Subgroups — C₁₃×#61645 #15747984

Order 3328.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3327	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3326	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3221	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3197	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#137	C₂²	1	2	yes	—
23	C₂×C₁₃×#137	C₂²	1	2	yes	—
24	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
26	C₁₃×#560	—	2	2	no	—
27	C₁₃×#553	—	2	2	no	—
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#552	C₂²	1	2	yes	—
30	C₁₃×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₁₃	—	2	2	no	—
32	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#548	—	2	2	no	—
35	C₁₃×#548	C₂²	1	2	yes	—
36	C₁₃×#548	C₂²	1	2	yes	—
37	C₁₃×#547	C₂²	1	2	yes	—
38	C₁₃×#541	C₂²	1	1	yes	characteristic
39	C₁₃×#540	—	2	2	no	—
40	C₁₃×#540	C₂²	1	1	yes	characteristic
41	C₁₃×#539	—	2	2	no	—
42	C₁₃×#537	C₂²	1	2	yes	—
43	C₁₃×#536	—	2	2	no	—
44	C₁₃×#536	C₂²	1	1	yes	characteristic
45	C₁₃×#536	C₂²	1	1	yes	characteristic
46	C₁₃×#525	—	2	2	no	—
47	C₁₃×#525	C₂²	1	2	yes	—
48	C₁₃×#525	C₂²	1	1	yes	characteristic
49	C₁₃×#525	C₂²	1	1	yes	characteristic
50	C₁₃×#519	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#496	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#488	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#485	C₂²	1	2	yes	—
60	C₁₃×#485	C₂²	1	2	yes	—
61	C₁₃×#484	C₂²	1	2	yes	complemented
62	C₁₃×#483	C₂²	1	2	yes	complemented
63	C₁₃×#482	C₂²	1	2	yes	—
64	C₁₃×#482	C₂²	1	2	yes	—
65	C₁₃×#479	C₂²	1	2	yes	complemented
66	C₁₃×#479	C₂²	1	2	yes	complemented
67	C₁₃×#470	C₂²	1	2	yes	—
68	C₁₃×#470	C₂²	1	2	yes	complemented
69	C₁₃×#469	C₂²	1	2	yes	—
70	C₁₃×#468	C₂²	1	2	yes	—
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#468	C₂²	1	2	yes	complemented
73	C₁₃×#467	C₂²	1	2	yes	complemented
74	C₁₃×#465	C₂²	1	2	yes	complemented
75	C₁₃×#464	C₂²	1	2	yes	complemented
76	C₁₃×#463	C₂²	1	2	yes	complemented
77	C₁₃×#462	C₂²	1	2	yes	complemented
78	C₁₃×#462	C₂²	1	2	yes	complemented
79	C₁₃×#461	C₂²	1	2	yes	complemented
80	C₁₃×#460	C₂²	1	2	yes	complemented
81	C₁₃×#452	C₂²	1	2	yes	—
82	C₁₃×#452	C₂²	1	2	yes	—
83	C₁₃×#452	C₂²	1	2	yes	complemented
84	C₁₃×#452	C₂²	1	2	yes	complemented
85	C₁₃×#452	C₂²	1	2	yes	complemented
86	C₁₃×#451	C₂²	1	2	yes	—
87	C₁₃×#451	C₂²	1	2	yes	—
88	C₁₃×#451	C₂²	1	2	yes	—
89	C₁₃×#451	C₂²	1	2	yes	—
90	C₁₃×#451	C₂²	1	2	yes	complemented
91	C₁₃×#449	C₂²	1	2	yes	—
92	C₁₃×#449	C₂²	1	2	yes	—
93	C₁₃×#449	C₂²	1	2	yes	complemented
94	C₁₃×#448	C₂²	1	2	yes	—
95	C₁₃×#448	C₂²	1	2	yes	—
96	C₁₃×#448	C₂²	1	2	yes	—
97	C₁₃×#448	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	2	yes	complemented
99	C₁₃×#441	C₂²	1	2	yes	complemented
100	C₁₃×#440	C₂²	1	2	yes	complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
103	C₁₃×#436	C₂²	1	2	yes	—
104	C₁₃×#436	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	—
106	C₁₃×#435	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	1	yes	characteristic
108	C₁₃×#433	C₂²	1	1	yes	characteristic
109	C₁₃×#419	C₂²	1	2	yes	—
110	C₁₃×#419	C₂²	1	2	yes	—
111	C₁₃×#417	C₂²	1	2	yes	complemented
112	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
113	C₁₃×#408	C₂²	1	2	yes	—
114	C₁₃×#407	C₂²	1	2	yes	—
115	C₁₃×2₋¹⁺⁴	—	4	4	no	—
116	C₂×C₁₃×#41	—	2	2	no	—
117	C₂×C₁₃×#41	—	2	1	no	—
118	C₂×C₁₃×#41	C₂³	1	2	yes	—
119	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂×C₁₃×#41	C₂³	1	2	yes	—
122	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	—	2	1	no	—
124	C₂²×Q₈×C₁₃	—	2	1	no	—
125	C₂²×Q₈×C₁₃	—	2	2	no	—
126	C₂²×Q₈×C₁₃	—	4	4	no	—
127	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
129	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₁₃	—	2	1	no	—
133	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₁₃×#137	—	4	4	no	—
135	C₁₃×#137	—	4	4	no	—
136	C₁₃×#137	—	4	4	no	—
137	C₁₃×#135	—	4	4	no	—
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
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×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×D₈	C₂³	1	2	yes	—
150	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	—	2	1	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	—	2	2	no	—
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×#127	—	2	2	no	—
161	C₁₃×#127	C₂³	1	1	yes	characteristic
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#125	—	2	2	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
173	C₁₃×#124	C₂³	1	1	yes	characteristic
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	1	no	—
177	C₁₃×#123	—	2	2	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×#123	—	2	2	no	—
183	C₁₃×#123	D₄	1	2	yes	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
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	D₄	1	2	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×#121	—	2	2	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	D₄	1	2	yes	—
210	C₁₃×#121	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	2	yes	—
212	C₁₃×#121	C₂³	1	2	yes	—
213	C₁₃×#121	C₂³	1	2	yes	—
214	C₁₃×#120	—	2	1	no	—
215	C₁₃×#120	—	2	2	no	—
216	C₁₃×#120	D₄	1	2	yes	—
217	C₄×Q₈×C₁₃	—	2	2	no	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
221	C₄×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	—	2	2	no	—
230	C₄×D₄×C₁₃	C₂³	1	2	yes	—
231	C₄×D₄×C₁₃	C₂³	1	2	yes	—
232	C₄×D₄×C₁₃	C₂³	1	2	yes	—
233	C₁₃×#117	—	2	2	no	—
234	C₁₃×#117	—	2	2	no	—
235	C₁₃×#117	C₂³	1	2	yes	—
236	C₁₃×#117	C₂³	1	1	yes	characteristic
237	C₁₃×#117	C₂³	1	1	yes	characteristic
238	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#103	C₂³	1	2	yes	—
251	C₁₃×#103	C₂³	1	2	yes	—
252	C₁₃×#103	C₂³	1	2	yes	—
253	C₁₃×#103	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#103	C₂³	1	2	yes	—
258	C₁₃×#102	C₂³	1	2	yes	—
259	C₁₃×#102	C₂³	1	2	yes	—
260	C₁₃×#102	C₂³	1	2	yes	—
261	C₁₃×#102	C₂³	1	2	yes	—
262	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₁₃×#97	C₂³	1	1	yes	characteristic
269	C₁₃×#97	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
272	#61645	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₁₃×#41	—	2	4	no	—
275	C₁₃×#41	—	4	2	no	—
276	C₁₃×#41	—	4	2	no	—
277	C₁₃×#41	—	4	2	no	—
278	C₁₃×#41	—	4	8	no	—
279	C₁₃×#41	—	4	2	no	—
280	C₁₃×#41	—	4	2	no	—
281	C₁₃×#41	—	4	2	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	4	4	no	—
284	C₂×Q₈×C₁₃	—	2	4	no	—
285	C₂×Q₈×C₁₃	—	2	1	no	—
286	C₂×Q₈×C₁₃	—	2	2	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	4	no	—
291	C₂×Q₈×C₁₃	—	2	4	no	—
292	C₂×Q₈×C₁₃	—	2	4	no	—
293	C₂×Q₈×C₁₃	—	4	2	no	—
294	C₂×Q₈×C₁₃	—	4	2	no	—
295	C₂×Q₈×C₁₃	—	4	2	no	—
296	C₂×Q₈×C₁₃	—	4	2	no	—
297	C₂×Q₈×C₁₃	—	4	4	no	—
298	C₂×Q₈×C₁₃	—	4	8	no	—
299	C₂×Q₈×C₁₃	—	4	4	no	—
300	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
306	C₂×D₄×C₁₃	—	2	2	no	—
307	C₂×D₄×C₁₃	—	2	1	no	—
308	C₂×D₄×C₁₃	—	2	2	no	—
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	2	no	—
315	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
326	C₂²×C₄×C₁₃	—	2	2	no	—
327	C₂²×C₄×C₁₃	—	2	2	no	—
328	C₂²×C₄×C₁₃	—	2	1	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	—	4	2	no	—
333	C₂²×C₄×C₁₃	—	4	4	no	—
334	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
339	C₁₃×Q₁₆	—	2	4	no	—
340	C₁₃×Q₁₆	—	2	4	no	—
341	C₁₃×Q₁₆	—	4	2	no	—
342	C₁₃×Q₁₆	—	4	2	no	—
343	C₁₃×Q₁₆	—	4	2	no	—
344	C₁₃×SD₁₆	—	2	4	no	—
345	C₁₃×SD₁₆	—	2	4	no	—
346	C₁₃×SD₁₆	—	4	2	no	—
347	C₁₃×SD₁₆	—	4	2	no	—
348	C₁₃×SD₁₆	—	4	2	no	—
349	C₁₃×SD₁₆	—	4	2	no	—
350	C₁₃×D₈	—	4	2	no	—
351	C₁₃×M₁₆	—	4	2	no	—
352	C₁₃×M₁₆	—	4	2	no	—
353	C₁₃×M₁₆	—	4	2	no	—
354	C₂×C₈×C₁₃	—	4	2	no	—
355	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
357	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
358	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
375	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
379	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
396	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
397	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
398	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
400	C₄²×C₁₃	—	2	2	no	—
401	C₄²×C₁₃	—	2	2	no	—
402	C₄²×C₁₃	—	2	2	no	—
403	C₄²×C₁₃	—	2	2	no	—
404	C₄²×C₁₃	—	2	1	no	—
405	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
406	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
407	#3539	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3486	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3327	C₂×C₁₃	1	2	yes	complemented
410	#3326	C₂×C₁₃	1	2	yes	complemented
411	#3320	C₂×C₁₃	1	2	yes	complemented
412	#3312	C₂×C₁₃	1	2	yes	complemented
413	#3278	C₂×C₁₃	1	2	yes	complemented
414	#3276	C₂×C₁₃	1	2	yes	complemented
415	#3271	C₂×C₁₃	1	2	yes	complemented
416	#3269	C₂×C₁₃	1	2	yes	complemented
417	#3223	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3221	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3201	C₂×C₁₃	1	2	yes	complemented
420	#3197	C₂×C₁₃	1	2	yes	complemented
421	#3127	C₂×C₁₃	1	1	yes	characteristic, complemented
422	#3126	C₂×C₁₃	1	1	yes	characteristic, complemented
423	#3013	C₂×C₁₃	1	2	yes	complemented
424	#3004	C₂×C₁₃	1	2	yes	complemented
425	#2978	C₂×C₁₃	1	1	yes	characteristic, complemented
426	C₂³×C₁₃	—	2	1	no	—
427	C₂³×C₁₃	—	2	2	no	—
428	C₂³×C₁₃	—	4	1	no	—
429	C₂³×C₁₃	—	4	2	no	—
430	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
431	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
433	Q₈×C₁₃	—	2	4	no	—
434	Q₈×C₁₃	—	2	2	no	—
435	Q₈×C₁₃	—	2	2	no	—
436	Q₈×C₁₃	—	2	2	no	—
437	Q₈×C₁₃	—	2	2	no	—
438	Q₈×C₁₃	—	2	2	no	—
439	Q₈×C₁₃	—	2	2	no	—
440	Q₈×C₁₃	—	4	1	no	—
441	Q₈×C₁₃	—	4	4	no	—
442	Q₈×C₁₃	—	4	4	no	—
443	Q₈×C₁₃	—	4	4	no	—
444	Q₈×C₁₃	—	4	2	no	—
445	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
446	D₄×C₁₃	—	2	2	no	—
447	D₄×C₁₃	—	2	2	no	—
448	D₄×C₁₃	—	2	2	no	—
449	D₄×C₁₃	—	4	2	no	—
450	D₄×C₁₃	—	4	2	no	—
451	D₄×C₁₃	—	4	1	no	—
452	D₄×C₁₃	—	4	2	no	—
453	D₄×C₁₃	—	4	4	no	—
454	D₄×C₁₃	—	4	4	no	—
455	D₄×C₁₃	—	4	2	no	—
456	D₄×C₁₃	—	8	2	no	—
457	D₄×C₁₃	—	8	2	no	—
458	D₄×C₁₃	—	8	2	no	—
459	D₄×C₁₃	—	8	2	no	—
460	D₄×C₁₃	—	8	2	no	—
461	D₄×C₁₃	—	8	2	no	—
462	C₂×C₄×C₁₃	—	2	4	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	2	2	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	2	no	—
469	C₂×C₄×C₁₃	—	2	2	no	—
470	C₂×C₄×C₁₃	—	2	2	no	—
471	C₂×C₄×C₁₃	—	2	2	no	—
472	C₂×C₄×C₁₃	—	2	2	no	—
473	C₂×C₄×C₁₃	—	2	1	no	—
474	C₂×C₄×C₁₃	—	2	1	no	—
475	C₂×C₄×C₁₃	—	2	1	no	—
476	C₂×C₄×C₁₃	—	4	2	no	—
477	C₂×C₄×C₁₃	—	4	1	no	—
478	C₂×C₄×C₁₃	—	4	4	no	—
479	C₂×C₄×C₁₃	—	4	4	no	—
480	C₂×C₄×C₁₃	—	4	4	no	—
481	C₂×C₄×C₁₃	—	4	4	no	—
482	C₂×C₄×C₁₃	—	4	2	no	—
483	C₂×C₄×C₁₃	—	4	2	no	—
484	C₂×C₄×C₁₃	—	8	2	no	—
485	C₂×C₄×C₁₃	—	8	2	no	—
486	C₂×C₄×C₁₃	—	8	2	no	—
487	C₂×C₄×C₁₃	—	8	2	no	—
488	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
494	C₈×C₁₃	—	2	2	no	—
495	C₈×C₁₃	—	2	2	no	—
496	C₈×C₁₃	—	2	2	no	—
497	C₈×C₁₃	—	2	2	no	—
498	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
499	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×#137	C₂²×C₁₃	1	2	yes	—
501	C₂×#137	C₂²×C₁₃	1	2	yes	—
502	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
503	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
504	#560	—	2	2	no	—
505	#553	—	2	2	no	—
506	#553	C₂²×C₁₃	1	2	yes	—
507	#552	C₂²×C₁₃	1	2	yes	—
508	#550	C₂²×C₁₃	1	2	yes	—
509	D₄×Q₈	—	2	2	no	—
510	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
511	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
512	#548	—	2	2	no	—
513	#548	C₂²×C₁₃	1	2	yes	—
514	#548	C₂²×C₁₃	1	2	yes	—
515	#547	C₂²×C₁₃	1	2	yes	—
516	#541	C₂²×C₁₃	1	1	yes	characteristic
517	#540	—	2	2	no	—
518	#540	C₂²×C₁₃	1	1	yes	characteristic
519	#539	—	2	2	no	—
520	#537	C₂²×C₁₃	1	2	yes	—
521	#536	—	2	2	no	—
522	#536	C₂²×C₁₃	1	1	yes	characteristic
523	#536	C₂²×C₁₃	1	1	yes	characteristic
524	#525	—	2	2	no	—
525	#525	C₂²×C₁₃	1	1	yes	characteristic
526	#525	C₂²×C₁₃	1	2	yes	—
527	#525	C₂²×C₁₃	1	1	yes	characteristic
528	#519	C₂²×C₁₃	1	1	yes	characteristic
529	#497	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	#496	C₂²×C₁₃	1	1	yes	characteristic, complemented
531	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
534	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
536	#488	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	#485	C₂²×C₁₃	1	2	yes	—
538	#485	C₂²×C₁₃	1	2	yes	—
539	#484	C₂²×C₁₃	1	2	yes	complemented
540	#483	C₂²×C₁₃	1	2	yes	complemented
541	#482	C₂²×C₁₃	1	2	yes	—
542	#482	C₂²×C₁₃	1	2	yes	—
543	#479	C₂²×C₁₃	1	2	yes	complemented
544	#479	C₂²×C₁₃	1	2	yes	complemented
545	#470	C₂²×C₁₃	1	2	yes	—
546	#470	C₂²×C₁₃	1	2	yes	complemented
547	#469	C₂²×C₁₃	1	2	yes	—
548	#468	C₂²×C₁₃	1	2	yes	—
549	#468	C₂²×C₁₃	1	2	yes	—
550	#468	C₂²×C₁₃	1	2	yes	complemented
551	#467	C₂²×C₁₃	1	2	yes	complemented
552	#465	C₂²×C₁₃	1	2	yes	complemented
553	#464	C₂²×C₁₃	1	2	yes	complemented
554	#463	C₂²×C₁₃	1	2	yes	complemented
555	#462	C₂²×C₁₃	1	2	yes	complemented
556	#462	C₂²×C₁₃	1	2	yes	complemented
557	#461	C₂²×C₁₃	1	2	yes	complemented
558	#460	C₂²×C₁₃	1	2	yes	complemented
559	#452	C₂²×C₁₃	1	2	yes	—
560	#452	C₂²×C₁₃	1	2	yes	—
561	#452	C₂²×C₁₃	1	2	yes	complemented
562	#452	C₂²×C₁₃	1	2	yes	complemented
563	#452	C₂²×C₁₃	1	2	yes	complemented
564	#451	C₂²×C₁₃	1	2	yes	—
565	#451	C₂²×C₁₃	1	2	yes	—
566	#451	C₂²×C₁₃	1	2	yes	—
567	#451	C₂²×C₁₃	1	2	yes	—
568	#451	C₂²×C₁₃	1	2	yes	complemented
569	#449	C₂²×C₁₃	1	2	yes	—
570	#449	C₂²×C₁₃	1	2	yes	—
571	#449	C₂²×C₁₃	1	2	yes	complemented
572	#448	C₂²×C₁₃	1	2	yes	—
573	#448	C₂²×C₁₃	1	2	yes	—
574	#448	C₂²×C₁₃	1	2	yes	—
575	#448	C₂²×C₁₃	1	2	yes	—
576	#448	C₂²×C₁₃	1	2	yes	complemented
577	#441	C₂²×C₁₃	1	2	yes	complemented
578	#440	C₂²×C₁₃	1	2	yes	complemented
579	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
580	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
581	#436	C₂²×C₁₃	1	2	yes	—
582	#436	C₂²×C₁₃	1	2	yes	—
583	#435	C₂²×C₁₃	1	2	yes	—
584	#435	C₂²×C₁₃	1	2	yes	—
585	#433	C₂²×C₁₃	1	1	yes	characteristic
586	#433	C₂²×C₁₃	1	1	yes	characteristic
587	#419	C₂²×C₁₃	1	2	yes	—
588	#419	C₂²×C₁₃	1	2	yes	—
589	#417	C₂²×C₁₃	1	2	yes	complemented
590	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
591	#408	C₂²×C₁₃	1	2	yes	—
592	#407	C₂²×C₁₃	1	2	yes	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	2	2	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	2	2	no	—
597	C₂²×C₁₃	—	2	2	no	—
598	C₂²×C₁₃	—	2	1	no	—
599	C₂²×C₁₃	—	2	2	no	—
600	C₂²×C₁₃	—	2	2	no	—
601	C₂²×C₁₃	—	4	4	no	—
602	C₂²×C₁₃	—	4	2	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	2	no	—
605	C₂²×C₁₃	—	4	1	no	—
606	C₂²×C₁₃	—	4	2	no	—
607	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₁₃	—	2	2	no	—
609	C₄×C₁₃	—	2	2	no	—
610	C₄×C₁₃	—	2	4	no	—
611	C₄×C₁₃	—	2	1	no	—
612	C₄×C₁₃	—	2	2	no	—
613	C₄×C₁₃	—	2	2	no	—
614	C₄×C₁₃	—	4	2	no	—
615	C₄×C₁₃	—	4	2	no	—
616	C₄×C₁₃	—	4	2	no	—
617	C₄×C₁₃	—	4	1	no	—
618	C₄×C₁₃	—	4	1	no	—
619	C₄×C₁₃	—	4	1	no	—
620	C₄×C₁₃	—	4	2	no	—
621	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
622	2₋¹⁺⁴	—	4	4	no	—
623	C₂×#41	—	2	2	no	—
624	C₂×#41	—	2	1	no	—
625	C₂×#41	C₂³×C₁₃	1	2	yes	—
626	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×#41	C₂³×C₁₃	1	2	yes	—
628	C₂×#41	C₂³×C₁₃	1	2	yes	—
629	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
630	C₂²×Q₈	—	2	1	no	—
631	C₂²×Q₈	—	2	1	no	—
632	C₂²×Q₈	—	2	2	no	—
633	C₂²×Q₈	—	4	4	no	—
634	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
637	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
638	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₂³×C₄	—	2	1	no	—
640	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
641	#137	—	4	4	no	—
642	#137	—	4	4	no	—
643	#137	—	4	4	no	—
644	#135	—	4	4	no	—
645	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
646	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
647	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
648	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
649	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
650	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
651	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
652	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
653	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
654	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
655	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
656	C₂×D₈	C₂³×C₁₃	1	2	yes	—
657	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
658	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
659	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
660	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
661	C₄⋊Q₈	—	2	1	no	—
662	C₄⋊Q₈	—	2	2	no	—
663	C₄⋊Q₈	—	2	2	no	—
664	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
665	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
666	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
667	#127	—	2	2	no	—
668	#127	C₂³×C₁₃	1	1	yes	characteristic
669	#126	—	2	2	no	—
670	#126	—	2	2	no	—
671	#126	—	2	2	no	—
672	#125	—	2	2	no	—
673	#125	—	2	2	no	—
674	#125	C₂³×C₁₃	1	1	yes	characteristic
675	#125	C₂³×C₁₃	1	1	yes	characteristic
676	#124	—	2	1	no	—
677	#124	—	2	2	no	—
678	#124	—	2	2	no	—
679	#124	C₂³×C₁₃	1	1	yes	characteristic
680	#124	C₂³×C₁₃	1	1	yes	characteristic
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	1	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	D₄×C₁₃	1	2	yes	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
701	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
704	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
705	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	2	no	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	D₄×C₁₃	1	2	yes	—
717	#121	C₂³×C₁₃	1	2	yes	—
718	#121	C₂³×C₁₃	1	2	yes	—
719	#121	C₂³×C₁₃	1	2	yes	—
720	#121	C₂³×C₁₃	1	2	yes	—
721	#120	—	2	1	no	—
722	#120	—	2	2	no	—
723	#120	D₄×C₁₃	1	2	yes	—
724	C₄×Q₈	—	2	2	no	—
725	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
726	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
727	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
728	C₄×D₄	—	2	2	no	—
729	C₄×D₄	—	2	2	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	C₂³×C₁₃	1	2	yes	—
738	C₄×D₄	C₂³×C₁₃	1	2	yes	—
739	C₄×D₄	C₂³×C₁₃	1	2	yes	—
740	#117	—	2	2	no	—
741	#117	—	2	2	no	—
742	#117	C₂³×C₁₃	1	1	yes	characteristic
743	#117	C₂³×C₁₃	1	2	yes	—
744	#117	C₂³×C₁₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	—	2	2	no	—
746	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
747	#107	C₂³×C₁₃	1	2	yes	—
748	#107	C₂³×C₁₃	1	2	yes	—
749	#106	C₂³×C₁₃	1	2	yes	—
750	#106	C₂³×C₁₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
753	#103	C₂³×C₁₃	1	2	yes	—
754	#103	C₂³×C₁₃	1	2	yes	—
755	#103	C₂³×C₁₃	1	2	yes	—
756	#103	C₂³×C₁₃	1	2	yes	—
757	#103	C₂³×C₁₃	1	2	yes	—
758	#103	C₂³×C₁₃	1	2	yes	—
759	#103	C₂³×C₁₃	1	2	yes	—
760	#103	C₂³×C₁₃	1	2	yes	—
761	#103	C₂³×C₁₃	1	2	yes	—
762	#103	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#102	C₂³×C₁₃	1	2	yes	—
766	#102	C₂³×C₁₃	1	2	yes	—
767	#102	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
775	#97	C₂³×C₁₃	1	1	yes	characteristic
776	#97	C₂³×C₁₃	1	1	yes	characteristic
777	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×C₁₃	—	4	2	no	—
780	C₂×C₁₃	—	4	2	no	—
781	C₂×C₁₃	—	4	1	no	—
782	C₂×C₁₃	—	8	2	no	—
783	C₂×C₁₃	—	8	1	no	—
784	C₂×C₁₃	#3484	1	1	yes	characteristic
785	C₂×C₁₃	#3586	1	2	yes	—
786	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
787	#41	—	2	4	no	—
788	#41	—	4	2	no	—
789	#41	—	4	2	no	—
790	#41	—	4	2	no	—
791	#41	—	4	8	no	—
792	#41	—	4	2	no	—
793	#41	—	4	2	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	4	no	—
797	C₂×Q₈	—	2	4	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	4	no	—
804	C₂×Q₈	—	2	4	no	—
805	C₂×Q₈	—	2	4	no	—
806	C₂×Q₈	—	4	2	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	—	4	4	no	—
811	C₂×Q₈	—	4	8	no	—
812	C₂×Q₈	—	4	4	no	—
813	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
815	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
816	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
817	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
818	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
829	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
830	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	4	no	—
847	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
848	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
852	Q₁₆	—	2	4	no	—
853	Q₁₆	—	2	4	no	—
854	Q₁₆	—	4	2	no	—
855	Q₁₆	—	4	2	no	—
856	Q₁₆	—	4	2	no	—
857	SD₁₆	—	2	4	no	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	4	2	no	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	D₈	—	4	2	no	—
864	M₁₆	—	4	2	no	—
865	M₁₆	—	4	2	no	—
866	M₁₆	—	4	2	no	—
867	C₂×C₈	—	4	2	no	—
868	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
869	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
870	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
871	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄×C₁₃	1	2	yes	—
888	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
889	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
909	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
910	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
911	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
913	C₄²	—	2	2	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	1	no	—
918	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
919	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
920	C₁₃	#61645	1	1	yes	characteristic, direct product factor, Sylow
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	2	no	—
925	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
926	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
927	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
928	Q₈	—	2	4	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	2	2	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	4	no	—
937	Q₈	—	4	4	no	—
938	Q₈	—	4	4	no	—
939	Q₈	—	4	2	no	—
940	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	4	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	8	2	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
986	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
988	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
989	C₈	—	2	2	no	—
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	4	4	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	2	no	—
1026	C₂	—	8	1	no	—
1027	C₂	C₁₃×#3484	1	1	yes	characteristic
1028	C₂	C₁₃×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3539	C₂	semidirect
2. C₁₃×#3486	C₂	semidirect
3. C₁₃×#3327	C₂	semidirect
4. C₁₃×#3326	C₂	semidirect
5. C₁₃×#3320	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3278	C₂	semidirect
8. C₁₃×#3276	C₂	semidirect
9. C₁₃×#3271	C₂	semidirect
10. C₁₃×#3269	C₂	semidirect
11. C₁₃×#3223	C₂	semidirect
12. C₁₃×#3221	C₂	semidirect
13. C₁₃×#3201	C₂	semidirect
14. C₁₃×#3197	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
16. C₁₃×#3126	C₂	semidirect
17. C₁₃×#3013	C₂	semidirect
18. C₁₃×#3004	C₂	semidirect
19. C₁₃×#2978	C₂	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#496	C₂²	semidirect
53. C₁₃×#494	C₂²	semidirect
54. C₁₃×#492	C₂²	semidirect
55. C₁₃×#491	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
57. C₁₃×#488	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
61. C₁₃×#484	C₂²	semidirect
62. C₁₃×#483	C₂²	semidirect
65. C₁₃×#479	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
68. C₁₃×#470	C₂²	semidirect
72. C₁₃×#468	C₂²	semidirect
73. C₁₃×#467	C₂²	semidirect
74. C₁₃×#465	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#463	C₂²	semidirect
77. C₁₃×#462	C₂²	semidirect
78. C₁₃×#462	C₂²	semidirect
79. C₁₃×#461	C₂²	semidirect
80. C₁₃×#460	C₂²	semidirect
83. C₁₃×#452	C₂²	semidirect
84. C₁₃×#452	C₂²	semidirect
85. C₁₃×#452	C₂²	semidirect
90. C₁₃×#451	C₂²	semidirect
93. C₁₃×#449	C₂²	semidirect
98. C₁₃×#448	C₂²	semidirect
99. C₁₃×#441	C₂²	semidirect
100. C₁₃×#440	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
102. C₄×C₁₃×SD₁₆	C₂²	semidirect
111. C₁₃×#417	C₂²	semidirect
112. C₂×C₁₃×#103	C₂²	semidirect
272. #61645	C₁₃	direct (N × H)
407. #3539	C₂×C₁₃	semidirect
408. #3486	C₂×C₁₃	semidirect
409. #3327	C₂×C₁₃	semidirect
410. #3326	C₂×C₁₃	semidirect
411. #3320	C₂×C₁₃	semidirect
412. #3312	C₂×C₁₃	semidirect
413. #3278	C₂×C₁₃	semidirect
414. #3276	C₂×C₁₃	semidirect
415. #3271	C₂×C₁₃	semidirect
416. #3269	C₂×C₁₃	semidirect
417. #3223	C₂×C₁₃	semidirect
418. #3221	C₂×C₁₃	semidirect
419. #3201	C₂×C₁₃	semidirect
420. #3197	C₂×C₁₃	semidirect
421. #3127	C₂×C₁₃	semidirect
422. #3126	C₂×C₁₃	semidirect
423. #3013	C₂×C₁₃	semidirect
424. #3004	C₂×C₁₃	semidirect
425. #2978	C₂×C₁₃	semidirect
502. C₂×#137	C₂²×C₁₃	semidirect
503. C₂×#135	C₂²×C₁₃	semidirect
529. #497	C₂²×C₁₃	semidirect
530. #496	C₂²×C₁₃	semidirect
531. #494	C₂²×C₁₃	semidirect
532. #492	C₂²×C₁₃	semidirect
533. #491	C₂²×C₁₃	semidirect
534. #491	C₂²×C₁₃	semidirect
535. #488	C₂²×C₁₃	semidirect
536. #488	C₂²×C₁₃	semidirect
539. #484	C₂²×C₁₃	semidirect
540. #483	C₂²×C₁₃	semidirect
543. #479	C₂²×C₁₃	semidirect
544. #479	C₂²×C₁₃	semidirect
546. #470	C₂²×C₁₃	semidirect
550. #468	C₂²×C₁₃	semidirect
551. #467	C₂²×C₁₃	semidirect
552. #465	C₂²×C₁₃	semidirect
553. #464	C₂²×C₁₃	semidirect
554. #463	C₂²×C₁₃	semidirect
555. #462	C₂²×C₁₃	semidirect
556. #462	C₂²×C₁₃	semidirect
557. #461	C₂²×C₁₃	semidirect
558. #460	C₂²×C₁₃	semidirect
561. #452	C₂²×C₁₃	semidirect
562. #452	C₂²×C₁₃	semidirect
563. #452	C₂²×C₁₃	semidirect
568. #451	C₂²×C₁₃	semidirect
571. #449	C₂²×C₁₃	semidirect
576. #448	C₂²×C₁₃	semidirect
577. #441	C₂²×C₁₃	semidirect
578. #440	C₂²×C₁₃	semidirect
579. C₄×Q₁₆	C₂²×C₁₃	semidirect
580. C₄×SD₁₆	C₂²×C₁₃	semidirect
589. #417	C₂²×C₁₃	semidirect
590. C₂×#103	C₂²×C₁₃	semidirect
920. C₁₃	#61645	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×#3539	2
C₁₃×#3486	2
C₁₃×#3327	2
C₁₃×#3326	2
C₁₃×#3320	2
C₁₃×#3312	2
C₁₃×#3278	2
C₁₃×#3276	2
C₁₃×#3271	2
C₁₃×#3269	2
C₁₃×#3223	2
C₁₃×#3221	2
C₁₃×#3201	2
C₁₃×#3197	2
C₁₃×#3127	2
C₁₃×#3126	2
C₁₃×#3013	2
C₁₃×#3004	2
C₁₃×#2978	2
#61645	13

Subgroups — C13×#61645 #15747984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61645 #15747984