Subgroups — C₁₃×#17679 #15704018

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1536	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1530	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1527	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1527	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₄	1	1	yes	characteristic
17	C₁₃×#556	C₄	1	1	yes	characteristic
18	C₁₃×#555	—	2	1	no	—
19	C₁₃×#551	—	2	1	no	—
20	C₁₃×#551	—	2	1	no	—
21	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
22	C₁₃×#548	C₄	1	1	yes	characteristic
23	C₁₃×#548	C₄	1	1	yes	characteristic
24	C₁₃×#546	—	2	1	no	—
25	C₁₃×#546	C₄	1	1	yes	characteristic
26	C₁₃×#546	C₄	1	1	yes	characteristic
27	D₄²×C₁₃	C₄	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#538	—	2	1	no	—
30	C₁₃×#538	—	2	1	no	—
31	C₁₃×#532	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#529	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₁₃×#518	—	2	1	no	—
38	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
39	C₁₃×#446	—	2	1	no	—
40	C₁₃×#435	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₈×D₄×C₁₃	—	2	1	no	—
43	C₁₃×#433	—	2	1	no	—
44	C₁₃×#433	—	2	1	no	—
45	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#424	—	2	1	no	—
53	C₁₃×#408	—	2	1	no	—
54	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#329	C₂²	1	1	yes	characteristic
64	C₁₃×#329	C₂²	1	1	yes	characteristic
65	C₁₃×#329	C₂²	1	1	yes	characteristic
66	C₁₃×#329	C₂²	1	1	yes	characteristic
67	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#329	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₁₃×M₁₆	—	2	1	no	—
84	C₂×C₁₃×M₁₆	—	2	1	no	—
85	C₂²×C₈×C₁₃	—	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
90	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
97	C₁₃×#124	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	—	2	1	no	—
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
107	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
108	C₁₃×#124	C₂³	1	1	yes	characteristic
109	C₁₃×#124	C₂³	1	1	yes	characteristic
110	C₁₃×#124	C₂³	1	1	yes	characteristic
111	C₁₃×#123	—	2	1	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×#123	—	2	1	no	—
114	C₁₃×#123	—	2	1	no	—
115	C₁₃×#123	—	2	1	no	—
116	C₁₃×#123	—	2	1	no	—
117	C₁₃×#123	—	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×#121	—	2	1	no	—
127	C₁₃×#121	—	2	1	no	—
128	C₁₃×#121	—	2	1	no	—
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
134	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
135	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
136	C₁₃×#120	—	2	1	no	—
137	C₁₃×#120	—	2	1	no	—
138	C₁₃×#120	—	2	1	no	—
139	C₁₃×#120	—	2	1	no	—
140	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
142	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
143	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
144	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
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
158	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
159	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
160	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
161	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
162	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
163	C₁₃×#117	—	2	1	no	—
164	C₁₃×#117	—	2	1	no	—
165	C₁₃×#117	—	2	1	no	—
166	C₁₃×#117	—	2	1	no	—
167	C₁₃×#117	D₄	1	1	yes	characteristic
168	C₁₃×#117	D₄	1	1	yes	characteristic
169	C₁₃×#117	D₄	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
172	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊C₈	—	2	1	no	—
180	C₁₃×C₄⋊C₈	—	2	1	no	—
181	C₁₃×C₄⋊C₈	—	2	1	no	—
182	C₁₃×C₄⋊C₈	—	2	1	no	—
183	C₁₃×C₄⋊C₈	—	2	1	no	—
184	C₁₃×C₄⋊C₈	—	2	1	no	—
185	C₁₃×C₄⋊C₈	—	2	1	no	—
186	C₁₃×C₂²⋊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	—	2	1	no	—
192	C₁₃×C₂²⋊C₈	—	2	1	no	—
193	C₁₃×#97	—	2	1	no	—
194	C₁₃×#97	—	2	1	no	—
195	C₁₃×#97	—	2	1	no	—
196	C₁₃×#97	C₂³	1	1	yes	characteristic
197	C₁₃×#97	C₂³	1	1	yes	characteristic
198	C₁₃×#97	C₂³	1	1	yes	characteristic
199	C₁₃×#97	C₂³	1	1	yes	characteristic
200	C₁₃×#97	C₂³	1	1	yes	characteristic
201	C₁₃×#97	C₂³	1	1	yes	characteristic
202	C₁₃×#97	C₂³	1	1	yes	characteristic
203	C₁₃×#97	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₁₃	—	2	1	no	—
205	C₄×C₈×C₁₃	—	2	1	no	—
206	#17679	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂⁴×C₁₃	—	2	1	no	—
208	C₂⁴×C₁₃	—	2	1	no	—
209	C₁₃×#41	—	4	2	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	—	8	1	no	—
215	C₂×Q₈×C₁₃	—	8	1	no	—
216	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	4	4	no	—
230	C₂×D₄×C₁₃	—	8	1	no	—
231	C₂×D₄×C₁₃	—	8	1	no	—
232	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
235	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
236	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
237	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	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	C₁₃×M₁₆	—	4	2	no	—
255	C₁₃×M₁₆	—	4	2	no	—
256	C₂×C₈×C₁₃	—	2	1	no	—
257	C₂×C₈×C₁₃	—	2	1	no	—
258	C₂×C₈×C₁₃	—	2	1	no	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	4	2	no	—
265	C₂×C₈×C₁₃	—	4	2	no	—
266	C₂×C₈×C₁₃	—	4	2	no	—
267	C₁₃×C₄⋊C₄	—	2	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	C₂²⋊C₄	1	1	yes	characteristic
278	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
282	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
283	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
284	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	1	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
310	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
311	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
312	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
313	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
314	C₄²×C₁₃	—	2	1	no	—
315	C₄²×C₁₃	—	2	1	no	—
316	C₄²×C₁₃	—	2	1	no	—
317	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
320	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
327	#3514	C₂×C₁₃	1	1	yes	characteristic
328	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
329	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#1536	C₂×C₁₃	1	1	yes	characteristic, complemented
331	#1535	C₂×C₁₃	1	1	yes	characteristic, complemented
332	#1535	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#1533	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#1532	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#1532	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#1530	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#1527	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#1527	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#329	C₂×C₁₃	1	1	yes	characteristic, complemented
342	C₂³×C₁₃	—	2	1	no	—
343	C₂³×C₁₃	—	2	1	no	—
344	C₂³×C₁₃	—	2	1	no	—
345	C₂³×C₁₃	—	4	2	no	—
346	C₂³×C₁₃	—	4	2	no	—
347	C₂³×C₁₃	—	8	1	no	—
348	C₂³×C₁₃	—	8	1	no	—
349	C₂³×C₁₃	—	8	1	no	—
350	C₂³×C₁₃	—	8	1	no	—
351	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	Q₈×C₁₃	—	4	1	no	—
355	Q₈×C₁₃	—	4	1	no	—
356	Q₈×C₁₃	—	4	1	no	—
357	Q₈×C₁₃	—	4	1	no	—
358	Q₈×C₁₃	—	8	1	no	—
359	Q₈×C₁₃	—	8	1	no	—
360	D₄×C₁₃	—	2	2	no	—
361	D₄×C₁₃	—	2	2	no	—
362	D₄×C₁₃	—	4	1	no	—
363	D₄×C₁₃	—	4	2	no	—
364	D₄×C₁₃	—	4	1	no	—
365	D₄×C₁₃	—	4	1	no	—
366	D₄×C₁₃	—	4	1	no	—
367	D₄×C₁₃	—	4	2	no	—
368	D₄×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	8	1	no	—
370	D₄×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	8	1	no	—
372	D₄×C₁₃	—	8	1	no	—
373	D₄×C₁₃	—	8	1	no	—
374	D₄×C₁₃	—	8	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	1	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	1	no	—
383	C₂×C₄×C₁₃	—	4	1	no	—
384	C₂×C₄×C₁₃	—	4	1	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	8	1	no	—
391	C₂×C₄×C₁₃	—	8	1	no	—
392	C₂×C₄×C₁₃	—	8	1	no	—
393	C₂×C₄×C₁₃	—	8	1	no	—
394	C₂×C₄×C₁₃	—	8	1	no	—
395	C₂×C₄×C₁₃	—	8	1	no	—
396	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₈×C₁₃	—	2	2	no	—
409	C₈×C₁₃	—	4	1	no	—
410	C₈×C₁₃	—	4	1	no	—
411	C₈×C₁₃	—	4	1	no	—
412	C₈×C₁₃	—	4	1	no	—
413	C₈×C₁₃	—	4	1	no	—
414	C₈×C₁₃	—	4	1	no	—
415	C₈×C₁₃	—	4	1	no	—
416	#559	C₄×C₁₃	1	1	yes	characteristic
417	#556	C₄×C₁₃	1	1	yes	characteristic
418	#555	—	2	1	no	—
419	#551	—	2	1	no	—
420	#551	—	2	1	no	—
421	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
422	#548	C₄×C₁₃	1	1	yes	characteristic
423	#548	C₄×C₁₃	1	1	yes	characteristic
424	#546	—	2	1	no	—
425	#546	C₄×C₁₃	1	1	yes	characteristic
426	#546	C₄×C₁₃	1	1	yes	characteristic
427	D₄²	C₄×C₁₃	1	1	yes	characteristic
428	#542	—	2	1	no	—
429	#538	—	2	1	no	—
430	#538	—	2	1	no	—
431	#532	C₂²×C₁₃	1	1	yes	characteristic
432	#529	C₂²×C₁₃	1	1	yes	characteristic
433	#529	C₂²×C₁₃	1	1	yes	characteristic
434	#529	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
437	#518	—	2	1	no	—
438	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
439	#446	—	2	1	no	—
440	#435	—	2	1	no	—
441	#435	—	2	1	no	—
442	C₈×D₄	—	2	1	no	—
443	#433	—	2	1	no	—
444	#433	—	2	1	no	—
445	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
446	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
447	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#424	—	2	1	no	—
453	#408	—	2	1	no	—
454	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
462	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#329	C₂²×C₁₃	1	1	yes	characteristic
464	#329	C₂²×C₁₃	1	1	yes	characteristic
465	#329	C₂²×C₁₃	1	1	yes	characteristic
466	#329	C₂²×C₁₃	1	1	yes	characteristic
467	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#329	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	2	1	no	—
478	C₂²×C₁₃	—	2	1	no	—
479	C₂²×C₁₃	—	2	1	no	—
480	C₂²×C₁₃	—	2	1	no	—
481	C₂²×C₁₃	—	2	1	no	—
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	4	1	no	—
484	C₂²×C₁₃	—	4	1	no	—
485	C₂²×C₁₃	—	4	1	no	—
486	C₂²×C₁₃	—	4	1	no	—
487	C₂²×C₁₃	—	4	1	no	—
488	C₂²×C₁₃	—	4	1	no	—
489	C₂²×C₁₃	—	4	1	no	—
490	C₂²×C₁₃	—	4	1	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	16	2	no	—
493	C₂²×C₁₃	—	16	2	no	—
494	C₂²×C₁₃	#421	1	2	yes	—
495	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
496	C₄×C₁₃	—	2	1	no	—
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	1	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	—	4	1	no	—
511	C₄×C₁₃	—	4	1	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
514	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
515	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
517	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
520	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
521	C₂×M₁₆	—	2	1	no	—
522	C₂×M₁₆	—	2	1	no	—
523	C₂²×C₈	—	2	1	no	—
524	C₂²×C₈	—	2	1	no	—
525	C₂²×C₈	—	2	1	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
528	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
529	#126	—	2	1	no	—
530	#126	—	2	1	no	—
531	#126	—	2	1	no	—
532	#126	—	2	1	no	—
533	#126	—	2	1	no	—
534	#125	C₂³×C₁₃	1	1	yes	characteristic
535	#124	—	2	1	no	—
536	#124	—	2	1	no	—
537	#124	—	2	1	no	—
538	#124	—	2	1	no	—
539	#124	—	2	1	no	—
540	#124	—	2	1	no	—
541	#124	—	2	1	no	—
542	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
543	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
544	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
545	#124	C₂×C₄×C₁₃	1	1	yes	characteristic
546	#124	C₂³×C₁₃	1	1	yes	characteristic
547	#124	C₂³×C₁₃	1	1	yes	characteristic
548	#124	C₂³×C₁₃	1	1	yes	characteristic
549	#123	—	2	1	no	—
550	#123	—	2	1	no	—
551	#123	—	2	1	no	—
552	#123	—	2	1	no	—
553	#123	—	2	1	no	—
554	#123	—	2	1	no	—
555	#123	—	2	1	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
562	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
563	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
564	#121	—	2	1	no	—
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
572	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
573	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
574	#120	—	2	1	no	—
575	#120	—	2	1	no	—
576	#120	—	2	1	no	—
577	#120	—	2	1	no	—
578	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
579	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
580	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
581	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
593	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
594	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
595	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
596	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
597	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
598	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
599	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
600	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
601	#117	—	2	1	no	—
602	#117	—	2	1	no	—
603	#117	—	2	1	no	—
604	#117	—	2	1	no	—
605	#117	D₄×C₁₃	1	1	yes	characteristic
606	#117	D₄×C₁₃	1	1	yes	characteristic
607	#117	D₄×C₁₃	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
617	C₄⋊C₈	—	2	1	no	—
618	C₄⋊C₈	—	2	1	no	—
619	C₄⋊C₈	—	2	1	no	—
620	C₄⋊C₈	—	2	1	no	—
621	C₄⋊C₈	—	2	1	no	—
622	C₄⋊C₈	—	2	1	no	—
623	C₄⋊C₈	—	2	1	no	—
624	C₂²⋊C₈	—	2	1	no	—
625	C₂²⋊C₈	—	2	1	no	—
626	C₂²⋊C₈	—	2	1	no	—
627	C₂²⋊C₈	—	2	1	no	—
628	C₂²⋊C₈	—	2	1	no	—
629	C₂²⋊C₈	—	2	1	no	—
630	C₂²⋊C₈	—	2	1	no	—
631	#97	—	2	1	no	—
632	#97	—	2	1	no	—
633	#97	—	2	1	no	—
634	#97	C₂³×C₁₃	1	1	yes	characteristic
635	#97	C₂³×C₁₃	1	1	yes	characteristic
636	#97	C₂³×C₁₃	1	1	yes	characteristic
637	#97	C₂³×C₁₃	1	1	yes	characteristic
638	#97	C₂³×C₁₃	1	1	yes	characteristic
639	#97	C₂³×C₁₃	1	1	yes	characteristic
640	#97	C₂³×C₁₃	1	1	yes	characteristic
641	#97	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×C₈	—	2	1	no	—
643	C₄×C₈	—	2	1	no	—
644	C₂×C₁₃	—	2	2	no	—
645	C₂×C₁₃	—	4	1	no	—
646	C₂×C₁₃	—	4	1	no	—
647	C₂×C₁₃	—	8	1	no	—
648	C₂×C₁₃	—	8	1	no	—
649	C₂×C₁₃	—	8	1	no	—
650	C₂×C₁₃	#2888	1	1	yes	characteristic
651	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
652	C₂×C₁₃	#2901	1	1	yes	characteristic
653	C₂⁴	—	2	1	no	—
654	C₂⁴	—	2	1	no	—
655	#41	—	4	2	no	—
656	#41	—	8	1	no	—
657	#41	—	8	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	8	1	no	—
661	C₂×Q₈	—	8	1	no	—
662	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
663	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
664	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
665	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	8	1	no	—
677	C₂×D₄	—	8	1	no	—
678	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
679	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
680	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
681	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
682	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
683	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
693	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
700	M₁₆	—	4	2	no	—
701	M₁₆	—	4	2	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	4	2	no	—
711	C₂×C₈	—	4	2	no	—
712	C₂×C₈	—	4	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
724	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
725	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
726	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
727	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
728	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
755	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
756	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
757	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
758	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
759	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	1	no	—
763	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
764	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
768	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
771	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₁₃	#17679	1	1	yes	characteristic, direct product factor, Sylow
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	4	2	no	—
779	C₂³	—	8	1	no	—
780	C₂³	—	8	1	no	—
781	C₂³	—	8	1	no	—
782	C₂³	—	8	1	no	—
783	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
784	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
785	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
786	Q₈	—	4	1	no	—
787	Q₈	—	4	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	4	1	no	—
790	Q₈	—	8	1	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	2	no	—
793	D₄	—	2	2	no	—
794	D₄	—	4	1	no	—
795	D₄	—	4	1	no	—
796	D₄	—	4	1	no	—
797	D₄	—	4	1	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	1	no	—
803	D₄	—	8	1	no	—
804	D₄	—	8	1	no	—
805	D₄	—	8	1	no	—
806	D₄	—	8	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	1	no	—
823	C₂×C₄	—	8	1	no	—
824	C₂×C₄	—	8	1	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	—	8	1	no	—
828	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
829	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
830	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
831	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
832	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
833	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
834	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
835	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
836	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
837	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₈	—	2	2	no	—
841	C₈	—	4	1	no	—
842	C₈	—	4	1	no	—
843	C₈	—	4	1	no	—
844	C₈	—	4	1	no	—
845	C₈	—	4	1	no	—
846	C₈	—	4	1	no	—
847	C₈	—	4	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	16	2	no	—
866	C₂²	—	16	2	no	—
867	C₂²	C₁₃×#421	1	2	yes	—
868	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	4	1	no	—
889	C₂	—	8	1	no	—
890	C₂	—	8	1	no	—
891	C₂	—	8	1	no	—
892	C₂	C₁₃×#2888	1	1	yes	characteristic
893	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
894	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#2923	C₂	semidirect
4. C₁₃×#1536	C₂	semidirect
5. C₁₃×#1535	C₂	semidirect
6. C₁₃×#1535	C₂	semidirect
7. C₁₃×#1533	C₂	semidirect
8. C₁₃×#1532	C₂	semidirect
9. C₁₃×#1532	C₂	semidirect
10. C₁₃×#1530	C₂	semidirect
11. C₁₃×#1529	C₂	semidirect
12. C₁₃×#1527	C₂	semidirect
13. C₁₃×#1527	C₂	semidirect
14. C₁₃×#1524	C₂	semidirect
15. C₂×C₁₃×#329	C₂	semidirect
45. C₁₃×#432	C₂²	semidirect
46. C₁₃×#432	C₂²	semidirect
47. C₁₃×#432	C₂²	semidirect
48. C₁₃×#432	C₂²	semidirect
49. C₁₃×#432	C₂²	semidirect
50. C₁₃×#432	C₂²	semidirect
51. C₁₃×#432	C₂²	semidirect
54. C₄×C₁₃×M₁₆	C₂²	semidirect
55. C₄×C₁₃×M₁₆	C₂²	semidirect
56. C₂×C₁₃×#97	C₂²	semidirect
57. C₂×C₁₃×#97	C₂²	semidirect
58. C₂×C₁₃×#97	C₂²	semidirect
59. C₁₃×#330	C₂²	semidirect
60. C₁₃×#330	C₂²	semidirect
61. C₁₃×#330	C₂²	semidirect
62. C₁₃×#330	C₂²	semidirect
67. C₁₃×#329	C₂²	semidirect
68. C₁₃×#329	C₂²	semidirect
69. C₁₃×#329	C₂²	semidirect
70. C₁₃×#329	C₂²	semidirect
71. C₁₃×#329	C₂²	semidirect
72. C₁₃×#329	C₂²	semidirect
73. C₁₃×#329	C₂²	semidirect
74. C₁₃×#329	C₂²	semidirect
206. #17679	C₁₃	direct (N × H)
328. #2970	C₂×C₁₃	semidirect
329. #2923	C₂×C₁₃	semidirect
330. #1536	C₂×C₁₃	semidirect
331. #1535	C₂×C₁₃	semidirect
332. #1535	C₂×C₁₃	semidirect
333. #1533	C₂×C₁₃	semidirect
334. #1532	C₂×C₁₃	semidirect
335. #1532	C₂×C₁₃	semidirect
336. #1530	C₂×C₁₃	semidirect
337. #1529	C₂×C₁₃	semidirect
338. #1527	C₂×C₁₃	semidirect
339. #1527	C₂×C₁₃	semidirect
340. #1524	C₂×C₁₃	semidirect
341. C₂×#329	C₂×C₁₃	semidirect
445. #432	C₂²×C₁₃	semidirect
446. #432	C₂²×C₁₃	semidirect
447. #432	C₂²×C₁₃	semidirect
448. #432	C₂²×C₁₃	semidirect
449. #432	C₂²×C₁₃	semidirect
450. #432	C₂²×C₁₃	semidirect
451. #432	C₂²×C₁₃	semidirect
454. C₄×M₁₆	C₂²×C₁₃	semidirect
455. C₄×M₁₆	C₂²×C₁₃	semidirect
456. C₂×#97	C₂²×C₁₃	semidirect
457. C₂×#97	C₂²×C₁₃	semidirect
458. C₂×#97	C₂²×C₁₃	semidirect
459. #330	C₂²×C₁₃	semidirect
460. #330	C₂²×C₁₃	semidirect
461. #330	C₂²×C₁₃	semidirect
462. #330	C₂²×C₁₃	semidirect
467. #329	C₂²×C₁₃	semidirect
468. #329	C₂²×C₁₃	semidirect
469. #329	C₂²×C₁₃	semidirect
470. #329	C₂²×C₁₃	semidirect
471. #329	C₂²×C₁₃	semidirect
472. #329	C₂²×C₁₃	semidirect
473. #329	C₂²×C₁₃	semidirect
474. #329	C₂²×C₁₃	semidirect
773. C₁₃	#17679	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×#3514	2
C₁₃×#2970	2
C₁₃×#2923	2
C₁₃×#1536	2
C₁₃×#1535	2
C₁₃×#1533	2
C₁₃×#1532	2
C₁₃×#1530	2
C₁₃×#1529	2
C₁₃×#1527	2
C₁₃×#1524	2
C₂×C₁₃×#329	2
#17679	13

Subgroups — C13×#17679 #15704018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17679 #15704018