Subgroups — C₁₃×#60701 #15747040

Order 3328.

1976 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3185	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3182	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3181	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3172	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3170	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3167	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3056	C₂	1	4	yes	maximal, complemented
14	C₄×C₁₃×#137	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	4	yes	—
17	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	—	2	1	no	—
21	C₁₃×#533	—	2	1	no	—
22	C₁₃×#533	C₂²	1	2	yes	—
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	2	yes	—
26	C₁₃×#533	C₂²	1	2	yes	—
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₁₃×#532	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×#529	—	2	1	no	—
35	C₁₃×#529	—	2	1	no	—
36	C₁₃×#529	—	2	1	no	—
37	C₁₃×#529	—	2	1	no	—
38	C₁₃×#529	C₂²	1	2	yes	—
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₂×C₁₃×#125	—	2	1	no	—
41	C₁₃×#525	—	2	1	no	—
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#525	C₂²	1	2	yes	—
44	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	—	2	1	no	—
48	C₄×C₁₃×#41	C₂²	1	2	yes	—
49	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
51	C₂×C₁₃×#117	—	2	1	no	—
52	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#501	C₂²	1	4	yes	complemented
54	C₁₃×#500	C₂²	1	2	yes	complemented
55	C₁₃×#498	C₂²	1	2	yes	complemented
56	C₁₃×#497	C₂²	1	4	yes	complemented
57	C₁₃×#494	C₂²	1	2	yes	complemented
58	C₁₃×#492	C₂²	1	2	yes	complemented
59	C₁₃×#491	C₂²	1	4	yes	complemented
60	C₁₃×#489	C₂²	1	4	yes	complemented
61	C₁₃×#487	C₂²	1	2	yes	complemented
62	C₁₃×#487	C₂²	1	2	yes	complemented
63	C₁₃×#487	C₂²	1	2	yes	complemented
64	C₁₃×#486	C₂²	1	2	yes	complemented
65	C₁₃×#470	C₂²	1	8	yes	—
66	C₁₃×#468	C₂²	1	8	yes	—
67	C₁₃×#467	C₂²	1	8	yes	—
68	C₁₃×#465	C₂²	1	8	yes	—
69	C₁₃×#441	C₂²	1	8	yes	complemented
70	C₁₃×#440	C₂²	1	8	yes	complemented
71	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
72	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
73	C₁₃×#428	C₂²	1	4	yes	—
74	C₁₃×#419	C₂²	1	4	yes	—
75	C₁₃×#417	C₂²	1	4	yes	—
76	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
77	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
78	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
81	C₂×C₁₃×#97	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
83	C₂×C₁₃×#41	—	2	1	no	—
84	C₂×C₁₃×#41	—	2	1	no	—
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	—	2	1	no	—
87	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#137	—	2	16	no	—
92	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
94	C₂×C₁₃×M₁₆	—	2	8	no	—
95	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
97	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
98	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
99	C₁₃×C₄⋊Q₈	—	2	1	no	—
100	C₁₃×C₄⋊Q₈	—	2	1	no	—
101	C₁₃×C₄⋊Q₈	—	2	1	no	—
102	C₁₃×C₄⋊Q₈	—	2	1	no	—
103	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₃×#127	C₂³	1	1	yes	characteristic
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#125	—	2	2	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	—	2	2	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	—	2	1	no	—
118	C₁₃×#125	—	2	1	no	—
119	C₁₃×#125	C₂³	1	2	yes	—
120	C₁₃×#124	—	2	1	no	—
121	C₁₃×#124	—	2	1	no	—
122	C₁₃×#124	C₂³	1	2	yes	—
123	C₁₃×#123	—	2	2	no	—
124	C₁₃×#123	—	2	2	no	—
125	C₁₃×#123	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	2	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×#121	—	2	1	no	—
141	C₁₃×#121	—	2	1	no	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	1	no	—
144	C₁₃×#121	C₂³	1	2	yes	—
145	C₁₃×#121	C₂³	1	2	yes	—
146	C₁₃×#120	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	2	no	—
163	C₄×D₄×C₁₃	—	2	2	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	C₂³	1	2	yes	—
172	C₄×D₄×C₁₃	C₂³	1	2	yes	—
173	C₁₃×#117	—	2	2	no	—
174	C₁₃×#117	—	2	2	no	—
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	2	no	—
177	C₁₃×#117	—	2	1	no	—
178	C₁₃×#117	—	2	1	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	—	2	2	no	—
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	C₂³	1	2	yes	—
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₂×C₄²×C₁₃	—	2	2	no	—
191	C₂×C₄²×C₁₃	—	2	2	no	—
192	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₁₃×#107	C₂³	1	8	yes	—
205	C₁₃×#106	C₂³	1	8	yes	—
206	C₁₃×#103	C₂³	1	8	yes	—
207	C₁₃×#103	C₂³	1	8	yes	—
208	C₁₃×#103	C₂³	1	8	yes	—
209	C₁₃×#102	C₂³	1	8	yes	—
210	C₁₃×#97	C₂³	1	4	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	2	yes	—
213	C₄×C₈×C₁₃	C₂³	1	4	yes	—
214	C₄×C₈×C₁₃	C₂³	1	2	yes	—
215	C₄×C₈×C₁₃	C₂³	1	2	yes	—
216	#60701	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₁₃×#41	—	2	8	no	—
219	C₁₃×#41	—	4	4	no	—
220	C₁₃×#41	—	4	4	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	2	8	no	—
227	C₂×Q₈×C₁₃	—	4	4	no	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	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	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	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₁₃×Q₁₆	—	2	16	no	—
263	C₁₃×SD₁₆	—	2	16	no	—
264	C₁₃×M₁₆	—	2	4	no	—
265	C₁₃×M₁₆	—	2	8	no	—
266	C₁₃×M₁₆	#41	1	8	yes	complemented
267	C₂×C₈×C₁₃	—	2	8	no	—
268	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
269	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	—	2	4	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
292	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	—	2	2	no	—
297	C₁₃×C₂²⋊C₄	—	2	2	no	—
298	C₁₃×C₂²⋊C₄	—	2	2	no	—
299	C₁₃×C₂²⋊C₄	—	2	2	no	—
300	C₁₃×C₂²⋊C₄	—	2	2	no	—
301	C₁₃×C₂²⋊C₄	—	2	2	no	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₄²×C₁₃	—	2	2	no	—
306	C₄²×C₁₃	—	2	4	no	—
307	C₄²×C₁₃	—	2	2	no	—
308	C₄²×C₁₃	—	2	2	no	—
309	C₄²×C₁₃	—	2	4	no	—
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
323	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
326	#3444	C₂×C₁₃	1	1	yes	characteristic
327	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3185	C₂×C₁₃	1	2	yes	complemented
329	#3182	C₂×C₁₃	1	2	yes	complemented
330	#3181	C₂×C₁₃	1	4	yes	complemented
331	#3172	C₂×C₁₃	1	4	yes	complemented
332	#3170	C₂×C₁₃	1	2	yes	complemented
333	#3167	C₂×C₁₃	1	2	yes	complemented
334	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3056	C₂×C₁₃	1	4	yes	complemented
339	C₄×#137	C₂×C₁₃	1	4	yes	complemented
340	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	2	2	no	—
343	C₂³×C₁₃	—	2	2	no	—
344	C₂³×C₁₃	—	4	1	no	—
345	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
346	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
347	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
348	Q₈×C₁₃	—	2	8	no	—
349	Q₈×C₁₃	—	2	4	no	—
350	Q₈×C₁₃	—	4	4	no	—
351	Q₈×C₁₃	—	4	4	no	—
352	Q₈×C₁₃	—	4	2	no	—
353	Q₈×C₁₃	—	4	4	no	—
354	Q₈×C₁₃	—	4	2	no	—
355	D₄×C₁₃	—	2	4	no	—
356	D₄×C₁₃	—	4	4	no	—
357	D₄×C₁₃	—	4	4	no	—
358	D₄×C₁₃	—	4	4	no	—
359	D₄×C₁₃	—	4	2	no	—
360	D₄×C₁₃	—	4	2	no	—
361	C₂×C₄×C₁₃	—	2	2	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	2	2	no	—
365	C₂×C₄×C₁₃	—	2	2	no	—
366	C₂×C₄×C₁₃	—	2	2	no	—
367	C₂×C₄×C₁₃	—	2	2	no	—
368	C₂×C₄×C₁₃	—	2	2	no	—
369	C₂×C₄×C₁₃	—	2	2	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	4	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	—	4	4	no	—
383	C₂×C₄×C₁₃	—	4	4	no	—
384	C₂×C₄×C₁₃	—	4	4	no	—
385	C₂×C₄×C₁₃	—	4	4	no	—
386	C₂×C₄×C₁₃	—	4	4	no	—
387	C₂×C₄×C₁₃	#137	1	4	yes	complemented
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
400	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
401	C₈×C₁₃	—	2	4	no	—
402	C₈×C₁₃	C₂×#41	1	8	yes	—
403	C₂×#137	C₂²×C₁₃	1	4	yes	—
404	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
405	#533	—	2	1	no	—
406	#533	—	2	1	no	—
407	#533	—	2	1	no	—
408	#533	—	2	1	no	—
409	#533	C₂²×C₁₃	1	2	yes	—
410	#533	C₂²×C₁₃	1	1	yes	characteristic
411	#533	C₂²×C₁₃	1	2	yes	—
412	#533	C₂²×C₁₃	1	2	yes	—
413	#533	C₂²×C₁₃	1	2	yes	—
414	#533	C₂²×C₁₃	1	1	yes	characteristic
415	#533	C₂²×C₁₃	1	1	yes	characteristic
416	#532	C₂²×C₁₃	1	1	yes	characteristic
417	#532	C₂²×C₁₃	1	1	yes	characteristic
418	#532	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	#529	—	2	1	no	—
422	#529	—	2	1	no	—
423	#529	—	2	1	no	—
424	#529	—	2	1	no	—
425	#529	C₂²×C₁₃	1	2	yes	—
426	#529	C₂²×C₁₃	1	2	yes	—
427	C₂×#125	—	2	1	no	—
428	#525	—	2	1	no	—
429	#525	—	2	1	no	—
430	#525	C₂²×C₁₃	1	2	yes	—
431	C₂×C₂²⋊Q₈	—	2	1	no	—
432	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
433	C₄×#41	—	2	1	no	—
434	C₄×#41	—	2	1	no	—
435	C₄×#41	C₂²×C₁₃	1	2	yes	—
436	C₂×C₄×Q₈	—	2	1	no	—
437	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
438	C₂×#117	—	2	1	no	—
439	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
440	#501	C₂²×C₁₃	1	4	yes	complemented
441	#500	C₂²×C₁₃	1	2	yes	complemented
442	#498	C₂²×C₁₃	1	2	yes	complemented
443	#497	C₂²×C₁₃	1	4	yes	complemented
444	#494	C₂²×C₁₃	1	2	yes	complemented
445	#492	C₂²×C₁₃	1	2	yes	complemented
446	#491	C₂²×C₁₃	1	4	yes	complemented
447	#489	C₂²×C₁₃	1	4	yes	complemented
448	#487	C₂²×C₁₃	1	2	yes	complemented
449	#487	C₂²×C₁₃	1	2	yes	complemented
450	#487	C₂²×C₁₃	1	2	yes	complemented
451	#486	C₂²×C₁₃	1	2	yes	complemented
452	#470	C₂²×C₁₃	1	8	yes	—
453	#468	C₂²×C₁₃	1	8	yes	—
454	#467	C₂²×C₁₃	1	8	yes	—
455	#465	C₂²×C₁₃	1	8	yes	—
456	#441	C₂²×C₁₃	1	8	yes	complemented
457	#440	C₂²×C₁₃	1	8	yes	complemented
458	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
459	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
460	#428	C₂²×C₁₃	1	4	yes	—
461	#419	C₂²×C₁₃	1	4	yes	—
462	#417	C₂²×C₁₃	1	4	yes	—
463	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
464	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
465	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
466	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
467	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
468	C₂×#97	C₂²×C₁₃	1	2	yes	—
469	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
470	C₂²×C₁₃	—	2	1	no	—
471	C₂²×C₁₃	—	2	1	no	—
472	C₂²×C₁₃	—	2	1	no	—
473	C₂²×C₁₃	—	2	1	no	—
474	C₂²×C₁₃	—	2	1	no	—
475	C₂²×C₁₃	—	2	1	no	—
476	C₂²×C₁₃	—	2	1	no	—
477	C₂²×C₁₃	—	4	4	no	—
478	C₂²×C₁₃	—	4	2	no	—
479	C₂²×C₁₃	—	4	2	no	—
480	C₂²×C₁₃	—	4	2	no	—
481	C₂²×C₁₃	#532	1	2	yes	—
482	C₂²×C₁₃	C₂×#137	1	2	yes	—
483	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₁₃	—	2	1	no	—
485	C₄×C₁₃	—	2	1	no	—
486	C₄×C₁₃	—	2	1	no	—
487	C₄×C₁₃	—	2	1	no	—
488	C₄×C₁₃	—	2	1	no	—
489	C₄×C₁₃	—	2	1	no	—
490	C₄×C₁₃	—	2	1	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	4	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	—	4	4	no	—
496	C₄×C₁₃	#532	1	2	yes	—
497	C₄×C₁₃	C₂×#137	1	2	yes	—
498	C₄×C₁₃	C₂×#137	1	2	yes	—
499	C₄×C₁₃	#575	1	2	yes	—
500	C₄×C₁₃	C₂²×#41	1	2	yes	—
501	C₂×#41	—	2	1	no	—
502	C₂×#41	—	2	1	no	—
503	C₂×#41	C₂³×C₁₃	1	2	yes	—
504	C₂²×Q₈	—	2	1	no	—
505	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
506	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
507	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	#137	—	2	16	no	—
510	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
511	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
512	C₂×M₁₆	—	2	8	no	—
513	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
514	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
515	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
516	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
517	C₄⋊Q₈	—	2	1	no	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	1	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
523	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
525	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
527	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
528	#127	C₂³×C₁₃	1	1	yes	characteristic
529	#126	—	2	2	no	—
530	#126	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	2	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	1	no	—
536	#125	—	2	1	no	—
537	#125	C₂³×C₁₃	1	2	yes	—
538	#124	—	2	1	no	—
539	#124	—	2	1	no	—
540	#124	C₂³×C₁₃	1	2	yes	—
541	#123	—	2	2	no	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	1	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
555	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
556	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
557	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
558	#121	—	2	1	no	—
559	#121	—	2	1	no	—
560	#121	—	2	1	no	—
561	#121	—	2	1	no	—
562	#121	C₂³×C₁₃	1	2	yes	—
563	#121	C₂³×C₁₃	1	2	yes	—
564	#120	—	2	2	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	2	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
576	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	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	C₂³×C₁₃	1	2	yes	—
590	C₄×D₄	C₂³×C₁₃	1	2	yes	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	—	2	2	no	—
594	#117	—	2	2	no	—
595	#117	—	2	1	no	—
596	#117	—	2	1	no	—
597	#117	—	2	2	no	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	C₂³×C₁₃	1	2	yes	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	2	no	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
607	C₂×C₂²⋊C₄	—	2	2	no	—
608	C₂×C₄²	—	2	2	no	—
609	C₂×C₄²	—	2	2	no	—
610	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
611	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
612	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
613	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
614	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
615	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
622	#107	C₂³×C₁₃	1	8	yes	—
623	#106	C₂³×C₁₃	1	8	yes	—
624	#103	C₂³×C₁₃	1	8	yes	—
625	#103	C₂³×C₁₃	1	8	yes	—
626	#103	C₂³×C₁₃	1	8	yes	—
627	#102	C₂³×C₁₃	1	8	yes	—
628	#97	C₂³×C₁₃	1	4	yes	—
629	#97	C₂³×C₁₃	1	2	yes	—
630	#97	C₂³×C₁₃	1	2	yes	—
631	C₄×C₈	C₂³×C₁₃	1	4	yes	—
632	C₄×C₈	C₂³×C₁₃	1	2	yes	—
633	C₄×C₈	C₂³×C₁₃	1	2	yes	—
634	C₂×C₁₃	—	2	2	no	—
635	C₂×C₁₃	—	2	2	no	—
636	C₂×C₁₃	—	4	1	no	—
637	C₂×C₁₃	—	8	2	no	—
638	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
639	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
640	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
641	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
642	#41	—	2	8	no	—
643	#41	—	4	4	no	—
644	#41	—	4	4	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	2	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	8	no	—
651	C₂×Q₈	—	4	4	no	—
652	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
653	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
686	Q₁₆	—	2	16	no	—
687	SD₁₆	—	2	16	no	—
688	M₁₆	—	2	4	no	—
689	M₁₆	—	2	8	no	—
690	M₁₆	C₁₃×#41	1	8	yes	complemented
691	C₂×C₈	—	2	8	no	—
692	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
693	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
716	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	2	4	no	—
732	C₄²	—	2	4	no	—
733	C₄²	—	2	2	no	—
734	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
742	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
747	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₁₃	#60701	1	1	yes	characteristic, direct product factor, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	4	1	no	—
755	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
757	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	Q₈	—	2	8	no	—
759	Q₈	—	2	4	no	—
760	Q₈	—	4	4	no	—
761	Q₈	—	4	4	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	2	no	—
765	D₄	—	2	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	2	no	—
770	D₄	—	4	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	4	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	4	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	C₁₃×#137	1	4	yes	complemented
798	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₈	—	2	4	no	—
812	C₈	C₂×C₁₃×#41	1	8	yes	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	C₁₃×#532	1	2	yes	—
825	C₂²	C₂×C₁₃×#137	1	2	yes	—
826	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	4	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	4	no	—
839	C₄	C₁₃×#532	1	2	yes	—
840	C₄	C₂×C₁₃×#137	1	2	yes	—
841	C₄	C₂×C₁₃×#137	1	2	yes	—
842	C₄	C₁₃×#575	1	2	yes	—
843	C₄	C₂²×C₁₃×#41	1	2	yes	—
844	C₂	—	2	2	no	—
845	C₂	—	2	2	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
849	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3185	C₂	semidirect
4. C₁₃×#3182	C₂	semidirect
5. C₁₃×#3181	C₂	semidirect
6. C₁₃×#3172	C₂	semidirect
7. C₁₃×#3170	C₂	semidirect
8. C₁₃×#3167	C₂	semidirect
9. C₁₃×#3165	C₂	semidirect
10. C₁₃×#3152	C₂	semidirect
11. C₁₃×#3141	C₂	semidirect
12. C₁₃×#3139	C₂	semidirect
13. C₁₃×#3056	C₂	semidirect
14. C₄×C₁₃×#137	C₂	semidirect
15. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
53. C₁₃×#501	C₂²	semidirect
54. C₁₃×#500	C₂²	semidirect
55. C₁₃×#498	C₂²	semidirect
56. C₁₃×#497	C₂²	semidirect
57. C₁₃×#494	C₂²	semidirect
58. C₁₃×#492	C₂²	semidirect
59. C₁₃×#491	C₂²	semidirect
60. C₁₃×#489	C₂²	semidirect
61. C₁₃×#487	C₂²	semidirect
62. C₁₃×#487	C₂²	semidirect
63. C₁₃×#487	C₂²	semidirect
64. C₁₃×#486	C₂²	semidirect
69. C₁₃×#441	C₂²	semidirect
70. C₁₃×#440	C₂²	semidirect
71. C₄×C₁₃×Q₁₆	C₂²	semidirect
72. C₄×C₁₃×SD₁₆	C₂²	semidirect
216. #60701	C₁₃	direct (N × H)
266. C₁₃×M₁₆	#41	semidirect
327. C₂×#533	C₂×C₁₃	semidirect
328. #3185	C₂×C₁₃	semidirect
329. #3182	C₂×C₁₃	semidirect
330. #3181	C₂×C₁₃	semidirect
331. #3172	C₂×C₁₃	semidirect
332. #3170	C₂×C₁₃	semidirect
333. #3167	C₂×C₁₃	semidirect
334. #3165	C₂×C₁₃	semidirect
335. #3152	C₂×C₁₃	semidirect
336. #3141	C₂×C₁₃	semidirect
337. #3139	C₂×C₁₃	semidirect
338. #3056	C₂×C₁₃	semidirect
339. C₄×#137	C₂×C₁₃	semidirect
340. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
387. C₂×C₄×C₁₃	#137	semidirect
440. #501	C₂²×C₁₃	semidirect
441. #500	C₂²×C₁₃	semidirect
442. #498	C₂²×C₁₃	semidirect
443. #497	C₂²×C₁₃	semidirect
444. #494	C₂²×C₁₃	semidirect
445. #492	C₂²×C₁₃	semidirect
446. #491	C₂²×C₁₃	semidirect
447. #489	C₂²×C₁₃	semidirect
448. #487	C₂²×C₁₃	semidirect
449. #487	C₂²×C₁₃	semidirect
450. #487	C₂²×C₁₃	semidirect
451. #486	C₂²×C₁₃	semidirect
456. #441	C₂²×C₁₃	semidirect
457. #440	C₂²×C₁₃	semidirect
458. C₄×Q₁₆	C₂²×C₁₃	semidirect
459. C₄×SD₁₆	C₂²×C₁₃	semidirect
690. M₁₆	C₁₃×#41	semidirect
750. C₁₃	#60701	direct (N × H)
797. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3444	2
C₂×C₁₃×#533	2
C₁₃×#3185	2
C₁₃×#3182	2
C₁₃×#3181	2
C₁₃×#3172	2
C₁₃×#3170	2
C₁₃×#3167	2
C₁₃×#3165	2
C₁₃×#3152	2
C₁₃×#3141	2
C₁₃×#3139	2
C₁₃×#3056	2
C₄×C₁₃×#137	2
C₂×C₄×C₁₃×M₁₆	2
#60701	13

Subgroups — C13×#60701 #15747040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60701 #15747040