Subgroups — C₁₃×#61480 #15747819

Order 3328.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3318	C₂	1	4	yes	maximal, complemented
9	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
10	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3176	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3122	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2948	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
20	C₁₃×#555	C₂²	1	2	yes	complemented
21	C₁₃×#554	C₂²	1	2	yes	complemented
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#553	C₂²	1	4	yes	complemented
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	—	2	4	no	—
27	D₄²×C₁₃	C₂²	1	4	yes	complemented
28	D₄²×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#540	C₂²	1	4	yes	complemented
30	C₁₃×#538	—	2	4	no	—
31	C₁₃×#532	C₂²	1	2	yes	complemented
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#525	—	2	2	no	—
34	C₂×C₁₃×#121	—	2	2	no	—
35	C₁₃×#518	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#499	C₂²	1	2	yes	complemented
39	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#493	C₂²	1	2	yes	complemented
41	C₁₃×#490	C₂²	1	4	yes	complemented
42	C₁₃×#486	C₂²	1	2	yes	complemented
43	C₁₃×#482	C₂²	1	4	yes	complemented
44	C₁₃×#482	C₂²	1	4	yes	complemented
45	C₁₃×#481	C₂²	1	4	yes	complemented
46	C₁₃×#478	C₂²	1	4	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#476	C₂²	1	2	yes	complemented
49	C₁₃×#476	C₂²	1	2	yes	complemented
50	C₁₃×#469	C₂²	1	4	yes	complemented
51	C₁₃×#466	C₂²	1	2	yes	complemented
52	C₁₃×#466	C₂²	1	2	yes	complemented
53	C₁₃×#466	C₂²	1	2	yes	complemented
54	C₁₃×#466	C₂²	1	2	yes	complemented
55	C₁₃×#459	C₂²	1	2	yes	complemented
56	C₁₃×#459	C₂²	1	4	yes	complemented
57	C₁₃×#459	C₂²	1	4	yes	complemented
58	C₁₃×#459	C₂²	1	2	yes	complemented
59	C₁₃×#447	C₂²	1	4	yes	complemented
60	C₁₃×#447	C₂²	1	4	yes	complemented
61	C₁₃×#447	C₂²	1	4	yes	complemented
62	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#442	C₂²	1	4	yes	complemented
65	C₁₃×#442	C₂²	1	4	yes	complemented
66	C₁₃×#442	C₂²	1	4	yes	complemented
67	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×D₈	C₂²	1	2	yes	—
69	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
71	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
72	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
74	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
76	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#435	C₂²	1	2	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#433	C₂²	1	2	yes	complemented
82	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#427	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
85	C₁₃×#418	C₂²	1	4	yes	complemented
86	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
87	C₁₃×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	—	2	2	no	—
91	C₂²×D₄×C₁₃	—	2	2	no	—
92	C₂²×D₄×C₁₃	—	2	4	no	—
93	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃	—	2	2	no	—
96	C₂×C₁₃×D₈	—	2	4	no	—
97	C₂×C₁₃×D₈	—	2	8	no	—
98	C₂×C₁₃×D₈	C₂³	1	2	yes	—
99	C₂×C₁₃×D₈	C₂³	1	2	yes	—
100	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×D₈	C₂³	1	4	yes	—
102	C₂×C₁₃×D₈	C₂³	1	2	yes	—
103	C₂×C₁₃×D₈	C₂³	1	4	yes	—
104	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#127	C₂³	1	2	yes	—
111	C₁₃×#127	C₂³	1	4	yes	—
112	C₁₃×#126	—	2	4	no	—
113	C₁₃×#126	D₄	1	2	yes	—
114	C₁₃×#125	D₄	1	1	yes	characteristic
115	C₁₃×#125	C₂³	1	4	yes	—
116	C₁₃×#124	—	2	4	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	D₄	1	1	yes	characteristic
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	D₄	1	2	yes	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	4	no	—
125	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
126	C₁₃×#121	—	2	4	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	4	no	—
132	C₁₃×#121	—	2	4	no	—
133	C₁₃×#121	—	2	4	no	—
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	D₄	1	1	yes	characteristic
136	C₁₃×#121	C₂³	1	4	yes	—
137	C₁₃×#121	C₂³	1	4	yes	—
138	C₁₃×#121	C₂³	1	4	yes	—
139	C₁₃×#120	—	2	4	no	—
140	C₁₃×#120	—	2	4	no	—
141	C₁₃×#120	—	2	4	no	—
142	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₁₃	—	2	4	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	—	2	2	no	—
147	C₄×D₄×C₁₃	—	2	2	no	—
148	C₄×D₄×C₁₃	—	2	2	no	—
149	C₄×D₄×C₁₃	C₂³	1	2	yes	—
150	C₄×D₄×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₄×D₄×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	C₂³	1	4	yes	—
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₄×D₄×C₁₃	C₂³	1	4	yes	—
156	C₄×D₄×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#117	—	2	2	no	—
159	C₁₃×#117	C₂³	1	4	yes	—
160	C₁₃×#117	C₂³	1	2	yes	—
161	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	2	yes	—
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	4	yes	—
173	C₁₃×#106	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×#102	C₂³	1	2	yes	—
179	C₁₃×#102	C₂³	1	2	yes	—
180	C₁₃×#102	C₂³	1	2	yes	—
181	C₁₃×#102	C₂³	1	2	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₁₃×#97	C₂³	1	2	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#61480	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂⁴×C₁₃	—	2	2	no	—
200	C₂⁴×C₁₃	—	2	4	no	—
201	C₁₃×#41	—	8	4	no	—
202	C₁₃×#41	—	8	4	no	—
203	C₂×Q₈×C₁₃	—	2	2	no	—
204	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂×D₄×C₁₃	—	2	4	no	—
206	C₂×D₄×C₁₃	—	2	8	no	—
207	C₂×D₄×C₁₃	—	2	4	no	—
208	C₂×D₄×C₁₃	—	2	4	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	4	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	4	no	—
216	C₂×D₄×C₁₃	—	4	2	no	—
217	C₂×D₄×C₁₃	—	4	4	no	—
218	C₂×D₄×C₁₃	—	8	4	no	—
219	C₂×D₄×C₁₃	—	8	8	no	—
220	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	2	no	—
227	C₂²×C₄×C₁₃	—	2	2	no	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	4	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	4	no	—
232	C₂²×C₄×C₁₃	—	2	2	no	—
233	C₂²×C₄×C₁₃	—	8	4	no	—
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₁₃×D₈	—	2	4	no	—
239	C₁₃×D₈	—	2	8	no	—
240	C₁₃×D₈	—	2	2	no	—
241	C₁₃×D₈	—	2	4	no	—
242	C₁₃×D₈	—	4	2	no	—
243	C₁₃×D₈	—	4	4	no	—
244	C₁₃×D₈	#41	1	4	yes	complemented
245	C₁₃×M₁₆	—	4	2	no	—
246	C₂×C₈×C₁₃	—	2	2	no	—
247	C₂×C₈×C₁₃	—	2	4	no	—
248	C₂×C₈×C₁₃	—	4	1	no	—
249	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	4	no	—
277	C₁₃×C₂²⋊C₄	—	2	4	no	—
278	C₁₃×C₂²⋊C₄	—	2	4	no	—
279	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
282	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
283	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
284	C₄²×C₁₃	—	2	4	no	—
285	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₁₃	C₂⁴	1	2	yes	—
290	#3519	C₂×C₁₃	1	2	yes	complemented
291	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3380	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3366	C₂×C₁₃	1	2	yes	complemented
294	#3341	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3339	C₂×C₁₃	1	2	yes	complemented
296	#3325	C₂×C₁₃	1	2	yes	complemented
297	#3318	C₂×C₁₃	1	4	yes	complemented
298	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
299	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3176	C₂×C₁₃	1	2	yes	complemented
301	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#3122	C₂×C₁₃	1	4	yes	complemented
303	#3109	C₂×C₁₃	1	2	yes	complemented
304	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#2948	C₂×C₁₃	1	2	yes	complemented
306	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	2	no	—
309	C₂³×C₁₃	—	2	4	no	—
310	C₂³×C₁₃	—	4	4	no	—
311	C₂³×C₁₃	—	4	8	no	—
312	C₂³×C₁₃	—	4	4	no	—
313	C₂³×C₁₃	—	8	2	no	—
314	C₂³×C₁₃	—	8	4	no	—
315	C₂³×C₁₃	—	8	4	no	—
316	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
317	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	8	2	no	—
320	D₄×C₁₃	—	2	4	no	—
321	D₄×C₁₃	—	2	2	no	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	4	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	2	4	no	—
327	D₄×C₁₃	—	4	4	no	—
328	D₄×C₁₃	—	4	8	no	—
329	D₄×C₁₃	—	4	8	no	—
330	D₄×C₁₃	—	4	4	no	—
331	D₄×C₁₃	—	8	4	no	—
332	D₄×C₁₃	—	8	2	no	—
333	D₄×C₁₃	—	8	4	no	—
334	D₄×C₁₃	—	8	4	no	—
335	D₄×C₁₃	—	8	4	no	—
336	D₄×C₁₃	C₂×#41	1	4	yes	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	8	2	no	—
349	C₂×C₄×C₁₃	—	8	2	no	—
350	C₂×C₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	8	4	no	—
352	C₂×C₄×C₁₃	—	8	4	no	—
353	C₂×C₄×C₁₃	—	8	2	no	—
354	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
363	C₈×C₁₃	—	2	1	no	—
364	C₈×C₁₃	—	2	2	no	—
365	C₈×C₁₃	—	2	1	no	—
366	C₈×C₁₃	—	2	1	no	—
367	C₈×C₁₃	—	2	2	no	—
368	C₈×C₁₃	C₂×#41	1	2	yes	—
369	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
371	#555	C₂²×C₁₃	1	2	yes	complemented
372	#554	C₂²×C₁₃	1	2	yes	complemented
373	#553	—	2	2	no	—
374	#553	C₂²×C₁₃	1	4	yes	complemented
375	#550	C₂²×C₁₃	1	2	yes	complemented
376	#546	—	2	2	no	—
377	#546	—	2	4	no	—
378	D₄²	C₂²×C₁₃	1	4	yes	complemented
379	D₄²	C₂²×C₁₃	1	2	yes	complemented
380	#540	C₂²×C₁₃	1	4	yes	complemented
381	#538	—	2	4	no	—
382	#532	C₂²×C₁₃	1	2	yes	complemented
383	#529	C₂²×C₁₃	1	1	yes	characteristic
384	#525	—	2	2	no	—
385	C₂×#121	—	2	2	no	—
386	#518	C₂²×C₁₃	1	4	yes	complemented
387	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
388	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#499	C₂²×C₁₃	1	2	yes	complemented
390	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
391	#493	C₂²×C₁₃	1	2	yes	complemented
392	#490	C₂²×C₁₃	1	4	yes	complemented
393	#486	C₂²×C₁₃	1	2	yes	complemented
394	#482	C₂²×C₁₃	1	4	yes	complemented
395	#482	C₂²×C₁₃	1	4	yes	complemented
396	#481	C₂²×C₁₃	1	4	yes	complemented
397	#478	C₂²×C₁₃	1	4	yes	complemented
398	#478	C₂²×C₁₃	1	4	yes	complemented
399	#476	C₂²×C₁₃	1	2	yes	complemented
400	#476	C₂²×C₁₃	1	2	yes	complemented
401	#469	C₂²×C₁₃	1	4	yes	complemented
402	#466	C₂²×C₁₃	1	2	yes	complemented
403	#466	C₂²×C₁₃	1	2	yes	complemented
404	#466	C₂²×C₁₃	1	2	yes	complemented
405	#466	C₂²×C₁₃	1	2	yes	complemented
406	#459	C₂²×C₁₃	1	2	yes	complemented
407	#459	C₂²×C₁₃	1	2	yes	complemented
408	#459	C₂²×C₁₃	1	4	yes	complemented
409	#459	C₂²×C₁₃	1	4	yes	complemented
410	#447	C₂²×C₁₃	1	4	yes	complemented
411	#447	C₂²×C₁₃	1	4	yes	complemented
412	#447	C₂²×C₁₃	1	4	yes	complemented
413	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#442	C₂²×C₁₃	1	4	yes	complemented
416	#442	C₂²×C₁₃	1	4	yes	complemented
417	#442	C₂²×C₁₃	1	4	yes	complemented
418	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
419	C₄×D₈	C₂²×C₁₃	1	2	yes	—
420	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
421	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
422	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
424	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
425	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
426	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
427	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	#435	C₂²×C₁₃	1	2	yes	complemented
430	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
431	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	#433	C₂²×C₁₃	1	2	yes	complemented
433	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#427	C₂²×C₁₃	1	2	yes	complemented
435	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#418	C₂²×C₁₃	1	4	yes	complemented
437	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
438	#405	C₂²×C₁₃	1	2	yes	complemented
439	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	2	4	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	2	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	4	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	4	no	—
452	C₂²×C₁₃	—	4	4	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	8	8	no	—
455	C₂²×C₁₃	—	16	8	no	—
456	C₂²×C₁₃	#576	1	2	yes	—
457	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
458	C₄×C₁₃	—	2	1	no	—
459	C₄×C₁₃	—	2	2	no	—
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	1	no	—
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	2	2	no	—
464	C₄×C₁₃	—	2	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	4	no	—
468	C₄×C₁₃	#576	1	2	yes	—
469	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
470	C₄×C₁₃	#585	1	1	yes	characteristic
471	C₂×#41	—	2	2	no	—
472	C₂×#41	—	2	2	no	—
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	4	no	—
475	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
477	C₂³×C₄	—	2	2	no	—
478	C₂×D₈	—	2	4	no	—
479	C₂×D₈	—	2	8	no	—
480	C₂×D₈	C₂³×C₁₃	1	2	yes	—
481	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×D₈	C₂³×C₁₃	1	2	yes	—
483	C₂×D₈	C₂³×C₁₃	1	4	yes	—
484	C₂×D₈	C₂³×C₁₃	1	2	yes	—
485	C₂×D₈	C₂³×C₁₃	1	4	yes	—
486	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
490	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
491	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
492	#127	C₂³×C₁₃	1	2	yes	—
493	#127	C₂³×C₁₃	1	4	yes	—
494	#126	—	2	4	no	—
495	#126	D₄×C₁₃	1	2	yes	—
496	#125	D₄×C₁₃	1	1	yes	characteristic
497	#125	C₂³×C₁₃	1	4	yes	—
498	#124	—	2	4	no	—
499	#124	—	2	2	no	—
500	#124	D₄×C₁₃	1	1	yes	characteristic
501	#123	—	2	4	no	—
502	#123	—	2	4	no	—
503	#123	—	2	4	no	—
504	#123	D₄×C₁₃	1	2	yes	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
508	#121	—	2	4	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	—	2	4	no	—
516	#121	—	2	4	no	—
517	#121	D₄×C₁₃	1	1	yes	characteristic
518	#121	C₂³×C₁₃	1	4	yes	—
519	#121	C₂³×C₁₃	1	4	yes	—
520	#121	C₂³×C₁₃	1	4	yes	—
521	#120	—	2	4	no	—
522	#120	—	2	4	no	—
523	#120	—	2	4	no	—
524	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	4	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	C₂³×C₁₃	1	2	yes	—
532	C₄×D₄	C₂³×C₁₃	1	2	yes	—
533	C₄×D₄	C₂³×C₁₃	1	2	yes	—
534	C₄×D₄	C₂³×C₁₃	1	2	yes	—
535	C₄×D₄	C₂³×C₁₃	1	4	yes	—
536	C₄×D₄	C₂³×C₁₃	1	4	yes	—
537	C₄×D₄	C₂³×C₁₃	1	4	yes	—
538	C₄×D₄	C₂³×C₁₃	1	2	yes	—
539	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
540	#117	—	2	2	no	—
541	#117	C₂³×C₁₃	1	4	yes	—
542	#117	C₂³×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₂²⋊C₄	—	2	2	no	—
546	C₂×C₂²⋊C₄	—	2	4	no	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
549	#107	C₂³×C₁₃	1	1	yes	characteristic
550	#107	C₂³×C₁₃	1	1	yes	characteristic
551	#107	C₂³×C₁₃	1	2	yes	—
552	#107	C₂³×C₁₃	1	2	yes	—
553	#107	C₂³×C₁₃	1	2	yes	—
554	#106	C₂³×C₁₃	1	4	yes	—
555	#106	C₂³×C₁₃	1	4	yes	—
556	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
559	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
560	#102	C₂³×C₁₃	1	2	yes	—
561	#102	C₂³×C₁₃	1	2	yes	—
562	#102	C₂³×C₁₃	1	2	yes	—
563	#102	C₂³×C₁₃	1	2	yes	—
564	#102	C₂³×C₁₃	1	4	yes	—
565	#102	C₂³×C₁₃	1	4	yes	—
566	#102	C₂³×C₁₃	1	4	yes	—
567	#102	C₂³×C₁₃	1	4	yes	—
568	#102	C₂³×C₁₃	1	4	yes	—
569	#102	C₂³×C₁₃	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
571	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
572	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
573	#97	C₂³×C₁₃	1	2	yes	—
574	#97	C₂³×C₁₃	1	2	yes	—
575	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
579	C₄×C₈	C₂³×C₁₃	1	2	yes	—
580	C₂×C₁₃	—	2	2	no	—
581	C₂×C₁₃	—	4	2	no	—
582	C₂×C₁₃	—	4	4	no	—
583	C₂×C₁₃	—	8	2	no	—
584	C₂×C₁₃	—	8	4	no	—
585	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
586	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
587	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	4	no	—
590	#41	—	8	4	no	—
591	#41	—	8	4	no	—
592	C₂×Q₈	—	2	2	no	—
593	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	8	4	no	—
608	C₂×D₄	—	8	8	no	—
609	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
610	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
611	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
613	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	8	4	no	—
623	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
627	D₈	—	2	4	no	—
628	D₈	—	2	8	no	—
629	D₈	—	2	2	no	—
630	D₈	—	2	4	no	—
631	D₈	—	4	2	no	—
632	D₈	—	4	4	no	—
633	D₈	C₁₃×#41	1	4	yes	complemented
634	M₁₆	—	4	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	4	no	—
637	C₂×C₈	—	4	1	no	—
638	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
642	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
643	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
673	C₄²	—	2	4	no	—
674	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₄²	C₂⁴×C₁₃	1	2	yes	—
679	C₁₃	#61480	1	1	yes	characteristic, direct product factor, Sylow
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	8	2	no	—
687	C₂³	—	8	4	no	—
688	C₂³	—	8	4	no	—
689	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
690	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
691	Q₈	—	2	2	no	—
692	Q₈	—	8	2	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	8	no	—
702	D₄	—	4	8	no	—
703	D₄	—	4	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	4	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	C₂×C₁₃×#41	1	4	yes	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	4	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	2	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
735	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
736	C₈	—	2	1	no	—
737	C₈	—	2	2	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×C₁₃×#41	1	2	yes	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	8	8	no	—
757	C₂²	—	16	8	no	—
758	C₂²	C₁₃×#576	1	2	yes	—
759	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	4	no	—
770	C₄	C₁₃×#576	1	2	yes	—
771	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
772	C₄	C₁₃×#585	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	4	no	—
776	C₂	—	8	2	no	—
777	C₂	—	8	4	no	—
778	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
779	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
780	C₂	C₂×C₁₃×#576	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 ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3519	C₂	semidirect
2. C₁₃×#3391	C₂	semidirect
3. C₁₃×#3380	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3341	C₂	semidirect
6. C₁₃×#3339	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3318	C₂	semidirect
9. D₄×C₁₃×D₈	C₂	semidirect
10. D₄×C₁₃×D₈	C₂	semidirect
11. C₁₃×#3176	C₂	semidirect
12. C₁₃×#3169	C₂	semidirect
13. C₁₃×#3122	C₂	semidirect
14. C₁₃×#3109	C₂	semidirect
15. C₁₃×#2966	C₂	semidirect
16. C₁₃×#2948	C₂	semidirect
17. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#555	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
23. C₁₃×#553	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
27. D₄²×C₁₃	C₂²	semidirect
28. D₄²×C₁₃	C₂²	semidirect
29. C₁₃×#540	C₂²	semidirect
31. C₁₃×#532	C₂²	semidirect
35. C₁₃×#518	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#500	C₂²	semidirect
38. C₁₃×#499	C₂²	semidirect
39. C₁₃×#493	C₂²	semidirect
40. C₁₃×#493	C₂²	semidirect
41. C₁₃×#490	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
43. C₁₃×#482	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#481	C₂²	semidirect
46. C₁₃×#478	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#476	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#469	C₂²	semidirect
51. C₁₃×#466	C₂²	semidirect
52. C₁₃×#466	C₂²	semidirect
53. C₁₃×#466	C₂²	semidirect
54. C₁₃×#466	C₂²	semidirect
55. C₁₃×#459	C₂²	semidirect
56. C₁₃×#459	C₂²	semidirect
57. C₁₃×#459	C₂²	semidirect
58. C₁₃×#459	C₂²	semidirect
59. C₁₃×#447	C₂²	semidirect
60. C₁₃×#447	C₂²	semidirect
61. C₁₃×#447	C₂²	semidirect
62. C₁₃×#446	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
64. C₁₃×#442	C₂²	semidirect
65. C₁₃×#442	C₂²	semidirect
66. C₁₃×#442	C₂²	semidirect
70. C₄×C₁₃×D₈	C₂²	semidirect
71. C₄×C₁₃×D₈	C₂²	semidirect
72. C₄×C₁₃×D₈	C₂²	semidirect
73. C₄×C₁₃×D₈	C₂²	semidirect
74. C₄×C₁₃×D₈	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
76. C₄×C₁₃×D₈	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₈×D₄×C₁₃	C₂²	semidirect
81. C₁₃×#433	C₂²	semidirect
82. C₁₃×#432	C₂²	semidirect
83. C₁₃×#427	C₂²	semidirect
84. C₂×C₁₃×#107	C₂²	semidirect
85. C₁₃×#418	C₂²	semidirect
86. C₂×C₁₃×#102	C₂²	semidirect
87. C₁₃×#405	C₂²	semidirect
88. C₂×C₄×C₈×C₁₃	C₂²	semidirect
198. #61480	C₁₃	direct (N × H)
244. C₁₃×D₈	#41	semidirect
290. #3519	C₂×C₁₃	semidirect
291. #3391	C₂×C₁₃	semidirect
292. #3380	C₂×C₁₃	semidirect
293. #3366	C₂×C₁₃	semidirect
294. #3341	C₂×C₁₃	semidirect
295. #3339	C₂×C₁₃	semidirect
296. #3325	C₂×C₁₃	semidirect
297. #3318	C₂×C₁₃	semidirect
298. D₄×D₈	C₂×C₁₃	semidirect
299. D₄×D₈	C₂×C₁₃	semidirect
300. #3176	C₂×C₁₃	semidirect
301. #3169	C₂×C₁₃	semidirect
302. #3122	C₂×C₁₃	semidirect
303. #3109	C₂×C₁₃	semidirect
304. #2966	C₂×C₁₃	semidirect
305. #2948	C₂×C₁₃	semidirect
306. C₂×C₄×D₈	C₂×C₁₃	semidirect
371. #555	C₂²×C₁₃	semidirect
372. #554	C₂²×C₁₃	semidirect
374. #553	C₂²×C₁₃	semidirect
375. #550	C₂²×C₁₃	semidirect
378. D₄²	C₂²×C₁₃	semidirect
379. D₄²	C₂²×C₁₃	semidirect
380. #540	C₂²×C₁₃	semidirect
382. #532	C₂²×C₁₃	semidirect
386. #518	C₂²×C₁₃	semidirect
387. C₂×C₄×D₄	C₂²×C₁₃	semidirect
388. #500	C₂²×C₁₃	semidirect
389. #499	C₂²×C₁₃	semidirect
390. #493	C₂²×C₁₃	semidirect
391. #493	C₂²×C₁₃	semidirect
392. #490	C₂²×C₁₃	semidirect
393. #486	C₂²×C₁₃	semidirect
394. #482	C₂²×C₁₃	semidirect
395. #482	C₂²×C₁₃	semidirect
396. #481	C₂²×C₁₃	semidirect
397. #478	C₂²×C₁₃	semidirect
398. #478	C₂²×C₁₃	semidirect
399. #476	C₂²×C₁₃	semidirect
400. #476	C₂²×C₁₃	semidirect
401. #469	C₂²×C₁₃	semidirect
402. #466	C₂²×C₁₃	semidirect
403. #466	C₂²×C₁₃	semidirect
404. #466	C₂²×C₁₃	semidirect
405. #466	C₂²×C₁₃	semidirect
406. #459	C₂²×C₁₃	semidirect
407. #459	C₂²×C₁₃	semidirect
408. #459	C₂²×C₁₃	semidirect
409. #459	C₂²×C₁₃	semidirect
410. #447	C₂²×C₁₃	semidirect
411. #447	C₂²×C₁₃	semidirect
412. #447	C₂²×C₁₃	semidirect
413. #446	C₂²×C₁₃	semidirect
414. C₈×Q₈	C₂²×C₁₃	semidirect
415. #442	C₂²×C₁₃	semidirect
416. #442	C₂²×C₁₃	semidirect
417. #442	C₂²×C₁₃	semidirect
421. C₄×D₈	C₂²×C₁₃	semidirect
422. C₄×D₈	C₂²×C₁₃	semidirect
423. C₄×D₈	C₂²×C₁₃	semidirect
424. C₄×D₈	C₂²×C₁₃	semidirect
425. C₄×D₈	C₂²×C₁₃	semidirect
426. C₄×D₈	C₂²×C₁₃	semidirect
427. C₄×D₈	C₂²×C₁₃	semidirect
428. #436	C₂²×C₁₃	semidirect
429. #435	C₂²×C₁₃	semidirect
430. C₈×D₄	C₂²×C₁₃	semidirect
431. C₈×D₄	C₂²×C₁₃	semidirect
432. #433	C₂²×C₁₃	semidirect
433. #432	C₂²×C₁₃	semidirect
434. #427	C₂²×C₁₃	semidirect
435. C₂×#107	C₂²×C₁₃	semidirect
436. #418	C₂²×C₁₃	semidirect
437. C₂×#102	C₂²×C₁₃	semidirect
438. #405	C₂²×C₁₃	semidirect
439. C₂×C₄×C₈	C₂²×C₁₃	semidirect
633. D₈	C₁₃×#41	semidirect
679. C₁₃	#61480	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×#3519	2
C₁₃×#3391	2
C₁₃×#3380	2
C₁₃×#3366	2
C₁₃×#3341	2
C₁₃×#3339	2
C₁₃×#3325	2
C₁₃×#3318	2
D₄×C₁₃×D₈	2
C₁₃×#3176	2
C₁₃×#3169	2
C₁₃×#3122	2
C₁₃×#3109	2
C₁₃×#2966	2
C₁₃×#2948	2
C₂×C₄×C₁₃×D₈	2
#61480	13

Subgroups — C13×#61480 #15747819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61480 #15747819