Subgroups — C₁₃×#62861 #15749200

Order 3328.

6854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3523	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3521	C₂	1	12	yes	maximal, complemented
3	C₁₃×#3516	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3515	C₂	1	12	yes	maximal, complemented
5	C₁₃×#3512	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3509	C₂	1	3	yes	maximal, complemented
7	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3495	C₂	1	6	yes	maximal, complemented
10	C₁₃×#3489	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3461	C₂	1	6	yes	maximal, complemented
12	C₁₃×#3455	C₂	1	3	yes	maximal, complemented
13	C₂×C₁₃×#541	C₂	1	3	yes	maximal, complemented
14	C₄×C₁₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₁₃×#557	C₂²	1	4	yes	complemented
19	C₁₃×#557	C₂²	1	12	yes	complemented
20	C₁₃×#556	C₂²	1	12	yes	—
21	C₁₃×#556	C₂²	1	12	yes	complemented
22	C₁₃×#554	C₂²	1	12	yes	complemented
23	C₁₃×#554	C₂²	1	12	yes	complemented
24	C₁₃×#553	C₂²	1	24	yes	complemented
25	C₁₃×#553	C₂²	1	12	yes	complemented
26	C₁₃×#552	C₂²	1	12	yes	—
27	C₁₃×#552	C₂²	1	24	yes	complemented
28	C₁₃×#552	C₂²	1	12	yes	complemented
29	C₁₃×#552	C₂²	1	24	yes	complemented
30	C₁₃×#552	C₂²	1	12	yes	complemented
31	C₁₃×#551	C₂²	1	24	yes	—
32	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
33	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
34	C₁₃×#548	C₂²	1	4	yes	—
35	C₁₃×#547	C₂²	1	12	yes	—
36	C₁₃×#547	C₂²	1	12	yes	complemented
37	C₁₃×#546	C₂²	1	12	yes	—
38	C₁₃×#544	C₂²	1	6	yes	complemented
39	C₁₃×#542	C₂²	1	6	yes	—
40	C₁₃×#542	C₂²	1	12	yes	complemented
41	C₁₃×#542	C₂²	1	6	yes	complemented
42	C₁₃×#541	C₂²	1	12	yes	—
43	C₁₃×#541	C₂²	1	3	yes	—
44	C₁₃×#541	C₂²	1	6	yes	—
45	C₁₃×#541	C₂²	1	12	yes	complemented
46	C₁₃×#541	C₂²	1	6	yes	complemented
47	C₁₃×#541	C₂²	1	6	yes	complemented
48	C₁₃×#541	C₂²	1	12	yes	complemented
49	C₁₃×#541	C₂²	1	3	yes	complemented
50	C₁₃×#540	C₂²	1	1	yes	characteristic
51	C₁₃×#540	C₂²	1	3	yes	complemented
52	C₁₃×#539	C₂²	1	24	yes	complemented
53	C₁₃×#539	C₂²	1	12	yes	complemented
54	C₁₃×#538	C₂²	1	12	yes	—
55	C₁₃×#537	C₂²	1	6	yes	—
56	C₁₃×#536	C₂²	1	6	yes	—
57	C₁₃×#536	C₂²	1	6	yes	complemented
58	C₁₃×#533	C₂²	1	12	yes	complemented
59	C₁₃×#533	C₂²	1	3	yes	complemented
60	C₁₃×#533	C₂²	1	12	yes	complemented
61	C₁₃×#532	C₂²	1	3	yes	complemented
62	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
63	C₁₃×#529	C₂²	1	12	yes	—
64	C₁₃×#529	C₂²	1	24	yes	complemented
65	C₁₃×#529	C₂²	1	12	yes	complemented
66	C₁₃×#529	C₂²	1	12	yes	complemented
67	C₁₃×#529	C₂²	1	12	yes	complemented
68	C₂×C₁₃×#126	C₂²	1	12	yes	—
69	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
70	C₂×C₁₃×#125	C₂²	1	12	yes	complemented
71	C₁₃×#525	C₂²	1	6	yes	—
72	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
73	C₁₃×#520	C₂²	1	6	yes	—
74	C₁₃×#520	C₂²	1	2	yes	—
75	C₁₃×#520	C₂²	1	2	yes	—
76	C₁₃×#520	C₂²	1	12	yes	complemented
77	C₁₃×#520	C₂²	1	6	yes	complemented
78	C₁₃×#519	C₂²	1	2	yes	—
79	C₁₃×#519	C₂²	1	4	yes	complemented
80	C₁₃×#519	C₂²	1	6	yes	complemented
81	C₁₃×#518	C₂²	1	6	yes	—
82	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
83	C₄×C₁₃×#41	C₂²	1	3	yes	—
84	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
85	C₄×C₁₃×#41	C₂²	1	3	yes	—
86	C₄×C₁₃×#41	C₂²	1	12	yes	complemented
87	C₄×C₁₃×#41	C₂²	1	6	yes	complemented
88	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
89	C₂×C₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
90	C₂×C₁₃×#117	C₂²	1	3	yes	—
91	C₂×C₁₃×#117	C₂²	1	3	yes	—
92	C₁₃×2₋¹⁺⁴	—	2	16	no	—
93	C₂×C₁₃×#41	—	2	8	no	—
94	C₂×C₁₃×#41	C₂³	1	3	yes	—
95	C₂×C₁₃×#41	C₂³	1	6	yes	—
96	C₂×C₁₃×#41	C₂³	1	12	yes	—
97	C₂×C₁₃×#41	C₂³	1	3	yes	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
101	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
105	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
108	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
109	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
110	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
111	C₁₃×#127	C₂³	1	1	yes	characteristic
112	C₁₃×#126	C₂³	1	12	yes	—
113	C₁₃×#126	C₂³	1	24	yes	—
114	C₁₃×#126	C₂³	1	24	yes	—
115	C₁₃×#126	C₂³	1	24	yes	—
116	C₁₃×#126	C₂³	1	12	yes	—
117	C₁₃×#126	C₂³	1	12	yes	—
118	C₁₃×#126	C₂³	1	24	yes	—
119	C₁₃×#126	C₂³	1	12	yes	—
120	C₁₃×#125	C₂³	1	12	yes	—
121	C₁₃×#125	C₂³	1	3	yes	—
122	C₁₃×#125	C₂³	1	6	yes	—
123	C₁₃×#125	C₂³	1	24	yes	—
124	C₁₃×#125	C₂³	1	24	yes	—
125	C₁₃×#125	C₂³	1	24	yes	—
126	C₁₃×#125	C₂³	1	12	yes	—
127	C₁₃×#125	C₂³	1	12	yes	—
128	C₁₃×#125	C₂³	1	12	yes	—
129	C₁₃×#125	C₂³	1	1	yes	characteristic
130	C₁₃×#125	C₂³	1	24	yes	—
131	C₁₃×#124	C₂³	1	12	yes	—
132	C₁₃×#124	C₂³	1	12	yes	—
133	C₁₃×#124	C₂³	1	6	yes	—
134	C₁₃×#124	C₂³	1	12	yes	—
135	C₁₃×#123	C₂³	1	12	yes	—
136	C₁₃×#123	C₂³	1	12	yes	—
137	C₁₃×#123	C₂³	1	12	yes	—
138	C₁₃×#123	C₂³	1	12	yes	—
139	C₁₃×#123	C₂³	1	4	yes	—
140	C₁₃×#123	C₂³	1	24	yes	—
141	C₁₃×#123	C₂³	1	24	yes	—
142	C₁₃×#123	C₂³	1	24	yes	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₁₃×#121	C₂³	1	6	yes	—
158	C₁₃×#121	C₂³	1	4	yes	—
159	C₁₃×#121	C₂³	1	24	yes	—
160	C₁₃×#121	C₂³	1	12	yes	—
161	C₁₃×#121	C₂³	1	12	yes	—
162	C₁₃×#121	C₂³	1	12	yes	—
163	C₁₃×#120	C₂³	1	12	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
177	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
178	C₄×D₄×C₁₃	C₂³	1	6	yes	—
179	C₄×D₄×C₁₃	C₂³	1	12	yes	—
180	C₄×D₄×C₁₃	C₂³	1	6	yes	—
181	C₄×D₄×C₁₃	C₂³	1	6	yes	—
182	C₄×D₄×C₁₃	C₂³	1	12	yes	—
183	C₄×D₄×C₁₃	C₂³	1	6	yes	—
184	C₄×D₄×C₁₃	C₂³	1	12	yes	—
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	12	yes	—
187	C₄×D₄×C₁₃	C₂³	1	12	yes	—
188	C₄×D₄×C₁₃	C₂³	1	6	yes	—
189	C₄×D₄×C₁₃	C₂³	1	24	yes	—
190	C₄×D₄×C₁₃	C₂³	1	12	yes	—
191	C₄×D₄×C₁₃	C₂³	1	12	yes	—
192	C₄×D₄×C₁₃	C₂³	1	12	yes	—
193	C₄×D₄×C₁₃	C₂³	1	24	yes	—
194	C₁₃×#117	C₂³	1	1	yes	characteristic
195	C₁₃×#117	C₂³	1	3	yes	—
196	C₁₃×#117	C₂³	1	3	yes	—
197	C₁₃×#117	C₂³	1	3	yes	—
198	C₁₃×#117	C₂³	1	3	yes	—
199	C₁₃×#117	C₂³	1	3	yes	—
200	C₁₃×#117	C₂³	1	6	yes	—
201	C₁₃×#117	C₂³	1	6	yes	—
202	C₁₃×#117	C₂³	1	6	yes	—
203	C₁₃×#117	C₂³	1	6	yes	—
204	C₁₃×#117	C₂³	1	6	yes	—
205	C₁₃×#117	C₂³	1	12	yes	—
206	C₁₃×#117	C₂³	1	24	yes	—
207	C₁₃×#117	C₂³	1	12	yes	—
208	C₁₃×#117	C₂³	1	24	yes	—
209	C₁₃×#117	C₂³	1	24	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
211	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
212	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
213	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
214	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
215	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
216	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
217	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
221	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
222	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
223	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
224	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
225	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
226	#62861	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
228	C₁₃×#41	—	2	4	no	—
229	C₁₃×#41	—	2	12	no	—
230	C₁₃×#41	—	2	48	no	—
231	C₁₃×#41	—	2	12	no	—
232	C₁₃×#41	—	2	24	no	—
233	C₁₃×#41	#41	1	8	yes	—
234	C₂×Q₈×C₁₃	—	2	4	no	—
235	C₂×Q₈×C₁₃	—	2	16	no	—
236	C₂×Q₈×C₁₃	—	2	24	no	—
237	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
238	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₁₃	—	2	12	no	—
243	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
245	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
251	C₂²×C₄×C₁₃	—	2	12	no	—
252	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
262	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
263	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
273	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
287	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
288	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
289	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
290	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₁₃	C₂⁴	1	3	yes	—
305	C₄²×C₁₃	C₂⁴	1	6	yes	—
306	C₄²×C₁₃	C₂⁴	1	3	yes	—
307	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₄²×C₁₃	C₂⁴	1	12	yes	—
309	C₄²×C₁₃	C₂⁴	1	12	yes	—
310	C₄²×C₁₃	C₂⁴	1	24	yes	—
311	C₄²×C₁₃	C₂⁴	1	12	yes	—
312	C₄²×C₁₃	C₂⁴	1	6	yes	—
313	C₄²×C₁₃	C₂⁴	1	12	yes	—
314	#3523	C₂×C₁₃	1	4	yes	complemented
315	#3521	C₂×C₁₃	1	12	yes	complemented
316	#3516	C₂×C₁₃	1	4	yes	complemented
317	#3515	C₂×C₁₃	1	12	yes	complemented
318	#3512	C₂×C₁₃	1	3	yes	complemented
319	#3509	C₂×C₁₃	1	3	yes	complemented
320	#3504	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3495	C₂×C₁₃	1	6	yes	complemented
323	#3489	C₂×C₁₃	1	2	yes	complemented
324	#3461	C₂×C₁₃	1	6	yes	complemented
325	#3455	C₂×C₁₃	1	3	yes	complemented
326	C₂×#541	C₂×C₁₃	1	3	yes	complemented
327	C₄×2₋¹⁺⁴	C₂×C₁₃	1	2	yes	complemented
328	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂³×C₁₃	—	2	6	no	—
330	C₂³×C₁₃	—	4	6	no	—
331	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
332	C₂³×C₁₃	C₂⁵	1	3	yes	—
333	C₂³×C₁₃	C₂⁵	1	4	yes	—
334	C₂³×C₁₃	C₂⁵	1	3	yes	—
335	Q₈×C₁₃	—	2	24	no	—
336	Q₈×C₁₃	—	2	12	no	—
337	Q₈×C₁₃	—	2	6	no	—
338	Q₈×C₁₃	—	4	12	no	—
339	Q₈×C₁₃	C₂×#41	1	4	yes	—
340	D₄×C₁₃	—	2	12	no	—
341	D₄×C₁₃	—	2	24	no	—
342	D₄×C₁₃	—	2	6	no	—
343	D₄×C₁₃	—	2	4	no	—
344	D₄×C₁₃	—	4	4	no	—
345	D₄×C₁₃	—	4	12	no	—
346	D₄×C₁₃	—	4	4	no	—
347	D₄×C₁₃	C₂×#41	1	12	yes	—
348	C₂×C₄×C₁₃	—	2	6	no	—
349	C₂×C₄×C₁₃	—	2	24	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	6	no	—
352	C₂×C₄×C₁₃	—	2	6	no	—
353	C₂×C₄×C₁₃	—	2	6	no	—
354	C₂×C₄×C₁₃	—	2	24	no	—
355	C₂×C₄×C₁₃	—	4	6	no	—
356	C₂×C₄×C₁₃	—	4	12	no	—
357	C₂×C₄×C₁₃	—	4	12	no	—
358	C₂×C₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	4	6	no	—
360	C₂×C₄×C₁₃	—	4	12	no	—
361	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
362	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
363	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
365	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
367	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
368	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
370	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
373	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
374	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
375	#557	C₂²×C₁₃	1	4	yes	complemented
376	#557	C₂²×C₁₃	1	12	yes	complemented
377	#556	C₂²×C₁₃	1	12	yes	—
378	#556	C₂²×C₁₃	1	12	yes	complemented
379	#554	C₂²×C₁₃	1	12	yes	complemented
380	#554	C₂²×C₁₃	1	12	yes	complemented
381	#553	C₂²×C₁₃	1	24	yes	complemented
382	#553	C₂²×C₁₃	1	12	yes	complemented
383	#552	C₂²×C₁₃	1	12	yes	—
384	#552	C₂²×C₁₃	1	24	yes	complemented
385	#552	C₂²×C₁₃	1	12	yes	complemented
386	#552	C₂²×C₁₃	1	24	yes	complemented
387	#552	C₂²×C₁₃	1	12	yes	complemented
388	#551	C₂²×C₁₃	1	24	yes	—
389	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
390	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
391	#548	C₂²×C₁₃	1	4	yes	—
392	#547	C₂²×C₁₃	1	12	yes	—
393	#547	C₂²×C₁₃	1	12	yes	complemented
394	#546	C₂²×C₁₃	1	12	yes	—
395	#544	C₂²×C₁₃	1	6	yes	complemented
396	#542	C₂²×C₁₃	1	6	yes	—
397	#542	C₂²×C₁₃	1	6	yes	complemented
398	#542	C₂²×C₁₃	1	12	yes	complemented
399	#541	C₂²×C₁₃	1	3	yes	—
400	#541	C₂²×C₁₃	1	6	yes	—
401	#541	C₂²×C₁₃	1	12	yes	—
402	#541	C₂²×C₁₃	1	6	yes	complemented
403	#541	C₂²×C₁₃	1	6	yes	complemented
404	#541	C₂²×C₁₃	1	12	yes	complemented
405	#541	C₂²×C₁₃	1	3	yes	complemented
406	#541	C₂²×C₁₃	1	12	yes	complemented
407	#540	C₂²×C₁₃	1	1	yes	characteristic
408	#540	C₂²×C₁₃	1	3	yes	complemented
409	#539	C₂²×C₁₃	1	12	yes	complemented
410	#539	C₂²×C₁₃	1	24	yes	complemented
411	#538	C₂²×C₁₃	1	12	yes	—
412	#537	C₂²×C₁₃	1	6	yes	—
413	#536	C₂²×C₁₃	1	6	yes	—
414	#536	C₂²×C₁₃	1	6	yes	complemented
415	#533	C₂²×C₁₃	1	3	yes	complemented
416	#533	C₂²×C₁₃	1	12	yes	complemented
417	#533	C₂²×C₁₃	1	12	yes	complemented
418	#532	C₂²×C₁₃	1	3	yes	complemented
419	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
420	#529	C₂²×C₁₃	1	12	yes	—
421	#529	C₂²×C₁₃	1	12	yes	complemented
422	#529	C₂²×C₁₃	1	12	yes	complemented
423	#529	C₂²×C₁₃	1	24	yes	complemented
424	#529	C₂²×C₁₃	1	12	yes	complemented
425	C₂×#126	C₂²×C₁₃	1	12	yes	—
426	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
427	C₂×#125	C₂²×C₁₃	1	12	yes	complemented
428	#525	C₂²×C₁₃	1	6	yes	—
429	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
430	#520	C₂²×C₁₃	1	6	yes	—
431	#520	C₂²×C₁₃	1	2	yes	—
432	#520	C₂²×C₁₃	1	2	yes	—
433	#520	C₂²×C₁₃	1	6	yes	complemented
434	#520	C₂²×C₁₃	1	12	yes	complemented
435	#519	C₂²×C₁₃	1	2	yes	—
436	#519	C₂²×C₁₃	1	6	yes	complemented
437	#519	C₂²×C₁₃	1	4	yes	complemented
438	#518	C₂²×C₁₃	1	6	yes	—
439	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
440	C₄×#41	C₂²×C₁₃	1	3	yes	—
441	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
442	C₄×#41	C₂²×C₁₃	1	3	yes	—
443	C₄×#41	C₂²×C₁₃	1	6	yes	complemented
444	C₄×#41	C₂²×C₁₃	1	12	yes	complemented
445	C₂×C₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
446	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
447	C₂×#117	C₂²×C₁₃	1	3	yes	—
448	C₂×#117	C₂²×C₁₃	1	3	yes	—
449	C₂²×C₁₃	—	2	6	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	3	no	—
453	C₂²×C₁₃	—	2	4	no	—
454	C₂²×C₁₃	—	2	6	no	—
455	C₂²×C₁₃	—	2	4	no	—
456	C₂²×C₁₃	—	2	2	no	—
457	C₂²×C₁₃	—	8	6	no	—
458	C₂²×C₁₃	C₂²×#41	1	6	yes	—
459	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	3	no	—
462	C₄×C₁₃	—	2	12	no	—
463	C₄×C₁₃	—	2	2	no	—
464	C₄×C₁₃	—	2	6	no	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	2	12	no	—
467	C₄×C₁₃	—	2	6	no	—
468	C₄×C₁₃	—	2	4	no	—
469	C₄×C₁₃	C₂²×#41	1	6	yes	—
470	C₄×C₁₃	C₂²×#41	1	2	yes	—
471	2₋¹⁺⁴	—	2	16	no	—
472	C₂×#41	—	2	8	no	—
473	C₂×#41	C₂³×C₁₃	1	3	yes	—
474	C₂×#41	C₂³×C₁₃	1	6	yes	—
475	C₂×#41	C₂³×C₁₃	1	12	yes	—
476	C₂×#41	C₂³×C₁₃	1	3	yes	—
477	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
480	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
481	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
483	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
484	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
485	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
486	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
487	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
488	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
489	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
490	#127	C₂³×C₁₃	1	1	yes	characteristic
491	#126	C₂³×C₁₃	1	12	yes	—
492	#126	C₂³×C₁₃	1	24	yes	—
493	#126	C₂³×C₁₃	1	24	yes	—
494	#126	C₂³×C₁₃	1	24	yes	—
495	#126	C₂³×C₁₃	1	12	yes	—
496	#126	C₂³×C₁₃	1	12	yes	—
497	#126	C₂³×C₁₃	1	24	yes	—
498	#126	C₂³×C₁₃	1	12	yes	—
499	#125	C₂³×C₁₃	1	12	yes	—
500	#125	C₂³×C₁₃	1	3	yes	—
501	#125	C₂³×C₁₃	1	6	yes	—
502	#125	C₂³×C₁₃	1	24	yes	—
503	#125	C₂³×C₁₃	1	24	yes	—
504	#125	C₂³×C₁₃	1	24	yes	—
505	#125	C₂³×C₁₃	1	12	yes	—
506	#125	C₂³×C₁₃	1	12	yes	—
507	#125	C₂³×C₁₃	1	12	yes	—
508	#125	C₂³×C₁₃	1	1	yes	characteristic
509	#125	C₂³×C₁₃	1	24	yes	—
510	#124	C₂³×C₁₃	1	12	yes	—
511	#124	C₂³×C₁₃	1	12	yes	—
512	#124	C₂³×C₁₃	1	6	yes	—
513	#124	C₂³×C₁₃	1	12	yes	—
514	#123	C₂³×C₁₃	1	12	yes	—
515	#123	C₂³×C₁₃	1	12	yes	—
516	#123	C₂³×C₁₃	1	12	yes	—
517	#123	C₂³×C₁₃	1	12	yes	—
518	#123	C₂³×C₁₃	1	4	yes	—
519	#123	C₂³×C₁₃	1	24	yes	—
520	#123	C₂³×C₁₃	1	24	yes	—
521	#123	C₂³×C₁₃	1	24	yes	—
522	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
523	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
524	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
525	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
526	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
527	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
528	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
529	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
530	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
531	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
532	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
533	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
534	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
535	#121	C₂³×C₁₃	1	2	yes	—
536	#121	C₂³×C₁₃	1	6	yes	—
537	#121	C₂³×C₁₃	1	4	yes	—
538	#121	C₂³×C₁₃	1	24	yes	—
539	#121	C₂³×C₁₃	1	12	yes	—
540	#121	C₂³×C₁₃	1	12	yes	—
541	#121	C₂³×C₁₃	1	12	yes	—
542	#120	C₂³×C₁₃	1	12	yes	—
543	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
549	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
550	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
551	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
553	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
554	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
555	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
556	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
557	C₄×D₄	C₂³×C₁₃	1	6	yes	—
558	C₄×D₄	C₂³×C₁₃	1	12	yes	—
559	C₄×D₄	C₂³×C₁₃	1	6	yes	—
560	C₄×D₄	C₂³×C₁₃	1	6	yes	—
561	C₄×D₄	C₂³×C₁₃	1	12	yes	—
562	C₄×D₄	C₂³×C₁₃	1	6	yes	—
563	C₄×D₄	C₂³×C₁₃	1	12	yes	—
564	C₄×D₄	C₂³×C₁₃	1	2	yes	—
565	C₄×D₄	C₂³×C₁₃	1	12	yes	—
566	C₄×D₄	C₂³×C₁₃	1	12	yes	—
567	C₄×D₄	C₂³×C₁₃	1	6	yes	—
568	C₄×D₄	C₂³×C₁₃	1	24	yes	—
569	C₄×D₄	C₂³×C₁₃	1	12	yes	—
570	C₄×D₄	C₂³×C₁₃	1	12	yes	—
571	C₄×D₄	C₂³×C₁₃	1	12	yes	—
572	C₄×D₄	C₂³×C₁₃	1	24	yes	—
573	#117	C₂³×C₁₃	1	1	yes	characteristic
574	#117	C₂³×C₁₃	1	3	yes	—
575	#117	C₂³×C₁₃	1	3	yes	—
576	#117	C₂³×C₁₃	1	3	yes	—
577	#117	C₂³×C₁₃	1	3	yes	—
578	#117	C₂³×C₁₃	1	3	yes	—
579	#117	C₂³×C₁₃	1	6	yes	—
580	#117	C₂³×C₁₃	1	6	yes	—
581	#117	C₂³×C₁₃	1	6	yes	—
582	#117	C₂³×C₁₃	1	6	yes	—
583	#117	C₂³×C₁₃	1	6	yes	—
584	#117	C₂³×C₁₃	1	12	yes	—
585	#117	C₂³×C₁₃	1	24	yes	—
586	#117	C₂³×C₁₃	1	12	yes	—
587	#117	C₂³×C₁₃	1	24	yes	—
588	#117	C₂³×C₁₃	1	24	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
591	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
592	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
600	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
601	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
602	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
603	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
604	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
605	C₂×C₁₃	—	2	6	no	—
606	C₂×C₁₃	—	4	4	no	—
607	C₂×C₁₃	—	4	3	no	—
608	C₂×C₁₃	—	4	1	no	—
609	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
610	C₂×C₁₃	2₋¹⁺⁶	1	2	yes	—
611	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
612	#41	—	2	4	no	—
613	#41	—	2	12	no	—
614	#41	—	2	48	no	—
615	#41	—	2	12	no	—
616	#41	—	2	24	no	—
617	#41	C₁₃×#41	1	8	yes	—
618	C₂×Q₈	—	2	4	no	—
619	C₂×Q₈	—	2	16	no	—
620	C₂×Q₈	—	2	24	no	—
621	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
622	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
623	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
624	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
625	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂×D₄	—	2	12	no	—
627	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
628	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
629	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
630	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
631	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
632	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
633	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
634	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
635	C₂²×C₄	—	2	12	no	—
636	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
641	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
644	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
645	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
646	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
648	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
649	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
650	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
651	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
652	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
654	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
655	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
656	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
657	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
658	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
659	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
660	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
661	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
662	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
663	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
671	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
673	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
674	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
675	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
676	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
677	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
678	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
679	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
680	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
681	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
682	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
683	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
684	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
685	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
686	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
687	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
688	C₄²	C₂⁴×C₁₃	1	3	yes	—
689	C₄²	C₂⁴×C₁₃	1	6	yes	—
690	C₄²	C₂⁴×C₁₃	1	3	yes	—
691	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₄²	C₂⁴×C₁₃	1	12	yes	—
693	C₄²	C₂⁴×C₁₃	1	12	yes	—
694	C₄²	C₂⁴×C₁₃	1	24	yes	—
695	C₄²	C₂⁴×C₁₃	1	12	yes	—
696	C₄²	C₂⁴×C₁₃	1	6	yes	—
697	C₄²	C₂⁴×C₁₃	1	12	yes	—
698	C₁₃	#62861	1	1	yes	characteristic, direct product factor, Sylow
699	C₂³	—	2	6	no	—
700	C₂³	—	4	6	no	—
701	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
702	C₂³	C₂⁵×C₁₃	1	3	yes	—
703	C₂³	C₂⁵×C₁₃	1	4	yes	—
704	C₂³	C₂⁵×C₁₃	1	3	yes	—
705	Q₈	—	2	24	no	—
706	Q₈	—	2	12	no	—
707	Q₈	—	2	6	no	—
708	Q₈	—	4	12	no	—
709	Q₈	C₂×C₁₃×#41	1	4	yes	—
710	D₄	—	2	12	no	—
711	D₄	—	2	24	no	—
712	D₄	—	2	6	no	—
713	D₄	—	2	4	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	12	no	—
716	D₄	—	4	4	no	—
717	D₄	C₂×C₁₃×#41	1	12	yes	—
718	C₂×C₄	—	2	6	no	—
719	C₂×C₄	—	2	24	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	6	no	—
722	C₂×C₄	—	2	6	no	—
723	C₂×C₄	—	2	6	no	—
724	C₂×C₄	—	2	24	no	—
725	C₂×C₄	—	4	6	no	—
726	C₂×C₄	—	4	12	no	—
727	C₂×C₄	—	4	12	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	6	no	—
730	C₂×C₄	—	4	12	no	—
731	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
732	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
733	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
734	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
735	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
736	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
737	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
738	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
739	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
740	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
741	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
742	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
743	C₂²	—	2	6	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	3	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	6	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	8	6	no	—
752	C₂²	C₂²×C₁₃×#41	1	6	yes	—
753	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
754	C₄	—	2	1	no	—
755	C₄	—	2	3	no	—
756	C₄	—	2	12	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	6	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	12	no	—
761	C₄	—	2	6	no	—
762	C₄	—	2	4	no	—
763	C₄	C₂²×C₁₃×#41	1	6	yes	—
764	C₄	C₂²×C₁₃×#41	1	2	yes	—
765	C₂	—	2	6	no	—
766	C₂	—	4	1	no	—
767	C₂	—	4	3	no	—
768	C₂	—	4	4	no	—
769	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
770	C₂	C₁₃×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3523	C₂	semidirect
2. C₁₃×#3521	C₂	semidirect
3. C₁₃×#3516	C₂	semidirect
4. C₁₃×#3515	C₂	semidirect
5. C₁₃×#3512	C₂	semidirect
6. C₁₃×#3509	C₂	semidirect
7. C₁₃×#3504	C₂	semidirect
8. C₁₃×#3499	C₂	semidirect
9. C₁₃×#3495	C₂	semidirect
10. C₁₃×#3489	C₂	semidirect
11. C₁₃×#3461	C₂	semidirect
12. C₁₃×#3455	C₂	semidirect
13. C₂×C₁₃×#541	C₂	semidirect
14. C₄×C₁₃×2₋¹⁺⁴	C₂	semidirect
15. C₁₃×#3428	C₂	semidirect
18. C₁₃×#557	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
25. C₁₃×#553	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
30. C₁₃×#552	C₂²	semidirect
33. D₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#547	C₂²	semidirect
38. C₁₃×#544	C₂²	semidirect
40. C₁₃×#542	C₂²	semidirect
41. C₁₃×#542	C₂²	semidirect
45. C₁₃×#541	C₂²	semidirect
46. C₁₃×#541	C₂²	semidirect
47. C₁₃×#541	C₂²	semidirect
48. C₁₃×#541	C₂²	semidirect
49. C₁₃×#541	C₂²	semidirect
51. C₁₃×#540	C₂²	semidirect
52. C₁₃×#539	C₂²	semidirect
53. C₁₃×#539	C₂²	semidirect
57. C₁₃×#536	C₂²	semidirect
58. C₁₃×#533	C₂²	semidirect
59. C₁₃×#533	C₂²	semidirect
60. C₁₃×#533	C₂²	semidirect
61. C₁₃×#532	C₂²	semidirect
62. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
64. C₁₃×#529	C₂²	semidirect
65. C₁₃×#529	C₂²	semidirect
66. C₁₃×#529	C₂²	semidirect
67. C₁₃×#529	C₂²	semidirect
69. C₂×C₁₃×#125	C₂²	semidirect
70. C₂×C₁₃×#125	C₂²	semidirect
76. C₁₃×#520	C₂²	semidirect
77. C₁₃×#520	C₂²	semidirect
79. C₁₃×#519	C₂²	semidirect
80. C₁₃×#519	C₂²	semidirect
86. C₄×C₁₃×#41	C₂²	semidirect
87. C₄×C₁₃×#41	C₂²	semidirect
88. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
89. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
226. #62861	C₁₃	direct (N × H)
314. #3523	C₂×C₁₃	semidirect
315. #3521	C₂×C₁₃	semidirect
316. #3516	C₂×C₁₃	semidirect
317. #3515	C₂×C₁₃	semidirect
318. #3512	C₂×C₁₃	semidirect
319. #3509	C₂×C₁₃	semidirect
320. #3504	C₂×C₁₃	semidirect
321. #3499	C₂×C₁₃	semidirect
322. #3495	C₂×C₁₃	semidirect
323. #3489	C₂×C₁₃	semidirect
324. #3461	C₂×C₁₃	semidirect
325. #3455	C₂×C₁₃	semidirect
326. C₂×#541	C₂×C₁₃	semidirect
327. C₄×2₋¹⁺⁴	C₂×C₁₃	semidirect
328. #3428	C₂×C₁₃	semidirect
375. #557	C₂²×C₁₃	semidirect
376. #557	C₂²×C₁₃	semidirect
378. #556	C₂²×C₁₃	semidirect
379. #554	C₂²×C₁₃	semidirect
380. #554	C₂²×C₁₃	semidirect
381. #553	C₂²×C₁₃	semidirect
382. #553	C₂²×C₁₃	semidirect
384. #552	C₂²×C₁₃	semidirect
385. #552	C₂²×C₁₃	semidirect
386. #552	C₂²×C₁₃	semidirect
387. #552	C₂²×C₁₃	semidirect
390. D₄×Q₈	C₂²×C₁₃	semidirect
393. #547	C₂²×C₁₃	semidirect
395. #544	C₂²×C₁₃	semidirect
397. #542	C₂²×C₁₃	semidirect
398. #542	C₂²×C₁₃	semidirect
402. #541	C₂²×C₁₃	semidirect
403. #541	C₂²×C₁₃	semidirect
404. #541	C₂²×C₁₃	semidirect
405. #541	C₂²×C₁₃	semidirect
406. #541	C₂²×C₁₃	semidirect
408. #540	C₂²×C₁₃	semidirect
409. #539	C₂²×C₁₃	semidirect
410. #539	C₂²×C₁₃	semidirect
414. #536	C₂²×C₁₃	semidirect
415. #533	C₂²×C₁₃	semidirect
416. #533	C₂²×C₁₃	semidirect
417. #533	C₂²×C₁₃	semidirect
418. #532	C₂²×C₁₃	semidirect
419. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
421. #529	C₂²×C₁₃	semidirect
422. #529	C₂²×C₁₃	semidirect
423. #529	C₂²×C₁₃	semidirect
424. #529	C₂²×C₁₃	semidirect
426. C₂×#125	C₂²×C₁₃	semidirect
427. C₂×#125	C₂²×C₁₃	semidirect
433. #520	C₂²×C₁₃	semidirect
434. #520	C₂²×C₁₃	semidirect
436. #519	C₂²×C₁₃	semidirect
437. #519	C₂²×C₁₃	semidirect
443. C₄×#41	C₂²×C₁₃	semidirect
444. C₄×#41	C₂²×C₁₃	semidirect
445. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
446. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
698. C₁₃	#62861	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×#3523	2
C₁₃×#3521	2
C₁₃×#3516	2
C₁₃×#3515	2
C₁₃×#3512	2
C₁₃×#3509	2
C₁₃×#3504	2
C₁₃×#3499	2
C₁₃×#3495	2
C₁₃×#3489	2
C₁₃×#3461	2
C₁₃×#3455	2
C₂×C₁₃×#541	2
C₄×C₁₃×2₋¹⁺⁴	2
C₁₃×#3428	2
#62861	13

Subgroups — C13×#62861 #15749200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62861 #15749200