Subgroups — C₁₃×#60759 #15747098

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3202	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3195	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3189	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3059	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	—
24	D₄×Q₈×C₁₃	—	2	1	no	—
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#547	—	2	2	no	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#546	—	2	2	no	—
29	C₁₃×#546	—	2	1	no	—
30	C₁₃×#537	C₂²	1	1	yes	characteristic
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#536	—	2	2	no	—
33	C₁₃×#536	—	2	1	no	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#536	C₂²	1	1	yes	characteristic
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#536	C₂²	1	4	yes	—
39	C₁₃×#536	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×#124	—	2	1	no	—
42	C₁₃×#525	C₂²	1	1	yes	characteristic
43	C₁₃×#525	C₂²	1	2	yes	—
44	C₂×C₁₃×#123	—	2	2	no	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₁₃×#520	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
51	C₁₃×#485	C₂²	1	2	yes	complemented
52	C₁₃×#485	C₂²	1	4	yes	complemented
53	C₁₃×#485	C₂²	1	4	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#484	C₂²	1	1	yes	characteristic
56	C₁₃×#484	C₂²	1	2	yes	—
57	C₁₃×#484	C₂²	1	4	yes	complemented
58	C₁₃×#483	C₂²	1	1	yes	characteristic
59	C₁₃×#483	C₂²	1	2	yes	—
60	C₁₃×#483	C₂²	1	4	yes	complemented
61	C₁₃×#482	C₂²	1	2	yes	complemented
62	C₁₃×#481	C₂²	1	1	yes	characteristic
63	C₁₃×#480	C₂²	1	1	yes	characteristic
64	C₁₃×#470	C₂²	1	4	yes	complemented
65	C₁₃×#470	C₂²	1	4	yes	complemented
66	C₁₃×#470	C₂²	1	4	yes	complemented
67	C₁₃×#468	C₂²	1	4	yes	complemented
68	C₁₃×#467	C₂²	1	4	yes	complemented
69	C₁₃×#467	C₂²	1	4	yes	complemented
70	C₁₃×#467	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#452	C₂²	1	4	yes	complemented
73	C₁₃×#452	C₂²	1	4	yes	complemented
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	2	yes	—
76	C₁₃×#451	C₂²	1	2	yes	—
77	C₁₃×#451	C₂²	1	4	yes	complemented
78	C₁₃×#451	C₂²	1	4	yes	complemented
79	C₁₃×#451	C₂²	1	4	yes	complemented
80	C₁₃×#451	C₂²	1	2	yes	complemented
81	C₁₃×#448	C₂²	1	2	yes	—
82	C₁₃×#448	C₂²	1	2	yes	complemented
83	C₁₃×#428	C₂²	1	2	yes	complemented
84	C₁₃×#427	C₂²	1	2	yes	complemented
85	C₁₃×#419	C₂²	1	2	yes	complemented
86	C₁₃×#419	C₂²	1	2	yes	complemented
87	C₁₃×#416	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
89	C₁₃×#408	C₂²	1	2	yes	—
90	C₁₃×#408	C₂²	1	4	yes	—
91	C₁₃×#407	C₂²	1	1	yes	characteristic
92	C₁₃×#407	C₂²	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	4	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	D₄	1	2	yes	—
100	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
101	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×#41	C₂³	1	2	yes	—
107	C₂²×Q₈×C₁₃	—	2	1	no	—
108	C₂²×Q₈×C₁₃	—	2	1	no	—
109	C₂²×Q₈×C₁₃	—	2	1	no	—
110	C₂²×Q₈×C₁₃	—	2	1	no	—
111	C₂²×Q₈×C₁₃	—	4	4	no	—
112	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
114	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	D₄	1	2	yes	—
119	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	—	2	1	no	—
121	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
123	C₁₃×#137	—	4	4	no	—
124	C₂×C₁₃×Q₁₆	—	4	4	no	—
125	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
126	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
129	C₁₃×#131	—	4	4	no	—
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	—	2	4	no	—
137	C₁₃×C₄⋊Q₈	—	2	1	no	—
138	C₁₃×C₄⋊Q₈	—	2	2	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	—	2	2	no	—
141	C₁₃×#124	—	2	4	no	—
142	C₁₃×#124	—	2	1	no	—
143	C₁₃×#124	—	2	2	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×#123	—	2	2	no	—
150	C₁₃×#123	—	2	2	no	—
151	C₁₃×#123	—	2	1	no	—
152	C₁₃×#123	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	1	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	—	2	2	no	—
157	C₁₃×C₂²⋊Q₈	—	2	2	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	1	no	—
160	C₁₃×C₂²⋊Q₈	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	1	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
170	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	1	no	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	C₂³	1	1	yes	characteristic
180	C₁₃×#121	C₂³	1	1	yes	characteristic
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#120	—	2	1	no	—
183	C₁₃×#120	—	2	2	no	—
184	C₄×Q₈×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	—	2	1	no	—
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	1	no	—
193	C₁₃×#117	C₂³	1	2	yes	—
194	C₁₃×#117	C₂³	1	1	yes	characteristic
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₁₃×#117	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²×C₁₃	—	2	1	no	—
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	2	yes	—
213	C₁₃×#107	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	2	yes	—
215	C₁₃×#106	C₂³	1	2	yes	—
216	C₁₃×#106	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
230	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
233	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
234	#60759	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₁₃×#41	—	4	4	no	—
242	C₁₃×#41	—	4	2	no	—
243	C₁₃×#41	—	4	2	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₁₃×#41	—	4	8	no	—
246	C₁₃×#41	—	4	4	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	1	no	—
250	C₂×Q₈×C₁₃	—	2	2	no	—
251	C₂×Q₈×C₁₃	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	2	4	no	—
253	C₂×Q₈×C₁₃	—	2	4	no	—
254	C₂×Q₈×C₁₃	—	2	4	no	—
255	C₂×Q₈×C₁₃	—	4	4	no	—
256	C₂×Q₈×C₁₃	—	4	4	no	—
257	C₂×Q₈×C₁₃	—	4	2	no	—
258	C₂×Q₈×C₁₃	—	4	4	no	—
259	C₂×Q₈×C₁₃	—	4	4	no	—
260	C₂×Q₈×C₁₃	—	4	4	no	—
261	C₂×Q₈×C₁₃	—	4	4	no	—
262	C₂×Q₈×C₁₃	—	4	4	no	—
263	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
266	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
267	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
268	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	1	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	1	no	—
274	C₂×D₄×C₁₃	—	4	2	no	—
275	C₂×D₄×C₁₃	—	4	4	no	—
276	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
281	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	1	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	1	no	—
296	C₂²×C₄×C₁₃	—	4	4	no	—
297	C₂²×C₄×C₁₃	—	4	4	no	—
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₁₃×Q₁₆	—	4	4	no	—
310	C₁₃×Q₁₆	—	4	4	no	—
311	C₁₃×Q₁₆	—	4	4	no	—
312	C₁₃×SD₁₆	—	4	4	no	—
313	C₁₃×M₁₆	—	2	4	no	—
314	C₁₃×M₁₆	—	4	4	no	—
315	C₂×C₈×C₁₃	—	2	4	no	—
316	C₂×C₈×C₁₃	—	4	4	no	—
317	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	1	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	4	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	4	no	—
328	C₁₃×C₄⋊C₄	—	2	4	no	—
329	C₁₃×C₄⋊C₄	—	2	1	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	1	no	—
333	C₁₃×C₄⋊C₄	—	2	1	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
339	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	1	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	4	no	—
348	C₁₃×C₂²⋊C₄	—	2	4	no	—
349	C₁₃×C₂²⋊C₄	—	2	4	no	—
350	C₁₃×C₂²⋊C₄	—	2	4	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	1	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	1	no	—
355	C₁₃×C₂²⋊C₄	—	2	1	no	—
356	C₁₃×C₂²⋊C₄	—	2	1	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	2	no	—
360	C₄²×C₁₃	—	2	2	no	—
361	C₄²×C₁₃	—	2	1	no	—
362	#3489	C₂×C₁₃	1	1	yes	characteristic
363	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3202	C₂×C₁₃	1	4	yes	complemented
365	#3201	C₂×C₁₃	1	4	yes	complemented
366	#3196	C₂×C₁₃	1	2	yes	complemented
367	#3195	C₂×C₁₃	1	2	yes	complemented
368	#3190	C₂×C₁₃	1	2	yes	complemented
369	#3189	C₂×C₁₃	1	2	yes	complemented
370	#3097	C₂×C₁₃	1	2	yes	complemented
371	#3095	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#3091	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#3063	C₂×C₁₃	1	2	yes	complemented
374	#3059	C₂×C₁₃	1	2	yes	complemented
375	#3011	C₂×C₁₃	1	2	yes	complemented
376	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
377	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	4	no	—
382	C₂³×C₁₃	—	2	1	no	—
383	C₂³×C₁₃	—	4	1	no	—
384	C₂³×C₁₃	—	4	2	no	—
385	C₂³×C₁₃	—	4	2	no	—
386	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
387	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
388	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	Q₈×C₁₃	—	2	2	no	—
392	Q₈×C₁₃	—	2	2	no	—
393	Q₈×C₁₃	—	2	4	no	—
394	Q₈×C₁₃	—	2	4	no	—
395	Q₈×C₁₃	—	2	4	no	—
396	Q₈×C₁₃	—	2	2	no	—
397	Q₈×C₁₃	—	4	2	no	—
398	Q₈×C₁₃	—	4	4	no	—
399	Q₈×C₁₃	—	4	4	no	—
400	Q₈×C₁₃	—	4	4	no	—
401	Q₈×C₁₃	—	4	4	no	—
402	Q₈×C₁₃	—	4	2	no	—
403	D₄×C₁₃	—	2	4	no	—
404	D₄×C₁₃	—	2	4	no	—
405	D₄×C₁₃	—	2	2	no	—
406	D₄×C₁₃	—	2	2	no	—
407	D₄×C₁₃	—	2	2	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	4	2	no	—
410	D₄×C₁₃	—	4	2	no	—
411	D₄×C₁₃	—	4	4	no	—
412	D₄×C₁₃	—	4	2	no	—
413	D₄×C₁₃	—	4	2	no	—
414	D₄×C₁₃	—	8	1	no	—
415	D₄×C₁₃	—	8	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	4	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	4	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	4	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	4	4	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	2	no	—
441	C₂×C₄×C₁₃	—	4	2	no	—
442	C₂×C₄×C₁₃	—	4	2	no	—
443	C₂×C₄×C₁₃	—	8	1	no	—
444	C₂×C₄×C₁₃	—	8	2	no	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
451	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
452	C₈×C₁₃	—	2	2	no	—
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	4	no	—
455	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
456	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
457	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
459	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#131	C₂²×C₁₃	1	2	yes	—
461	D₄×Q₈	—	2	1	no	—
462	#548	—	2	1	no	—
463	#547	—	2	2	no	—
464	#547	—	2	1	no	—
465	#546	—	2	2	no	—
466	#546	—	2	1	no	—
467	#537	C₂²×C₁₃	1	2	yes	—
468	#537	C₂²×C₁₃	1	1	yes	characteristic
469	#536	—	2	2	no	—
470	#536	—	2	1	no	—
471	#536	—	2	1	no	—
472	#536	C₂²×C₁₃	1	2	yes	—
473	#536	C₂²×C₁₃	1	4	yes	—
474	#536	C₂²×C₁₃	1	2	yes	—
475	#536	C₂²×C₁₃	1	2	yes	—
476	#536	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×C₄⋊Q₈	—	2	1	no	—
478	C₂×#124	—	2	1	no	—
479	#525	C₂²×C₁₃	1	1	yes	characteristic
480	#525	C₂²×C₁₃	1	2	yes	—
481	C₂×#123	—	2	2	no	—
482	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
485	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
486	#520	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
488	#485	C₂²×C₁₃	1	2	yes	complemented
489	#485	C₂²×C₁₃	1	4	yes	complemented
490	#485	C₂²×C₁₃	1	4	yes	complemented
491	#485	C₂²×C₁₃	1	4	yes	complemented
492	#484	C₂²×C₁₃	1	1	yes	characteristic
493	#484	C₂²×C₁₃	1	2	yes	—
494	#484	C₂²×C₁₃	1	4	yes	complemented
495	#483	C₂²×C₁₃	1	1	yes	characteristic
496	#483	C₂²×C₁₃	1	2	yes	—
497	#483	C₂²×C₁₃	1	4	yes	complemented
498	#482	C₂²×C₁₃	1	2	yes	complemented
499	#481	C₂²×C₁₃	1	1	yes	characteristic
500	#480	C₂²×C₁₃	1	1	yes	characteristic
501	#470	C₂²×C₁₃	1	4	yes	complemented
502	#470	C₂²×C₁₃	1	4	yes	complemented
503	#470	C₂²×C₁₃	1	4	yes	complemented
504	#468	C₂²×C₁₃	1	4	yes	complemented
505	#467	C₂²×C₁₃	1	4	yes	complemented
506	#467	C₂²×C₁₃	1	4	yes	complemented
507	#467	C₂²×C₁₃	1	4	yes	complemented
508	#465	C₂²×C₁₃	1	4	yes	complemented
509	#452	C₂²×C₁₃	1	4	yes	complemented
510	#452	C₂²×C₁₃	1	4	yes	complemented
511	#451	C₂²×C₁₃	1	2	yes	—
512	#451	C₂²×C₁₃	1	2	yes	—
513	#451	C₂²×C₁₃	1	2	yes	—
514	#451	C₂²×C₁₃	1	4	yes	complemented
515	#451	C₂²×C₁₃	1	4	yes	complemented
516	#451	C₂²×C₁₃	1	4	yes	complemented
517	#451	C₂²×C₁₃	1	2	yes	complemented
518	#448	C₂²×C₁₃	1	2	yes	—
519	#448	C₂²×C₁₃	1	2	yes	complemented
520	#428	C₂²×C₁₃	1	2	yes	complemented
521	#427	C₂²×C₁₃	1	2	yes	complemented
522	#419	C₂²×C₁₃	1	2	yes	complemented
523	#419	C₂²×C₁₃	1	2	yes	complemented
524	#416	C₂²×C₁₃	1	2	yes	complemented
525	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
526	#408	C₂²×C₁₃	1	2	yes	—
527	#408	C₂²×C₁₃	1	4	yes	—
528	#407	C₂²×C₁₃	1	1	yes	characteristic
529	#407	C₂²×C₁₃	1	2	yes	—
530	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
532	C₂²×C₁₃	—	2	1	no	—
533	C₂²×C₁₃	—	2	1	no	—
534	C₂²×C₁₃	—	2	1	no	—
535	C₂²×C₁₃	—	2	1	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	1	no	—
538	C₂²×C₁₃	—	2	2	no	—
539	C₂²×C₁₃	—	2	1	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	2	1	no	—
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	4	4	no	—
546	C₂²×C₁₃	—	4	1	no	—
547	C₂²×C₁₃	—	4	1	no	—
548	C₂²×C₁₃	—	4	1	no	—
549	C₂²×C₁₃	—	8	4	no	—
550	C₂²×C₁₃	#534	1	2	yes	—
551	C₂²×C₁₃	#578	1	2	yes	—
552	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₁₃	—	2	1	no	—
554	C₄×C₁₃	—	2	1	no	—
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	4	2	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	—	4	1	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₄×C₁₃	—	4	4	no	—
563	C₄×C₁₃	—	4	2	no	—
564	C₄×C₁₃	—	4	1	no	—
565	C₄×C₁₃	#534	1	2	yes	—
566	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
567	2₋¹⁺⁴	—	4	4	no	—
568	C₂×#41	—	2	2	no	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	4	4	no	—
571	C₂×#41	D₄×C₁₃	1	2	yes	—
572	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
573	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
574	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
575	C₂×#41	C₂³×C₁₃	1	2	yes	—
576	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×#41	C₂³×C₁₃	1	2	yes	—
579	C₂²×Q₈	—	2	1	no	—
580	C₂²×Q₈	—	2	1	no	—
581	C₂²×Q₈	—	2	1	no	—
582	C₂²×Q₈	—	2	1	no	—
583	C₂²×Q₈	—	4	4	no	—
584	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
587	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
589	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₂²×D₄	D₄×C₁₃	1	2	yes	—
591	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
592	C₂³×C₄	—	2	1	no	—
593	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
595	#137	—	4	4	no	—
596	C₂×Q₁₆	—	4	4	no	—
597	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
598	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
599	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
600	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
601	#131	—	4	4	no	—
602	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
603	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
604	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
605	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
606	C₄⋊Q₈	—	2	2	no	—
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	4	no	—
609	C₄⋊Q₈	—	2	1	no	—
610	C₄⋊Q₈	—	2	2	no	—
611	#124	—	2	2	no	—
612	#124	—	2	2	no	—
613	#124	—	2	4	no	—
614	#124	—	2	1	no	—
615	#124	—	2	2	no	—
616	#123	—	2	4	no	—
617	#123	—	2	4	no	—
618	#123	—	2	4	no	—
619	#123	—	2	4	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	1	no	—
624	#123	—	2	2	no	—
625	C₂²⋊Q₈	—	2	1	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	1	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
637	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
641	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
645	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	1	no	—
650	#121	—	2	2	no	—
651	#121	C₂³×C₁₃	1	1	yes	characteristic
652	#121	C₂³×C₁₃	1	1	yes	characteristic
653	#121	C₂³×C₁₃	1	2	yes	—
654	#120	—	2	1	no	—
655	#120	—	2	2	no	—
656	C₄×Q₈	—	2	1	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	2	no	—
663	#117	—	2	1	no	—
664	#117	—	2	1	no	—
665	#117	C₂³×C₁₃	1	2	yes	—
666	#117	C₂³×C₁₃	1	2	yes	—
667	#117	C₂³×C₁₃	1	1	yes	characteristic
668	#117	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄⋊C₄	—	2	2	no	—
670	C₂×C₄⋊C₄	—	2	2	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	—	2	2	no	—
673	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	2	no	—
679	C₂×C₂²⋊C₄	—	2	2	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₄²	—	2	1	no	—
683	#107	C₂³×C₁₃	1	2	yes	—
684	#107	C₂³×C₁₃	1	2	yes	—
685	#107	C₂³×C₁₃	1	4	yes	—
686	#106	C₂³×C₁₃	1	2	yes	—
687	#106	C₂³×C₁₃	1	2	yes	—
688	#106	C₂³×C₁₃	1	4	yes	—
689	#103	C₂³×C₁₃	1	4	yes	—
690	#103	C₂³×C₁₃	1	4	yes	—
691	#103	C₂³×C₁₃	1	2	yes	—
692	#103	C₂³×C₁₃	1	2	yes	—
693	#103	C₂³×C₁₃	1	4	yes	—
694	#103	C₂³×C₁₃	1	4	yes	—
695	#103	C₂³×C₁₃	1	4	yes	—
696	#103	C₂³×C₁₃	1	4	yes	—
697	#102	C₂³×C₁₃	1	2	yes	—
698	#102	C₂³×C₁₃	1	2	yes	—
699	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
700	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
701	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
704	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
706	C₂×C₁₃	—	2	2	no	—
707	C₂×C₁₃	—	2	2	no	—
708	C₂×C₁₃	—	4	1	no	—
709	C₂×C₁₃	—	4	2	no	—
710	C₂×C₁₃	—	4	2	no	—
711	C₂×C₁₃	—	8	1	no	—
712	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
713	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
714	C₂×C₁₃	#3586	1	1	yes	characteristic
715	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
717	#41	—	2	4	no	—
718	#41	—	2	4	no	—
719	#41	—	2	4	no	—
720	#41	—	4	4	no	—
721	#41	—	4	4	no	—
722	#41	—	4	2	no	—
723	#41	—	4	2	no	—
724	#41	—	4	4	no	—
725	#41	—	4	8	no	—
726	#41	—	4	4	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	1	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	4	4	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×Q₈	—	4	4	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	—	4	4	no	—
743	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
746	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
747	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
748	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	1	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	4	no	—
756	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
759	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
762	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
763	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	1	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	4	4	no	—
777	C₂²×C₄	—	4	4	no	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
789	Q₁₆	—	4	4	no	—
790	Q₁₆	—	4	4	no	—
791	Q₁₆	—	4	4	no	—
792	SD₁₆	—	4	4	no	—
793	M₁₆	—	2	4	no	—
794	M₁₆	—	4	4	no	—
795	C₂×C₈	—	2	4	no	—
796	C₂×C₈	—	4	4	no	—
797	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
798	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
799	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	1	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	4	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	4	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	4	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	—	2	1	no	—
836	C₂²⋊C₄	—	2	1	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	1	no	—
842	C₁₃	#60759	1	1	yes	characteristic, direct product factor, Sylow
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	4	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	2	no	—
849	C₂³	—	4	2	no	—
850	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
851	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
852	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
853	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
854	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	4	no	—
858	Q₈	—	2	4	no	—
859	Q₈	—	2	4	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	4	2	no	—
862	Q₈	—	4	4	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	—	4	4	no	—
866	Q₈	—	4	2	no	—
867	D₄	—	2	4	no	—
868	D₄	—	2	4	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	2	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	2	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	2	no	—
877	D₄	—	4	2	no	—
878	D₄	—	8	1	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	4	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	2	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	8	1	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
913	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
915	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
916	C₈	—	2	2	no	—
917	C₈	—	2	2	no	—
918	C₈	—	2	4	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	4	4	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	8	4	no	—
937	C₂²	C₁₃×#534	1	2	yes	—
938	C₂²	C₁₃×#578	1	2	yes	—
939	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	4	no	—
952	C₄	C₁₃×#534	1	2	yes	—
953	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
954	C₂	—	2	2	no	—
955	C₂	—	2	2	no	—
956	C₂	—	4	1	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	2	no	—
959	C₂	—	8	1	no	—
960	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
961	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
962	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3202	C₂	semidirect
4. C₁₃×#3201	C₂	semidirect
5. C₁₃×#3196	C₂	semidirect
6. C₁₃×#3195	C₂	semidirect
7. C₁₃×#3190	C₂	semidirect
8. C₁₃×#3189	C₂	semidirect
9. C₁₃×#3097	C₂	semidirect
10. C₁₃×#3095	C₂	semidirect
11. C₁₃×#3091	C₂	semidirect
12. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3059	C₂	semidirect
14. C₁₃×#3011	C₂	semidirect
15. C₁₃×#3004	C₂	semidirect
16. C₂×C₁₃×#451	C₂	semidirect
17. C₁₃×#2880	C₂	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂²×C₁₃×Q₁₆	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
57. C₁₃×#484	C₂²	semidirect
60. C₁₃×#483	C₂²	semidirect
61. C₁₃×#482	C₂²	semidirect
64. C₁₃×#470	C₂²	semidirect
65. C₁₃×#470	C₂²	semidirect
66. C₁₃×#470	C₂²	semidirect
67. C₁₃×#468	C₂²	semidirect
68. C₁₃×#467	C₂²	semidirect
69. C₁₃×#467	C₂²	semidirect
70. C₁₃×#467	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#452	C₂²	semidirect
73. C₁₃×#452	C₂²	semidirect
77. C₁₃×#451	C₂²	semidirect
78. C₁₃×#451	C₂²	semidirect
79. C₁₃×#451	C₂²	semidirect
80. C₁₃×#451	C₂²	semidirect
82. C₁₃×#448	C₂²	semidirect
83. C₁₃×#428	C₂²	semidirect
84. C₁₃×#427	C₂²	semidirect
85. C₁₃×#419	C₂²	semidirect
86. C₁₃×#419	C₂²	semidirect
87. C₁₃×#416	C₂²	semidirect
88. C₂×C₁₃×#103	C₂²	semidirect
234. #60759	C₁₃	direct (N × H)
363. C₂×#536	C₂×C₁₃	semidirect
364. #3202	C₂×C₁₃	semidirect
365. #3201	C₂×C₁₃	semidirect
366. #3196	C₂×C₁₃	semidirect
367. #3195	C₂×C₁₃	semidirect
368. #3190	C₂×C₁₃	semidirect
369. #3189	C₂×C₁₃	semidirect
370. #3097	C₂×C₁₃	semidirect
371. #3095	C₂×C₁₃	semidirect
372. #3091	C₂×C₁₃	semidirect
373. #3063	C₂×C₁₃	semidirect
374. #3059	C₂×C₁₃	semidirect
375. #3011	C₂×C₁₃	semidirect
376. #3004	C₂×C₁₃	semidirect
377. C₂×#451	C₂×C₁₃	semidirect
378. #2880	C₂×C₁₃	semidirect
458. C₂×#137	C₂²×C₁₃	semidirect
459. C₂²×Q₁₆	C₂²×C₁₃	semidirect
488. #485	C₂²×C₁₃	semidirect
489. #485	C₂²×C₁₃	semidirect
490. #485	C₂²×C₁₃	semidirect
491. #485	C₂²×C₁₃	semidirect
494. #484	C₂²×C₁₃	semidirect
497. #483	C₂²×C₁₃	semidirect
498. #482	C₂²×C₁₃	semidirect
501. #470	C₂²×C₁₃	semidirect
502. #470	C₂²×C₁₃	semidirect
503. #470	C₂²×C₁₃	semidirect
504. #468	C₂²×C₁₃	semidirect
505. #467	C₂²×C₁₃	semidirect
506. #467	C₂²×C₁₃	semidirect
507. #467	C₂²×C₁₃	semidirect
508. #465	C₂²×C₁₃	semidirect
509. #452	C₂²×C₁₃	semidirect
510. #452	C₂²×C₁₃	semidirect
514. #451	C₂²×C₁₃	semidirect
515. #451	C₂²×C₁₃	semidirect
516. #451	C₂²×C₁₃	semidirect
517. #451	C₂²×C₁₃	semidirect
519. #448	C₂²×C₁₃	semidirect
520. #428	C₂²×C₁₃	semidirect
521. #427	C₂²×C₁₃	semidirect
522. #419	C₂²×C₁₃	semidirect
523. #419	C₂²×C₁₃	semidirect
524. #416	C₂²×C₁₃	semidirect
525. C₂×#103	C₂²×C₁₃	semidirect
842. C₁₃	#60759	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×#3489	2
C₂×C₁₃×#536	2
C₁₃×#3202	2
C₁₃×#3201	2
C₁₃×#3196	2
C₁₃×#3195	2
C₁₃×#3190	2
C₁₃×#3189	2
C₁₃×#3097	2
C₁₃×#3095	2
C₁₃×#3091	2
C₁₃×#3063	2
C₁₃×#3059	2
C₁₃×#3011	2
C₁₃×#3004	2
C₂×C₁₃×#451	2
C₁₃×#2880	2
#60759	13

Subgroups — C13×#60759 #15747098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60759 #15747098