Subgroups — C₁₃×#61564 #15747903

Order 3328.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3301	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3300	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3282	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3108	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	C₂²	1	2	yes	complemented
23	C₁₃×#552	C₂²	1	2	yes	complemented
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#548	—	2	2	no	—
27	C₁₃×#548	C₂²	1	4	yes	—
28	C₁₃×#548	C₂²	1	2	yes	complemented
29	C₁₃×#548	C₂²	1	4	yes	complemented
30	C₁₃×#546	C₂²	1	2	yes	complemented
31	C₁₃×#539	—	2	1	no	—
32	C₁₃×#538	—	2	1	no	—
33	C₁₃×#534	—	2	1	no	—
34	C₁₃×#529	C₂²	1	2	yes	—
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#525	C₂²	1	2	yes	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#121	—	2	1	no	—
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
44	C₁₃×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#495	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#485	C₂²	1	4	yes	complemented
51	C₁₃×#483	C₂²	1	2	yes	complemented
52	C₁₃×#481	C₂²	1	2	yes	complemented
53	C₁₃×#480	C₂²	1	2	yes	—
54	C₁₃×#480	C₂²	1	2	yes	complemented
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#467	C₂²	1	4	yes	complemented
57	C₁₃×#466	C₂²	1	4	yes	complemented
58	C₁₃×#465	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#452	C₂²	1	4	yes	complemented
64	C₁₃×#452	C₂²	1	4	yes	complemented
65	C₁₃×#451	C₂²	1	4	yes	complemented
66	C₁₃×#451	C₂²	1	2	yes	complemented
67	C₁₃×#451	C₂²	1	2	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#448	C₂²	1	2	yes	—
71	C₁₃×#448	C₂²	1	2	yes	—
72	C₁₃×#448	C₂²	1	2	yes	complemented
73	C₁₃×#448	C₂²	1	4	yes	complemented
74	C₁₃×#447	C₂²	1	2	yes	—
75	C₁₃×#447	C₂²	1	2	yes	complemented
76	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
77	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
78	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
80	C₁₃×#431	C₂²	1	2	yes	complemented
81	C₁₃×#416	C₂²	1	4	yes	complemented
82	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
84	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	4	4	no	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	—	2	1	no	—
93	C₂²×Q₈×C₁₃	—	2	1	no	—
94	C₂²×Q₈×C₁₃	—	4	4	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₂³×C₄×C₁₃	—	2	1	no	—
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#135	—	4	8	no	—
111	C₂×C₁₃×Q₁₆	—	4	4	no	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	—	4	4	no	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	4	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	C₂³	1	2	yes	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	4	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	C₂³	1	4	yes	—
132	C₁₃×#124	C₂³	1	2	yes	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#121	—	2	4	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	4	no	—
171	C₄×D₄×C₁₃	—	2	4	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	D₄	1	2	yes	—
175	C₄×D₄×C₁₃	D₄	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	C₂³	1	2	yes	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	4	yes	—
201	C₁₃×#106	C₂³	1	4	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	4	yes	—
207	C₁₃×#103	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₄×C₈×C₁₃	C₂³	1	4	yes	—
217	#61564	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	—	2	1	no	—
219	C₂⁴×C₁₃	—	2	1	no	—
220	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₁₃×#41	—	2	8	no	—
223	C₁₃×#41	—	4	4	no	—
224	C₁₃×#41	—	4	4	no	—
225	C₁₃×#41	—	4	8	no	—
226	C₂×Q₈×C₁₃	—	2	4	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	2	no	—
229	C₂×Q₈×C₁₃	—	2	2	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	4	no	—
233	C₂×Q₈×C₁₃	—	2	4	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	2	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	4	2	no	—
239	C₂×Q₈×C₁₃	—	4	4	no	—
240	C₂×Q₈×C₁₃	—	4	4	no	—
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	4	4	no	—
258	C₂×D₄×C₁₃	—	4	4	no	—
259	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	2	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	4	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	—	4	4	no	—
277	C₂²×C₄×C₁₃	—	4	4	no	—
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₁₃×Q₁₆	—	2	8	no	—
290	C₁₃×Q₁₆	—	4	4	no	—
291	C₁₃×SD₁₆	—	2	8	no	—
292	C₁₃×SD₁₆	—	4	4	no	—
293	C₁₃×SD₁₆	—	4	4	no	—
294	C₁₃×D₈	—	4	4	no	—
295	C₂×C₈×C₁₃	—	4	2	no	—
296	C₂×C₈×C₁₃	—	4	2	no	—
297	C₂×C₈×C₁₃	—	4	4	no	—
298	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₄²×C₁₃	—	2	4	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	—	2	2	no	—
338	C₄²×C₁₃	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	C₂⁴	1	2	yes	—
340	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3301	C₂×C₁₃	1	4	yes	complemented
343	#3300	C₂×C₁₃	1	4	yes	complemented
344	#3285	C₂×C₁₃	1	4	yes	complemented
345	#3282	C₂×C₁₃	1	4	yes	complemented
346	#3211	C₂×C₁₃	1	2	yes	complemented
347	#3190	C₂×C₁₃	1	2	yes	complemented
348	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3186	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3108	C₂×C₁₃	1	2	yes	complemented
351	#3002	C₂×C₁₃	1	2	yes	complemented
352	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	2	no	—
357	C₂³×C₁₃	—	2	2	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	1	no	—
361	C₂³×C₁₃	—	4	1	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	4	2	no	—
365	C₂³×C₁₃	—	4	2	no	—
366	C₂³×C₁₃	—	8	1	no	—
367	C₂³×C₁₃	—	8	1	no	—
368	C₂³×C₁₃	#135	1	4	yes	complemented
369	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
370	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	Q₈×C₁₃	—	2	4	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	2	4	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	4	4	no	—
379	Q₈×C₁₃	—	4	4	no	—
380	Q₈×C₁₃	—	4	2	no	—
381	Q₈×C₁₃	—	8	1	no	—
382	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
383	D₄×C₁₃	—	2	4	no	—
384	D₄×C₁₃	—	2	4	no	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	2	4	no	—
387	D₄×C₁₃	—	4	8	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	8	1	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	2	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	4	1	no	—
409	C₂×C₄×C₁₃	—	4	1	no	—
410	C₂×C₄×C₁₃	—	4	1	no	—
411	C₂×C₄×C₁₃	—	4	1	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	4	1	no	—
414	C₂×C₄×C₁₃	—	4	8	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	8	2	no	—
421	C₂×C₄×C₁₃	—	8	2	no	—
422	C₂×C₄×C₁₃	—	8	1	no	—
423	C₂×C₄×C₁₃	—	8	1	no	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
431	C₈×C₁₃	—	2	4	no	—
432	C₈×C₁₃	—	2	4	no	—
433	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
436	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
437	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
438	#553	—	2	2	no	—
439	#553	C₂²×C₁₃	1	2	yes	complemented
440	#552	C₂²×C₁₃	1	2	yes	complemented
441	#551	—	2	2	no	—
442	#548	—	2	2	no	—
443	#548	—	2	2	no	—
444	#548	C₂²×C₁₃	1	4	yes	—
445	#548	C₂²×C₁₃	1	4	yes	complemented
446	#548	C₂²×C₁₃	1	2	yes	complemented
447	#546	C₂²×C₁₃	1	2	yes	complemented
448	#539	—	2	1	no	—
449	#538	—	2	1	no	—
450	#534	—	2	1	no	—
451	#529	C₂²×C₁₃	1	2	yes	—
452	C₂×#124	—	2	1	no	—
453	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
454	#525	C₂²×C₁₃	1	2	yes	—
455	C₂×C₂²⋊Q₈	—	2	1	no	—
456	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×#121	—	2	1	no	—
459	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
461	#518	—	2	1	no	—
462	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	C₂×C₄×D₄	—	2	1	no	—
464	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
465	#495	C₂²×C₁₃	1	4	yes	complemented
466	#488	C₂²×C₁₃	1	4	yes	complemented
467	#485	C₂²×C₁₃	1	4	yes	complemented
468	#483	C₂²×C₁₃	1	2	yes	complemented
469	#481	C₂²×C₁₃	1	2	yes	complemented
470	#480	C₂²×C₁₃	1	2	yes	—
471	#480	C₂²×C₁₃	1	2	yes	complemented
472	#479	C₂²×C₁₃	1	4	yes	complemented
473	#467	C₂²×C₁₃	1	4	yes	complemented
474	#466	C₂²×C₁₃	1	4	yes	complemented
475	#465	C₂²×C₁₃	1	4	yes	complemented
476	#465	C₂²×C₁₃	1	4	yes	complemented
477	#464	C₂²×C₁₃	1	4	yes	complemented
478	#464	C₂²×C₁₃	1	4	yes	complemented
479	#463	C₂²×C₁₃	1	4	yes	complemented
480	#452	C₂²×C₁₃	1	4	yes	complemented
481	#452	C₂²×C₁₃	1	4	yes	complemented
482	#451	C₂²×C₁₃	1	2	yes	complemented
483	#451	C₂²×C₁₃	1	2	yes	complemented
484	#451	C₂²×C₁₃	1	4	yes	complemented
485	#450	C₂²×C₁₃	1	2	yes	complemented
486	#449	C₂²×C₁₃	1	4	yes	complemented
487	#448	C₂²×C₁₃	1	2	yes	—
488	#448	C₂²×C₁₃	1	2	yes	—
489	#448	C₂²×C₁₃	1	2	yes	complemented
490	#448	C₂²×C₁₃	1	4	yes	complemented
491	#447	C₂²×C₁₃	1	2	yes	—
492	#447	C₂²×C₁₃	1	2	yes	complemented
493	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
494	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
495	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
496	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
497	#431	C₂²×C₁₃	1	2	yes	complemented
498	#416	C₂²×C₁₃	1	4	yes	complemented
499	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
500	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
501	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	2	1	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	2	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	4	4	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	4	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	2	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	8	2	no	—
521	C₂²×C₁₃	—	8	4	no	—
522	C₂²×C₁₃	—	16	2	no	—
523	C₂²×C₁₃	C₂×#135	1	2	yes	—
524	C₂²×C₁₃	C₂×#135	1	2	yes	—
525	C₂²×C₁₃	C₂×#135	1	2	yes	—
526	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	4	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	1	no	—
532	C₄×C₁₃	—	2	1	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	4	2	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
540	C₂×#41	—	2	2	no	—
541	C₂×#41	—	4	4	no	—
542	C₂×#41	C₂³×C₁₃	1	4	yes	—
543	C₂×#41	C₂³×C₁₃	1	2	yes	—
544	C₂²×Q₈	—	2	1	no	—
545	C₂²×Q₈	—	2	1	no	—
546	C₂²×Q₈	—	2	1	no	—
547	C₂²×Q₈	—	4	4	no	—
548	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
563	#135	—	4	8	no	—
564	C₂×Q₁₆	—	4	4	no	—
565	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
566	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×SD₁₆	—	4	4	no	—
568	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
569	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂×D₈	C₂³×C₁₃	1	4	yes	—
572	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
573	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
574	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#125	—	2	2	no	—
579	#125	C₂³×C₁₃	1	2	yes	—
580	#124	—	2	4	no	—
581	#124	—	2	4	no	—
582	#124	—	2	2	no	—
583	#124	—	2	2	no	—
584	#124	C₂³×C₁₃	1	4	yes	—
585	#124	C₂³×C₁₃	1	2	yes	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	4	no	—
595	C₂²⋊Q₈	—	2	4	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
601	#121	—	2	4	no	—
602	#121	—	2	4	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	C₂³×C₁₃	1	2	yes	—
611	#121	C₂³×C₁₃	1	2	yes	—
612	#121	C₂³×C₁₃	1	2	yes	—
613	#121	C₂³×C₁₃	1	2	yes	—
614	#121	C₂³×C₁₃	1	2	yes	—
615	#120	—	2	2	no	—
616	#120	—	2	2	no	—
617	C₄×Q₈	—	2	2	no	—
618	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
619	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	2	4	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	D₄×C₁₃	1	2	yes	—
628	C₄×D₄	D₄×C₁₃	1	2	yes	—
629	C₄×D₄	C₂³×C₁₃	1	2	yes	—
630	C₄×D₄	C₂³×C₁₃	1	2	yes	—
631	C₄×D₄	C₂³×C₁₃	1	2	yes	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	C₂³×C₁₃	1	2	yes	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
653	#107	C₂³×C₁₃	1	4	yes	—
654	#106	C₂³×C₁₃	1	4	yes	—
655	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	4	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#103	C₂³×C₁₃	1	4	yes	—
661	#102	C₂³×C₁₃	1	4	yes	—
662	#102	C₂³×C₁₃	1	4	yes	—
663	#102	C₂³×C₁₃	1	4	yes	—
664	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
665	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
666	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
669	C₄×C₈	C₂³×C₁₃	1	4	yes	—
670	C₂×C₁₃	—	2	2	no	—
671	C₂×C₁₃	—	2	2	no	—
672	C₂×C₁₃	—	2	2	no	—
673	C₂×C₁₃	—	4	2	no	—
674	C₂×C₁₃	—	8	2	no	—
675	C₂×C₁₃	—	8	2	no	—
676	C₂×C₁₃	#3484	1	1	yes	characteristic
677	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
678	C₂×C₁₃	#3586	1	1	yes	characteristic
679	C₂⁴	—	2	1	no	—
680	C₂⁴	—	2	1	no	—
681	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
683	#41	—	2	8	no	—
684	#41	—	4	4	no	—
685	#41	—	4	4	no	—
686	#41	—	4	8	no	—
687	C₂×Q₈	—	2	4	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	4	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	4	2	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	4	no	—
699	C₂×Q₈	—	4	2	no	—
700	C₂×Q₈	—	4	4	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
703	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
722	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
723	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
750	Q₁₆	—	2	8	no	—
751	Q₁₆	—	4	4	no	—
752	SD₁₆	—	2	8	no	—
753	SD₁₆	—	4	4	no	—
754	SD₁₆	—	4	4	no	—
755	D₈	—	4	4	no	—
756	C₂×C₈	—	4	2	no	—
757	C₂×C₈	—	4	2	no	—
758	C₂×C₈	—	4	4	no	—
759	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
760	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
793	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	C₂×D₄×C₁₃	1	2	yes	—
800	C₄²	C₂⁴×C₁₃	1	2	yes	—
801	C₁₃	#61564	1	1	yes	characteristic, direct product factor, Sylow
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	C₁₃×#135	1	4	yes	complemented
816	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	4	4	no	—
826	Q₈	—	4	4	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
830	D₄	—	2	4	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	4	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	8	1	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	—	8	1	no	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
878	C₈	—	2	4	no	—
879	C₈	—	2	4	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	16	2	no	—
899	C₂²	C₂×C₁₃×#135	1	2	yes	—
900	C₂²	C₂×C₁₃×#135	1	2	yes	—
901	C₂²	C₂×C₁₃×#135	1	2	yes	—
902	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	2	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₁₃×#3484	1	1	yes	characteristic
923	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
924	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3505	C₂	semidirect
2. C₂×C₁₃×#548	C₂	semidirect
3. C₁₃×#3301	C₂	semidirect
4. C₁₃×#3300	C₂	semidirect
5. C₁₃×#3285	C₂	semidirect
6. C₁₃×#3282	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3190	C₂	semidirect
9. C₁₃×#3187	C₂	semidirect
10. C₁₃×#3186	C₂	semidirect
11. C₁₃×#3108	C₂	semidirect
12. C₁₃×#3002	C₂	semidirect
13. C₂×C₁₃×#451	C₂	semidirect
14. C₂×C₁₃×#448	C₂	semidirect
15. C₁₃×#2972	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
19. C₂²×C₁₃×Q₁₆	C₂²	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
36. C₂×C₁₃×#124	C₂²	semidirect
40. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
48. C₁₃×#495	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#485	C₂²	semidirect
51. C₁₃×#483	C₂²	semidirect
52. C₁₃×#481	C₂²	semidirect
54. C₁₃×#480	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#467	C₂²	semidirect
57. C₁₃×#466	C₂²	semidirect
58. C₁₃×#465	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#451	C₂²	semidirect
67. C₁₃×#451	C₂²	semidirect
68. C₁₃×#450	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
72. C₁₃×#448	C₂²	semidirect
73. C₁₃×#448	C₂²	semidirect
75. C₁₃×#447	C₂²	semidirect
76. C₄×C₁₃×Q₁₆	C₂²	semidirect
77. C₄×C₁₃×SD₁₆	C₂²	semidirect
78. C₈×D₄×C₁₃	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#431	C₂²	semidirect
81. C₁₃×#416	C₂²	semidirect
82. C₂×C₁₃×#103	C₂²	semidirect
83. C₂×C₁₃×#103	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
217. #61564	C₁₃	direct (N × H)
340. #3505	C₂×C₁₃	semidirect
341. C₂×#548	C₂×C₁₃	semidirect
342. #3301	C₂×C₁₃	semidirect
343. #3300	C₂×C₁₃	semidirect
344. #3285	C₂×C₁₃	semidirect
345. #3282	C₂×C₁₃	semidirect
346. #3211	C₂×C₁₃	semidirect
347. #3190	C₂×C₁₃	semidirect
348. #3187	C₂×C₁₃	semidirect
349. #3186	C₂×C₁₃	semidirect
350. #3108	C₂×C₁₃	semidirect
351. #3002	C₂×C₁₃	semidirect
352. C₂×#451	C₂×C₁₃	semidirect
353. C₂×#448	C₂×C₁₃	semidirect
354. #2972	C₂×C₁₃	semidirect
368. C₂³×C₁₃	#135	semidirect
433. C₂²×#41	C₂²×C₁₃	semidirect
435. C₂×#135	C₂²×C₁₃	semidirect
436. C₂²×Q₁₆	C₂²×C₁₃	semidirect
437. C₂²×SD₁₆	C₂²×C₁₃	semidirect
439. #553	C₂²×C₁₃	semidirect
440. #552	C₂²×C₁₃	semidirect
445. #548	C₂²×C₁₃	semidirect
446. #548	C₂²×C₁₃	semidirect
447. #546	C₂²×C₁₃	semidirect
453. C₂×#124	C₂²×C₁₃	semidirect
457. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
462. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
465. #495	C₂²×C₁₃	semidirect
466. #488	C₂²×C₁₃	semidirect
467. #485	C₂²×C₁₃	semidirect
468. #483	C₂²×C₁₃	semidirect
469. #481	C₂²×C₁₃	semidirect
471. #480	C₂²×C₁₃	semidirect
472. #479	C₂²×C₁₃	semidirect
473. #467	C₂²×C₁₃	semidirect
474. #466	C₂²×C₁₃	semidirect
475. #465	C₂²×C₁₃	semidirect
476. #465	C₂²×C₁₃	semidirect
477. #464	C₂²×C₁₃	semidirect
478. #464	C₂²×C₁₃	semidirect
479. #463	C₂²×C₁₃	semidirect
480. #452	C₂²×C₁₃	semidirect
481. #452	C₂²×C₁₃	semidirect
482. #451	C₂²×C₁₃	semidirect
483. #451	C₂²×C₁₃	semidirect
484. #451	C₂²×C₁₃	semidirect
485. #450	C₂²×C₁₃	semidirect
486. #449	C₂²×C₁₃	semidirect
489. #448	C₂²×C₁₃	semidirect
490. #448	C₂²×C₁₃	semidirect
492. #447	C₂²×C₁₃	semidirect
493. C₄×Q₁₆	C₂²×C₁₃	semidirect
494. C₄×SD₁₆	C₂²×C₁₃	semidirect
495. C₈×D₄	C₂²×C₁₃	semidirect
496. C₈×D₄	C₂²×C₁₃	semidirect
497. #431	C₂²×C₁₃	semidirect
498. #416	C₂²×C₁₃	semidirect
499. C₂×#103	C₂²×C₁₃	semidirect
500. C₂×#103	C₂²×C₁₃	semidirect
503. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
801. C₁₃	#61564	direct (N × H)
815. C₂³	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3505	2
C₂×C₁₃×#548	2
C₁₃×#3301	2
C₁₃×#3300	2
C₁₃×#3285	2
C₁₃×#3282	2
C₁₃×#3211	2
C₁₃×#3190	2
C₁₃×#3187	2
C₁₃×#3186	2
C₁₃×#3108	2
C₁₃×#3002	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₁₃×#2972	2
#61564	13

Subgroups — C13×#61564 #15747903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61564 #15747903