Subgroups — C₁₃×#62913 #15749252

Order 3328.

6974 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3554	C₂	1	6	yes	maximal, complemented
2	C₁₃×#3552	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3550	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3547	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3541	C₂	1	12	yes	maximal, complemented
6	C₁₃×#3523	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3518	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3511	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3506	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3503	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3499	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3497	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3486	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3460	C₂	1	3	yes	maximal, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
19	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
20	C₁₃×#563	C₂²	1	24	yes	complemented
21	C₁₃×#562	C₂²	1	24	yes	complemented
22	C₁₃×#559	C₂²	1	12	yes	—
23	C₁₃×#559	C₂²	1	3	yes	complemented
24	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	Q₈²×C₁₃	C₂²	1	6	yes	complemented
26	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#557	C₂²	1	6	yes	complemented
28	C₁₃×#557	C₂²	1	3	yes	complemented
29	C₁₃×#556	C₂²	1	6	yes	—
30	C₁₃×#556	C₂²	1	12	yes	complemented
31	C₁₃×#556	C₂²	1	6	yes	complemented
32	C₁₃×#556	C₂²	1	3	yes	complemented
33	C₁₃×#555	C₂²	1	6	yes	—
34	C₁₃×#555	C₂²	1	6	yes	complemented
35	C₁₃×#554	C₂²	1	6	yes	—
36	C₁₃×#554	C₂²	1	12	yes	—
37	C₁₃×#554	C₂²	1	3	yes	complemented
38	C₁₃×#554	C₂²	1	6	yes	complemented
39	C₁₃×#554	C₂²	1	6	yes	complemented
40	C₁₃×#553	C₂²	1	6	yes	—
41	C₁₃×#553	C₂²	1	12	yes	—
42	C₁₃×#553	C₂²	1	12	yes	—
43	C₁₃×#552	C₂²	1	12	yes	complemented
44	C₁₃×#550	C₂²	1	6	yes	—
45	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
46	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
47	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
48	D₄×Q₈×C₁₃	C₂²	1	12	yes	—
49	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
50	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
51	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
52	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
53	D₄×Q₈×C₁₃	C₂²	1	12	yes	complemented
54	D₄×Q₈×C₁₃	C₂²	1	6	yes	complemented
55	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#548	C₂²	1	12	yes	—
57	C₁₃×#548	C₂²	1	2	yes	—
58	C₁₃×#548	C₂²	1	4	yes	complemented
59	C₁₃×#548	C₂²	1	12	yes	complemented
60	C₁₃×#548	C₂²	1	12	yes	complemented
61	C₁₃×#547	C₂²	1	6	yes	—
62	C₁₃×#547	C₂²	1	12	yes	complemented
63	C₁₃×#547	C₂²	1	6	yes	complemented
64	C₁₃×#544	C₂²	1	3	yes	—
65	C₁₃×#544	C₂²	1	12	yes	complemented
66	C₁₃×#542	C₂²	1	6	yes	—
67	C₁₃×#542	C₂²	1	6	yes	—
68	C₁₃×#542	C₂²	1	12	yes	complemented
69	C₁₃×#542	C₂²	1	24	yes	complemented
70	C₁₃×#542	C₂²	1	12	yes	complemented
71	C₁₃×#541	C₂²	1	12	yes	complemented
72	C₁₃×#540	C₂²	1	6	yes	—
73	C₁₃×#540	C₂²	1	6	yes	—
74	C₁₃×#539	C₂²	1	24	yes	complemented
75	C₁₃×#538	C₂²	1	12	yes	—
76	C₁₃×#538	C₂²	1	12	yes	—
77	C₁₃×#537	C₂²	1	3	yes	—
78	C₁₃×#537	C₂²	1	12	yes	complemented
79	C₁₃×#536	C₂²	1	12	yes	complemented
80	C₁₃×#536	C₂²	1	12	yes	complemented
81	C₁₃×#536	C₂²	1	12	yes	complemented
82	C₁₃×#535	C₂²	1	1	yes	characteristic
83	C₁₃×#535	C₂²	1	3	yes	—
84	C₁₃×#533	C₂²	1	3	yes	—
85	C₁₃×#533	C₂²	1	6	yes	complemented
86	C₁₃×#533	C₂²	1	6	yes	complemented
87	C₁₃×#533	C₂²	1	6	yes	complemented
88	C₁₃×#532	C₂²	1	6	yes	—
89	C₁₃×#532	C₂²	1	6	yes	—
90	C₁₃×#532	C₂²	1	3	yes	—
91	C₁₃×#532	C₂²	1	6	yes	complemented
92	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
93	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	complemented
94	C₁₃×#529	C₂²	1	6	yes	—
95	C₁₃×#529	C₂²	1	6	yes	—
96	C₁₃×#529	C₂²	1	6	yes	complemented
97	C₁₃×#525	C₂²	1	12	yes	—
98	C₁₃×#525	C₂²	1	12	yes	—
99	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	—
100	C₁₃×#520	C₂²	1	6	yes	—
101	C₁₃×#519	C₂²	1	4	yes	complemented
102	C₄×C₁₃×#41	C₂²	1	3	yes	—
103	C₄×C₁₃×#41	C₂²	1	3	yes	—
104	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
106	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
108	C₁₃×2₋¹⁺⁴	—	4	16	no	—
109	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×#41	C₂³	1	3	yes	—
111	C₂×C₁₃×#41	C₂³	1	2	yes	—
112	C₂×C₁₃×#41	C₂³	1	12	yes	—
113	C₂×C₁₃×#41	C₂³	1	12	yes	—
114	C₂×C₁₃×#41	C₂³	1	12	yes	—
115	C₂²×Q₈×C₁₃	—	4	8	no	—
116	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
118	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
119	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
120	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
121	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
138	C₁₃×#127	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	3	yes	—
140	C₁₃×#127	C₂³	1	6	yes	—
141	C₁₃×#126	C₂³	1	12	yes	—
142	C₁₃×#126	C₂³	1	12	yes	—
143	C₁₃×#126	C₂³	1	12	yes	—
144	C₁₃×#126	C₂³	1	24	yes	—
145	C₁₃×#126	C₂³	1	24	yes	—
146	C₁₃×#125	C₂³	1	6	yes	—
147	C₁₃×#125	C₂³	1	6	yes	—
148	C₁₃×#125	C₂³	1	6	yes	—
149	C₁₃×#125	C₂³	1	6	yes	—
150	C₁₃×#125	C₂³	1	12	yes	—
151	C₁₃×#125	C₂³	1	12	yes	—
152	C₁₃×#125	C₂³	1	24	yes	—
153	C₁₃×#124	C₂³	1	2	yes	—
154	C₁₃×#124	C₂³	1	6	yes	—
155	C₁₃×#124	C₂³	1	6	yes	—
156	C₁₃×#124	C₂³	1	12	yes	—
157	C₁₃×#124	C₂³	1	12	yes	—
158	C₁₃×#124	C₂³	1	6	yes	—
159	C₁₃×#124	C₂³	1	12	yes	—
160	C₁₃×#124	C₂³	1	24	yes	—
161	C₁₃×#124	C₂³	1	24	yes	—
162	C₁₃×#123	C₂³	1	12	yes	—
163	C₁₃×#123	C₂³	1	12	yes	—
164	C₁₃×#123	C₂³	1	24	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	24	yes	—
169	C₁₃×#123	C₂³	1	24	yes	—
170	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	6	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	12	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
190	C₁₃×#121	C₂³	1	6	yes	—
191	C₁₃×#121	C₂³	1	12	yes	—
192	C₁₃×#121	C₂³	1	12	yes	—
193	C₁₃×#121	C₂³	1	12	yes	—
194	C₁₃×#121	C₂³	1	2	yes	—
195	C₁₃×#121	C₂³	1	6	yes	—
196	C₁₃×#121	C₂³	1	6	yes	—
197	C₁₃×#121	C₂³	1	2	yes	—
198	C₁₃×#121	C₂³	1	6	yes	—
199	C₁₃×#121	C₂³	1	6	yes	—
200	C₁₃×#121	C₂³	1	6	yes	—
201	C₁₃×#121	C₂³	1	12	yes	—
202	C₁₃×#121	C₂³	1	6	yes	—
203	C₁₃×#121	C₂³	1	12	yes	—
204	C₁₃×#121	C₂³	1	12	yes	—
205	C₁₃×#121	C₂³	1	24	yes	—
206	C₁₃×#120	C₂³	1	4	yes	—
207	C₁₃×#120	C₂³	1	12	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
225	C₄×D₄×C₁₃	C₂³	1	6	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	6	yes	—
231	C₄×D₄×C₁₃	C₂³	1	3	yes	—
232	C₄×D₄×C₁₃	C₂³	1	3	yes	—
233	C₄×D₄×C₁₃	C₂³	1	6	yes	—
234	C₄×D₄×C₁₃	C₂³	1	6	yes	—
235	C₄×D₄×C₁₃	C₂³	1	3	yes	—
236	C₄×D₄×C₁₃	C₂³	1	3	yes	—
237	C₄×D₄×C₁₃	C₂³	1	6	yes	—
238	C₄×D₄×C₁₃	C₂³	1	6	yes	—
239	C₄×D₄×C₁₃	C₂³	1	24	yes	—
240	C₄×D₄×C₁₃	C₂³	1	12	yes	—
241	C₄×D₄×C₁₃	C₂³	1	12	yes	—
242	C₄×D₄×C₁₃	C₂³	1	12	yes	—
243	C₄×D₄×C₁₃	C₂³	1	24	yes	—
244	C₄×D₄×C₁₃	C₂³	1	6	yes	—
245	C₄×D₄×C₁₃	C₂³	1	12	yes	—
246	C₁₃×#117	C₂³	1	1	yes	characteristic
247	C₁₃×#117	C₂³	1	3	yes	—
248	C₁₃×#117	C₂³	1	6	yes	—
249	C₁₃×#117	C₂³	1	6	yes	—
250	C₁₃×#117	C₂³	1	6	yes	—
251	C₁₃×#117	C₂³	1	12	yes	—
252	C₁₃×#117	C₂³	1	12	yes	—
253	C₁₃×#117	C₂³	1	12	yes	—
254	C₁₃×#117	C₂³	1	12	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	12	yes	—
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
261	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
262	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
263	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
264	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
265	#62913	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
267	C₁₃×#41	—	2	8	no	—
268	C₁₃×#41	—	2	4	no	—
269	C₁₃×#41	—	2	12	no	—
270	C₁₃×#41	—	4	24	no	—
271	C₁₃×#41	—	4	24	no	—
272	C₁₃×#41	—	4	24	no	—
273	C₂×Q₈×C₁₃	—	2	4	no	—
274	C₂×Q₈×C₁₃	—	2	16	no	—
275	C₂×Q₈×C₁₃	—	2	8	no	—
276	C₂×Q₈×C₁₃	—	4	12	no	—
277	C₂×Q₈×C₁₃	—	4	24	no	—
278	C₂×Q₈×C₁₃	—	4	24	no	—
279	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
281	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
282	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
283	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
284	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
285	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
286	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
287	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂×D₄×C₁₃	—	2	4	no	—
289	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
291	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
295	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
296	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
297	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
298	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
299	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
300	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
301	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
302	C₂²×C₄×C₁₃	—	4	12	no	—
303	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
308	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
334	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
336	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
341	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
349	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
350	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
351	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
352	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
353	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
354	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
355	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
356	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
357	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
358	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
359	C₄²×C₁₃	C₂⁴	1	2	yes	—
360	C₄²×C₁₃	C₂⁴	1	3	yes	—
361	C₄²×C₁₃	C₂⁴	1	3	yes	—
362	C₄²×C₁₃	C₂⁴	1	3	yes	—
363	C₄²×C₁₃	C₂⁴	1	6	yes	—
364	C₄²×C₁₃	C₂⁴	1	6	yes	—
365	C₄²×C₁₃	C₂⁴	1	3	yes	—
366	C₄²×C₁₃	C₂⁴	1	6	yes	—
367	C₄²×C₁₃	C₂⁴	1	6	yes	—
368	C₄²×C₁₃	C₂⁴	1	6	yes	—
369	C₄²×C₁₃	C₂⁴	1	24	yes	—
370	#3554	C₂×C₁₃	1	6	yes	complemented
371	#3552	C₂×C₁₃	1	6	yes	complemented
372	#3550	C₂×C₁₃	1	6	yes	complemented
373	#3547	C₂×C₁₃	1	6	yes	complemented
374	#3541	C₂×C₁₃	1	12	yes	complemented
375	#3523	C₂×C₁₃	1	2	yes	complemented
376	#3518	C₂×C₁₃	1	2	yes	complemented
377	#3511	C₂×C₁₃	1	3	yes	complemented
378	#3506	C₂×C₁₃	1	3	yes	complemented
379	#3503	C₂×C₁₃	1	3	yes	complemented
380	#3499	C₂×C₁₃	1	2	yes	complemented
381	#3497	C₂×C₁₃	1	2	yes	complemented
382	#3486	C₂×C₁₃	1	4	yes	complemented
383	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
384	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
385	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#3460	C₂×C₁₃	1	3	yes	complemented
387	C₂³×C₁₃	—	2	4	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	4	2	no	—
390	C₂³×C₁₃	C₂⁵	1	4	yes	—
391	C₂³×C₁₃	C₂⁵	1	2	yes	—
392	C₂³×C₁₃	C₂⁵	1	6	yes	—
393	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
394	Q₈×C₁₃	—	2	6	no	—
395	Q₈×C₁₃	—	2	24	no	—
396	Q₈×C₁₃	—	2	12	no	—
397	Q₈×C₁₃	—	2	2	no	—
398	Q₈×C₁₃	—	2	6	no	—
399	Q₈×C₁₃	—	4	12	no	—
400	Q₈×C₁₃	—	4	12	no	—
401	Q₈×C₁₃	—	4	6	no	—
402	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
403	D₄×C₁₃	—	2	4	no	—
404	D₄×C₁₃	—	2	12	no	—
405	D₄×C₁₃	—	2	12	no	—
406	D₄×C₁₃	—	2	4	no	—
407	D₄×C₁₃	—	2	4	no	—
408	D₄×C₁₃	—	2	2	no	—
409	D₄×C₁₃	—	2	6	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	4	6	no	—
412	D₄×C₁₃	—	4	12	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	12	no	—
415	D₄×C₁₃	—	4	12	no	—
416	C₂×C₄×C₁₃	—	2	6	no	—
417	C₂×C₄×C₁₃	—	2	24	no	—
418	C₂×C₄×C₁₃	—	2	12	no	—
419	C₂×C₄×C₁₃	—	2	12	no	—
420	C₂×C₄×C₁₃	—	2	12	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	4	6	no	—
423	C₂×C₄×C₁₃	—	4	12	no	—
424	C₂×C₄×C₁₃	—	4	3	no	—
425	C₂×C₄×C₁₃	—	4	6	no	—
426	C₂×C₄×C₁₃	—	4	6	no	—
427	C₂×C₄×C₁₃	—	4	24	no	—
428	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	complemented
429	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
431	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
432	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
433	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
434	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
435	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
436	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
437	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
438	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
439	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
440	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
441	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
442	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
443	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
444	#563	C₂²×C₁₃	1	24	yes	complemented
445	#562	C₂²×C₁₃	1	24	yes	complemented
446	#559	C₂²×C₁₃	1	12	yes	—
447	#559	C₂²×C₁₃	1	3	yes	complemented
448	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	Q₈²	C₂²×C₁₃	1	6	yes	complemented
450	#557	C₂²×C₁₃	1	3	yes	complemented
451	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	#557	C₂²×C₁₃	1	6	yes	complemented
453	#556	C₂²×C₁₃	1	6	yes	—
454	#556	C₂²×C₁₃	1	3	yes	complemented
455	#556	C₂²×C₁₃	1	6	yes	complemented
456	#556	C₂²×C₁₃	1	12	yes	complemented
457	#555	C₂²×C₁₃	1	6	yes	—
458	#555	C₂²×C₁₃	1	6	yes	complemented
459	#554	C₂²×C₁₃	1	6	yes	—
460	#554	C₂²×C₁₃	1	12	yes	—
461	#554	C₂²×C₁₃	1	3	yes	complemented
462	#554	C₂²×C₁₃	1	6	yes	complemented
463	#554	C₂²×C₁₃	1	6	yes	complemented
464	#553	C₂²×C₁₃	1	6	yes	—
465	#553	C₂²×C₁₃	1	12	yes	—
466	#553	C₂²×C₁₃	1	12	yes	—
467	#552	C₂²×C₁₃	1	12	yes	complemented
468	#550	C₂²×C₁₃	1	6	yes	—
469	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
471	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
472	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
473	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
474	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
475	D₄×Q₈	C₂²×C₁₃	1	12	yes	—
476	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
478	D₄×Q₈	C₂²×C₁₃	1	12	yes	complemented
479	D₄×Q₈	C₂²×C₁₃	1	6	yes	complemented
480	#548	C₂²×C₁₃	1	2	yes	—
481	#548	C₂²×C₁₃	1	12	yes	—
482	#548	C₂²×C₁₃	1	4	yes	complemented
483	#548	C₂²×C₁₃	1	12	yes	complemented
484	#548	C₂²×C₁₃	1	12	yes	complemented
485	#547	C₂²×C₁₃	1	6	yes	—
486	#547	C₂²×C₁₃	1	6	yes	complemented
487	#547	C₂²×C₁₃	1	12	yes	complemented
488	#544	C₂²×C₁₃	1	3	yes	—
489	#544	C₂²×C₁₃	1	12	yes	complemented
490	#542	C₂²×C₁₃	1	6	yes	—
491	#542	C₂²×C₁₃	1	6	yes	—
492	#542	C₂²×C₁₃	1	12	yes	complemented
493	#542	C₂²×C₁₃	1	12	yes	complemented
494	#542	C₂²×C₁₃	1	24	yes	complemented
495	#541	C₂²×C₁₃	1	12	yes	complemented
496	#540	C₂²×C₁₃	1	6	yes	—
497	#540	C₂²×C₁₃	1	6	yes	—
498	#539	C₂²×C₁₃	1	24	yes	complemented
499	#538	C₂²×C₁₃	1	12	yes	—
500	#538	C₂²×C₁₃	1	12	yes	—
501	#537	C₂²×C₁₃	1	3	yes	—
502	#537	C₂²×C₁₃	1	12	yes	complemented
503	#536	C₂²×C₁₃	1	12	yes	complemented
504	#536	C₂²×C₁₃	1	12	yes	complemented
505	#536	C₂²×C₁₃	1	12	yes	complemented
506	#535	C₂²×C₁₃	1	1	yes	characteristic
507	#535	C₂²×C₁₃	1	3	yes	—
508	#533	C₂²×C₁₃	1	3	yes	—
509	#533	C₂²×C₁₃	1	6	yes	complemented
510	#533	C₂²×C₁₃	1	6	yes	complemented
511	#533	C₂²×C₁₃	1	6	yes	complemented
512	#532	C₂²×C₁₃	1	6	yes	—
513	#532	C₂²×C₁₃	1	6	yes	—
514	#532	C₂²×C₁₃	1	3	yes	—
515	#532	C₂²×C₁₃	1	6	yes	complemented
516	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
517	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	complemented
518	#529	C₂²×C₁₃	1	6	yes	—
519	#529	C₂²×C₁₃	1	6	yes	—
520	#529	C₂²×C₁₃	1	6	yes	complemented
521	#525	C₂²×C₁₃	1	12	yes	—
522	#525	C₂²×C₁₃	1	12	yes	—
523	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	6	yes	—
524	#520	C₂²×C₁₃	1	6	yes	—
525	#519	C₂²×C₁₃	1	4	yes	complemented
526	C₄×#41	C₂²×C₁₃	1	3	yes	—
527	C₄×#41	C₂²×C₁₃	1	3	yes	—
528	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
529	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
530	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
531	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
532	C₂²×C₁₃	—	2	1	no	—
533	C₂²×C₁₃	—	2	1	no	—
534	C₂²×C₁₃	—	2	4	no	—
535	C₂²×C₁₃	—	2	2	no	—
536	C₂²×C₁₃	—	2	6	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	6	no	—
539	C₂²×C₁₃	—	2	4	no	—
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	6	no	—
542	C₂²×C₁₃	—	2	4	no	—
543	C₂²×C₁₃	—	4	8	no	—
544	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
545	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	2	6	no	—
548	C₄×C₁₃	—	2	12	no	—
549	C₄×C₁₃	—	2	3	no	—
550	C₄×C₁₃	—	2	6	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	3	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	2	3	no	—
555	C₄×C₁₃	—	2	6	no	—
556	C₄×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
557	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
558	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
559	2₋¹⁺⁴	—	4	16	no	—
560	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×#41	C₂³×C₁₃	1	3	yes	—
562	C₂×#41	C₂³×C₁₃	1	2	yes	—
563	C₂×#41	C₂³×C₁₃	1	12	yes	—
564	C₂×#41	C₂³×C₁₃	1	12	yes	—
565	C₂×#41	C₂³×C₁₃	1	12	yes	—
566	C₂²×Q₈	—	4	8	no	—
567	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
569	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
570	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
571	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
572	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
573	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
575	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
576	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
577	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
578	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
579	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
580	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
581	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
582	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
583	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
584	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
585	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
586	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
587	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
588	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
589	#127	C₂³×C₁₃	1	2	yes	—
590	#127	C₂³×C₁₃	1	3	yes	—
591	#127	C₂³×C₁₃	1	6	yes	—
592	#126	C₂³×C₁₃	1	12	yes	—
593	#126	C₂³×C₁₃	1	12	yes	—
594	#126	C₂³×C₁₃	1	12	yes	—
595	#126	C₂³×C₁₃	1	24	yes	—
596	#126	C₂³×C₁₃	1	24	yes	—
597	#125	C₂³×C₁₃	1	6	yes	—
598	#125	C₂³×C₁₃	1	6	yes	—
599	#125	C₂³×C₁₃	1	6	yes	—
600	#125	C₂³×C₁₃	1	6	yes	—
601	#125	C₂³×C₁₃	1	12	yes	—
602	#125	C₂³×C₁₃	1	12	yes	—
603	#125	C₂³×C₁₃	1	24	yes	—
604	#124	C₂³×C₁₃	1	2	yes	—
605	#124	C₂³×C₁₃	1	6	yes	—
606	#124	C₂³×C₁₃	1	6	yes	—
607	#124	C₂³×C₁₃	1	12	yes	—
608	#124	C₂³×C₁₃	1	12	yes	—
609	#124	C₂³×C₁₃	1	6	yes	—
610	#124	C₂³×C₁₃	1	12	yes	—
611	#124	C₂³×C₁₃	1	24	yes	—
612	#124	C₂³×C₁₃	1	24	yes	—
613	#123	C₂³×C₁₃	1	12	yes	—
614	#123	C₂³×C₁₃	1	12	yes	—
615	#123	C₂³×C₁₃	1	24	yes	—
616	#123	C₂³×C₁₃	1	12	yes	—
617	#123	C₂³×C₁₃	1	12	yes	—
618	#123	C₂³×C₁₃	1	12	yes	—
619	#123	C₂³×C₁₃	1	24	yes	—
620	#123	C₂³×C₁₃	1	24	yes	—
621	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
622	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
623	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
624	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
625	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
627	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
628	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
629	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
630	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
631	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
632	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
633	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
634	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
641	#121	C₂³×C₁₃	1	6	yes	—
642	#121	C₂³×C₁₃	1	12	yes	—
643	#121	C₂³×C₁₃	1	12	yes	—
644	#121	C₂³×C₁₃	1	12	yes	—
645	#121	C₂³×C₁₃	1	2	yes	—
646	#121	C₂³×C₁₃	1	6	yes	—
647	#121	C₂³×C₁₃	1	6	yes	—
648	#121	C₂³×C₁₃	1	2	yes	—
649	#121	C₂³×C₁₃	1	6	yes	—
650	#121	C₂³×C₁₃	1	6	yes	—
651	#121	C₂³×C₁₃	1	6	yes	—
652	#121	C₂³×C₁₃	1	12	yes	—
653	#121	C₂³×C₁₃	1	6	yes	—
654	#121	C₂³×C₁₃	1	12	yes	—
655	#121	C₂³×C₁₃	1	12	yes	—
656	#121	C₂³×C₁₃	1	24	yes	—
657	#120	C₂³×C₁₃	1	4	yes	—
658	#120	C₂³×C₁₃	1	12	yes	—
659	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
660	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
662	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
663	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
664	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
665	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
666	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
667	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
668	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
669	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
670	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
671	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
672	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
673	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
674	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
675	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
676	C₄×D₄	C₂³×C₁₃	1	6	yes	—
677	C₄×D₄	C₂³×C₁₃	1	6	yes	—
678	C₄×D₄	C₂³×C₁₃	1	6	yes	—
679	C₄×D₄	C₂³×C₁₃	1	6	yes	—
680	C₄×D₄	C₂³×C₁₃	1	6	yes	—
681	C₄×D₄	C₂³×C₁₃	1	6	yes	—
682	C₄×D₄	C₂³×C₁₃	1	3	yes	—
683	C₄×D₄	C₂³×C₁₃	1	3	yes	—
684	C₄×D₄	C₂³×C₁₃	1	6	yes	—
685	C₄×D₄	C₂³×C₁₃	1	6	yes	—
686	C₄×D₄	C₂³×C₁₃	1	3	yes	—
687	C₄×D₄	C₂³×C₁₃	1	3	yes	—
688	C₄×D₄	C₂³×C₁₃	1	6	yes	—
689	C₄×D₄	C₂³×C₁₃	1	6	yes	—
690	C₄×D₄	C₂³×C₁₃	1	24	yes	—
691	C₄×D₄	C₂³×C₁₃	1	12	yes	—
692	C₄×D₄	C₂³×C₁₃	1	12	yes	—
693	C₄×D₄	C₂³×C₁₃	1	12	yes	—
694	C₄×D₄	C₂³×C₁₃	1	24	yes	—
695	C₄×D₄	C₂³×C₁₃	1	6	yes	—
696	C₄×D₄	C₂³×C₁₃	1	12	yes	—
697	#117	C₂³×C₁₃	1	1	yes	characteristic
698	#117	C₂³×C₁₃	1	3	yes	—
699	#117	C₂³×C₁₃	1	6	yes	—
700	#117	C₂³×C₁₃	1	6	yes	—
701	#117	C₂³×C₁₃	1	6	yes	—
702	#117	C₂³×C₁₃	1	12	yes	—
703	#117	C₂³×C₁₃	1	12	yes	—
704	#117	C₂³×C₁₃	1	12	yes	—
705	#117	C₂³×C₁₃	1	12	yes	—
706	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
707	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
708	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
710	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
711	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
713	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
714	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
715	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
716	C₂×C₁₃	—	2	2	no	—
717	C₂×C₁₃	—	4	2	no	—
718	C₂×C₁₃	—	4	6	no	—
719	C₂×C₁₃	—	4	4	no	—
720	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
721	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
722	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
723	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
724	#41	—	2	8	no	—
725	#41	—	2	4	no	—
726	#41	—	2	12	no	—
727	#41	—	4	24	no	—
728	#41	—	4	24	no	—
729	#41	—	4	24	no	—
730	C₂×Q₈	—	2	4	no	—
731	C₂×Q₈	—	2	16	no	—
732	C₂×Q₈	—	2	8	no	—
733	C₂×Q₈	—	4	12	no	—
734	C₂×Q₈	—	4	24	no	—
735	C₂×Q₈	—	4	24	no	—
736	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
738	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
739	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
740	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
741	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
742	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
743	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
744	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
748	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
749	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
751	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
752	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
753	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
754	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
755	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
756	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
757	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
758	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
759	C₂²×C₄	—	4	12	no	—
760	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
762	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
766	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
768	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
769	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
770	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
771	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
772	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
774	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
775	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
776	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
777	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
778	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
779	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
780	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
785	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
786	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
787	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
788	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
789	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
792	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
793	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
794	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
795	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
796	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
797	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
798	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
799	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
800	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
801	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
802	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
803	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
804	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
805	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
806	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
807	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
808	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
809	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
810	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
811	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
812	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
813	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
814	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
815	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
816	C₄²	C₂⁴×C₁₃	1	2	yes	—
817	C₄²	C₂⁴×C₁₃	1	3	yes	—
818	C₄²	C₂⁴×C₁₃	1	3	yes	—
819	C₄²	C₂⁴×C₁₃	1	3	yes	—
820	C₄²	C₂⁴×C₁₃	1	6	yes	—
821	C₄²	C₂⁴×C₁₃	1	6	yes	—
822	C₄²	C₂⁴×C₁₃	1	3	yes	—
823	C₄²	C₂⁴×C₁₃	1	6	yes	—
824	C₄²	C₂⁴×C₁₃	1	6	yes	—
825	C₄²	C₂⁴×C₁₃	1	6	yes	—
826	C₄²	C₂⁴×C₁₃	1	24	yes	—
827	C₁₃	#62913	1	1	yes	characteristic, direct product factor, Sylow
828	C₂³	—	2	4	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	2	no	—
831	C₂³	C₂⁵×C₁₃	1	4	yes	—
832	C₂³	C₂⁵×C₁₃	1	2	yes	—
833	C₂³	C₂⁵×C₁₃	1	6	yes	—
834	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
835	Q₈	—	2	6	no	—
836	Q₈	—	2	24	no	—
837	Q₈	—	2	12	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	6	no	—
840	Q₈	—	4	12	no	—
841	Q₈	—	4	12	no	—
842	Q₈	—	4	6	no	—
843	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	12	no	—
846	D₄	—	2	12	no	—
847	D₄	—	2	4	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	6	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	6	no	—
853	D₄	—	4	12	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	12	no	—
856	D₄	—	4	12	no	—
857	C₂×C₄	—	2	6	no	—
858	C₂×C₄	—	2	24	no	—
859	C₂×C₄	—	2	12	no	—
860	C₂×C₄	—	2	12	no	—
861	C₂×C₄	—	2	12	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	4	6	no	—
864	C₂×C₄	—	4	12	no	—
865	C₂×C₄	—	4	3	no	—
866	C₂×C₄	—	4	6	no	—
867	C₂×C₄	—	4	6	no	—
868	C₂×C₄	—	4	24	no	—
869	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	complemented
870	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
871	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
872	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
873	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
874	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
875	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
876	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
877	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
878	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
879	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
880	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
881	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
882	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	6	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	6	no	—
890	C₂²	—	2	4	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	6	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	4	8	no	—
895	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
896	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	6	no	—
899	C₄	—	2	12	no	—
900	C₄	—	2	3	no	—
901	C₄	—	2	6	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	3	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	3	no	—
906	C₄	—	2	6	no	—
907	C₄	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
908	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
909	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	4	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	6	no	—
914	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
916	C₂	C₁₃×2₋¹⁺⁶	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×#3554	C₂	semidirect
2. C₁₃×#3552	C₂	semidirect
3. C₁₃×#3550	C₂	semidirect
4. C₁₃×#3547	C₂	semidirect
5. C₁₃×#3541	C₂	semidirect
6. C₁₃×#3523	C₂	semidirect
7. C₁₃×#3518	C₂	semidirect
8. C₁₃×#3511	C₂	semidirect
9. C₁₃×#3506	C₂	semidirect
10. C₁₃×#3503	C₂	semidirect
11. C₁₃×#3499	C₂	semidirect
12. C₁₃×#3497	C₂	semidirect
13. C₁₃×#3486	C₂	semidirect
14. C₁₃×#3480	C₂	semidirect
15. Q₈×C₁₃×#41	C₂	semidirect
16. C₂×D₄×Q₈×C₁₃	C₂	semidirect
17. C₁₃×#3460	C₂	semidirect
18. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
20. C₁₃×#563	C₂²	semidirect
21. C₁₃×#562	C₂²	semidirect
23. C₁₃×#559	C₂²	semidirect
24. Q₈²×C₁₃	C₂²	semidirect
25. Q₈²×C₁₃	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
32. C₁₃×#556	C₂²	semidirect
34. C₁₃×#555	C₂²	semidirect
37. C₁₃×#554	C₂²	semidirect
38. C₁₃×#554	C₂²	semidirect
39. C₁₃×#554	C₂²	semidirect
43. C₁₃×#552	C₂²	semidirect
45. C₁₃×#550	C₂²	semidirect
52. D₄×Q₈×C₁₃	C₂²	semidirect
53. D₄×Q₈×C₁₃	C₂²	semidirect
54. D₄×Q₈×C₁₃	C₂²	semidirect
55. D₄×Q₈×C₁₃	C₂²	semidirect
58. C₁₃×#548	C₂²	semidirect
59. C₁₃×#548	C₂²	semidirect
60. C₁₃×#548	C₂²	semidirect
62. C₁₃×#547	C₂²	semidirect
63. C₁₃×#547	C₂²	semidirect
65. C₁₃×#544	C₂²	semidirect
68. C₁₃×#542	C₂²	semidirect
69. C₁₃×#542	C₂²	semidirect
70. C₁₃×#542	C₂²	semidirect
71. C₁₃×#541	C₂²	semidirect
74. C₁₃×#539	C₂²	semidirect
78. C₁₃×#537	C₂²	semidirect
79. C₁₃×#536	C₂²	semidirect
80. C₁₃×#536	C₂²	semidirect
81. C₁₃×#536	C₂²	semidirect
85. C₁₃×#533	C₂²	semidirect
86. C₁₃×#533	C₂²	semidirect
87. C₁₃×#533	C₂²	semidirect
91. C₁₃×#532	C₂²	semidirect
93. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
96. C₁₃×#529	C₂²	semidirect
101. C₁₃×#519	C₂²	semidirect
104. C₄×C₁₃×#41	C₂²	semidirect
106. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
265. #62913	C₁₃	direct (N × H)
370. #3554	C₂×C₁₃	semidirect
371. #3552	C₂×C₁₃	semidirect
372. #3550	C₂×C₁₃	semidirect
373. #3547	C₂×C₁₃	semidirect
374. #3541	C₂×C₁₃	semidirect
375. #3523	C₂×C₁₃	semidirect
376. #3518	C₂×C₁₃	semidirect
377. #3511	C₂×C₁₃	semidirect
378. #3506	C₂×C₁₃	semidirect
379. #3503	C₂×C₁₃	semidirect
380. #3499	C₂×C₁₃	semidirect
381. #3497	C₂×C₁₃	semidirect
382. #3486	C₂×C₁₃	semidirect
383. #3480	C₂×C₁₃	semidirect
384. Q₈×#41	C₂×C₁₃	semidirect
385. C₂×D₄×Q₈	C₂×C₁₃	semidirect
386. #3460	C₂×C₁₃	semidirect
428. C₂×C₄×C₁₃	2₋¹⁺⁴	semidirect
442. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
444. #563	C₂²×C₁₃	semidirect
445. #562	C₂²×C₁₃	semidirect
447. #559	C₂²×C₁₃	semidirect
448. Q₈²	C₂²×C₁₃	semidirect
449. Q₈²	C₂²×C₁₃	semidirect
450. #557	C₂²×C₁₃	semidirect
451. #557	C₂²×C₁₃	semidirect
452. #557	C₂²×C₁₃	semidirect
454. #556	C₂²×C₁₃	semidirect
455. #556	C₂²×C₁₃	semidirect
456. #556	C₂²×C₁₃	semidirect
458. #555	C₂²×C₁₃	semidirect
461. #554	C₂²×C₁₃	semidirect
462. #554	C₂²×C₁₃	semidirect
463. #554	C₂²×C₁₃	semidirect
467. #552	C₂²×C₁₃	semidirect
469. #550	C₂²×C₁₃	semidirect
476. D₄×Q₈	C₂²×C₁₃	semidirect
477. D₄×Q₈	C₂²×C₁₃	semidirect
478. D₄×Q₈	C₂²×C₁₃	semidirect
479. D₄×Q₈	C₂²×C₁₃	semidirect
482. #548	C₂²×C₁₃	semidirect
483. #548	C₂²×C₁₃	semidirect
484. #548	C₂²×C₁₃	semidirect
486. #547	C₂²×C₁₃	semidirect
487. #547	C₂²×C₁₃	semidirect
489. #544	C₂²×C₁₃	semidirect
492. #542	C₂²×C₁₃	semidirect
493. #542	C₂²×C₁₃	semidirect
494. #542	C₂²×C₁₃	semidirect
495. #541	C₂²×C₁₃	semidirect
498. #539	C₂²×C₁₃	semidirect
502. #537	C₂²×C₁₃	semidirect
503. #536	C₂²×C₁₃	semidirect
504. #536	C₂²×C₁₃	semidirect
505. #536	C₂²×C₁₃	semidirect
509. #533	C₂²×C₁₃	semidirect
510. #533	C₂²×C₁₃	semidirect
511. #533	C₂²×C₁₃	semidirect
515. #532	C₂²×C₁₃	semidirect
517. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
520. #529	C₂²×C₁₃	semidirect
525. #519	C₂²×C₁₃	semidirect
528. C₄×#41	C₂²×C₁₃	semidirect
530. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
827. C₁₃	#62913	direct (N × H)
869. C₂×C₄	C₁₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3554	2
C₁₃×#3552	2
C₁₃×#3550	2
C₁₃×#3547	2
C₁₃×#3541	2
C₁₃×#3523	2
C₁₃×#3518	2
C₁₃×#3511	2
C₁₃×#3506	2
C₁₃×#3503	2
C₁₃×#3499	2
C₁₃×#3497	2
C₁₃×#3486	2
C₁₃×#3480	2
Q₈×C₁₃×#41	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3460	2
#62913	13

Subgroups — C13×#62913 #15749252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62913 #15749252