Subgroups — C₁₃×#17598 #15703937

Order 3328.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1521	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1520	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1516	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1515	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1511	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1508	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1504	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1501	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#328	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₄	1	1	yes	characteristic, complemented
17	C₁₃×#554	—	2	1	no	—
18	C₁₃×#552	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#552	C₄	1	1	yes	characteristic, complemented
20	C₁₃×#551	—	2	1	no	—
21	C₁₃×#551	—	2	1	no	—
22	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
23	C₁₃×#548	C₄	1	1	yes	characteristic, complemented
24	C₁₃×#548	C₄	1	1	yes	characteristic, complemented
25	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
26	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
27	C₁₃×#546	—	2	1	no	—
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#539	—	2	1	no	—
30	C₁₃×#539	—	2	1	no	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#525	C₂²	1	1	yes	characteristic
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₁₃×#520	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#436	—	2	1	no	—
40	C₁₃×#435	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₈×D₄×C₁₃	—	2	1	no	—
43	C₁₃×#432	C₂²	1	1	yes	characteristic
44	C₁₃×#431	C₂²	1	1	yes	characteristic
45	C₁₃×#407	C₂²	1	1	yes	characteristic
46	C₁₃×#407	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₁₃×#388	—	2	1	no	—
50	C₁₃×#387	—	2	1	no	—
51	C₁₃×#386	—	2	1	no	—
52	C₁₃×#385	—	2	1	no	—
53	C₁₃×#383	C₂²	1	1	yes	characteristic
54	C₁₃×#382	C₂²	1	1	yes	characteristic
55	C₁₃×#381	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
59	C₁₃×#328	C₂²	1	1	yes	characteristic
60	C₁₃×#328	C₂²	1	1	yes	characteristic
61	C₁₃×#328	C₂²	1	1	yes	characteristic
62	C₁₃×#328	C₂²	1	1	yes	characteristic
63	C₁₃×#328	C₂²	1	1	yes	characteristic
64	C₁₃×#328	C₂²	1	1	yes	characteristic
65	C₁₃×#328	C₂²	1	1	yes	characteristic
66	C₁₃×#328	C₂²	1	1	yes	characteristic
67	C₁₃×#328	C₂²	1	1	yes	characteristic
68	C₁₃×#328	C₂²	1	1	yes	characteristic
69	C₁₃×#328	C₂²	1	1	yes	characteristic
70	C₁₃×#328	C₂²	1	1	yes	characteristic
71	C₁₃×#327	C₂²	1	1	yes	characteristic
72	C₁₃×#327	C₂²	1	1	yes	characteristic
73	C₁₃×#327	C₂²	1	1	yes	characteristic
74	C₁₃×#327	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	—	2	1	no	—
85	C₂×C₁₃×M₁₆	—	2	1	no	—
86	C₂²×C₈×C₁₃	—	2	1	no	—
87	C₂²×C₈×C₁₃	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
90	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
91	C₁₃×#126	—	2	1	no	—
92	C₁₃×#126	—	2	1	no	—
93	C₁₃×#126	—	2	1	no	—
94	C₁₃×#126	—	2	1	no	—
95	C₁₃×#126	—	2	1	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×#125	—	2	1	no	—
98	C₁₃×#125	—	2	1	no	—
99	C₁₃×#125	C₂×C₄	1	1	yes	characteristic, complemented
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	C₂×C₄	1	1	yes	characteristic, complemented
104	C₁₃×#123	—	2	1	no	—
105	C₁₃×#123	—	2	1	no	—
106	C₁₃×#123	—	2	1	no	—
107	C₁₃×#123	—	2	1	no	—
108	C₁₃×#123	—	2	1	no	—
109	C₁₃×#123	—	2	1	no	—
110	C₁₃×#123	—	2	1	no	—
111	C₁₃×#123	—	2	1	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
125	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
126	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
127	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
128	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
129	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
136	C₁₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
137	C₁₃×#121	C₂³	1	1	yes	characteristic
138	C₁₃×#120	—	2	1	no	—
139	C₁₃×#120	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	1	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
143	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
144	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
145	C₄×D₄×C₁₃	—	2	1	no	—
146	C₄×D₄×C₁₃	—	2	1	no	—
147	C₄×D₄×C₁₃	—	2	1	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
157	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
158	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
159	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
160	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
161	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
162	C₁₃×#117	—	2	1	no	—
163	C₁₃×#117	—	2	1	no	—
164	C₁₃×#117	—	2	1	no	—
165	C₁₃×#117	—	2	1	no	—
166	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
167	C₁₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
174	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
175	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
176	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
179	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
182	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×C₄⋊C₈	—	2	1	no	—
186	C₁₃×C₄⋊C₈	—	2	1	no	—
187	C₁₃×C₂²⋊C₈	—	2	1	no	—
188	C₁₃×C₂²⋊C₈	—	2	1	no	—
189	C₁₃×C₂²⋊C₈	—	2	1	no	—
190	C₁₃×C₂²⋊C₈	—	2	1	no	—
191	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
195	C₁₃×#97	—	2	1	no	—
196	C₄×C₈×C₁₃	—	2	1	no	—
197	C₁₃×#95	—	2	1	no	—
198	C₁₃×#95	—	2	1	no	—
199	C₁₃×#95	—	2	1	no	—
200	C₁₃×#95	—	2	1	no	—
201	C₁₃×#95	—	2	1	no	—
202	C₁₃×#95	C₂³	1	1	yes	characteristic
203	C₁₃×#95	C₂³	1	1	yes	characteristic
204	C₁₃×#95	C₂³	1	1	yes	characteristic
205	C₁₃×#95	C₂³	1	1	yes	characteristic
206	#17598	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₁₃×#41	—	4	4	no	—
210	C₁₃×#41	—	8	1	no	—
211	C₁₃×#41	—	8	1	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	8	1	no	—
216	C₂×Q₈×C₁₃	—	8	1	no	—
217	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	1	no	—
223	C₂×D₄×C₁₃	—	2	1	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	4	2	no	—
226	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
228	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
229	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
230	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	—	2	1	no	—
232	C₂²×C₄×C₁₃	—	2	1	no	—
233	C₂²×C₄×C₁₃	—	2	1	no	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	4	2	no	—
243	C₂²×C₄×C₁₃	—	8	1	no	—
244	C₂²×C₄×C₁₃	—	8	1	no	—
245	C₂²×C₄×C₁₃	—	8	1	no	—
246	C₂²×C₄×C₁₃	—	8	1	no	—
247	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₁₃×M₁₆	—	8	1	no	—
261	C₁₃×M₁₆	—	8	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	8	1	no	—
267	C₂×C₈×C₁₃	—	8	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	1	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	1	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	8	1	no	—
288	C₁₃×C₄⋊C₄	—	8	1	no	—
289	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
290	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
294	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
295	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
297	C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₁₃×C₂²⋊C₄	—	2	1	no	—
302	C₁₃×C₂²⋊C₄	—	2	1	no	—
303	C₁₃×C₂²⋊C₄	—	2	1	no	—
304	C₁₃×C₂²⋊C₄	—	2	1	no	—
305	C₁₃×C₂²⋊C₄	—	2	1	no	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	1	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	1	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	4	2	no	—
315	C₁₃×C₂²⋊C₄	—	8	1	no	—
316	C₁₃×C₂²⋊C₄	—	8	1	no	—
317	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
318	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
321	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
322	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
323	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
324	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	8	1	no	—
331	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
333	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
335	#3520	C₂×C₁₃	1	1	yes	characteristic
336	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2318	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#1521	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#1520	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#1518	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#1516	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#1515	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#1513	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#1512	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#1511	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#1508	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#1504	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#1501	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂×#328	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	1	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	1	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	4	1	no	—
366	Q₈×C₁₃	—	4	1	no	—
367	Q₈×C₁₃	—	4	1	no	—
368	Q₈×C₁₃	—	8	1	no	—
369	Q₈×C₁₃	—	8	1	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	2	no	—
372	D₄×C₁₃	—	4	1	no	—
373	D₄×C₁₃	—	4	1	no	—
374	D₄×C₁₃	—	4	1	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	1	no	—
377	D₄×C₁₃	—	4	1	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	1	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	4	1	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	1	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	1	no	—
413	C₂×C₄×C₁₃	—	4	1	no	—
414	C₂×C₄×C₁₃	—	4	1	no	—
415	C₂×C₄×C₁₃	—	4	1	no	—
416	C₂×C₄×C₁₃	—	4	1	no	—
417	C₂×C₄×C₁₃	—	8	1	no	—
418	C₂×C₄×C₁₃	—	8	1	no	—
419	C₂×C₄×C₁₃	—	8	1	no	—
420	C₂×C₄×C₁₃	—	8	1	no	—
421	C₂×C₄×C₁₃	—	8	4	no	—
422	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₈×C₁₃	—	4	1	no	—
433	C₈×C₁₃	—	4	1	no	—
434	C₈×C₁₃	—	4	1	no	—
435	C₈×C₁₃	—	4	1	no	—
436	#556	C₄×C₁₃	1	1	yes	characteristic, complemented
437	#554	—	2	1	no	—
438	#552	C₄×C₁₃	1	1	yes	characteristic, complemented
439	#552	C₄×C₁₃	1	1	yes	characteristic, complemented
440	#551	—	2	1	no	—
441	#551	—	2	1	no	—
442	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
443	#548	C₄×C₁₃	1	1	yes	characteristic, complemented
444	#548	C₄×C₁₃	1	1	yes	characteristic, complemented
445	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
446	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
447	#546	—	2	1	no	—
448	#542	—	2	1	no	—
449	#539	—	2	1	no	—
450	#539	—	2	1	no	—
451	#533	C₂²×C₁₃	1	1	yes	characteristic
452	#529	C₂²×C₁₃	1	1	yes	characteristic
453	#525	C₂²×C₁₃	1	1	yes	characteristic
454	#525	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
456	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
457	#520	—	2	1	no	—
458	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
459	#436	—	2	1	no	—
460	#435	—	2	1	no	—
461	#435	—	2	1	no	—
462	C₈×D₄	—	2	1	no	—
463	#432	C₂²×C₁₃	1	1	yes	characteristic
464	#431	C₂²×C₁₃	1	1	yes	characteristic
465	#407	C₂²×C₁₃	1	1	yes	characteristic
466	#407	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
469	#388	—	2	1	no	—
470	#387	—	2	1	no	—
471	#386	—	2	1	no	—
472	#385	—	2	1	no	—
473	#383	C₂²×C₁₃	1	1	yes	characteristic
474	#382	C₂²×C₁₃	1	1	yes	characteristic
475	#381	C₂²×C₁₃	1	1	yes	characteristic
476	#380	C₂²×C₁₃	1	1	yes	characteristic
477	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
479	#328	C₂²×C₁₃	1	1	yes	characteristic
480	#328	C₂²×C₁₃	1	1	yes	characteristic
481	#328	C₂²×C₁₃	1	1	yes	characteristic
482	#328	C₂²×C₁₃	1	1	yes	characteristic
483	#328	C₂²×C₁₃	1	1	yes	characteristic
484	#328	C₂²×C₁₃	1	1	yes	characteristic
485	#328	C₂²×C₁₃	1	1	yes	characteristic
486	#328	C₂²×C₁₃	1	1	yes	characteristic
487	#328	C₂²×C₁₃	1	1	yes	characteristic
488	#328	C₂²×C₁₃	1	1	yes	characteristic
489	#328	C₂²×C₁₃	1	1	yes	characteristic
490	#328	C₂²×C₁₃	1	1	yes	characteristic
491	#327	C₂²×C₁₃	1	1	yes	characteristic
492	#327	C₂²×C₁₃	1	1	yes	characteristic
493	#327	C₂²×C₁₃	1	1	yes	characteristic
494	#327	C₂²×C₁₃	1	1	yes	characteristic
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	1	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
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	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	8	1	no	—
514	C₂²×C₁₃	—	8	1	no	—
515	C₂²×C₁₃	#421	1	2	yes	—
516	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
517	C₂²×C₁₃	#577	1	1	yes	characteristic
518	C₂²×C₁₃	#578	1	1	yes	characteristic
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	1	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	2	1	no	—
527	C₄×C₁₃	—	2	1	no	—
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	1	no	—
534	C₄×C₁₃	—	4	1	no	—
535	C₄×C₁₃	—	4	1	no	—
536	C₄×C₁₃	—	8	1	no	—
537	C₄×C₁₃	—	8	1	no	—
538	C₄×C₁₃	—	8	1	no	—
539	C₄×C₁₃	—	8	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
542	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
543	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
545	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
546	C₂³×C₄	—	2	1	no	—
547	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×M₁₆	—	2	1	no	—
550	C₂×M₁₆	—	2	1	no	—
551	C₂²×C₈	—	2	1	no	—
552	C₂²×C₈	—	2	1	no	—
553	C₄⋊Q₈	—	2	1	no	—
554	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
555	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
556	#126	—	2	1	no	—
557	#126	—	2	1	no	—
558	#126	—	2	1	no	—
559	#126	—	2	1	no	—
560	#126	—	2	1	no	—
561	#125	—	2	1	no	—
562	#125	—	2	1	no	—
563	#125	—	2	1	no	—
564	#125	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
565	#124	—	2	1	no	—
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
569	#123	—	2	1	no	—
570	#123	—	2	1	no	—
571	#123	—	2	1	no	—
572	#123	—	2	1	no	—
573	#123	—	2	1	no	—
574	#123	—	2	1	no	—
575	#123	—	2	1	no	—
576	#123	—	2	1	no	—
577	#123	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
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	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
589	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
590	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
591	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
592	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
593	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
594	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	#121	—	2	1	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
601	#121	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
602	#121	C₂³×C₁₃	1	1	yes	characteristic
603	#120	—	2	1	no	—
604	#120	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
608	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
609	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
619	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
620	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
621	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
622	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
623	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
624	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
625	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
626	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
627	#117	—	2	1	no	—
628	#117	—	2	1	no	—
629	#117	—	2	1	no	—
630	#117	—	2	1	no	—
631	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
632	#117	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
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	C₂×C₄×C₁₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
640	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₁₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
650	C₄⋊C₈	—	2	1	no	—
651	C₄⋊C₈	—	2	1	no	—
652	C₂²⋊C₈	—	2	1	no	—
653	C₂²⋊C₈	—	2	1	no	—
654	C₂²⋊C₈	—	2	1	no	—
655	C₂²⋊C₈	—	2	1	no	—
656	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
657	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
658	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
660	#97	—	2	1	no	—
661	C₄×C₈	—	2	1	no	—
662	#95	—	2	1	no	—
663	#95	—	2	1	no	—
664	#95	—	2	1	no	—
665	#95	—	2	1	no	—
666	#95	—	2	1	no	—
667	#95	C₂³×C₁₃	1	1	yes	characteristic
668	#95	C₂³×C₁₃	1	1	yes	characteristic
669	#95	C₂³×C₁₃	1	1	yes	characteristic
670	#95	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₁₃	—	2	1	no	—
672	C₂×C₁₃	—	2	1	no	—
673	C₂×C₁₃	—	2	2	no	—
674	C₂×C₁₃	—	4	1	no	—
675	C₂×C₁₃	—	4	1	no	—
676	C₂×C₁₃	—	4	1	no	—
677	C₂×C₁₃	—	8	1	no	—
678	C₂×C₁₃	#2883	1	1	yes	characteristic
679	C₂×C₁₃	#2898	1	1	yes	characteristic
680	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
681	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
683	#41	—	4	4	no	—
684	#41	—	8	1	no	—
685	#41	—	8	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	1	no	—
689	C₂×Q₈	—	8	1	no	—
690	C₂×Q₈	—	8	1	no	—
691	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
692	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
693	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
701	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
702	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
703	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
704	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	8	1	no	—
718	C₂²×C₄	—	8	1	no	—
719	C₂²×C₄	—	8	1	no	—
720	C₂²×C₄	—	8	1	no	—
721	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	M₁₆	—	8	1	no	—
735	M₁₆	—	8	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	2	1	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	8	1	no	—
741	C₂×C₈	—	8	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	8	1	no	—
762	C₄⋊C₄	—	8	1	no	—
763	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
764	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
765	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
766	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	1	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	8	1	no	—
790	C₂²⋊C₄	—	8	1	no	—
791	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
792	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
793	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
794	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
795	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
796	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
797	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
798	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
799	C₄²	—	2	1	no	—
800	C₄²	—	2	1	no	—
801	C₄²	—	2	1	no	—
802	C₄²	—	2	1	no	—
803	C₄²	—	2	1	no	—
804	C₄²	—	8	1	no	—
805	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
806	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
807	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₁₃	#17598	1	1	yes	characteristic, direct product factor, Sylow
810	C₂³	—	2	2	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	4	1	no	—
817	C₂³	—	4	1	no	—
818	C₂³	—	4	1	no	—
819	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
820	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
821	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
822	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
823	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	Q₈	—	4	1	no	—
825	Q₈	—	4	1	no	—
826	Q₈	—	4	1	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	Q₈	—	8	1	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	4	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	2	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	8	1	no	—
840	D₄	—	8	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	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	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	8	1	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	1	no	—
880	C₂×C₄	—	8	1	no	—
881	C₂×C₄	—	8	4	no	—
882	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
883	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
884	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
885	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
886	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
887	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
888	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
889	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
892	C₈	—	4	1	no	—
893	C₈	—	4	1	no	—
894	C₈	—	4	1	no	—
895	C₈	—	4	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	8	1	no	—
915	C₂²	—	8	1	no	—
916	C₂²	C₁₃×#421	1	2	yes	—
917	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
918	C₂²	C₁₃×#577	1	1	yes	characteristic
919	C₂²	C₁₃×#578	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	1	no	—
933	C₄	—	4	1	no	—
934	C₄	—	4	1	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	8	1	no	—
938	C₄	—	8	1	no	—
939	C₄	—	8	1	no	—
940	C₄	—	8	1	no	—
941	C₂	—	2	1	no	—
942	C₂	—	2	1	no	—
943	C₂	—	2	2	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	8	1	no	—
948	C₂	C₁₃×#2883	1	1	yes	characteristic
949	C₂	C₁₃×#2898	1	1	yes	characteristic
950	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3520	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₁₃×#2974	C₂	semidirect
3. C₁₃×#2318	C₂	semidirect
4. C₁₃×#1521	C₂	semidirect
5. C₁₃×#1520	C₂	semidirect
6. C₁₃×#1518	C₂	semidirect
7. C₁₃×#1516	C₂	semidirect
8. C₁₃×#1515	C₂	semidirect
9. C₁₃×#1513	C₂	semidirect
10. C₁₃×#1512	C₂	semidirect
11. C₁₃×#1511	C₂	semidirect
12. C₁₃×#1508	C₂	semidirect
13. C₁₃×#1504	C₂	semidirect
14. C₁₃×#1501	C₂	semidirect
15. C₂×C₁₃×#328	C₂	semidirect
16. C₁₃×#556	C₄	semidirect
18. C₁₃×#552	C₄	semidirect
19. C₁₃×#552	C₄	semidirect
22. D₄×Q₈×C₁₃	C₄	semidirect
23. C₁₃×#548	C₄	semidirect
24. C₁₃×#548	C₄	semidirect
25. C₁₃×#547	C₄	semidirect
26. C₁₃×#547	C₄	semidirect
77. C₂×C₁₃×#41	C₂×C₄	semidirect
79. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
89. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
90. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
99. C₁₃×#125	C₂×C₄	semidirect
103. C₁₃×#124	C₂×C₄	semidirect
126. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
127. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
128. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
136. C₁₃×#121	C₂×C₄	semidirect
142. C₄×Q₈×C₁₃	C₂×C₄	semidirect
143. C₄×Q₈×C₁₃	C₂×C₄	semidirect
144. C₄×Q₈×C₁₃	C₂×C₄	semidirect
157. C₄×D₄×C₁₃	C₂×C₄	semidirect
167. C₁₃×#117	C₂×C₄	semidirect
174. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
206. #17598	C₁₃	direct (N × H)
336. #2974	C₂×C₁₃	semidirect
337. #2318	C₂×C₁₃	semidirect
338. #1521	C₂×C₁₃	semidirect
339. #1520	C₂×C₁₃	semidirect
340. #1518	C₂×C₁₃	semidirect
341. #1516	C₂×C₁₃	semidirect
342. #1515	C₂×C₁₃	semidirect
343. #1513	C₂×C₁₃	semidirect
344. #1512	C₂×C₁₃	semidirect
345. #1511	C₂×C₁₃	semidirect
346. #1508	C₂×C₁₃	semidirect
347. #1504	C₂×C₁₃	semidirect
348. #1501	C₂×C₁₃	semidirect
349. C₂×#328	C₂×C₁₃	semidirect
436. #556	C₄×C₁₃	semidirect
438. #552	C₄×C₁₃	semidirect
439. #552	C₄×C₁₃	semidirect
442. D₄×Q₈	C₄×C₁₃	semidirect
443. #548	C₄×C₁₃	semidirect
444. #548	C₄×C₁₃	semidirect
445. #547	C₄×C₁₃	semidirect
446. #547	C₄×C₁₃	semidirect
542. C₂×#41	C₂×C₄×C₁₃	semidirect
544. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
554. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
555. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
564. #125	C₂×C₄×C₁₃	semidirect
568. #124	C₂×C₄×C₁₃	semidirect
591. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
592. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
593. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
601. #121	C₂×C₄×C₁₃	semidirect
607. C₄×Q₈	C₂×C₄×C₁₃	semidirect
608. C₄×Q₈	C₂×C₄×C₁₃	semidirect
609. C₄×Q₈	C₂×C₄×C₁₃	semidirect
622. C₄×D₄	C₂×C₄×C₁₃	semidirect
632. #117	C₂×C₄×C₁₃	semidirect
639. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
809. C₁₃	#17598	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×#3520	2
C₁₃×#2974	2
C₁₃×#2318	2
C₁₃×#1521	2
C₁₃×#1520	2
C₁₃×#1518	2
C₁₃×#1516	2
C₁₃×#1515	2
C₁₃×#1513	2
C₁₃×#1512	2
C₁₃×#1511	2
C₁₃×#1508	2
C₁₃×#1504	2
C₁₃×#1501	2
C₂×C₁₃×#328	2
#17598	13

Subgroups — C13×#17598 #15703937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17598 #15703937