Subgroups — C₁₃×#62903 #15749242

Order 3328.

6628 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3564	C₂	1	6	yes	maximal, complemented
2	C₁₃×#3564	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3561	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3538	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3535	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3535	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3520	C₂	1	6	yes	maximal, complemented
8	C₁₃×#3501	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3495	C₂	1	6	yes	maximal, complemented
10	C₁₃×#3491	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3490	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#551	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	C₂²	1	12	yes	complemented
17	C₁₃×#563	C₂²	1	12	yes	complemented
18	C₁₃×#563	C₂²	1	12	yes	complemented
19	C₁₃×#562	C₂²	1	12	yes	complemented
20	C₁₃×#556	C₂²	1	6	yes	complemented
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×#554	C₂²	1	12	yes	complemented
25	C₁₃×#552	C₂²	1	6	yes	complemented
26	C₁₃×#552	C₂²	1	12	yes	complemented
27	C₁₃×#552	C₂²	1	12	yes	complemented
28	C₁₃×#552	C₂²	1	12	yes	complemented
29	C₁₃×#552	C₂²	1	6	yes	complemented
30	C₁₃×#552	C₂²	1	12	yes	complemented
31	C₁₃×#551	C₂²	1	12	yes	complemented
32	C₁₃×#551	C₂²	1	12	yes	complemented
33	C₁₃×#551	C₂²	1	12	yes	complemented
34	C₁₃×#551	C₂²	1	12	yes	complemented
35	C₁₃×#551	C₂²	1	12	yes	complemented
36	C₁₃×#551	C₂²	1	12	yes	complemented
37	C₁₃×#551	C₂²	1	12	yes	complemented
38	C₁₃×#551	C₂²	1	12	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
40	D₄×Q₈×C₁₃	C₂²	1	12	yes	complemented
41	C₁₃×#548	C₂²	1	2	yes	complemented
42	C₁₃×#548	C₂²	1	6	yes	complemented
43	C₁₃×#547	C₂²	1	6	yes	complemented
44	C₁₃×#547	C₂²	1	6	yes	complemented
45	C₁₃×#546	C₂²	1	12	yes	complemented
46	C₁₃×#546	C₂²	1	12	yes	complemented
47	C₁₃×#544	C₂²	1	6	yes	complemented
48	C₁₃×#544	C₂²	1	6	yes	complemented
49	C₁₃×#544	C₂²	1	6	yes	complemented
50	C₁₃×#544	C₂²	1	6	yes	complemented
51	C₁₃×#543	C₂²	1	1	yes	characteristic
52	C₁₃×#543	C₂²	1	3	yes	—
53	C₁₃×#543	C₂²	1	3	yes	—
54	C₁₃×#543	C₂²	1	6	yes	complemented
55	C₁₃×#543	C₂²	1	6	yes	complemented
56	C₁₃×#543	C₂²	1	6	yes	complemented
57	C₁₃×#542	C₂²	1	6	yes	complemented
58	C₁₃×#542	C₂²	1	6	yes	complemented
59	C₁₃×#542	C₂²	1	12	yes	complemented
60	C₁₃×#542	C₂²	1	12	yes	complemented
61	C₁₃×#541	C₂²	1	12	yes	complemented
62	C₁₃×#541	C₂²	1	6	yes	complemented
63	C₁₃×#541	C₂²	1	6	yes	complemented
64	C₁₃×#539	C₂²	1	12	yes	complemented
65	C₁₃×#539	C₂²	1	6	yes	complemented
66	C₁₃×#539	C₂²	1	6	yes	complemented
67	C₁₃×#539	C₂²	1	6	yes	complemented
68	C₁₃×#539	C₂²	1	12	yes	complemented
69	C₁₃×#539	C₂²	1	12	yes	complemented
70	C₁₃×#538	C₂²	1	6	yes	—
71	C₁₃×#538	C₂²	1	6	yes	—
72	C₁₃×#538	C₂²	1	6	yes	complemented
73	C₁₃×#536	C₂²	1	6	yes	complemented
74	C₁₃×#536	C₂²	1	12	yes	complemented
75	C₁₃×#534	C₂²	1	3	yes	—
76	C₁₃×#533	C₂²	1	6	yes	complemented
77	C₁₃×#533	C₂²	1	6	yes	complemented
78	C₁₃×#533	C₂²	1	6	yes	complemented
79	C₁₃×#529	C₂²	1	6	yes	complemented
80	C₁₃×#529	C₂²	1	6	yes	complemented
81	C₁₃×#529	C₂²	1	6	yes	complemented
82	C₂×C₁₃×#126	C₂²	1	3	yes	complemented
83	C₂×C₁₃×#126	C₂²	1	3	yes	complemented
84	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
85	C₁₃×#525	C₂²	1	6	yes	—
86	C₁₃×#525	C₂²	1	6	yes	—
87	C₁₃×#525	C₂²	1	6	yes	complemented
88	C₂×C₁₃×#123	C₂²	1	3	yes	—
89	C₂×C₁₃×#123	C₂²	1	3	yes	complemented
90	C₂×C₁₃×#123	C₂²	1	3	yes	complemented
91	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
92	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
93	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
94	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
95	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
96	C₂×C₁₃×#120	C₂²	1	3	yes	—
97	C₁₃×#520	C₂²	1	6	yes	complemented
98	C₁₃×#519	C₂²	1	2	yes	complemented
99	C₁₃×#518	C₂²	1	6	yes	—
100	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
101	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
102	C₂×C₁₃×#117	C₂²	1	3	yes	—
103	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
104	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	—
105	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×#41	C₂³	1	6	yes	—
108	C₂×C₁₃×#41	C₂³	1	6	yes	—
109	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
112	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×Q₈×C₁₃	C₂³	1	6	yes	complemented
114	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
119	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
121	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
123	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
124	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
125	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
126	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
127	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	complemented
128	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	complemented
129	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	complemented
130	C₁₃×#126	C₂³	1	12	yes	—
131	C₁₃×#126	C₂³	1	12	yes	—
132	C₁₃×#126	C₂³	1	12	yes	—
133	C₁₃×#126	C₂³	1	12	yes	—
134	C₁₃×#126	C₂³	1	12	yes	—
135	C₁₃×#126	C₂³	1	12	yes	—
136	C₁₃×#126	C₂³	1	12	yes	complemented
137	C₁₃×#126	C₂³	1	12	yes	complemented
138	C₁₃×#126	C₂³	1	12	yes	complemented
139	C₁₃×#126	C₂³	1	12	yes	complemented
140	C₁₃×#126	C₂³	1	12	yes	complemented
141	C₁₃×#125	C₂³	1	6	yes	complemented
142	C₁₃×#125	C₂³	1	6	yes	complemented
143	C₁₃×#125	C₂³	1	6	yes	complemented
144	C₁₃×#125	C₂³	1	12	yes	complemented
145	C₁₃×#125	C₂³	1	12	yes	complemented
146	C₁₃×#125	C₂³	1	12	yes	complemented
147	C₁₃×#125	C₂³	1	12	yes	complemented
148	C₁₃×#125	C₂³	1	12	yes	complemented
149	C₁₃×#125	C₂³	1	12	yes	complemented
150	C₁₃×#125	C₂³	1	12	yes	complemented
151	C₁₃×#124	C₂³	1	12	yes	—
152	C₁₃×#124	C₂³	1	12	yes	—
153	C₁₃×#124	C₂³	1	12	yes	—
154	C₁₃×#124	C₂³	1	12	yes	—
155	C₁₃×#124	C₂³	1	6	yes	complemented
156	C₁₃×#124	C₂³	1	6	yes	complemented
157	C₁₃×#124	C₂³	1	6	yes	complemented
158	C₁₃×#123	C₂³	1	12	yes	—
159	C₁₃×#123	C₂³	1	12	yes	—
160	C₁₃×#123	C₂³	1	12	yes	—
161	C₁₃×#123	C₂³	1	12	yes	—
162	C₁₃×#123	C₂³	1	12	yes	—
163	C₁₃×#123	C₂³	1	12	yes	—
164	C₁₃×#123	C₂³	1	12	yes	—
165	C₁₃×#123	C₂³	1	12	yes	—
166	C₁₃×#123	C₂³	1	12	yes	—
167	C₁₃×#123	C₂³	1	12	yes	—
168	C₁₃×#123	C₂³	1	12	yes	—
169	C₁₃×#123	C₂³	1	12	yes	complemented
170	C₁₃×#123	C₂³	1	12	yes	complemented
171	C₁₃×#123	C₂³	1	12	yes	complemented
172	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
195	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
196	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
197	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	complemented
198	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
199	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
200	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
201	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
202	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
203	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	complemented
204	C₁₃×#121	C₂³	1	6	yes	—
205	C₁₃×#121	C₂³	1	6	yes	—
206	C₁₃×#121	C₂³	1	6	yes	—
207	C₁₃×#121	C₂³	1	6	yes	—
208	C₁₃×#121	C₂³	1	12	yes	—
209	C₁₃×#121	C₂³	1	12	yes	—
210	C₁₃×#121	C₂³	1	6	yes	complemented
211	C₁₃×#120	C₂³	1	12	yes	—
212	C₁₃×#120	C₂³	1	12	yes	—
213	C₁₃×#120	C₂³	1	12	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
215	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
217	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
218	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
219	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
220	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
222	C₄×Q₈×C₁₃	C₂³	1	6	yes	complemented
223	C₄×Q₈×C₁₃	C₂³	1	12	yes	complemented
224	C₄×D₄×C₁₃	C₂³	1	12	yes	—
225	C₄×D₄×C₁₃	C₂³	1	12	yes	—
226	C₄×D₄×C₁₃	C₂³	1	6	yes	—
227	C₄×D₄×C₁₃	C₂³	1	6	yes	—
228	C₄×D₄×C₁₃	C₂³	1	6	yes	—
229	C₄×D₄×C₁₃	C₂³	1	6	yes	—
230	C₄×D₄×C₁₃	C₂³	1	12	yes	—
231	C₄×D₄×C₁₃	C₂³	1	12	yes	—
232	C₄×D₄×C₁₃	C₂³	1	12	yes	—
233	C₄×D₄×C₁₃	C₂³	1	12	yes	—
234	C₄×D₄×C₁₃	C₂³	1	12	yes	—
235	C₄×D₄×C₁₃	C₂³	1	12	yes	—
236	C₄×D₄×C₁₃	C₂³	1	6	yes	complemented
237	C₄×D₄×C₁₃	C₂³	1	6	yes	complemented
238	C₄×D₄×C₁₃	C₂³	1	6	yes	complemented
239	C₁₃×#117	C₂³	1	12	yes	—
240	C₁₃×#117	C₂³	1	12	yes	—
241	C₁₃×#117	C₂³	1	6	yes	—
242	C₁₃×#117	C₂³	1	6	yes	—
243	C₁₃×#117	C₂³	1	6	yes	—
244	C₁₃×#117	C₂³	1	6	yes	—
245	C₁₃×#117	C₂³	1	12	yes	—
246	C₁₃×#117	C₂³	1	6	yes	—
247	C₁₃×#117	C₂³	1	6	yes	—
248	C₁₃×#117	C₂³	1	12	yes	complemented
249	C₁₃×#117	C₂³	1	6	yes	complemented
250	C₁₃×#117	C₂³	1	12	yes	complemented
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	complemented
263	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
264	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
265	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
266	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
269	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
270	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
271	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
277	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
278	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
279	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
280	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
281	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
282	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
283	#62903	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂⁴×C₁₃	—	2	4	no	—
285	C₂⁴×C₁₃	—	4	2	no	—
286	C₂⁴×C₁₃	—	8	1	no	—
287	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
288	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
289	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
290	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×#41	—	4	12	no	—
292	C₁₃×#41	—	8	6	no	—
293	C₁₃×#41	—	8	2	no	—
294	C₂×Q₈×C₁₃	—	4	4	no	—
295	C₂×Q₈×C₁₃	—	8	2	no	—
296	C₂×Q₈×C₁₃	—	8	3	no	—
297	C₂×Q₈×C₁₃	—	8	6	no	—
298	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
301	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
302	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
304	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
305	C₂×D₄×C₁₃	—	2	12	no	—
306	C₂×D₄×C₁₃	—	4	6	no	—
307	C₂×D₄×C₁₃	—	8	3	no	—
308	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
309	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
310	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
311	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
312	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
314	C₂²×C₄×C₁₃	—	2	4	no	—
315	C₂²×C₄×C₁₃	—	4	6	no	—
316	C₂²×C₄×C₁₃	—	8	1	no	—
317	C₂²×C₄×C₁₃	—	8	3	no	—
318	C₂²×C₄×C₁₃	—	8	3	no	—
319	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
322	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
323	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
324	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
326	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
328	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
329	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
330	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
331	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
332	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
333	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
334	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
335	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
336	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
341	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
342	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
343	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
344	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
349	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
350	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
351	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
352	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
353	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
354	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
355	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
356	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
363	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
364	C₁₃×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
365	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
366	C₁₃×C₂²⋊C₄	C₂⁴	1	3	yes	—
367	C₁₃×C₂²⋊C₄	C₂⁴	1	3	yes	—
368	C₁₃×C₂²⋊C₄	C₂⁴	1	3	yes	—
369	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
370	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
371	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
372	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
373	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
374	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
375	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
376	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
377	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
378	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
384	C₄²×C₁₃	C₂⁴	1	6	yes	—
385	C₄²×C₁₃	C₂⁴	1	6	yes	—
386	C₄²×C₁₃	C₂⁴	1	6	yes	—
387	C₄²×C₁₃	C₂⁴	1	6	yes	—
388	C₄²×C₁₃	C₂⁴	1	6	yes	—
389	C₄²×C₁₃	C₂⁴	1	6	yes	—
390	C₄²×C₁₃	C₂⁴	1	12	yes	—
391	C₄²×C₁₃	C₂⁴	1	12	yes	—
392	#3564	C₂×C₁₃	1	6	yes	complemented
393	#3564	C₂×C₁₃	1	6	yes	complemented
394	#3561	C₂×C₁₃	1	6	yes	complemented
395	#3538	C₂×C₁₃	1	6	yes	complemented
396	#3535	C₂×C₁₃	1	6	yes	complemented
397	#3535	C₂×C₁₃	1	6	yes	complemented
398	#3520	C₂×C₁₃	1	6	yes	complemented
399	#3501	C₂×C₁₃	1	3	yes	complemented
400	#3495	C₂×C₁₃	1	6	yes	complemented
401	#3491	C₂×C₁₃	1	3	yes	complemented
402	#3490	C₂×C₁₃	1	3	yes	complemented
403	C₂×#551	C₂×C₁₃	1	3	yes	complemented
404	#3459	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
406	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
407	C₂³×C₁₃	—	2	6	no	—
408	C₂³×C₁₃	—	2	6	no	—
409	C₂³×C₁₃	—	2	6	no	—
410	C₂³×C₁₃	—	2	6	no	—
411	C₂³×C₁₃	—	4	3	no	—
412	C₂³×C₁₃	—	4	1	no	—
413	C₂³×C₁₃	—	4	1	no	—
414	C₂³×C₁₃	—	4	3	no	—
415	C₂³×C₁₃	—	4	3	no	—
416	C₂³×C₁₃	—	4	3	no	—
417	C₂³×C₁₃	—	4	3	no	—
418	C₂³×C₁₃	—	8	8	no	—
419	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
420	C₂³×C₁₃	C₂⁵	1	3	yes	—
421	C₂³×C₁₃	C₂⁵	1	6	yes	—
422	C₂³×C₁₃	C₂⁵	1	3	yes	—
423	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
424	Q₈×C₁₃	—	4	6	no	—
425	Q₈×C₁₃	—	4	2	no	—
426	Q₈×C₁₃	—	4	6	no	—
427	Q₈×C₁₃	—	4	12	no	—
428	Q₈×C₁₃	—	4	2	no	—
429	Q₈×C₁₃	—	4	6	no	—
430	Q₈×C₁₃	—	4	6	no	—
431	D₄×C₁₃	—	2	24	no	—
432	D₄×C₁₃	—	2	12	no	—
433	D₄×C₁₃	—	4	6	no	—
434	D₄×C₁₃	—	4	12	no	—
435	D₄×C₁₃	—	4	6	no	—
436	D₄×C₁₃	—	4	6	no	—
437	C₂×C₄×C₁₃	—	2	6	no	—
438	C₂×C₄×C₁₃	—	2	6	no	—
439	C₂×C₄×C₁₃	—	2	6	no	—
440	C₂×C₄×C₁₃	—	2	12	no	—
441	C₂×C₄×C₁₃	—	4	3	no	—
442	C₂×C₄×C₁₃	—	4	6	no	—
443	C₂×C₄×C₁₃	—	4	3	no	—
444	C₂×C₄×C₁₃	—	4	3	no	—
445	C₂×C₄×C₁₃	—	4	3	no	—
446	C₂×C₄×C₁₃	—	4	6	no	—
447	C₂×C₄×C₁₃	—	4	6	no	—
448	C₂×C₄×C₁₃	—	4	3	no	—
449	C₂×C₄×C₁₃	—	4	3	no	—
450	C₂×C₄×C₁₃	—	4	6	no	—
451	C₂×C₄×C₁₃	—	4	6	no	—
452	C₂×C₄×C₁₃	—	4	3	no	—
453	C₂×C₄×C₁₃	—	4	3	no	—
454	C₂×C₄×C₁₃	—	4	12	no	—
455	C₂×C₄×C₁₃	—	4	12	no	—
456	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
458	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
460	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
461	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
462	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
463	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
464	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
465	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
466	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
467	#563	C₂²×C₁₃	1	12	yes	complemented
468	#563	C₂²×C₁₃	1	12	yes	complemented
469	#563	C₂²×C₁₃	1	12	yes	complemented
470	#562	C₂²×C₁₃	1	12	yes	complemented
471	#556	C₂²×C₁₃	1	12	yes	complemented
472	#556	C₂²×C₁₃	1	6	yes	complemented
473	#554	C₂²×C₁₃	1	12	yes	complemented
474	#554	C₂²×C₁₃	1	12	yes	complemented
475	#554	C₂²×C₁₃	1	12	yes	complemented
476	#552	C₂²×C₁₃	1	12	yes	complemented
477	#552	C₂²×C₁₃	1	12	yes	complemented
478	#552	C₂²×C₁₃	1	6	yes	complemented
479	#552	C₂²×C₁₃	1	12	yes	complemented
480	#552	C₂²×C₁₃	1	12	yes	complemented
481	#552	C₂²×C₁₃	1	6	yes	complemented
482	#551	C₂²×C₁₃	1	12	yes	complemented
483	#551	C₂²×C₁₃	1	12	yes	complemented
484	#551	C₂²×C₁₃	1	12	yes	complemented
485	#551	C₂²×C₁₃	1	12	yes	complemented
486	#551	C₂²×C₁₃	1	12	yes	complemented
487	#551	C₂²×C₁₃	1	12	yes	complemented
488	#551	C₂²×C₁₃	1	12	yes	complemented
489	#551	C₂²×C₁₃	1	12	yes	complemented
490	D₄×Q₈	C₂²×C₁₃	1	12	yes	complemented
491	D₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
492	#548	C₂²×C₁₃	1	2	yes	complemented
493	#548	C₂²×C₁₃	1	6	yes	complemented
494	#547	C₂²×C₁₃	1	6	yes	complemented
495	#547	C₂²×C₁₃	1	6	yes	complemented
496	#546	C₂²×C₁₃	1	12	yes	complemented
497	#546	C₂²×C₁₃	1	12	yes	complemented
498	#544	C₂²×C₁₃	1	6	yes	complemented
499	#544	C₂²×C₁₃	1	6	yes	complemented
500	#544	C₂²×C₁₃	1	6	yes	complemented
501	#544	C₂²×C₁₃	1	6	yes	complemented
502	#543	C₂²×C₁₃	1	1	yes	characteristic
503	#543	C₂²×C₁₃	1	3	yes	—
504	#543	C₂²×C₁₃	1	3	yes	—
505	#543	C₂²×C₁₃	1	6	yes	complemented
506	#543	C₂²×C₁₃	1	6	yes	complemented
507	#543	C₂²×C₁₃	1	6	yes	complemented
508	#542	C₂²×C₁₃	1	6	yes	complemented
509	#542	C₂²×C₁₃	1	6	yes	complemented
510	#542	C₂²×C₁₃	1	12	yes	complemented
511	#542	C₂²×C₁₃	1	12	yes	complemented
512	#541	C₂²×C₁₃	1	6	yes	complemented
513	#541	C₂²×C₁₃	1	6	yes	complemented
514	#541	C₂²×C₁₃	1	12	yes	complemented
515	#539	C₂²×C₁₃	1	6	yes	complemented
516	#539	C₂²×C₁₃	1	6	yes	complemented
517	#539	C₂²×C₁₃	1	6	yes	complemented
518	#539	C₂²×C₁₃	1	12	yes	complemented
519	#539	C₂²×C₁₃	1	12	yes	complemented
520	#539	C₂²×C₁₃	1	12	yes	complemented
521	#538	C₂²×C₁₃	1	6	yes	—
522	#538	C₂²×C₁₃	1	6	yes	—
523	#538	C₂²×C₁₃	1	6	yes	complemented
524	#536	C₂²×C₁₃	1	6	yes	complemented
525	#536	C₂²×C₁₃	1	12	yes	complemented
526	#534	C₂²×C₁₃	1	3	yes	—
527	#533	C₂²×C₁₃	1	6	yes	complemented
528	#533	C₂²×C₁₃	1	6	yes	complemented
529	#533	C₂²×C₁₃	1	6	yes	complemented
530	#529	C₂²×C₁₃	1	6	yes	complemented
531	#529	C₂²×C₁₃	1	6	yes	complemented
532	#529	C₂²×C₁₃	1	6	yes	complemented
533	C₂×#126	C₂²×C₁₃	1	3	yes	complemented
534	C₂×#126	C₂²×C₁₃	1	3	yes	complemented
535	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
536	#525	C₂²×C₁₃	1	6	yes	—
537	#525	C₂²×C₁₃	1	6	yes	—
538	#525	C₂²×C₁₃	1	6	yes	complemented
539	C₂×#123	C₂²×C₁₃	1	3	yes	—
540	C₂×#123	C₂²×C₁₃	1	3	yes	complemented
541	C₂×#123	C₂²×C₁₃	1	3	yes	complemented
542	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
543	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
544	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
545	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
546	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
547	C₂×#120	C₂²×C₁₃	1	3	yes	—
548	#520	C₂²×C₁₃	1	6	yes	complemented
549	#519	C₂²×C₁₃	1	2	yes	complemented
550	#518	C₂²×C₁₃	1	6	yes	—
551	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
552	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
553	C₂×#117	C₂²×C₁₃	1	3	yes	—
554	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
555	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	—
556	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
557	C₂²×C₁₃	—	2	1	no	—
558	C₂²×C₁₃	—	2	3	no	—
559	C₂²×C₁₃	—	2	1	no	—
560	C₂²×C₁₃	—	2	3	no	—
561	C₂²×C₁₃	—	2	6	no	—
562	C₂²×C₁₃	—	2	3	no	—
563	C₂²×C₁₃	—	2	6	no	—
564	C₂²×C₁₃	—	2	3	no	—
565	C₂²×C₁₃	—	2	6	no	—
566	C₂²×C₁₃	—	2	3	no	—
567	C₂²×C₁₃	—	4	4	no	—
568	C₂²×C₁₃	—	4	12	no	—
569	C₂²×C₁₃	—	8	6	no	—
570	C₂²×C₁₃	—	8	6	no	—
571	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
572	C₂²×C₁₃	#585	1	2	yes	—
573	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
574	C₄×C₁₃	—	2	1	no	—
575	C₄×C₁₃	—	2	3	no	—
576	C₄×C₁₃	—	2	6	no	—
577	C₄×C₁₃	—	2	6	no	—
578	C₄×C₁₃	—	2	6	no	—
579	C₄×C₁₃	—	2	6	no	—
580	C₄×C₁₃	—	2	1	no	—
581	C₄×C₁₃	—	2	6	no	—
582	C₄×C₁₃	—	2	3	no	—
583	C₄×C₁₃	—	2	6	no	—
584	C₄×C₁₃	—	2	6	no	—
585	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×#41	C₂³×C₁₃	1	6	yes	—
587	C₂×#41	C₂³×C₁₃	1	6	yes	—
588	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
589	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
591	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₂²×Q₈	C₂³×C₁₃	1	6	yes	complemented
593	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
594	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
595	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
596	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
598	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
600	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
601	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
602	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
603	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
604	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
605	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
606	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
607	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
608	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
609	#126	C₂³×C₁₃	1	12	yes	—
610	#126	C₂³×C₁₃	1	12	yes	—
611	#126	C₂³×C₁₃	1	12	yes	—
612	#126	C₂³×C₁₃	1	12	yes	—
613	#126	C₂³×C₁₃	1	12	yes	—
614	#126	C₂³×C₁₃	1	12	yes	—
615	#126	C₂³×C₁₃	1	12	yes	complemented
616	#126	C₂³×C₁₃	1	12	yes	complemented
617	#126	C₂³×C₁₃	1	12	yes	complemented
618	#126	C₂³×C₁₃	1	12	yes	complemented
619	#126	C₂³×C₁₃	1	12	yes	complemented
620	#125	C₂³×C₁₃	1	6	yes	complemented
621	#125	C₂³×C₁₃	1	6	yes	complemented
622	#125	C₂³×C₁₃	1	6	yes	complemented
623	#125	C₂³×C₁₃	1	12	yes	complemented
624	#125	C₂³×C₁₃	1	12	yes	complemented
625	#125	C₂³×C₁₃	1	12	yes	complemented
626	#125	C₂³×C₁₃	1	12	yes	complemented
627	#125	C₂³×C₁₃	1	12	yes	complemented
628	#125	C₂³×C₁₃	1	12	yes	complemented
629	#125	C₂³×C₁₃	1	12	yes	complemented
630	#124	C₂³×C₁₃	1	12	yes	—
631	#124	C₂³×C₁₃	1	12	yes	—
632	#124	C₂³×C₁₃	1	12	yes	—
633	#124	C₂³×C₁₃	1	12	yes	—
634	#124	C₂³×C₁₃	1	6	yes	complemented
635	#124	C₂³×C₁₃	1	6	yes	complemented
636	#124	C₂³×C₁₃	1	6	yes	complemented
637	#123	C₂³×C₁₃	1	12	yes	—
638	#123	C₂³×C₁₃	1	12	yes	—
639	#123	C₂³×C₁₃	1	12	yes	—
640	#123	C₂³×C₁₃	1	12	yes	—
641	#123	C₂³×C₁₃	1	12	yes	—
642	#123	C₂³×C₁₃	1	12	yes	—
643	#123	C₂³×C₁₃	1	12	yes	—
644	#123	C₂³×C₁₃	1	12	yes	—
645	#123	C₂³×C₁₃	1	12	yes	—
646	#123	C₂³×C₁₃	1	12	yes	—
647	#123	C₂³×C₁₃	1	12	yes	—
648	#123	C₂³×C₁₃	1	12	yes	complemented
649	#123	C₂³×C₁₃	1	12	yes	complemented
650	#123	C₂³×C₁₃	1	12	yes	complemented
651	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
652	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
653	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
654	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
655	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
656	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
657	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
658	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
659	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
660	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
661	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
662	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
663	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
664	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
665	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
666	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
667	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
668	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
669	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
670	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
671	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
672	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
673	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
674	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
675	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
676	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	complemented
677	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
678	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
679	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
680	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
681	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
682	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	complemented
683	#121	C₂³×C₁₃	1	6	yes	—
684	#121	C₂³×C₁₃	1	6	yes	—
685	#121	C₂³×C₁₃	1	6	yes	—
686	#121	C₂³×C₁₃	1	6	yes	—
687	#121	C₂³×C₁₃	1	12	yes	—
688	#121	C₂³×C₁₃	1	12	yes	—
689	#121	C₂³×C₁₃	1	6	yes	complemented
690	#120	C₂³×C₁₃	1	12	yes	—
691	#120	C₂³×C₁₃	1	12	yes	—
692	#120	C₂³×C₁₃	1	12	yes	—
693	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
694	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
695	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
696	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
697	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
698	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
699	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
700	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
701	C₄×Q₈	C₂³×C₁₃	1	6	yes	complemented
702	C₄×Q₈	C₂³×C₁₃	1	12	yes	complemented
703	C₄×D₄	C₂³×C₁₃	1	12	yes	—
704	C₄×D₄	C₂³×C₁₃	1	12	yes	—
705	C₄×D₄	C₂³×C₁₃	1	6	yes	—
706	C₄×D₄	C₂³×C₁₃	1	6	yes	—
707	C₄×D₄	C₂³×C₁₃	1	6	yes	—
708	C₄×D₄	C₂³×C₁₃	1	6	yes	—
709	C₄×D₄	C₂³×C₁₃	1	12	yes	—
710	C₄×D₄	C₂³×C₁₃	1	12	yes	—
711	C₄×D₄	C₂³×C₁₃	1	12	yes	—
712	C₄×D₄	C₂³×C₁₃	1	12	yes	—
713	C₄×D₄	C₂³×C₁₃	1	12	yes	—
714	C₄×D₄	C₂³×C₁₃	1	12	yes	—
715	C₄×D₄	C₂³×C₁₃	1	6	yes	complemented
716	C₄×D₄	C₂³×C₁₃	1	6	yes	complemented
717	C₄×D₄	C₂³×C₁₃	1	6	yes	complemented
718	#117	C₂³×C₁₃	1	12	yes	—
719	#117	C₂³×C₁₃	1	12	yes	—
720	#117	C₂³×C₁₃	1	6	yes	—
721	#117	C₂³×C₁₃	1	6	yes	—
722	#117	C₂³×C₁₃	1	6	yes	—
723	#117	C₂³×C₁₃	1	6	yes	—
724	#117	C₂³×C₁₃	1	12	yes	—
725	#117	C₂³×C₁₃	1	6	yes	—
726	#117	C₂³×C₁₃	1	6	yes	—
727	#117	C₂³×C₁₃	1	12	yes	complemented
728	#117	C₂³×C₁₃	1	6	yes	complemented
729	#117	C₂³×C₁₃	1	12	yes	complemented
730	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
731	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
732	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
733	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
734	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
735	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
736	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
737	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
738	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
739	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
740	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
741	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	complemented
742	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
759	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
760	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
761	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
762	C₂×C₁₃	—	2	2	no	—
763	C₂×C₁₃	—	2	6	no	—
764	C₂×C₁₃	—	4	3	no	—
765	C₂×C₁₃	—	4	6	no	—
766	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
767	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
768	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
769	C₂⁴	—	2	4	no	—
770	C₂⁴	—	4	2	no	—
771	C₂⁴	—	8	1	no	—
772	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
773	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
774	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
775	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
776	#41	—	4	12	no	—
777	#41	—	8	6	no	—
778	#41	—	8	2	no	—
779	C₂×Q₈	—	4	4	no	—
780	C₂×Q₈	—	8	2	no	—
781	C₂×Q₈	—	8	3	no	—
782	C₂×Q₈	—	8	6	no	—
783	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
784	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
785	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
786	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
787	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
788	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
789	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
790	C₂×D₄	—	2	12	no	—
791	C₂×D₄	—	4	6	no	—
792	C₂×D₄	—	8	3	no	—
793	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
794	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
795	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
796	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
797	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
798	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
799	C₂²×C₄	—	2	4	no	—
800	C₂²×C₄	—	4	6	no	—
801	C₂²×C₄	—	8	1	no	—
802	C₂²×C₄	—	8	3	no	—
803	C₂²×C₄	—	8	3	no	—
804	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
805	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
806	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
807	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
808	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
809	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
810	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
811	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
812	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
813	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
814	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
815	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
816	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
817	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
818	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
819	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
820	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
821	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
822	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
823	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
824	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
825	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
826	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
827	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
828	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
829	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
830	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
831	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
832	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
833	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
834	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
835	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
836	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
837	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
838	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
839	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
840	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
841	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
842	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
843	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
844	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
845	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
846	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
847	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
848	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
849	C₂²⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
850	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
851	C₂²⋊C₄	C₂⁴×C₁₃	1	3	yes	—
852	C₂²⋊C₄	C₂⁴×C₁₃	1	3	yes	—
853	C₂²⋊C₄	C₂⁴×C₁₃	1	3	yes	—
854	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
855	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
856	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
857	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
858	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
859	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
860	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
861	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
862	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
863	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
864	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
865	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
866	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
867	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
868	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
869	C₄²	C₂⁴×C₁₃	1	6	yes	—
870	C₄²	C₂⁴×C₁₃	1	6	yes	—
871	C₄²	C₂⁴×C₁₃	1	6	yes	—
872	C₄²	C₂⁴×C₁₃	1	6	yes	—
873	C₄²	C₂⁴×C₁₃	1	6	yes	—
874	C₄²	C₂⁴×C₁₃	1	6	yes	—
875	C₄²	C₂⁴×C₁₃	1	12	yes	—
876	C₄²	C₂⁴×C₁₃	1	12	yes	—
877	C₁₃	#62903	1	1	yes	characteristic, direct product factor, Sylow
878	C₂³	—	2	6	no	—
879	C₂³	—	2	6	no	—
880	C₂³	—	2	6	no	—
881	C₂³	—	2	6	no	—
882	C₂³	—	4	3	no	—
883	C₂³	—	4	1	no	—
884	C₂³	—	4	1	no	—
885	C₂³	—	4	3	no	—
886	C₂³	—	4	3	no	—
887	C₂³	—	4	3	no	—
888	C₂³	—	4	3	no	—
889	C₂³	—	8	8	no	—
890	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
891	C₂³	C₂⁵×C₁₃	1	3	yes	—
892	C₂³	C₂⁵×C₁₃	1	6	yes	—
893	C₂³	C₂⁵×C₁₃	1	3	yes	—
894	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
895	Q₈	—	4	6	no	—
896	Q₈	—	4	2	no	—
897	Q₈	—	4	6	no	—
898	Q₈	—	4	12	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	6	no	—
901	Q₈	—	4	6	no	—
902	D₄	—	2	24	no	—
903	D₄	—	2	12	no	—
904	D₄	—	4	6	no	—
905	D₄	—	4	12	no	—
906	D₄	—	4	6	no	—
907	D₄	—	4	6	no	—
908	C₂×C₄	—	2	6	no	—
909	C₂×C₄	—	2	6	no	—
910	C₂×C₄	—	2	6	no	—
911	C₂×C₄	—	2	12	no	—
912	C₂×C₄	—	4	3	no	—
913	C₂×C₄	—	4	6	no	—
914	C₂×C₄	—	4	3	no	—
915	C₂×C₄	—	4	3	no	—
916	C₂×C₄	—	4	3	no	—
917	C₂×C₄	—	4	6	no	—
918	C₂×C₄	—	4	6	no	—
919	C₂×C₄	—	4	3	no	—
920	C₂×C₄	—	4	3	no	—
921	C₂×C₄	—	4	6	no	—
922	C₂×C₄	—	4	6	no	—
923	C₂×C₄	—	4	3	no	—
924	C₂×C₄	—	4	3	no	—
925	C₂×C₄	—	4	12	no	—
926	C₂×C₄	—	4	12	no	—
927	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
929	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
931	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
932	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
933	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
934	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
935	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
936	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
937	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	3	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	3	no	—
942	C₂²	—	2	6	no	—
943	C₂²	—	2	3	no	—
944	C₂²	—	2	6	no	—
945	C₂²	—	2	3	no	—
946	C₂²	—	2	6	no	—
947	C₂²	—	2	3	no	—
948	C₂²	—	4	4	no	—
949	C₂²	—	4	12	no	—
950	C₂²	—	8	6	no	—
951	C₂²	—	8	6	no	—
952	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
953	C₂²	C₁₃×#585	1	2	yes	—
954	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
955	C₄	—	2	1	no	—
956	C₄	—	2	3	no	—
957	C₄	—	2	6	no	—
958	C₄	—	2	6	no	—
959	C₄	—	2	6	no	—
960	C₄	—	2	6	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	6	no	—
963	C₄	—	2	3	no	—
964	C₄	—	2	6	no	—
965	C₄	—	2	6	no	—
966	C₂	—	2	2	no	—
967	C₂	—	2	6	no	—
968	C₂	—	4	3	no	—
969	C₂	—	4	6	no	—
970	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
971	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
972	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic

	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×#3564	C₂	semidirect
2. C₁₃×#3564	C₂	semidirect
3. C₁₃×#3561	C₂	semidirect
4. C₁₃×#3538	C₂	semidirect
5. C₁₃×#3535	C₂	semidirect
6. C₁₃×#3535	C₂	semidirect
7. C₁₃×#3520	C₂	semidirect
8. C₁₃×#3501	C₂	semidirect
9. C₁₃×#3495	C₂	semidirect
10. C₁₃×#3491	C₂	semidirect
11. C₁₃×#3490	C₂	semidirect
12. C₂×C₁₃×#551	C₂	semidirect
13. C₁₃×#3459	C₂	semidirect
14. C₁₃×#3458	C₂	semidirect
15. C₂×C₁₃×#543	C₂	semidirect
16. C₁₃×#563	C₂²	semidirect
17. C₁₃×#563	C₂²	semidirect
18. C₁₃×#563	C₂²	semidirect
19. C₁₃×#562	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
23. C₁₃×#554	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
30. C₁₃×#552	C₂²	semidirect
31. C₁₃×#551	C₂²	semidirect
32. C₁₃×#551	C₂²	semidirect
33. C₁₃×#551	C₂²	semidirect
34. C₁₃×#551	C₂²	semidirect
35. C₁₃×#551	C₂²	semidirect
36. C₁₃×#551	C₂²	semidirect
37. C₁₃×#551	C₂²	semidirect
38. C₁₃×#551	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
40. D₄×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#548	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#544	C₂²	semidirect
48. C₁₃×#544	C₂²	semidirect
49. C₁₃×#544	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
54. C₁₃×#543	C₂²	semidirect
55. C₁₃×#543	C₂²	semidirect
56. C₁₃×#543	C₂²	semidirect
57. C₁₃×#542	C₂²	semidirect
58. C₁₃×#542	C₂²	semidirect
59. C₁₃×#542	C₂²	semidirect
60. C₁₃×#542	C₂²	semidirect
61. C₁₃×#541	C₂²	semidirect
62. C₁₃×#541	C₂²	semidirect
63. C₁₃×#541	C₂²	semidirect
64. C₁₃×#539	C₂²	semidirect
65. C₁₃×#539	C₂²	semidirect
66. C₁₃×#539	C₂²	semidirect
67. C₁₃×#539	C₂²	semidirect
68. C₁₃×#539	C₂²	semidirect
69. C₁₃×#539	C₂²	semidirect
72. C₁₃×#538	C₂²	semidirect
73. C₁₃×#536	C₂²	semidirect
74. C₁₃×#536	C₂²	semidirect
76. C₁₃×#533	C₂²	semidirect
77. C₁₃×#533	C₂²	semidirect
78. C₁₃×#533	C₂²	semidirect
79. C₁₃×#529	C₂²	semidirect
80. C₁₃×#529	C₂²	semidirect
81. C₁₃×#529	C₂²	semidirect
82. C₂×C₁₃×#126	C₂²	semidirect
83. C₂×C₁₃×#126	C₂²	semidirect
84. C₂×C₁₃×#124	C₂²	semidirect
87. C₁₃×#525	C₂²	semidirect
89. C₂×C₁₃×#123	C₂²	semidirect
90. C₂×C₁₃×#123	C₂²	semidirect
92. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
97. C₁₃×#520	C₂²	semidirect
98. C₁₃×#519	C₂²	semidirect
101. C₂×C₄×D₄×C₁₃	C₂²	semidirect
103. C₂×C₁₃×#117	C₂²	semidirect
109. C₂×C₁₃×#41	C₂³	semidirect
113. C₂²×Q₈×C₁₃	C₂³	semidirect
122. C₁₃×C₄⋊Q₈	C₂³	semidirect
123. C₁₃×C₄⋊Q₈	C₂³	semidirect
124. C₁₃×C₄⋊Q₈	C₂³	semidirect
125. C₁₃×C₄⋊Q₈	C₂³	semidirect
126. C₁₃×C₄⋊Q₈	C₂³	semidirect
127. C₁₃×C₄⋊Q₈	C₂³	semidirect
128. C₁₃×C₄⋊Q₈	C₂³	semidirect
129. C₁₃×C₄⋊Q₈	C₂³	semidirect
136. C₁₃×#126	C₂³	semidirect
137. C₁₃×#126	C₂³	semidirect
138. C₁₃×#126	C₂³	semidirect
139. C₁₃×#126	C₂³	semidirect
140. C₁₃×#126	C₂³	semidirect
141. C₁₃×#125	C₂³	semidirect
142. C₁₃×#125	C₂³	semidirect
143. C₁₃×#125	C₂³	semidirect
144. C₁₃×#125	C₂³	semidirect
145. C₁₃×#125	C₂³	semidirect
146. C₁₃×#125	C₂³	semidirect
147. C₁₃×#125	C₂³	semidirect
148. C₁₃×#125	C₂³	semidirect
149. C₁₃×#125	C₂³	semidirect
150. C₁₃×#125	C₂³	semidirect
155. C₁₃×#124	C₂³	semidirect
156. C₁₃×#124	C₂³	semidirect
157. C₁₃×#124	C₂³	semidirect
169. C₁₃×#123	C₂³	semidirect
170. C₁₃×#123	C₂³	semidirect
171. C₁₃×#123	C₂³	semidirect
194. C₁₃×C₂²⋊Q₈	C₂³	semidirect
195. C₁₃×C₂²⋊Q₈	C₂³	semidirect
196. C₁₃×C₂²⋊Q₈	C₂³	semidirect
197. C₁₃×C₂²⋊Q₈	C₂³	semidirect
198. C₁₃×C₂²⋊Q₈	C₂³	semidirect
199. C₁₃×C₂²⋊Q₈	C₂³	semidirect
200. C₁₃×C₂²⋊Q₈	C₂³	semidirect
201. C₁₃×C₂²⋊Q₈	C₂³	semidirect
202. C₁₃×C₂²⋊Q₈	C₂³	semidirect
203. C₁₃×C₂²⋊Q₈	C₂³	semidirect
210. C₁₃×#121	C₂³	semidirect
214. C₄×Q₈×C₁₃	C₂³	semidirect
215. C₄×Q₈×C₁₃	C₂³	semidirect
216. C₄×Q₈×C₁₃	C₂³	semidirect
217. C₄×Q₈×C₁₃	C₂³	semidirect
218. C₄×Q₈×C₁₃	C₂³	semidirect
219. C₄×Q₈×C₁₃	C₂³	semidirect
220. C₄×Q₈×C₁₃	C₂³	semidirect
221. C₄×Q₈×C₁₃	C₂³	semidirect
222. C₄×Q₈×C₁₃	C₂³	semidirect
223. C₄×Q₈×C₁₃	C₂³	semidirect
236. C₄×D₄×C₁₃	C₂³	semidirect
237. C₄×D₄×C₁₃	C₂³	semidirect
238. C₄×D₄×C₁₃	C₂³	semidirect
248. C₁₃×#117	C₂³	semidirect
249. C₁₃×#117	C₂³	semidirect
250. C₁₃×#117	C₂³	semidirect
261. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
262. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
283. #62903	C₁₃	direct (N × H)
392. #3564	C₂×C₁₃	semidirect
393. #3564	C₂×C₁₃	semidirect
394. #3561	C₂×C₁₃	semidirect
395. #3538	C₂×C₁₃	semidirect
396. #3535	C₂×C₁₃	semidirect
397. #3535	C₂×C₁₃	semidirect
398. #3520	C₂×C₁₃	semidirect
399. #3501	C₂×C₁₃	semidirect
400. #3495	C₂×C₁₃	semidirect
401. #3491	C₂×C₁₃	semidirect
402. #3490	C₂×C₁₃	semidirect
403. C₂×#551	C₂×C₁₃	semidirect
404. #3459	C₂×C₁₃	semidirect
405. #3458	C₂×C₁₃	semidirect
406. C₂×#543	C₂×C₁₃	semidirect
467. #563	C₂²×C₁₃	semidirect
468. #563	C₂²×C₁₃	semidirect
469. #563	C₂²×C₁₃	semidirect
470. #562	C₂²×C₁₃	semidirect
471. #556	C₂²×C₁₃	semidirect
472. #556	C₂²×C₁₃	semidirect
473. #554	C₂²×C₁₃	semidirect
474. #554	C₂²×C₁₃	semidirect
475. #554	C₂²×C₁₃	semidirect
476. #552	C₂²×C₁₃	semidirect
477. #552	C₂²×C₁₃	semidirect
478. #552	C₂²×C₁₃	semidirect
479. #552	C₂²×C₁₃	semidirect
480. #552	C₂²×C₁₃	semidirect
481. #552	C₂²×C₁₃	semidirect
482. #551	C₂²×C₁₃	semidirect
483. #551	C₂²×C₁₃	semidirect
484. #551	C₂²×C₁₃	semidirect
485. #551	C₂²×C₁₃	semidirect
486. #551	C₂²×C₁₃	semidirect
487. #551	C₂²×C₁₃	semidirect
488. #551	C₂²×C₁₃	semidirect
489. #551	C₂²×C₁₃	semidirect
490. D₄×Q₈	C₂²×C₁₃	semidirect
491. D₄×Q₈	C₂²×C₁₃	semidirect
492. #548	C₂²×C₁₃	semidirect
493. #548	C₂²×C₁₃	semidirect
494. #547	C₂²×C₁₃	semidirect
495. #547	C₂²×C₁₃	semidirect
496. #546	C₂²×C₁₃	semidirect
497. #546	C₂²×C₁₃	semidirect
498. #544	C₂²×C₁₃	semidirect
499. #544	C₂²×C₁₃	semidirect
500. #544	C₂²×C₁₃	semidirect
501. #544	C₂²×C₁₃	semidirect
505. #543	C₂²×C₁₃	semidirect
506. #543	C₂²×C₁₃	semidirect
507. #543	C₂²×C₁₃	semidirect
508. #542	C₂²×C₁₃	semidirect
509. #542	C₂²×C₁₃	semidirect
510. #542	C₂²×C₁₃	semidirect
511. #542	C₂²×C₁₃	semidirect
512. #541	C₂²×C₁₃	semidirect
513. #541	C₂²×C₁₃	semidirect
514. #541	C₂²×C₁₃	semidirect
515. #539	C₂²×C₁₃	semidirect
516. #539	C₂²×C₁₃	semidirect
517. #539	C₂²×C₁₃	semidirect
518. #539	C₂²×C₁₃	semidirect
519. #539	C₂²×C₁₃	semidirect
520. #539	C₂²×C₁₃	semidirect
523. #538	C₂²×C₁₃	semidirect
524. #536	C₂²×C₁₃	semidirect
525. #536	C₂²×C₁₃	semidirect
527. #533	C₂²×C₁₃	semidirect
528. #533	C₂²×C₁₃	semidirect
529. #533	C₂²×C₁₃	semidirect
530. #529	C₂²×C₁₃	semidirect
531. #529	C₂²×C₁₃	semidirect
532. #529	C₂²×C₁₃	semidirect
533. C₂×#126	C₂²×C₁₃	semidirect
534. C₂×#126	C₂²×C₁₃	semidirect
535. C₂×#124	C₂²×C₁₃	semidirect
538. #525	C₂²×C₁₃	semidirect
540. C₂×#123	C₂²×C₁₃	semidirect
541. C₂×#123	C₂²×C₁₃	semidirect
543. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
544. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
545. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
546. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
548. #520	C₂²×C₁₃	semidirect
549. #519	C₂²×C₁₃	semidirect
552. C₂×C₄×D₄	C₂²×C₁₃	semidirect
554. C₂×#117	C₂²×C₁₃	semidirect
588. C₂×#41	C₂³×C₁₃	semidirect
592. C₂²×Q₈	C₂³×C₁₃	semidirect
601. C₄⋊Q₈	C₂³×C₁₃	semidirect
602. C₄⋊Q₈	C₂³×C₁₃	semidirect
603. C₄⋊Q₈	C₂³×C₁₃	semidirect
604. C₄⋊Q₈	C₂³×C₁₃	semidirect
605. C₄⋊Q₈	C₂³×C₁₃	semidirect
606. C₄⋊Q₈	C₂³×C₁₃	semidirect
607. C₄⋊Q₈	C₂³×C₁₃	semidirect
608. C₄⋊Q₈	C₂³×C₁₃	semidirect
615. #126	C₂³×C₁₃	semidirect
616. #126	C₂³×C₁₃	semidirect
617. #126	C₂³×C₁₃	semidirect
618. #126	C₂³×C₁₃	semidirect
619. #126	C₂³×C₁₃	semidirect
620. #125	C₂³×C₁₃	semidirect
621. #125	C₂³×C₁₃	semidirect
622. #125	C₂³×C₁₃	semidirect
623. #125	C₂³×C₁₃	semidirect
624. #125	C₂³×C₁₃	semidirect
625. #125	C₂³×C₁₃	semidirect
626. #125	C₂³×C₁₃	semidirect
627. #125	C₂³×C₁₃	semidirect
628. #125	C₂³×C₁₃	semidirect
629. #125	C₂³×C₁₃	semidirect
634. #124	C₂³×C₁₃	semidirect
635. #124	C₂³×C₁₃	semidirect
636. #124	C₂³×C₁₃	semidirect
648. #123	C₂³×C₁₃	semidirect
649. #123	C₂³×C₁₃	semidirect
650. #123	C₂³×C₁₃	semidirect
673. C₂²⋊Q₈	C₂³×C₁₃	semidirect
674. C₂²⋊Q₈	C₂³×C₁₃	semidirect
675. C₂²⋊Q₈	C₂³×C₁₃	semidirect
676. C₂²⋊Q₈	C₂³×C₁₃	semidirect
677. C₂²⋊Q₈	C₂³×C₁₃	semidirect
678. C₂²⋊Q₈	C₂³×C₁₃	semidirect
679. C₂²⋊Q₈	C₂³×C₁₃	semidirect
680. C₂²⋊Q₈	C₂³×C₁₃	semidirect
681. C₂²⋊Q₈	C₂³×C₁₃	semidirect
682. C₂²⋊Q₈	C₂³×C₁₃	semidirect
689. #121	C₂³×C₁₃	semidirect
693. C₄×Q₈	C₂³×C₁₃	semidirect
694. C₄×Q₈	C₂³×C₁₃	semidirect
695. C₄×Q₈	C₂³×C₁₃	semidirect
696. C₄×Q₈	C₂³×C₁₃	semidirect
697. C₄×Q₈	C₂³×C₁₃	semidirect
698. C₄×Q₈	C₂³×C₁₃	semidirect
699. C₄×Q₈	C₂³×C₁₃	semidirect
700. C₄×Q₈	C₂³×C₁₃	semidirect
701. C₄×Q₈	C₂³×C₁₃	semidirect
702. C₄×Q₈	C₂³×C₁₃	semidirect
715. C₄×D₄	C₂³×C₁₃	semidirect
716. C₄×D₄	C₂³×C₁₃	semidirect
717. C₄×D₄	C₂³×C₁₃	semidirect
727. #117	C₂³×C₁₃	semidirect
728. #117	C₂³×C₁₃	semidirect
729. #117	C₂³×C₁₃	semidirect
740. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
741. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
877. C₁₃	#62903	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×#3564	2
C₁₃×#3561	2
C₁₃×#3538	2
C₁₃×#3535	2
C₁₃×#3520	2
C₁₃×#3501	2
C₁₃×#3495	2
C₁₃×#3491	2
C₁₃×#3490	2
C₂×C₁₃×#551	2
C₁₃×#3459	2
C₁₃×#3458	2
C₂×C₁₃×#543	2
#62903	13

Subgroups — C13×#62903 #15749242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62903 #15749242