Subgroups — C₁₃×#62814 #15749153

Order 3328.

7286 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3494	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3493	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3492	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3491	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3490	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3475	C₂	1	16	yes	maximal, complemented
8	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3455	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3444	C₂	1	4	yes	maximal, complemented
12	C₂×C₁₃×#525	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3428	C₂	1	2	yes	maximal, complemented
14	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#556	C₂²	1	16	yes	complemented
18	C₁₃×#555	C₂²	1	16	yes	complemented
19	C₁₃×#554	C₂²	1	16	yes	complemented
20	C₁₃×#553	C₂²	1	16	yes	complemented
21	C₁₃×#553	C₂²	1	16	yes	complemented
22	C₁₃×#552	C₂²	1	32	yes	complemented
23	C₁₃×#552	C₂²	1	16	yes	complemented
24	C₁₃×#552	C₂²	1	16	yes	complemented
25	C₁₃×#551	C₂²	1	32	yes	complemented
26	C₁₃×#551	C₂²	1	32	yes	complemented
27	C₁₃×#547	C₂²	1	16	yes	complemented
28	C₁₃×#546	C₂²	1	32	yes	complemented
29	C₁₃×#544	C₂²	1	4	yes	complemented
30	C₁₃×#544	C₂²	1	8	yes	complemented
31	C₁₃×#543	C₂²	1	4	yes	—
32	C₁₃×#542	C₂²	1	16	yes	complemented
33	C₁₃×#541	C₂²	1	8	yes	complemented
34	C₁₃×#540	C₂²	1	8	yes	complemented
35	C₁₃×#539	C₂²	1	16	yes	complemented
36	C₁₃×#538	C₂²	1	16	yes	complemented
37	C₁₃×#537	C₂²	1	4	yes	complemented
38	C₁₃×#536	C₂²	1	4	yes	complemented
39	C₁₃×#535	C₂²	1	4	yes	complemented
40	C₁₃×#534	C₂²	1	4	yes	—
41	C₁₃×#533	C₂²	1	4	yes	complemented
42	C₁₃×#533	C₂²	1	8	yes	complemented
43	C₁₃×#533	C₂²	1	8	yes	complemented
44	C₁₃×#532	C₂²	1	4	yes	complemented
45	C₁₃×#532	C₂²	1	8	yes	complemented
46	C₁₃×#529	C₂²	1	16	yes	complemented
47	C₁₃×#529	C₂²	1	16	yes	complemented
48	C₁₃×#529	C₂²	1	16	yes	complemented
49	C₁₃×#529	C₂²	1	32	yes	complemented
50	C₁₃×#525	C₂²	1	8	yes	—
51	C₁₃×#525	C₂²	1	8	yes	—
52	C₁₃×#525	C₂²	1	4	yes	complemented
53	C₁₃×#525	C₂²	1	4	yes	complemented
54	C₁₃×#525	C₂²	1	4	yes	complemented
55	C₁₃×#525	C₂²	1	4	yes	complemented
56	C₁₃×#525	C₂²	1	16	yes	complemented
57	C₁₃×#525	C₂²	1	8	yes	complemented
58	C₂×C₁₃×#123	C₂²	1	4	yes	—
59	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
61	C₂×C₁₃×#120	C₂²	1	4	yes	—
62	C₁₃×#520	C₂²	1	8	yes	complemented
63	C₁₃×#520	C₂²	1	8	yes	complemented
64	C₁₃×#519	C₂²	1	4	yes	complemented
65	C₁₃×#518	C₂²	1	8	yes	—
66	C₁₃×#518	C₂²	1	4	yes	complemented
67	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
68	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
69	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
70	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
71	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#117	C₂²	1	2	yes	—
74	C₂×C₁₃×#117	C₂²	1	2	yes	—
75	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
76	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
77	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
78	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
79	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
80	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
83	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×#41	—	2	16	no	—
85	C₂×C₁₃×#41	C₂³	1	4	yes	—
86	C₂×C₁₃×#41	C₂³	1	4	yes	—
87	C₂×C₁₃×#41	C₂³	1	4	yes	—
88	C₂×C₁₃×#41	C₂³	1	4	yes	—
89	C₂×C₁₃×#41	C₂³	1	16	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
94	C₂³×C₄×C₁₃	—	2	8	no	—
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
106	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
107	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
108	C₁₃×#127	C₂³	1	4	yes	complemented
109	C₁₃×#126	C₂³	1	32	yes	—
110	C₁₃×#126	C₂³	1	32	yes	complemented
111	C₁₃×#126	C₂³	1	32	yes	complemented
112	C₁₃×#125	C₂³	1	8	yes	complemented
113	C₁₃×#125	C₂³	1	16	yes	complemented
114	C₁₃×#125	C₂³	1	32	yes	complemented
115	C₁₃×#125	C₂³	1	16	yes	complemented
116	C₁₃×#124	C₂³	1	32	yes	—
117	C₁₃×#124	C₂³	1	8	yes	complemented
118	C₁₃×#124	C₂³	1	16	yes	complemented
119	C₁₃×#123	C₂³	1	16	yes	—
120	C₁₃×#123	C₂³	1	8	yes	—
121	C₁₃×#123	C₂³	1	8	yes	—
122	C₁₃×#123	C₂³	1	32	yes	—
123	C₁₃×#123	C₂³	1	16	yes	—
124	C₁₃×#123	C₂³	1	32	yes	—
125	C₁₃×#123	C₂³	1	32	yes	complemented
126	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
129	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
130	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
131	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
134	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
135	C₁₃×#121	C₂³	1	8	yes	—
136	C₁₃×#121	C₂³	1	8	yes	—
137	C₁₃×#121	C₂³	1	8	yes	—
138	C₁₃×#121	C₂³	1	8	yes	—
139	C₁₃×#121	C₂³	1	16	yes	—
140	C₁₃×#121	C₂³	1	16	yes	—
141	C₁₃×#121	C₂³	1	32	yes	—
142	C₁₃×#121	C₂³	1	16	yes	complemented
143	C₁₃×#120	C₂³	1	16	yes	—
144	C₁₃×#120	C₂³	1	8	yes	—
145	C₁₃×#120	C₂³	1	8	yes	—
146	C₁₃×#120	C₂³	1	16	yes	—
147	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
148	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
149	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
150	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
151	C₄×D₄×C₁₃	C₂³	1	16	yes	—
152	C₄×D₄×C₁₃	C₂³	1	16	yes	—
153	C₄×D₄×C₁₃	C₂³	1	16	yes	—
154	C₄×D₄×C₁₃	C₂³	1	16	yes	—
155	C₄×D₄×C₁₃	C₂³	1	32	yes	—
156	C₄×D₄×C₁₃	C₂³	1	32	yes	—
157	C₄×D₄×C₁₃	C₂³	1	32	yes	—
158	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
159	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
160	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
161	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
162	C₁₃×#117	C₂³	1	4	yes	—
163	C₁₃×#117	C₂³	1	4	yes	—
164	C₁₃×#117	C₂³	1	4	yes	—
165	C₁₃×#117	C₂³	1	4	yes	—
166	C₁₃×#117	C₂³	1	4	yes	—
167	C₁₃×#117	C₂³	1	16	yes	—
168	C₁₃×#117	C₂³	1	4	yes	—
169	C₁₃×#117	C₂³	1	4	yes	—
170	C₁₃×#117	C₂³	1	4	yes	—
171	C₁₃×#117	C₂³	1	8	yes	—
172	C₁₃×#117	C₂³	1	8	yes	—
173	C₁₃×#117	C₂³	1	8	yes	—
174	C₁₃×#117	C₂³	1	8	yes	—
175	C₁₃×#117	C₂³	1	16	yes	—
176	C₁₃×#117	C₂³	1	16	yes	—
177	C₁₃×#117	C₂³	1	16	yes	complemented
178	C₁₃×#117	C₂³	1	16	yes	complemented
179	C₁₃×#117	C₂³	1	32	yes	complemented
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
187	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
196	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
198	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
200	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
203	#62814	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂⁴×C₁₃	—	2	4	no	—
205	C₂⁴×C₁₃	—	4	4	no	—
206	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
208	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
209	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₁₃×#41	—	2	16	no	—
212	C₁₃×#41	—	2	16	no	—
213	C₁₃×#41	—	2	16	no	—
214	C₁₃×#41	—	2	16	no	—
215	C₁₃×#41	—	4	32	no	—
216	C₂×Q₈×C₁₃	—	2	8	no	—
217	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
218	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
219	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
220	C₂×D₄×C₁₃	—	2	16	no	—
221	C₂×D₄×C₁₃	—	2	8	no	—
222	C₂×D₄×C₁₃	—	4	16	no	—
223	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
224	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
225	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
228	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
229	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	16	no	—
232	C₂²×C₄×C₁₃	—	2	16	no	—
233	C₂²×C₄×C₁₃	—	2	4	no	—
234	C₂²×C₄×C₁₃	—	2	4	no	—
235	C₂²×C₄×C₁₃	—	2	4	no	—
236	C₂²×C₄×C₁₃	—	2	4	no	—
237	C₂²×C₄×C₁₃	—	2	16	no	—
238	C₂²×C₄×C₁₃	—	4	8	no	—
239	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
240	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
243	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
255	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
258	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
268	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
269	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
270	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
271	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
272	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
273	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
274	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
275	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
276	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
277	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
278	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
279	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
280	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
281	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
282	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
283	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
284	C₄²×C₁₃	C₂⁴	1	8	yes	—
285	C₄²×C₁₃	C₂⁴	1	4	yes	—
286	C₄²×C₁₃	C₂⁴	1	8	yes	—
287	C₄²×C₁₃	C₂⁴	1	4	yes	—
288	C₄²×C₁₃	C₂⁴	1	8	yes	—
289	C₄²×C₁₃	C₂⁴	1	32	yes	—
290	C₄²×C₁₃	C₂⁴	1	4	yes	—
291	C₄²×C₁₃	C₂⁴	1	4	yes	—
292	C₄²×C₁₃	C₂⁴	1	8	yes	—
293	#3495	C₂×C₁₃	1	8	yes	complemented
294	#3494	C₂×C₁₃	1	8	yes	complemented
295	#3493	C₂×C₁₃	1	4	yes	complemented
296	#3492	C₂×C₁₃	1	4	yes	complemented
297	#3491	C₂×C₁₃	1	4	yes	complemented
298	#3490	C₂×C₁₃	1	4	yes	complemented
299	#3475	C₂×C₁₃	1	16	yes	complemented
300	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#3455	C₂×C₁₃	1	4	yes	complemented
302	#3449	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#3444	C₂×C₁₃	1	4	yes	complemented
304	C₂×#525	C₂×C₁₃	1	2	yes	complemented
305	#3428	C₂×C₁₃	1	2	yes	complemented
306	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	2	no	—
308	C₂³×C₁₃	—	2	4	no	—
309	C₂³×C₁₃	—	2	8	no	—
310	C₂³×C₁₃	—	2	2	no	—
311	C₂³×C₁₃	—	2	8	no	—
312	C₂³×C₁₃	—	2	8	no	—
313	C₂³×C₁₃	—	4	2	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	—	4	2	no	—
316	C₂³×C₁₃	—	4	8	no	—
317	C₂³×C₁₃	—	4	16	no	—
318	C₂³×C₁₃	C₂×#41	1	4	yes	—
319	C₂³×C₁₃	C₂⁵	1	2	yes	—
320	C₂³×C₁₃	C₂⁵	1	8	yes	—
321	C₂³×C₁₃	C₂⁵	1	2	yes	—
322	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
323	C₂³×C₁₃	C₂⁵	1	2	yes	—
324	Q₈×C₁₃	—	2	8	no	—
325	Q₈×C₁₃	—	2	8	no	—
326	Q₈×C₁₃	—	4	16	no	—
327	D₄×C₁₃	—	2	16	no	—
328	D₄×C₁₃	—	2	16	no	—
329	D₄×C₁₃	—	2	32	no	—
330	D₄×C₁₃	—	2	8	no	—
331	D₄×C₁₃	—	2	8	no	—
332	D₄×C₁₃	—	4	16	no	—
333	D₄×C₁₃	—	4	16	no	—
334	C₂×C₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	8	no	—
338	C₂×C₄×C₁₃	—	2	16	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	2	8	no	—
342	C₂×C₄×C₁₃	—	2	8	no	—
343	C₂×C₄×C₁₃	—	2	4	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	16	no	—
346	C₂×C₄×C₁₃	—	2	16	no	—
347	C₂×C₄×C₁₃	—	4	4	no	—
348	C₂×C₄×C₁₃	—	4	8	no	—
349	C₂×C₄×C₁₃	—	4	4	no	—
350	C₂×C₄×C₁₃	—	4	8	no	—
351	C₂×C₄×C₁₃	—	4	32	no	—
352	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
353	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
354	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
355	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
357	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
358	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
359	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
360	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
361	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
362	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
364	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
365	C₂²×#41	C₂²×C₁₃	1	2	yes	—
366	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
367	#556	C₂²×C₁₃	1	16	yes	complemented
368	#555	C₂²×C₁₃	1	16	yes	complemented
369	#554	C₂²×C₁₃	1	16	yes	complemented
370	#553	C₂²×C₁₃	1	16	yes	complemented
371	#553	C₂²×C₁₃	1	16	yes	complemented
372	#552	C₂²×C₁₃	1	32	yes	complemented
373	#552	C₂²×C₁₃	1	16	yes	complemented
374	#552	C₂²×C₁₃	1	16	yes	complemented
375	#551	C₂²×C₁₃	1	32	yes	complemented
376	#551	C₂²×C₁₃	1	32	yes	complemented
377	#547	C₂²×C₁₃	1	16	yes	complemented
378	#546	C₂²×C₁₃	1	32	yes	complemented
379	#544	C₂²×C₁₃	1	4	yes	complemented
380	#544	C₂²×C₁₃	1	8	yes	complemented
381	#543	C₂²×C₁₃	1	4	yes	—
382	#542	C₂²×C₁₃	1	16	yes	complemented
383	#541	C₂²×C₁₃	1	8	yes	complemented
384	#540	C₂²×C₁₃	1	8	yes	complemented
385	#539	C₂²×C₁₃	1	16	yes	complemented
386	#538	C₂²×C₁₃	1	16	yes	complemented
387	#537	C₂²×C₁₃	1	4	yes	complemented
388	#536	C₂²×C₁₃	1	4	yes	complemented
389	#535	C₂²×C₁₃	1	4	yes	complemented
390	#534	C₂²×C₁₃	1	4	yes	—
391	#533	C₂²×C₁₃	1	4	yes	complemented
392	#533	C₂²×C₁₃	1	8	yes	complemented
393	#533	C₂²×C₁₃	1	8	yes	complemented
394	#532	C₂²×C₁₃	1	4	yes	complemented
395	#532	C₂²×C₁₃	1	8	yes	complemented
396	#529	C₂²×C₁₃	1	16	yes	complemented
397	#529	C₂²×C₁₃	1	16	yes	complemented
398	#529	C₂²×C₁₃	1	16	yes	complemented
399	#529	C₂²×C₁₃	1	32	yes	complemented
400	#525	C₂²×C₁₃	1	8	yes	—
401	#525	C₂²×C₁₃	1	8	yes	—
402	#525	C₂²×C₁₃	1	4	yes	complemented
403	#525	C₂²×C₁₃	1	4	yes	complemented
404	#525	C₂²×C₁₃	1	4	yes	complemented
405	#525	C₂²×C₁₃	1	4	yes	complemented
406	#525	C₂²×C₁₃	1	16	yes	complemented
407	#525	C₂²×C₁₃	1	8	yes	complemented
408	C₂×#123	C₂²×C₁₃	1	4	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
410	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
411	C₂×#120	C₂²×C₁₃	1	4	yes	—
412	#520	C₂²×C₁₃	1	8	yes	complemented
413	#520	C₂²×C₁₃	1	8	yes	complemented
414	#519	C₂²×C₁₃	1	4	yes	complemented
415	#518	C₂²×C₁₃	1	8	yes	—
416	#518	C₂²×C₁₃	1	4	yes	complemented
417	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
418	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
419	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
420	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
421	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#117	C₂²×C₁₃	1	2	yes	—
424	C₂×#117	C₂²×C₁₃	1	2	yes	—
425	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
426	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
427	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
428	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
429	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
430	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
431	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
432	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
433	C₂²×C₁₃	—	2	8	no	—
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	2	4	no	—
438	C₂²×C₁₃	—	2	2	no	—
439	C₂²×C₁₃	—	2	8	no	—
440	C₂²×C₁₃	—	2	16	no	—
441	C₂²×C₁₃	—	2	4	no	—
442	C₂²×C₁₃	—	4	4	no	—
443	C₂²×C₁₃	—	4	16	no	—
444	C₂²×C₁₃	—	4	4	no	—
445	C₂²×C₁₃	—	8	8	no	—
446	C₂²×C₁₃	C₂²×#41	1	4	yes	—
447	C₂²×C₁₃	C₂²×#41	1	2	yes	—
448	C₂²×C₁₃	#585	1	4	yes	—
449	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	2	8	no	—
453	C₄×C₁₃	—	2	8	no	—
454	C₄×C₁₃	—	2	8	no	—
455	C₄×C₁₃	—	2	16	no	—
456	C₄×C₁₃	C₂²×#41	1	2	yes	—
457	C₄×C₁₃	C₂²×#41	1	4	yes	—
458	C₄×C₁₃	C₂²×#41	1	2	yes	—
459	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×#41	—	2	16	no	—
461	C₂×#41	C₂³×C₁₃	1	4	yes	—
462	C₂×#41	C₂³×C₁₃	1	4	yes	—
463	C₂×#41	C₂³×C₁₃	1	4	yes	—
464	C₂×#41	C₂³×C₁₃	1	4	yes	—
465	C₂×#41	C₂³×C₁₃	1	16	yes	—
466	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
468	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
469	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
470	C₂³×C₄	—	2	8	no	—
471	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
474	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
475	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
480	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
482	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
483	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
484	#127	C₂³×C₁₃	1	4	yes	complemented
485	#126	C₂³×C₁₃	1	32	yes	—
486	#126	C₂³×C₁₃	1	32	yes	complemented
487	#126	C₂³×C₁₃	1	32	yes	complemented
488	#125	C₂³×C₁₃	1	8	yes	complemented
489	#125	C₂³×C₁₃	1	16	yes	complemented
490	#125	C₂³×C₁₃	1	32	yes	complemented
491	#125	C₂³×C₁₃	1	16	yes	complemented
492	#124	C₂³×C₁₃	1	32	yes	—
493	#124	C₂³×C₁₃	1	8	yes	complemented
494	#124	C₂³×C₁₃	1	16	yes	complemented
495	#123	C₂³×C₁₃	1	16	yes	—
496	#123	C₂³×C₁₃	1	8	yes	—
497	#123	C₂³×C₁₃	1	8	yes	—
498	#123	C₂³×C₁₃	1	32	yes	—
499	#123	C₂³×C₁₃	1	16	yes	—
500	#123	C₂³×C₁₃	1	32	yes	—
501	#123	C₂³×C₁₃	1	32	yes	complemented
502	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
503	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
504	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
505	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
506	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
507	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
508	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
509	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
510	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
511	#121	C₂³×C₁₃	1	8	yes	—
512	#121	C₂³×C₁₃	1	8	yes	—
513	#121	C₂³×C₁₃	1	8	yes	—
514	#121	C₂³×C₁₃	1	8	yes	—
515	#121	C₂³×C₁₃	1	16	yes	—
516	#121	C₂³×C₁₃	1	16	yes	—
517	#121	C₂³×C₁₃	1	32	yes	—
518	#121	C₂³×C₁₃	1	16	yes	complemented
519	#120	C₂³×C₁₃	1	16	yes	—
520	#120	C₂³×C₁₃	1	8	yes	—
521	#120	C₂³×C₁₃	1	8	yes	—
522	#120	C₂³×C₁₃	1	16	yes	—
523	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
524	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
525	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
526	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
527	C₄×D₄	C₂³×C₁₃	1	16	yes	—
528	C₄×D₄	C₂³×C₁₃	1	16	yes	—
529	C₄×D₄	C₂³×C₁₃	1	16	yes	—
530	C₄×D₄	C₂³×C₁₃	1	16	yes	—
531	C₄×D₄	C₂³×C₁₃	1	32	yes	—
532	C₄×D₄	C₂³×C₁₃	1	32	yes	—
533	C₄×D₄	C₂³×C₁₃	1	32	yes	—
534	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
535	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
536	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
537	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
538	#117	C₂³×C₁₃	1	4	yes	—
539	#117	C₂³×C₁₃	1	4	yes	—
540	#117	C₂³×C₁₃	1	4	yes	—
541	#117	C₂³×C₁₃	1	4	yes	—
542	#117	C₂³×C₁₃	1	4	yes	—
543	#117	C₂³×C₁₃	1	16	yes	—
544	#117	C₂³×C₁₃	1	4	yes	—
545	#117	C₂³×C₁₃	1	4	yes	—
546	#117	C₂³×C₁₃	1	4	yes	—
547	#117	C₂³×C₁₃	1	8	yes	—
548	#117	C₂³×C₁₃	1	8	yes	—
549	#117	C₂³×C₁₃	1	8	yes	—
550	#117	C₂³×C₁₃	1	8	yes	—
551	#117	C₂³×C₁₃	1	16	yes	—
552	#117	C₂³×C₁₃	1	16	yes	—
553	#117	C₂³×C₁₃	1	16	yes	complemented
554	#117	C₂³×C₁₃	1	16	yes	complemented
555	#117	C₂³×C₁₃	1	32	yes	complemented
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
564	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
572	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
576	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
577	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
578	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
579	C₂×C₁₃	—	2	2	no	—
580	C₂×C₁₃	—	2	4	no	—
581	C₂×C₁₃	—	2	4	no	—
582	C₂×C₁₃	—	4	2	no	—
583	C₂×C₁₃	—	4	8	no	—
584	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
585	C₂×C₁₃	C₂×#585	1	2	yes	—
586	C₂⁴	—	2	4	no	—
587	C₂⁴	—	4	4	no	—
588	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
589	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
590	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
591	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
592	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
593	#41	—	2	16	no	—
594	#41	—	2	16	no	—
595	#41	—	2	16	no	—
596	#41	—	2	16	no	—
597	#41	—	4	32	no	—
598	C₂×Q₈	—	2	8	no	—
599	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
600	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
601	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
602	C₂×D₄	—	2	16	no	—
603	C₂×D₄	—	2	8	no	—
604	C₂×D₄	—	4	16	no	—
605	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
606	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
607	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
608	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
610	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
611	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	16	no	—
614	C₂²×C₄	—	2	16	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	16	no	—
620	C₂²×C₄	—	4	8	no	—
621	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
622	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
626	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
627	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
639	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
645	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
646	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
647	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
648	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
649	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
650	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
651	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
652	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
653	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
654	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
655	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
656	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
657	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
658	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
659	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
660	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
661	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
662	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
663	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
664	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
665	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
666	C₄²	C₂⁴×C₁₃	1	4	yes	—
667	C₄²	C₂⁴×C₁₃	1	8	yes	—
668	C₄²	C₂⁴×C₁₃	1	4	yes	—
669	C₄²	C₂⁴×C₁₃	1	4	yes	—
670	C₄²	C₂⁴×C₁₃	1	8	yes	—
671	C₄²	C₂⁴×C₁₃	1	4	yes	—
672	C₄²	C₂⁴×C₁₃	1	8	yes	—
673	C₄²	C₂⁴×C₁₃	1	8	yes	—
674	C₄²	C₂⁴×C₁₃	1	32	yes	—
675	C₁₃	#62814	1	1	yes	characteristic, direct product factor, Sylow
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	8	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	8	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	8	no	—
686	C₂³	—	4	16	no	—
687	C₂³	C₂×C₁₃×#41	1	4	yes	—
688	C₂³	C₂⁵×C₁₃	1	2	yes	—
689	C₂³	C₂⁵×C₁₃	1	8	yes	—
690	C₂³	C₂⁵×C₁₃	1	2	yes	—
691	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
692	C₂³	C₂⁵×C₁₃	1	2	yes	—
693	Q₈	—	2	8	no	—
694	Q₈	—	2	8	no	—
695	Q₈	—	4	16	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	16	no	—
698	D₄	—	2	32	no	—
699	D₄	—	2	8	no	—
700	D₄	—	2	8	no	—
701	D₄	—	4	16	no	—
702	D₄	—	4	16	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	16	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	16	no	—
715	C₂×C₄	—	2	16	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	8	no	—
720	C₂×C₄	—	4	32	no	—
721	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
722	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
723	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
724	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
725	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
726	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
727	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
728	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
729	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
730	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
731	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
732	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
733	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
734	C₂²	—	2	8	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	16	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	16	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	8	8	no	—
747	C₂²	C₂²×C₁₃×#41	1	4	yes	—
748	C₂²	C₂²×C₁₃×#41	1	2	yes	—
749	C₂²	C₁₃×#585	1	4	yes	—
750	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	8	no	—
754	C₄	—	2	8	no	—
755	C₄	—	2	8	no	—
756	C₄	—	2	16	no	—
757	C₄	C₂²×C₁₃×#41	1	2	yes	—
758	C₄	C₂²×C₁₃×#41	1	4	yes	—
759	C₄	C₂²×C₁₃×#41	1	2	yes	—
760	C₂	—	2	2	no	—
761	C₂	—	2	4	no	—
762	C₂	—	2	4	no	—
763	C₂	—	4	2	no	—
764	C₂	—	4	8	no	—
765	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
766	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3495	C₂	semidirect
2. C₁₃×#3494	C₂	semidirect
3. C₁₃×#3493	C₂	semidirect
4. C₁₃×#3492	C₂	semidirect
5. C₁₃×#3491	C₂	semidirect
6. C₁₃×#3490	C₂	semidirect
7. C₁₃×#3475	C₂	semidirect
8. C₁₃×#3458	C₂	semidirect
9. C₁₃×#3455	C₂	semidirect
10. C₁₃×#3449	C₂	semidirect
11. C₁₃×#3444	C₂	semidirect
12. C₂×C₁₃×#525	C₂	semidirect
13. C₁₃×#3428	C₂	semidirect
14. C₂²×C₁₃×#117	C₂	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#555	C₂²	semidirect
19. C₁₃×#554	C₂²	semidirect
20. C₁₃×#553	C₂²	semidirect
21. C₁₃×#553	C₂²	semidirect
22. C₁₃×#552	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
24. C₁₃×#552	C₂²	semidirect
25. C₁₃×#551	C₂²	semidirect
26. C₁₃×#551	C₂²	semidirect
27. C₁₃×#547	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. C₁₃×#544	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
32. C₁₃×#542	C₂²	semidirect
33. C₁₃×#541	C₂²	semidirect
34. C₁₃×#540	C₂²	semidirect
35. C₁₃×#539	C₂²	semidirect
36. C₁₃×#538	C₂²	semidirect
37. C₁₃×#537	C₂²	semidirect
38. C₁₃×#536	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
41. C₁₃×#533	C₂²	semidirect
42. C₁₃×#533	C₂²	semidirect
43. C₁₃×#533	C₂²	semidirect
44. C₁₃×#532	C₂²	semidirect
45. C₁₃×#532	C₂²	semidirect
46. C₁₃×#529	C₂²	semidirect
47. C₁₃×#529	C₂²	semidirect
48. C₁₃×#529	C₂²	semidirect
49. C₁₃×#529	C₂²	semidirect
52. C₁₃×#525	C₂²	semidirect
53. C₁₃×#525	C₂²	semidirect
54. C₁₃×#525	C₂²	semidirect
55. C₁₃×#525	C₂²	semidirect
56. C₁₃×#525	C₂²	semidirect
57. C₁₃×#525	C₂²	semidirect
59. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₁₃×#121	C₂²	semidirect
62. C₁₃×#520	C₂²	semidirect
63. C₁₃×#520	C₂²	semidirect
64. C₁₃×#519	C₂²	semidirect
66. C₁₃×#518	C₂²	semidirect
67. C₄×C₁₃×#41	C₂²	semidirect
68. C₄×C₁₃×#41	C₂²	semidirect
69. C₄×C₁₃×#41	C₂²	semidirect
70. C₂×C₄×D₄×C₁₃	C₂²	semidirect
75. C₂×C₁₃×#117	C₂²	semidirect
76. C₂×C₁₃×#117	C₂²	semidirect
77. C₂×C₁₃×#117	C₂²	semidirect
78. C₂×C₁₃×#117	C₂²	semidirect
79. C₂×C₁₃×#117	C₂²	semidirect
80. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
82. C₂²×C₄²×C₁₃	C₂²	semidirect
105. C₁₃×C₄⋊Q₈	C₂³	semidirect
106. C₁₃×C₄⋊Q₈	C₂³	semidirect
107. C₁₃×C₄⋊Q₈	C₂³	semidirect
108. C₁₃×#127	C₂³	semidirect
110. C₁₃×#126	C₂³	semidirect
111. C₁₃×#126	C₂³	semidirect
112. C₁₃×#125	C₂³	semidirect
113. C₁₃×#125	C₂³	semidirect
114. C₁₃×#125	C₂³	semidirect
115. C₁₃×#125	C₂³	semidirect
117. C₁₃×#124	C₂³	semidirect
118. C₁₃×#124	C₂³	semidirect
125. C₁₃×#123	C₂³	semidirect
133. C₁₃×C₂²⋊Q₈	C₂³	semidirect
134. C₁₃×C₂²⋊Q₈	C₂³	semidirect
142. C₁₃×#121	C₂³	semidirect
147. C₄×Q₈×C₁₃	C₂³	semidirect
148. C₄×Q₈×C₁₃	C₂³	semidirect
149. C₄×Q₈×C₁₃	C₂³	semidirect
150. C₄×Q₈×C₁₃	C₂³	semidirect
158. C₄×D₄×C₁₃	C₂³	semidirect
159. C₄×D₄×C₁₃	C₂³	semidirect
160. C₄×D₄×C₁₃	C₂³	semidirect
161. C₄×D₄×C₁₃	C₂³	semidirect
177. C₁₃×#117	C₂³	semidirect
178. C₁₃×#117	C₂³	semidirect
179. C₁₃×#117	C₂³	semidirect
187. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
202. C₂×C₄²×C₁₃	C₂³	semidirect
203. #62814	C₁₃	direct (N × H)
239. C₂²×C₄×C₁₃	#41	semidirect
293. #3495	C₂×C₁₃	semidirect
294. #3494	C₂×C₁₃	semidirect
295. #3493	C₂×C₁₃	semidirect
296. #3492	C₂×C₁₃	semidirect
297. #3491	C₂×C₁₃	semidirect
298. #3490	C₂×C₁₃	semidirect
299. #3475	C₂×C₁₃	semidirect
300. #3458	C₂×C₁₃	semidirect
301. #3455	C₂×C₁₃	semidirect
302. #3449	C₂×C₁₃	semidirect
303. #3444	C₂×C₁₃	semidirect
304. C₂×#525	C₂×C₁₃	semidirect
305. #3428	C₂×C₁₃	semidirect
306. C₂²×#117	C₂×C₁₃	semidirect
367. #556	C₂²×C₁₃	semidirect
368. #555	C₂²×C₁₃	semidirect
369. #554	C₂²×C₁₃	semidirect
370. #553	C₂²×C₁₃	semidirect
371. #553	C₂²×C₁₃	semidirect
372. #552	C₂²×C₁₃	semidirect
373. #552	C₂²×C₁₃	semidirect
374. #552	C₂²×C₁₃	semidirect
375. #551	C₂²×C₁₃	semidirect
376. #551	C₂²×C₁₃	semidirect
377. #547	C₂²×C₁₃	semidirect
378. #546	C₂²×C₁₃	semidirect
379. #544	C₂²×C₁₃	semidirect
380. #544	C₂²×C₁₃	semidirect
382. #542	C₂²×C₁₃	semidirect
383. #541	C₂²×C₁₃	semidirect
384. #540	C₂²×C₁₃	semidirect
385. #539	C₂²×C₁₃	semidirect
386. #538	C₂²×C₁₃	semidirect
387. #537	C₂²×C₁₃	semidirect
388. #536	C₂²×C₁₃	semidirect
389. #535	C₂²×C₁₃	semidirect
391. #533	C₂²×C₁₃	semidirect
392. #533	C₂²×C₁₃	semidirect
393. #533	C₂²×C₁₃	semidirect
394. #532	C₂²×C₁₃	semidirect
395. #532	C₂²×C₁₃	semidirect
396. #529	C₂²×C₁₃	semidirect
397. #529	C₂²×C₁₃	semidirect
398. #529	C₂²×C₁₃	semidirect
399. #529	C₂²×C₁₃	semidirect
402. #525	C₂²×C₁₃	semidirect
403. #525	C₂²×C₁₃	semidirect
404. #525	C₂²×C₁₃	semidirect
405. #525	C₂²×C₁₃	semidirect
406. #525	C₂²×C₁₃	semidirect
407. #525	C₂²×C₁₃	semidirect
409. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
410. C₂×#121	C₂²×C₁₃	semidirect
412. #520	C₂²×C₁₃	semidirect
413. #520	C₂²×C₁₃	semidirect
414. #519	C₂²×C₁₃	semidirect
416. #518	C₂²×C₁₃	semidirect
417. C₄×#41	C₂²×C₁₃	semidirect
418. C₄×#41	C₂²×C₁₃	semidirect
419. C₄×#41	C₂²×C₁₃	semidirect
420. C₂×C₄×D₄	C₂²×C₁₃	semidirect
425. C₂×#117	C₂²×C₁₃	semidirect
426. C₂×#117	C₂²×C₁₃	semidirect
427. C₂×#117	C₂²×C₁₃	semidirect
428. C₂×#117	C₂²×C₁₃	semidirect
429. C₂×#117	C₂²×C₁₃	semidirect
430. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
432. C₂²×C₄²	C₂²×C₁₃	semidirect
481. C₄⋊Q₈	C₂³×C₁₃	semidirect
482. C₄⋊Q₈	C₂³×C₁₃	semidirect
483. C₄⋊Q₈	C₂³×C₁₃	semidirect
484. #127	C₂³×C₁₃	semidirect
486. #126	C₂³×C₁₃	semidirect
487. #126	C₂³×C₁₃	semidirect
488. #125	C₂³×C₁₃	semidirect
489. #125	C₂³×C₁₃	semidirect
490. #125	C₂³×C₁₃	semidirect
491. #125	C₂³×C₁₃	semidirect
493. #124	C₂³×C₁₃	semidirect
494. #124	C₂³×C₁₃	semidirect
501. #123	C₂³×C₁₃	semidirect
509. C₂²⋊Q₈	C₂³×C₁₃	semidirect
510. C₂²⋊Q₈	C₂³×C₁₃	semidirect
518. #121	C₂³×C₁₃	semidirect
523. C₄×Q₈	C₂³×C₁₃	semidirect
524. C₄×Q₈	C₂³×C₁₃	semidirect
525. C₄×Q₈	C₂³×C₁₃	semidirect
526. C₄×Q₈	C₂³×C₁₃	semidirect
534. C₄×D₄	C₂³×C₁₃	semidirect
535. C₄×D₄	C₂³×C₁₃	semidirect
536. C₄×D₄	C₂³×C₁₃	semidirect
537. C₄×D₄	C₂³×C₁₃	semidirect
553. #117	C₂³×C₁₃	semidirect
554. #117	C₂³×C₁₃	semidirect
555. #117	C₂³×C₁₃	semidirect
563. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
578. C₂×C₄²	C₂³×C₁₃	semidirect
621. C₂²×C₄	C₁₃×#41	semidirect
675. C₁₃	#62814	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×#3495	2
C₁₃×#3494	2
C₁₃×#3493	2
C₁₃×#3492	2
C₁₃×#3491	2
C₁₃×#3490	2
C₁₃×#3475	2
C₁₃×#3458	2
C₁₃×#3455	2
C₁₃×#3449	2
C₁₃×#3444	2
C₂×C₁₃×#525	2
C₁₃×#3428	2
C₂²×C₁₃×#117	2
#62814	13

Subgroups — C13×#62814 #15749153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62814 #15749153