124	C₂³×C₁₃	1	2	yes	—
700	#124	C₂³×C₁₃	1	2	yes	—
701	#124	C₂³×C₁₃	1	2	yes	—
702	#123	—	2	2	no	—
703	#123	—	2	2	no	—
704	#123	—	2	2	no	—
705	#123	—	2	2	no	—
706	#123	—	2	2	no	—
707	#123	—	2	2	no	—
708	#123	—	2	2	no	—
709	#123	—	2	2	no	—
710	#123	D₄×C₁₃	1	2	yes	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
724	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
725	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
726	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	1	no	—
730	#121	—	2	2	no	—
731	#121	—	2	2	no	—
732	#121	D₄×C₁₃	1	1	yes	characteristic
733	#121	C₂³×C₁₃	1	2	yes	—
734	#121	C₂³×C₁₃	1	2	yes	—
735	#121	C₂³×C₁₃	1	2	yes	—
736	#120	—	2	2	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
742	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
746	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
747	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	1	no	—
758	C₄×D₄	C₂³×C₁₃	1	2	yes	—
759	C₄×D₄	C₂³×C₁₃	1	2	yes	—
760	C₄×D₄	C₂³×C₁₃	1	2	yes	—
761	C₄×D₄	C₂³×C₁₃	1	2	yes	—
762	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
763	#117	—	2	1	no	—
764	#117	—	2	2	no	—
765	#117	—	2	2	no	—
766	#117	C₂³×C₁₃	1	2	yes	—
767	C₂×C₄⋊C₄	—	2	1	no	—
768	C₂×C₄⋊C₄	—	2	2	no	—
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
771	C₂×C₂²⋊C₄	—	2	1	no	—
772	C₂×C₂²⋊C₄	—	2	1	no	—
773	C₂×C₂²⋊C₄	—	2	2	no	—
774	C₂×C₄²	—	2	1	no	—
775	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
776	#106	C₂³×C₁₃	1	2	yes	—
777	#106	C₂³×C₁₃	1	2	yes	—
778	#106	C₂³×C₁₃	1	2	yes	—
779	#106	C₂³×C₁₃	1	2	yes	—
780	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
781	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
782	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
784	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
785	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
786	#103	C₂³×C₁₃	1	2	yes	—
787	#103	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	2	yes	—
797	#102	C₂³×C₁₃	1	2	yes	—
798	#102	C₂³×C₁₃	1	2	yes	—
799	#102	C₂³×C₁₃	1	2	yes	—
800	#102	C₂³×C₁₃	1	2	yes	—
801	#102	C₂³×C₁₃	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
805	#97	C₂³×C₁₃	1	2	yes	—
806	#97	C₂³×C₁₃	1	2	yes	—
807	C₄×C₈	C₂³×C₁₃	1	2	yes	—
808	C₂×C₁₃	—	2	2	no	—
809	C₂×C₁₃	—	4	2	no	—
810	C₂×C₁₃	—	8	2	no	—
811	C₂×C₁₃	—	8	2	no	—
812	C₂×C₁₃	#3488	1	1	yes	characteristic
813	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
814	C₂×C₁₃	#3586	1	1	yes	characteristic
815	C₂⁴	—	2	1	no	—
816	#41	—	2	4	no	—
817	#41	—	4	2	no	—
818	#41	—	4	2	no	—
819	#41	—	4	2	no	—
820	#41	—	8	2	no	—
821	#41	—	8	4	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	2	1	no	—
826	C₂×Q₈	—	2	2	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	4	1	no	—
830	C₂×Q₈	—	4	1	no	—
831	C₂×Q₈	—	4	2	no	—
832	C₂×Q₈	—	4	1	no	—
833	C₂×Q₈	—	4	2	no	—
834	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
836	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
837	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	1	no	—
845	C₂×D₄	—	2	1	no	—
846	C₂×D₄	—	2	1	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	1	no	—
849	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
850	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
851	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
852	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
864	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
865	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
867	Q₁₆	—	2	4	no	—
868	Q₁₆	—	2	4	no	—
869	Q₁₆	—	4	2	no	—
870	Q₁₆	—	4	2	no	—
871	SD₁₆	—	2	4	no	—
872	SD₁₆	—	4	2	no	—
873	SD₁₆	—	4	2	no	—
874	SD₁₆	—	4	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	4	2	no	—
877	D₈	—	4	2	no	—
878	D₈	—	4	2	no	—
879	M₁₆	—	4	2	no	—
880	C₂×C₈	—	4	1	no	—
881	C₂×C₈	—	4	1	no	—
882	C₂×C₈	—	4	2	no	—
883	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
884	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
885	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
886	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	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	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
907	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
908	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
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	2	yes	—
912	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
914	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
934	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
935	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
936	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
938	C₄²	—	2	1	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
946	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
947	C₄²	C₂⁴×C₁₃	1	2	yes	—
948	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₁₃	#62021	1	1	yes	characteristic, direct product factor, Sylow
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	1	no	—
955	C₂³	—	8	1	no	—
956	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
957	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
958	Q₈	—	2	1	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	2	1	no	—
961	Q₈	—	2	2	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	4	1	no	—
966	Q₈	—	4	2	no	—
967	Q₈	—	8	2	no	—
968	Q₈	—	8	1	no	—
969	Q₈	—	8	1	no	—
970	Q₈	—	8	2	no	—
971	Q₈	—	8	1	no	—
972	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
973	D₄	—	2	4	no	—
974	D₄	—	2	2	no	—
975	D₄	—	2	2	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	2	no	—
978	D₄	—	4	1	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	2	no	—
981	D₄	—	4	4	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	1	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	2	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	4	1	no	—
1001	C₂×C₄	—	4	4	no	—
1002	C₂×C₄	—	4	2	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	8	2	no	—
1005	C₂×C₄	—	8	2	no	—
1006	C₂×C₄	—	8	2	no	—
1007	C₂×C₄	—	8	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	1	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1014	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1015	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1016	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1019	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1020	C₈	—	2	2	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	16	2	no	—
1036	C₂²	C₁₃×#577	1	2	yes	—
1037	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1055	C₄	C₁₃×#585	1	1	yes	characteristic
1056	C₂	—	2	2	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	8	2	no	—
1059	C₂	—	8	2	no	—
1060	C₂	C₁₃×#3488	1	1	yes	characteristic
1061	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1062	C₂	C₁₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3561	C₂	semidirect
2. C₁₃×#3522	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3316	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3298	C₂	semidirect
8. C₁₃×#3282	C₂	semidirect
9. C₁₃×#3271	C₂	semidirect
10. C₁₃×#3270	C₂	semidirect
11. C₁₃×#3263	C₂	semidirect
12. C₁₃×#3246	C₂	semidirect
13. C₁₃×#3225	C₂	semidirect
14. C₁₃×#3213	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3113	C₂	semidirect
17. C₁₃×#3046	C₂	semidirect
18. C₂×C₁₃×#464	C₂	semidirect
19. C₁₃×#2992	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
27. C₁₃×#559	C₂²	semidirect
28. Q₈²×C₁₃	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
44. C₁₃×#542	C₂²	semidirect
53. C₁₃×#520	C₂²	semidirect
55. C₁₃×#497	C₂²	semidirect
60. C₁₃×#487	C₂²	semidirect
62. C₁₃×#483	C₂²	semidirect
65. C₁₃×#476	C₂²	semidirect
66. C₁₃×#475	C₂²	semidirect
67. C₁₃×#475	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
69. C₁₃×#475	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
75. C₁₃×#465	C₂²	semidirect
81. C₁₃×#464	C₂²	semidirect
86. C₁₃×#462	C₂²	semidirect
87. C₁₃×#462	C₂²	semidirect
88. C₁₃×#462	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
93. C₁₃×#452	C₂²	semidirect
95. C₁₃×#451	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
103. C₁₃×#441	C₂²	semidirect
104. C₁₃×#441	C₂²	semidirect
105. C₁₃×#441	C₂²	semidirect
107. C₄×C₁₃×SD₁₆	C₂²	semidirect
109. C₁₃×#435	C₂²	semidirect
111. C₁₃×#433	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
117. C₂×C₁₃×#103	C₂²	semidirect
284. #62021	C₁₃	direct (N × H)
420. #3561	C₂×C₁₃	semidirect
421. #3522	C₂×C₁₃	semidirect
422. #3401	C₂×C₁₃	semidirect
423. #3369	C₂×C₁₃	semidirect
424. #3316	C₂×C₁₃	semidirect
425. #3306	C₂×C₁₃	semidirect
426. #3298	C₂×C₁₃	semidirect
427. #3282	C₂×C₁₃	semidirect
428. #3271	C₂×C₁₃	semidirect
429. #3270	C₂×C₁₃	semidirect
430. #3263	C₂×C₁₃	semidirect
431. #3246	C₂×C₁₃	semidirect
432. #3225	C₂×C₁₃	semidirect
433. #3213	C₂×C₁₃	semidirect
434. #3125	C₂×C₁₃	semidirect
435. #3113	C₂×C₁₃	semidirect
436. #3046	C₂×C₁₃	semidirect
437. C₂×#464	C₂×C₁₃	semidirect
438. #2992	C₂×C₁₃	semidirect
512. C₂×#137	C₂²×C₁₃	semidirect
519. #559	C₂²×C₁₃	semidirect
520. Q₈²	C₂²×C₁₃	semidirect
523. #554	C₂²×C₁₃	semidirect
525. #550	C₂²×C₁₃	semidirect
536. #542	C₂²×C₁₃	semidirect
545. #520	C₂²×C₁₃	semidirect
547. #497	C₂²×C₁₃	semidirect
552. #487	C₂²×C₁₃	semidirect
554. #483	C₂²×C₁₃	semidirect
557. #476	C₂²×C₁₃	semidirect
558. #475	C₂²×C₁₃	semidirect
559. #475	C₂²×C₁₃	semidirect
560. #475	C₂²×C₁₃	semidirect
561. #475	C₂²×C₁₃	semidirect
562. #470	C₂²×C₁₃	semidirect
567. #465	C₂²×C₁₃	semidirect
573. #464	C₂²×C₁₃	semidirect
578. #462	C₂²×C₁₃	semidirect
579. #462	C₂²×C₁₃	semidirect
580. #462	C₂²×C₁₃	semidirect
581. #461	C₂²×C₁₃	semidirect
582. #461	C₂²×C₁₃	semidirect
583. #460	C₂²×C₁₃	semidirect
585. #452	C₂²×C₁₃	semidirect
587. #451	C₂²×C₁₃	semidirect
591. #448	C₂²×C₁₃	semidirect
593. #446	C₂²×C₁₃	semidirect
595. #441	C₂²×C₁₃	semidirect
596. #441	C₂²×C₁₃	semidirect
597. #441	C₂²×C₁₃	semidirect
599. C₄×SD₁₆	C₂²×C₁₃	semidirect
601. #435	C₂²×C₁₃	semidirect
603. #433	C₂²×C₁₃	semidirect
605. #424	C₂²×C₁₃	semidirect
609. C₂×#103	C₂²×C₁₃	semidirect
950. C₁₃	#62021	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×#3561	2
C₁₃×#3522	2
C₁₃×#3401	2
C₁₃×#3369	2
C₁₃×#3316	2
C₁₃×#3306	2
C₁₃×#3298	2
C₁₃×#3282	2
C₁₃×#3271	2
C₁₃×#3270	2
C₁₃×#3263	2
C₁₃×#3246	2
C₁₃×#3225	2
C₁₃×#3213	2
C₁₃×#3125	2
C₁₃×#3113	2
C₁₃×#3046	2
C₂×C₁₃×#464	2
C₁₃×#2992	2
#62021	13

Subgroups — C13×#62021 #15748360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62021 #15748360