Subgroups — C₁₃×#62876 #15749215

Order 3328.

7414 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3562	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3558	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3546	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3543	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3534	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3532	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3510	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3508	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3500	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3498	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#562	C₂²	1	16	yes	complemented
22	C₁₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
23	C₁₃×#560	C₂²	1	16	yes	complemented
24	C₁₃×#560	C₂²	1	8	yes	complemented
25	C₁₃×#560	C₂²	1	16	yes	complemented
26	C₁₃×#559	C₂²	1	8	yes	complemented
27	C₁₃×#559	C₂²	1	8	yes	complemented
28	C₁₃×#556	C₂²	1	8	yes	complemented
29	C₁₃×#553	C₂²	1	16	yes	complemented
30	C₁₃×#551	C₂²	1	16	yes	complemented
31	C₁₃×#551	C₂²	1	8	yes	complemented
32	C₁₃×#550	C₂²	1	8	yes	complemented
33	C₁₃×#550	C₂²	1	8	yes	complemented
34	C₁₃×#550	C₂²	1	8	yes	complemented
35	C₁₃×#548	C₂²	1	8	yes	complemented
36	C₁₃×#548	C₂²	1	8	yes	complemented
37	C₁₃×#547	C₂²	1	8	yes	complemented
38	C₁₃×#546	C₂²	1	8	yes	complemented
39	C₁₃×#546	C₂²	1	8	yes	complemented
40	C₁₃×#546	C₂²	1	16	yes	complemented
41	C₁₃×#546	C₂²	1	16	yes	complemented
42	C₁₃×#546	C₂²	1	16	yes	complemented
43	C₁₃×#546	C₂²	1	8	yes	complemented
44	C₁₃×#546	C₂²	1	16	yes	complemented
45	C₁₃×#546	C₂²	1	8	yes	complemented
46	D₄²×C₁₃	C₂²	1	8	yes	complemented
47	D₄²×C₁₃	C₂²	1	8	yes	complemented
48	D₄²×C₁₃	C₂²	1	16	yes	complemented
49	D₄²×C₁₃	C₂²	1	8	yes	complemented
50	D₄²×C₁₃	C₂²	1	8	yes	complemented
51	C₁₃×#542	C₂²	1	4	yes	complemented
52	C₁₃×#542	C₂²	1	4	yes	complemented
53	C₁₃×#542	C₂²	1	8	yes	complemented
54	C₁₃×#541	C₂²	1	4	yes	complemented
55	C₁₃×#540	C₂²	1	4	yes	complemented
56	C₁₃×#540	C₂²	1	8	yes	complemented
57	C₁₃×#540	C₂²	1	16	yes	complemented
58	C₁₃×#539	C₂²	1	8	yes	complemented
59	C₁₃×#539	C₂²	1	8	yes	complemented
60	C₁₃×#538	C₂²	1	8	yes	complemented
61	C₁₃×#538	C₂²	1	16	yes	complemented
62	C₁₃×#538	C₂²	1	16	yes	complemented
63	C₁₃×#538	C₂²	1	16	yes	complemented
64	C₁₃×#538	C₂²	1	8	yes	complemented
65	C₁₃×#537	C₂²	1	8	yes	complemented
66	C₁₃×#536	C₂²	1	2	yes	complemented
67	C₁₃×#536	C₂²	1	4	yes	complemented
68	C₁₃×#535	C₂²	1	2	yes	—
69	C₁₃×#535	C₂²	1	4	yes	complemented
70	C₁₃×#535	C₂²	1	8	yes	complemented
71	C₁₃×#535	C₂²	1	8	yes	complemented
72	C₁₃×#535	C₂²	1	2	yes	complemented
73	C₁₃×#535	C₂²	1	2	yes	complemented
74	C₁₃×#535	C₂²	1	16	yes	complemented
75	C₁₃×#535	C₂²	1	4	yes	complemented
76	C₁₃×#535	C₂²	1	4	yes	complemented
77	C₁₃×#535	C₂²	1	4	yes	complemented
78	C₁₃×#534	C₂²	1	4	yes	complemented
79	C₁₃×#534	C₂²	1	8	yes	complemented
80	C₁₃×#534	C₂²	1	16	yes	complemented
81	C₁₃×#534	C₂²	1	8	yes	complemented
82	C₁₃×#533	C₂²	1	2	yes	complemented
83	C₁₃×#532	C₂²	1	2	yes	complemented
84	C₁₃×#532	C₂²	1	8	yes	complemented
85	C₁₃×#532	C₂²	1	4	yes	complemented
86	C₁₃×#532	C₂²	1	4	yes	complemented
87	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
89	C₁₃×#529	C₂²	1	8	yes	complemented
90	C₁₃×#529	C₂²	1	8	yes	complemented
91	C₁₃×#529	C₂²	1	8	yes	complemented
92	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
93	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
94	C₁₃×#525	C₂²	1	2	yes	complemented
95	C₁₃×#525	C₂²	1	2	yes	complemented
96	C₁₃×#525	C₂²	1	4	yes	complemented
97	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
98	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
99	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
100	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
101	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#518	C₂²	1	2	yes	complemented
103	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
105	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
106	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
107	C₂⁵×C₁₃	C₂³	1	2	yes	—
108	C₁₃×2₋¹⁺⁴	—	4	4	no	—
109	C₁₃×H(5,𝔽₂)	—	4	8	no	—
110	C₁₃×H(5,𝔽₂)	—	4	4	no	—
111	C₂×C₁₃×#41	—	4	4	no	—
112	C₂×C₁₃×#41	C₂³	1	2	yes	—
113	C₂×C₁₃×#41	C₂³	1	2	yes	—
114	C₂×C₁₃×#41	C₂³	1	4	yes	—
115	C₂×C₁₃×#41	C₂³	1	4	yes	—
116	C₂×C₁₃×#41	C₂³	1	4	yes	—
117	C₂×C₁₃×#41	C₂³	1	8	yes	—
118	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
119	C₂×C₁₃×#41	C₂³	1	4	yes	complemented
120	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
121	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
123	C₂²×D₄×C₁₃	—	4	4	no	—
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
130	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
131	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
132	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
133	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
136	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
137	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
140	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
141	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
142	C₁₃×#127	C₂³	1	4	yes	—
143	C₁₃×#127	C₂³	1	4	yes	—
144	C₁₃×#127	C₂³	1	4	yes	—
145	C₁₃×#127	C₂³	1	8	yes	—
146	C₁₃×#127	C₂³	1	4	yes	—
147	C₁₃×#127	C₂³	1	8	yes	—
148	C₁₃×#127	C₂³	1	2	yes	complemented
149	C₁₃×#127	C₂³	1	4	yes	complemented
150	C₁₃×#127	C₂³	1	16	yes	complemented
151	C₁₃×#126	C₂³	1	8	yes	—
152	C₁₃×#126	C₂³	1	8	yes	—
153	C₁₃×#126	C₂³	1	8	yes	complemented
154	C₁₃×#126	C₂³	1	16	yes	complemented
155	C₁₃×#126	C₂³	1	8	yes	complemented
156	C₁₃×#126	C₂³	1	16	yes	complemented
157	C₁₃×#125	C₂³	1	4	yes	complemented
158	C₁₃×#125	C₂³	1	8	yes	complemented
159	C₁₃×#125	C₂³	1	8	yes	complemented
160	C₁₃×#124	C₂³	1	4	yes	—
161	C₁₃×#124	C₂³	1	4	yes	—
162	C₁₃×#124	C₂³	1	8	yes	—
163	C₁₃×#124	C₂³	1	4	yes	—
164	C₁₃×#124	C₂³	1	8	yes	—
165	C₁₃×#124	C₂³	1	8	yes	—
166	C₁₃×#124	C₂³	1	4	yes	—
167	C₁₃×#124	C₂³	1	8	yes	—
168	C₁₃×#124	C₂³	1	2	yes	complemented
169	C₁₃×#124	C₂³	1	4	yes	complemented
170	C₁₃×#124	C₂³	1	16	yes	complemented
171	C₁₃×#124	C₂³	1	2	yes	complemented
172	C₁₃×#124	C₂³	1	4	yes	complemented
173	C₁₃×#124	C₂³	1	16	yes	complemented
174	C₁₃×#124	C₂³	1	16	yes	complemented
175	C₁₃×#123	C₂³	1	4	yes	—
176	C₁₃×#123	C₂³	1	8	yes	—
177	C₁₃×#123	C₂³	1	4	yes	—
178	C₁₃×#123	C₂³	1	8	yes	—
179	C₁₃×#123	C₂³	1	8	yes	—
180	C₁₃×#123	C₂³	1	8	yes	—
181	C₁₃×#123	C₂³	1	16	yes	—
182	C₁₃×#123	C₂³	1	16	yes	complemented
183	C₁₃×#123	C₂³	1	8	yes	complemented
184	C₁₃×#123	C₂³	1	16	yes	complemented
185	C₁₃×#123	C₂³	1	8	yes	complemented
186	C₁₃×#123	C₂³	1	16	yes	complemented
187	C₁₃×#123	C₂³	1	16	yes	complemented
188	C₁₃×#123	C₂³	1	16	yes	complemented
189	C₁₃×#123	C₂³	1	16	yes	complemented
190	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
194	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
195	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
196	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
197	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
198	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₁₃×#121	C₂³	1	8	yes	—
201	C₁₃×#121	C₂³	1	16	yes	—
202	C₁₃×#121	C₂³	1	4	yes	—
203	C₁₃×#121	C₂³	1	4	yes	—
204	C₁₃×#121	C₂³	1	8	yes	—
205	C₁₃×#121	C₂³	1	8	yes	—
206	C₁₃×#121	C₂³	1	8	yes	—
207	C₁₃×#121	C₂³	1	8	yes	—
208	C₁₃×#121	C₂³	1	8	yes	—
209	C₁₃×#121	C₂³	1	16	yes	—
210	C₁₃×#121	C₂³	1	16	yes	—
211	C₁₃×#121	C₂³	1	16	yes	—
212	C₁₃×#121	C₂³	1	16	yes	—
213	C₁₃×#121	C₂³	1	8	yes	complemented
214	C₁₃×#121	C₂³	1	16	yes	complemented
215	C₁₃×#121	C₂³	1	16	yes	complemented
216	C₁₃×#121	C₂³	1	8	yes	complemented
217	C₁₃×#121	C₂³	1	16	yes	complemented
218	C₁₃×#121	C₂³	1	16	yes	complemented
219	C₁₃×#121	C₂³	1	16	yes	complemented
220	C₁₃×#121	C₂³	1	16	yes	complemented
221	C₁₃×#121	C₂³	1	16	yes	complemented
222	C₁₃×#121	C₂³	1	16	yes	complemented
223	C₁₃×#120	C₂³	1	4	yes	—
224	C₁₃×#120	C₂³	1	4	yes	—
225	C₁₃×#120	C₂³	1	8	yes	—
226	C₁₃×#120	C₂³	1	16	yes	—
227	C₁₃×#120	C₂³	1	8	yes	—
228	C₁₃×#120	C₂³	1	16	yes	—
229	C₁₃×#120	C₂³	1	8	yes	—
230	C₁₃×#120	C₂³	1	8	yes	—
231	C₁₃×#120	C₂³	1	16	yes	—
232	C₁₃×#120	C₂³	1	8	yes	—
233	C₁₃×#120	C₂³	1	8	yes	—
234	C₁₃×#120	C₂³	1	16	yes	—
235	C₁₃×#120	C₂³	1	16	yes	complemented
236	C₁₃×#120	C₂³	1	16	yes	complemented
237	C₁₃×#120	C₂³	1	16	yes	complemented
238	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
239	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
240	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
241	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
242	C₄×D₄×C₁₃	C₂³	1	8	yes	—
243	C₄×D₄×C₁₃	C₂³	1	8	yes	—
244	C₄×D₄×C₁₃	C₂³	1	8	yes	—
245	C₄×D₄×C₁₃	C₂³	1	8	yes	—
246	C₄×D₄×C₁₃	C₂³	1	8	yes	—
247	C₄×D₄×C₁₃	C₂³	1	8	yes	—
248	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
249	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
250	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
251	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
252	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
253	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
254	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
255	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
256	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
257	C₁₃×#117	C₂³	1	4	yes	—
258	C₁₃×#117	C₂³	1	4	yes	—
259	C₁₃×#117	C₂³	1	2	yes	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₁₃×#117	C₂³	1	4	yes	—
262	C₁₃×#117	C₂³	1	4	yes	complemented
263	C₁₃×#117	C₂³	1	4	yes	complemented
264	C₁₃×#117	C₂³	1	16	yes	complemented
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
266	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
269	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
270	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
271	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
274	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
275	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
276	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
277	#62876	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂⁴×C₁₃	—	4	4	no	—
279	C₂⁴×C₁₃	—	8	4	no	—
280	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
281	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
283	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
284	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
285	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
286	C₁₃×#41	—	2	8	no	—
287	C₁₃×#41	—	2	8	no	—
288	C₁₃×#41	—	4	8	no	—
289	C₁₃×#41	—	4	16	no	—
290	C₁₃×#41	—	4	8	no	—
291	C₁₃×#41	—	4	8	no	—
292	C₁₃×#41	—	4	8	no	—
293	C₁₃×#41	—	4	8	no	—
294	C₁₃×#41	—	8	16	no	—
295	C₂×Q₈×C₁₃	—	2	4	no	—
296	C₂×Q₈×C₁₃	—	4	8	no	—
297	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
301	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
302	C₂×D₄×C₁₃	—	2	8	no	—
303	C₂×D₄×C₁₃	—	2	4	no	—
304	C₂×D₄×C₁₃	—	4	16	no	—
305	C₂×D₄×C₁₃	—	4	8	no	—
306	C₂×D₄×C₁₃	—	4	8	no	—
307	C₂×D₄×C₁₃	—	4	8	no	—
308	C₂×D₄×C₁₃	—	4	4	no	—
309	C₂×D₄×C₁₃	—	4	4	no	—
310	C₂×D₄×C₁₃	—	4	8	no	—
311	C₂×D₄×C₁₃	—	4	16	no	—
312	C₂×D₄×C₁₃	—	8	8	no	—
313	C₂×D₄×C₁₃	—	8	16	no	—
314	C₂×D₄×C₁₃	—	8	16	no	—
315	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
316	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
317	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
318	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
319	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
320	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
321	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
322	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
323	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
325	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
328	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
329	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
330	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
331	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
332	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
333	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
334	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₁₃	—	2	4	no	—
337	C₂²×C₄×C₁₃	—	4	4	no	—
338	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
349	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
354	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
355	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
356	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
369	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
370	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
372	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
373	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
374	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
375	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
376	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
377	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
378	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
387	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
388	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
389	C₄²×C₁₃	C₂⁴	1	2	yes	—
390	C₄²×C₁₃	C₂⁴	1	2	yes	—
391	C₄²×C₁₃	C₂⁴	1	4	yes	—
392	C₄²×C₁₃	C₂⁴	1	4	yes	—
393	C₄²×C₁₃	C₂⁴	1	4	yes	—
394	C₄²×C₁₃	C₂⁴	1	8	yes	—
395	C₄²×C₁₃	C₂⁴	1	8	yes	—
396	C₄²×C₁₃	C₂⁴	1	8	yes	—
397	#3562	C₂×C₁₃	1	8	yes	complemented
398	#3558	C₂×C₁₃	1	8	yes	complemented
399	#3546	C₂×C₁₃	1	8	yes	complemented
400	#3543	C₂×C₁₃	1	8	yes	complemented
401	#3534	C₂×C₁₃	1	8	yes	complemented
402	#3532	C₂×C₁₃	1	8	yes	complemented
403	#3510	C₂×C₁₃	1	2	yes	complemented
404	#3508	C₂×C₁₃	1	2	yes	complemented
405	#3500	C₂×C₁₃	1	2	yes	complemented
406	#3498	C₂×C₁₃	1	2	yes	complemented
407	#3487	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3485	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3484	C₂×C₁₃	1	2	yes	complemented
410	#3455	C₂×C₁₃	1	2	yes	complemented
411	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
412	C₂³×C₁₃	—	2	2	no	—
413	C₂³×C₁₃	—	2	4	no	—
414	C₂³×C₁₃	—	2	8	no	—
415	C₂³×C₁₃	—	4	2	no	—
416	C₂³×C₁₃	—	4	8	no	—
417	C₂³×C₁₃	—	4	4	no	—
418	C₂³×C₁₃	—	4	8	no	—
419	C₂³×C₁₃	—	4	16	no	—
420	C₂³×C₁₃	—	4	8	no	—
421	C₂³×C₁₃	—	4	4	no	—
422	C₂³×C₁₃	—	4	16	no	—
423	C₂³×C₁₃	—	4	8	no	—
424	C₂³×C₁₃	—	8	16	no	—
425	C₂³×C₁₃	C₂⁵	1	2	yes	—
426	C₂³×C₁₃	C₂⁵	1	4	yes	—
427	C₂³×C₁₃	C₂⁵	1	8	yes	—
428	C₂³×C₁₃	C₂⁵	1	4	yes	—
429	C₂³×C₁₃	C₂⁵	1	4	yes	—
430	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
431	Q₈×C₁₃	—	2	8	no	—
432	Q₈×C₁₃	—	2	4	no	—
433	Q₈×C₁₃	—	2	4	no	—
434	Q₈×C₁₃	—	4	4	no	—
435	Q₈×C₁₃	—	4	8	no	—
436	D₄×C₁₃	—	2	8	no	—
437	D₄×C₁₃	—	2	8	no	—
438	D₄×C₁₃	—	2	8	no	—
439	D₄×C₁₃	—	2	8	no	—
440	D₄×C₁₃	—	2	8	no	—
441	D₄×C₁₃	—	2	4	no	—
442	D₄×C₁₃	—	2	4	no	—
443	D₄×C₁₃	—	4	8	no	—
444	D₄×C₁₃	—	4	8	no	—
445	D₄×C₁₃	—	4	8	no	—
446	D₄×C₁₃	—	4	8	no	—
447	D₄×C₁₃	—	4	8	no	—
448	D₄×C₁₃	—	4	8	no	—
449	D₄×C₁₃	—	4	16	no	—
450	D₄×C₁₃	—	4	8	no	—
451	D₄×C₁₃	—	4	8	no	—
452	D₄×C₁₃	—	4	16	no	—
453	D₄×C₁₃	—	4	16	no	—
454	D₄×C₁₃	—	4	16	no	—
455	D₄×C₁₃	—	4	16	no	—
456	D₄×C₁₃	—	4	4	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	4	no	—
459	C₂×C₄×C₁₃	—	2	8	no	—
460	C₂×C₄×C₁₃	—	2	8	no	—
461	C₂×C₄×C₁₃	—	2	8	no	—
462	C₂×C₄×C₁₃	—	4	8	no	—
463	C₂×C₄×C₁₃	—	4	4	no	—
464	C₂×C₄×C₁₃	—	4	8	no	—
465	C₂×C₄×C₁₃	—	4	8	no	—
466	C₂×C₄×C₁₃	—	4	4	no	—
467	C₂×C₄×C₁₃	—	4	16	no	—
468	C₂×C₄×C₁₃	—	4	8	no	—
469	C₂×C₄×C₁₃	—	4	8	no	—
470	C₂×C₄×C₁₃	—	4	8	no	—
471	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
472	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
473	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
474	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
475	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
476	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
477	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
478	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
479	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
480	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
481	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
483	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
485	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	#562	C₂²×C₁₃	1	16	yes	complemented
487	H(3,𝔽₄)	C₂²×C₁₃	1	8	yes	complemented
488	#560	C₂²×C₁₃	1	16	yes	complemented
489	#560	C₂²×C₁₃	1	8	yes	complemented
490	#560	C₂²×C₁₃	1	16	yes	complemented
491	#559	C₂²×C₁₃	1	8	yes	complemented
492	#559	C₂²×C₁₃	1	8	yes	complemented
493	#556	C₂²×C₁₃	1	8	yes	complemented
494	#553	C₂²×C₁₃	1	16	yes	complemented
495	#551	C₂²×C₁₃	1	16	yes	complemented
496	#551	C₂²×C₁₃	1	8	yes	complemented
497	#550	C₂²×C₁₃	1	8	yes	complemented
498	#550	C₂²×C₁₃	1	8	yes	complemented
499	#550	C₂²×C₁₃	1	8	yes	complemented
500	#548	C₂²×C₁₃	1	8	yes	complemented
501	#548	C₂²×C₁₃	1	8	yes	complemented
502	#547	C₂²×C₁₃	1	8	yes	complemented
503	#546	C₂²×C₁₃	1	8	yes	complemented
504	#546	C₂²×C₁₃	1	8	yes	complemented
505	#546	C₂²×C₁₃	1	16	yes	complemented
506	#546	C₂²×C₁₃	1	16	yes	complemented
507	#546	C₂²×C₁₃	1	16	yes	complemented
508	#546	C₂²×C₁₃	1	8	yes	complemented
509	#546	C₂²×C₁₃	1	16	yes	complemented
510	#546	C₂²×C₁₃	1	8	yes	complemented
511	D₄²	C₂²×C₁₃	1	8	yes	complemented
512	D₄²	C₂²×C₁₃	1	8	yes	complemented
513	D₄²	C₂²×C₁₃	1	16	yes	complemented
514	D₄²	C₂²×C₁₃	1	8	yes	complemented
515	D₄²	C₂²×C₁₃	1	8	yes	complemented
516	#542	C₂²×C₁₃	1	4	yes	complemented
517	#542	C₂²×C₁₃	1	4	yes	complemented
518	#542	C₂²×C₁₃	1	8	yes	complemented
519	#541	C₂²×C₁₃	1	4	yes	complemented
520	#540	C₂²×C₁₃	1	4	yes	complemented
521	#540	C₂²×C₁₃	1	8	yes	complemented
522	#540	C₂²×C₁₃	1	16	yes	complemented
523	#539	C₂²×C₁₃	1	8	yes	complemented
524	#539	C₂²×C₁₃	1	8	yes	complemented
525	#538	C₂²×C₁₃	1	8	yes	complemented
526	#538	C₂²×C₁₃	1	16	yes	complemented
527	#538	C₂²×C₁₃	1	16	yes	complemented
528	#538	C₂²×C₁₃	1	16	yes	complemented
529	#538	C₂²×C₁₃	1	8	yes	complemented
530	#537	C₂²×C₁₃	1	8	yes	complemented
531	#536	C₂²×C₁₃	1	2	yes	complemented
532	#536	C₂²×C₁₃	1	4	yes	complemented
533	#535	C₂²×C₁₃	1	2	yes	—
534	#535	C₂²×C₁₃	1	8	yes	complemented
535	#535	C₂²×C₁₃	1	8	yes	complemented
536	#535	C₂²×C₁₃	1	2	yes	complemented
537	#535	C₂²×C₁₃	1	4	yes	complemented
538	#535	C₂²×C₁₃	1	2	yes	complemented
539	#535	C₂²×C₁₃	1	16	yes	complemented
540	#535	C₂²×C₁₃	1	4	yes	complemented
541	#535	C₂²×C₁₃	1	4	yes	complemented
542	#535	C₂²×C₁₃	1	4	yes	complemented
543	#534	C₂²×C₁₃	1	8	yes	complemented
544	#534	C₂²×C₁₃	1	4	yes	complemented
545	#534	C₂²×C₁₃	1	16	yes	complemented
546	#534	C₂²×C₁₃	1	8	yes	complemented
547	#533	C₂²×C₁₃	1	2	yes	complemented
548	#532	C₂²×C₁₃	1	2	yes	complemented
549	#532	C₂²×C₁₃	1	8	yes	complemented
550	#532	C₂²×C₁₃	1	4	yes	complemented
551	#532	C₂²×C₁₃	1	4	yes	complemented
552	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
553	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
554	#529	C₂²×C₁₃	1	8	yes	complemented
555	#529	C₂²×C₁₃	1	8	yes	complemented
556	#529	C₂²×C₁₃	1	8	yes	complemented
557	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
558	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
559	#525	C₂²×C₁₃	1	2	yes	complemented
560	#525	C₂²×C₁₃	1	2	yes	complemented
561	#525	C₂²×C₁₃	1	4	yes	complemented
562	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
563	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
564	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
565	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
566	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
567	#518	C₂²×C₁₃	1	2	yes	complemented
568	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
569	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
570	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
571	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
572	C₂²×C₁₃	—	2	2	no	—
573	C₂²×C₁₃	—	2	2	no	—
574	C₂²×C₁₃	—	2	4	no	—
575	C₂²×C₁₃	—	2	4	no	—
576	C₂²×C₁₃	—	2	4	no	—
577	C₂²×C₁₃	—	2	8	no	—
578	C₂²×C₁₃	—	2	8	no	—
579	C₂²×C₁₃	—	2	8	no	—
580	C₂²×C₁₃	—	2	16	no	—
581	C₂²×C₁₃	—	2	8	no	—
582	C₂²×C₁₃	—	2	4	no	—
583	C₂²×C₁₃	—	4	4	no	—
584	C₂²×C₁₃	—	8	4	no	—
585	C₂²×C₁₃	—	8	8	no	—
586	C₂²×C₁₃	—	8	16	no	—
587	C₂²×C₁₃	—	16	8	no	—
588	C₂²×C₁₃	—	16	4	no	—
589	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
590	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
591	C₄×C₁₃	—	2	2	no	—
592	C₄×C₁₃	—	2	4	no	—
593	C₄×C₁₃	—	2	4	no	—
594	C₄×C₁₃	—	2	4	no	—
595	C₄×C₁₃	—	2	8	no	—
596	C₄×C₁₃	—	2	4	no	—
597	C₄×C₁₃	—	2	8	no	—
598	C₄×C₁₃	—	2	4	no	—
599	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
600	C₂⁵	C₂³×C₁₃	1	2	yes	—
601	2₋¹⁺⁴	—	4	4	no	—
602	H(5,𝔽₂)	—	4	8	no	—
603	H(5,𝔽₂)	—	4	4	no	—
604	C₂×#41	—	4	4	no	—
605	C₂×#41	C₂³×C₁₃	1	2	yes	—
606	C₂×#41	C₂³×C₁₃	1	2	yes	—
607	C₂×#41	C₂³×C₁₃	1	4	yes	—
608	C₂×#41	C₂³×C₁₃	1	4	yes	—
609	C₂×#41	C₂³×C₁₃	1	4	yes	—
610	C₂×#41	C₂³×C₁₃	1	8	yes	—
611	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
612	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
613	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
614	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
616	C₂²×D₄	—	4	4	no	—
617	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
618	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
619	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
620	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
621	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
622	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
623	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
624	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
625	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
626	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
627	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
628	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
629	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
630	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
632	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
633	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
634	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
635	#127	C₂³×C₁₃	1	4	yes	—
636	#127	C₂³×C₁₃	1	4	yes	—
637	#127	C₂³×C₁₃	1	4	yes	—
638	#127	C₂³×C₁₃	1	8	yes	—
639	#127	C₂³×C₁₃	1	4	yes	—
640	#127	C₂³×C₁₃	1	8	yes	—
641	#127	C₂³×C₁₃	1	2	yes	complemented
642	#127	C₂³×C₁₃	1	4	yes	complemented
643	#127	C₂³×C₁₃	1	16	yes	complemented
644	#126	C₂³×C₁₃	1	8	yes	—
645	#126	C₂³×C₁₃	1	8	yes	—
646	#126	C₂³×C₁₃	1	8	yes	complemented
647	#126	C₂³×C₁₃	1	16	yes	complemented
648	#126	C₂³×C₁₃	1	8	yes	complemented
649	#126	C₂³×C₁₃	1	16	yes	complemented
650	#125	C₂³×C₁₃	1	4	yes	complemented
651	#125	C₂³×C₁₃	1	8	yes	complemented
652	#125	C₂³×C₁₃	1	8	yes	complemented
653	#124	C₂³×C₁₃	1	4	yes	—
654	#124	C₂³×C₁₃	1	4	yes	—
655	#124	C₂³×C₁₃	1	8	yes	—
656	#124	C₂³×C₁₃	1	4	yes	—
657	#124	C₂³×C₁₃	1	8	yes	—
658	#124	C₂³×C₁₃	1	8	yes	—
659	#124	C₂³×C₁₃	1	4	yes	—
660	#124	C₂³×C₁₃	1	8	yes	—
661	#124	C₂³×C₁₃	1	2	yes	complemented
662	#124	C₂³×C₁₃	1	4	yes	complemented
663	#124	C₂³×C₁₃	1	16	yes	complemented
664	#124	C₂³×C₁₃	1	2	yes	complemented
665	#124	C₂³×C₁₃	1	4	yes	complemented
666	#124	C₂³×C₁₃	1	16	yes	complemented
667	#124	C₂³×C₁₃	1	16	yes	complemented
668	#123	C₂³×C₁₃	1	4	yes	—
669	#123	C₂³×C₁₃	1	8	yes	—
670	#123	C₂³×C₁₃	1	4	yes	—
671	#123	C₂³×C₁₃	1	8	yes	—
672	#123	C₂³×C₁₃	1	8	yes	—
673	#123	C₂³×C₁₃	1	8	yes	—
674	#123	C₂³×C₁₃	1	16	yes	—
675	#123	C₂³×C₁₃	1	16	yes	complemented
676	#123	C₂³×C₁₃	1	8	yes	complemented
677	#123	C₂³×C₁₃	1	16	yes	complemented
678	#123	C₂³×C₁₃	1	8	yes	complemented
679	#123	C₂³×C₁₃	1	16	yes	complemented
680	#123	C₂³×C₁₃	1	16	yes	complemented
681	#123	C₂³×C₁₃	1	16	yes	complemented
682	#123	C₂³×C₁₃	1	16	yes	complemented
683	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
684	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
685	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
687	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
688	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
689	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
690	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
691	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
692	#121	C₂³×C₁₃	1	8	yes	—
693	#121	C₂³×C₁₃	1	8	yes	—
694	#121	C₂³×C₁₃	1	16	yes	—
695	#121	C₂³×C₁₃	1	4	yes	—
696	#121	C₂³×C₁₃	1	4	yes	—
697	#121	C₂³×C₁₃	1	8	yes	—
698	#121	C₂³×C₁₃	1	8	yes	—
699	#121	C₂³×C₁₃	1	8	yes	—
700	#121	C₂³×C₁₃	1	8	yes	—
701	#121	C₂³×C₁₃	1	8	yes	—
702	#121	C₂³×C₁₃	1	16	yes	—
703	#121	C₂³×C₁₃	1	16	yes	—
704	#121	C₂³×C₁₃	1	16	yes	—
705	#121	C₂³×C₁₃	1	16	yes	—
706	#121	C₂³×C₁₃	1	8	yes	complemented
707	#121	C₂³×C₁₃	1	16	yes	complemented
708	#121	C₂³×C₁₃	1	16	yes	complemented
709	#121	C₂³×C₁₃	1	8	yes	complemented
710	#121	C₂³×C₁₃	1	16	yes	complemented
711	#121	C₂³×C₁₃	1	16	yes	complemented
712	#121	C₂³×C₁₃	1	16	yes	complemented
713	#121	C₂³×C₁₃	1	16	yes	complemented
714	#121	C₂³×C₁₃	1	16	yes	complemented
715	#121	C₂³×C₁₃	1	16	yes	complemented
716	#120	C₂³×C₁₃	1	4	yes	—
717	#120	C₂³×C₁₃	1	4	yes	—
718	#120	C₂³×C₁₃	1	8	yes	—
719	#120	C₂³×C₁₃	1	16	yes	—
720	#120	C₂³×C₁₃	1	8	yes	—
721	#120	C₂³×C₁₃	1	16	yes	—
722	#120	C₂³×C₁₃	1	8	yes	—
723	#120	C₂³×C₁₃	1	8	yes	—
724	#120	C₂³×C₁₃	1	16	yes	—
725	#120	C₂³×C₁₃	1	8	yes	—
726	#120	C₂³×C₁₃	1	8	yes	—
727	#120	C₂³×C₁₃	1	16	yes	—
728	#120	C₂³×C₁₃	1	16	yes	complemented
729	#120	C₂³×C₁₃	1	16	yes	complemented
730	#120	C₂³×C₁₃	1	16	yes	complemented
731	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
732	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
733	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
734	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
735	C₄×D₄	C₂³×C₁₃	1	8	yes	—
736	C₄×D₄	C₂³×C₁₃	1	8	yes	—
737	C₄×D₄	C₂³×C₁₃	1	8	yes	—
738	C₄×D₄	C₂³×C₁₃	1	8	yes	—
739	C₄×D₄	C₂³×C₁₃	1	8	yes	—
740	C₄×D₄	C₂³×C₁₃	1	8	yes	—
741	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
742	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
743	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
744	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
745	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
746	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
747	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
748	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
749	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
750	#117	C₂³×C₁₃	1	4	yes	—
751	#117	C₂³×C₁₃	1	4	yes	—
752	#117	C₂³×C₁₃	1	2	yes	—
753	#117	C₂³×C₁₃	1	2	yes	—
754	#117	C₂³×C₁₃	1	4	yes	—
755	#117	C₂³×C₁₃	1	4	yes	complemented
756	#117	C₂³×C₁₃	1	4	yes	complemented
757	#117	C₂³×C₁₃	1	16	yes	complemented
758	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
760	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
766	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
767	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
768	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
769	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
770	C₂×C₁₃	—	2	2	no	—
771	C₂×C₁₃	—	4	2	no	—
772	C₂×C₁₃	—	4	8	no	—
773	C₂×C₁₃	—	4	4	no	—
774	C₂×C₁₃	—	4	4	no	—
775	C₂×C₁₃	—	4	4	no	—
776	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
777	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
778	C₂⁴	—	4	4	no	—
779	C₂⁴	—	8	4	no	—
780	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
781	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
783	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
784	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
785	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
786	#41	—	2	8	no	—
787	#41	—	2	8	no	—
788	#41	—	4	8	no	—
789	#41	—	4	16	no	—
790	#41	—	4	8	no	—
791	#41	—	4	8	no	—
792	#41	—	4	8	no	—
793	#41	—	4	8	no	—
794	#41	—	8	16	no	—
795	C₂×Q₈	—	2	4	no	—
796	C₂×Q₈	—	4	8	no	—
797	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
798	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
799	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
800	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
801	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
802	C₂×D₄	—	2	8	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	4	16	no	—
805	C₂×D₄	—	4	8	no	—
806	C₂×D₄	—	4	8	no	—
807	C₂×D₄	—	4	8	no	—
808	C₂×D₄	—	4	4	no	—
809	C₂×D₄	—	4	4	no	—
810	C₂×D₄	—	4	8	no	—
811	C₂×D₄	—	4	16	no	—
812	C₂×D₄	—	8	8	no	—
813	C₂×D₄	—	8	16	no	—
814	C₂×D₄	—	8	16	no	—
815	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
816	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
817	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
818	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
819	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
820	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
821	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
822	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
823	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
824	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
825	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
826	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
827	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
828	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
829	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
830	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
831	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
832	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
833	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
834	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
835	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
836	C₂²×C₄	—	2	4	no	—
837	C₂²×C₄	—	4	4	no	—
838	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
839	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
843	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
844	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
845	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
847	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
848	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
849	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
850	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
851	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
852	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
855	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
857	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
858	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
859	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
860	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
861	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
862	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
865	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
866	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
868	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
869	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
870	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
871	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
872	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
873	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
874	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
875	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
876	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
877	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
878	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
879	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
880	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
883	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
884	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
885	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
887	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
888	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
889	C₄²	C₂⁴×C₁₃	1	2	yes	—
890	C₄²	C₂⁴×C₁₃	1	2	yes	—
891	C₄²	C₂⁴×C₁₃	1	4	yes	—
892	C₄²	C₂⁴×C₁₃	1	4	yes	—
893	C₄²	C₂⁴×C₁₃	1	4	yes	—
894	C₄²	C₂⁴×C₁₃	1	8	yes	—
895	C₄²	C₂⁴×C₁₃	1	8	yes	—
896	C₄²	C₂⁴×C₁₃	1	8	yes	—
897	C₁₃	#62876	1	1	yes	characteristic, direct product factor, Sylow
898	C₂³	—	2	2	no	—
899	C₂³	—	2	4	no	—
900	C₂³	—	2	8	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	8	no	—
903	C₂³	—	4	4	no	—
904	C₂³	—	4	8	no	—
905	C₂³	—	4	16	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	4	16	no	—
909	C₂³	—	4	8	no	—
910	C₂³	—	8	16	no	—
911	C₂³	C₂⁵×C₁₃	1	2	yes	—
912	C₂³	C₂⁵×C₁₃	1	4	yes	—
913	C₂³	C₂⁵×C₁₃	1	8	yes	—
914	C₂³	C₂⁵×C₁₃	1	4	yes	—
915	C₂³	C₂⁵×C₁₃	1	4	yes	—
916	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
917	Q₈	—	2	8	no	—
918	Q₈	—	2	4	no	—
919	Q₈	—	2	4	no	—
920	Q₈	—	4	4	no	—
921	Q₈	—	4	8	no	—
922	D₄	—	2	8	no	—
923	D₄	—	2	8	no	—
924	D₄	—	2	8	no	—
925	D₄	—	2	8	no	—
926	D₄	—	2	8	no	—
927	D₄	—	2	4	no	—
928	D₄	—	2	4	no	—
929	D₄	—	4	8	no	—
930	D₄	—	4	8	no	—
931	D₄	—	4	8	no	—
932	D₄	—	4	8	no	—
933	D₄	—	4	8	no	—
934	D₄	—	4	8	no	—
935	D₄	—	4	16	no	—
936	D₄	—	4	8	no	—
937	D₄	—	4	8	no	—
938	D₄	—	4	16	no	—
939	D₄	—	4	16	no	—
940	D₄	—	4	16	no	—
941	D₄	—	4	16	no	—
942	D₄	—	4	4	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	4	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	2	8	no	—
948	C₂×C₄	—	4	8	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	16	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
958	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
959	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
960	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
961	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
962	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
963	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
964	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
965	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
966	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	4	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	8	no	—
973	C₂²	—	2	8	no	—
974	C₂²	—	2	8	no	—
975	C₂²	—	2	16	no	—
976	C₂²	—	2	8	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	4	4	no	—
979	C₂²	—	8	4	no	—
980	C₂²	—	8	8	no	—
981	C₂²	—	8	16	no	—
982	C₂²	—	16	8	no	—
983	C₂²	—	16	4	no	—
984	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
985	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	4	no	—
989	C₄	—	2	4	no	—
990	C₄	—	2	8	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	8	no	—
993	C₄	—	2	4	no	—
994	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
995	C₂	—	2	2	no	—
996	C₂	—	4	2	no	—
997	C₂	—	4	8	no	—
998	C₂	—	4	4	no	—
999	C₂	—	4	4	no	—
1000	C₂	—	4	4	no	—
1001	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1002	C₂	C₁₃×H(7,𝔽₂)	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3562	C₂	semidirect
2. C₁₃×#3558	C₂	semidirect
3. C₁₃×#3546	C₂	semidirect
4. C₁₃×#3543	C₂	semidirect
5. C₁₃×#3534	C₂	semidirect
6. C₁₃×#3532	C₂	semidirect
7. C₁₃×#3510	C₂	semidirect
8. C₁₃×#3508	C₂	semidirect
9. C₁₃×#3500	C₂	semidirect
10. C₁₃×#3498	C₂	semidirect
11. C₁₃×#3487	C₂	semidirect
12. C₁₃×#3485	C₂	semidirect
13. C₁₃×#3484	C₂	semidirect
14. C₁₃×#3455	C₂	semidirect
15. C₂×C₁₃×#535	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂³×D₄×C₁₃	C₂²	semidirect
21. C₁₃×#562	C₂²	semidirect
22. C₁₃×H(3,𝔽₄)	C₂²	semidirect
23. C₁₃×#560	C₂²	semidirect
24. C₁₃×#560	C₂²	semidirect
25. C₁₃×#560	C₂²	semidirect
26. C₁₃×#559	C₂²	semidirect
27. C₁₃×#559	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#551	C₂²	semidirect
31. C₁₃×#551	C₂²	semidirect
32. C₁₃×#550	C₂²	semidirect
33. C₁₃×#550	C₂²	semidirect
34. C₁₃×#550	C₂²	semidirect
35. C₁₃×#548	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
37. C₁₃×#547	C₂²	semidirect
38. C₁₃×#546	C₂²	semidirect
39. C₁₃×#546	C₂²	semidirect
40. C₁₃×#546	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
43. C₁₃×#546	C₂²	semidirect
44. C₁₃×#546	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. D₄²×C₁₃	C₂²	semidirect
47. D₄²×C₁₃	C₂²	semidirect
48. D₄²×C₁₃	C₂²	semidirect
49. D₄²×C₁₃	C₂²	semidirect
50. D₄²×C₁₃	C₂²	semidirect
51. C₁₃×#542	C₂²	semidirect
52. C₁₃×#542	C₂²	semidirect
53. C₁₃×#542	C₂²	semidirect
54. C₁₃×#541	C₂²	semidirect
55. C₁₃×#540	C₂²	semidirect
56. C₁₃×#540	C₂²	semidirect
57. C₁₃×#540	C₂²	semidirect
58. C₁₃×#539	C₂²	semidirect
59. C₁₃×#539	C₂²	semidirect
60. C₁₃×#538	C₂²	semidirect
61. C₁₃×#538	C₂²	semidirect
62. C₁₃×#538	C₂²	semidirect
63. C₁₃×#538	C₂²	semidirect
64. C₁₃×#538	C₂²	semidirect
65. C₁₃×#537	C₂²	semidirect
66. C₁₃×#536	C₂²	semidirect
67. C₁₃×#536	C₂²	semidirect
69. C₁₃×#535	C₂²	semidirect
70. C₁₃×#535	C₂²	semidirect
71. C₁₃×#535	C₂²	semidirect
72. C₁₃×#535	C₂²	semidirect
73. C₁₃×#535	C₂²	semidirect
74. C₁₃×#535	C₂²	semidirect
75. C₁₃×#535	C₂²	semidirect
76. C₁₃×#535	C₂²	semidirect
77. C₁₃×#535	C₂²	semidirect
78. C₁₃×#534	C₂²	semidirect
79. C₁₃×#534	C₂²	semidirect
80. C₁₃×#534	C₂²	semidirect
81. C₁₃×#534	C₂²	semidirect
82. C₁₃×#533	C₂²	semidirect
83. C₁₃×#532	C₂²	semidirect
84. C₁₃×#532	C₂²	semidirect
85. C₁₃×#532	C₂²	semidirect
86. C₁₃×#532	C₂²	semidirect
87. C₂×C₁₃×#127	C₂²	semidirect
88. C₂×C₁₃×#127	C₂²	semidirect
89. C₁₃×#529	C₂²	semidirect
90. C₁₃×#529	C₂²	semidirect
91. C₁₃×#529	C₂²	semidirect
92. C₂×C₁₃×#124	C₂²	semidirect
93. C₂×C₁₃×#124	C₂²	semidirect
94. C₁₃×#525	C₂²	semidirect
95. C₁₃×#525	C₂²	semidirect
96. C₁₃×#525	C₂²	semidirect
97. C₂×C₁₃×#123	C₂²	semidirect
98. C₂×C₁₃×#121	C₂²	semidirect
99. C₂×C₁₃×#120	C₂²	semidirect
100. C₂×C₁₃×#120	C₂²	semidirect
101. C₁₃×#519	C₂²	semidirect
102. C₁₃×#518	C₂²	semidirect
103. C₁₃×#518	C₂²	semidirect
104. C₄×C₁₃×#41	C₂²	semidirect
105. C₄×C₁₃×#41	C₂²	semidirect
106. C₂×C₁₃×#117	C₂²	semidirect
118. C₂×C₁₃×#41	C₂³	semidirect
119. C₂×C₁₃×#41	C₂³	semidirect
120. C₂×C₁₃×#41	C₂³	semidirect
122. C₂²×Q₈×C₁₃	C₂³	semidirect
135. C₂²×D₄×C₁₃	C₂³	semidirect
136. C₂²×D₄×C₁₃	C₂³	semidirect
139. C₁₃×C₄⋊Q₈	C₂³	semidirect
140. C₁₃×C₄⋊Q₈	C₂³	semidirect
141. C₁₃×C₄⋊Q₈	C₂³	semidirect
148. C₁₃×#127	C₂³	semidirect
149. C₁₃×#127	C₂³	semidirect
150. C₁₃×#127	C₂³	semidirect
153. C₁₃×#126	C₂³	semidirect
154. C₁₃×#126	C₂³	semidirect
155. C₁₃×#126	C₂³	semidirect
156. C₁₃×#126	C₂³	semidirect
157. C₁₃×#125	C₂³	semidirect
158. C₁₃×#125	C₂³	semidirect
159. C₁₃×#125	C₂³	semidirect
168. C₁₃×#124	C₂³	semidirect
169. C₁₃×#124	C₂³	semidirect
170. C₁₃×#124	C₂³	semidirect
171. C₁₃×#124	C₂³	semidirect
172. C₁₃×#124	C₂³	semidirect
173. C₁₃×#124	C₂³	semidirect
174. C₁₃×#124	C₂³	semidirect
182. C₁₃×#123	C₂³	semidirect
183. C₁₃×#123	C₂³	semidirect
184. C₁₃×#123	C₂³	semidirect
185. C₁₃×#123	C₂³	semidirect
186. C₁₃×#123	C₂³	semidirect
187. C₁₃×#123	C₂³	semidirect
188. C₁₃×#123	C₂³	semidirect
189. C₁₃×#123	C₂³	semidirect
193. C₁₃×C₂²⋊Q₈	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
213. C₁₃×#121	C₂³	semidirect
214. C₁₃×#121	C₂³	semidirect
215. C₁₃×#121	C₂³	semidirect
216. C₁₃×#121	C₂³	semidirect
217. C₁₃×#121	C₂³	semidirect
218. C₁₃×#121	C₂³	semidirect
219. C₁₃×#121	C₂³	semidirect
220. C₁₃×#121	C₂³	semidirect
221. C₁₃×#121	C₂³	semidirect
222. C₁₃×#121	C₂³	semidirect
235. C₁₃×#120	C₂³	semidirect
236. C₁₃×#120	C₂³	semidirect
237. C₁₃×#120	C₂³	semidirect
238. C₄×Q₈×C₁₃	C₂³	semidirect
239. C₄×Q₈×C₁₃	C₂³	semidirect
240. C₄×Q₈×C₁₃	C₂³	semidirect
241. C₄×Q₈×C₁₃	C₂³	semidirect
248. C₄×D₄×C₁₃	C₂³	semidirect
249. C₄×D₄×C₁₃	C₂³	semidirect
250. C₄×D₄×C₁₃	C₂³	semidirect
251. C₄×D₄×C₁₃	C₂³	semidirect
252. C₄×D₄×C₁₃	C₂³	semidirect
253. C₄×D₄×C₁₃	C₂³	semidirect
254. C₄×D₄×C₁₃	C₂³	semidirect
255. C₄×D₄×C₁₃	C₂³	semidirect
256. C₄×D₄×C₁₃	C₂³	semidirect
262. C₁₃×#117	C₂³	semidirect
263. C₁₃×#117	C₂³	semidirect
264. C₁₃×#117	C₂³	semidirect
266. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
272. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
273. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
275. C₂×C₄²×C₁₃	C₂³	semidirect
276. C₂×C₄²×C₁₃	C₂³	semidirect
277. #62876	C₁₃	direct (N × H)
397. #3562	C₂×C₁₃	semidirect
398. #3558	C₂×C₁₃	semidirect
399. #3546	C₂×C₁₃	semidirect
400. #3543	C₂×C₁₃	semidirect
401. #3534	C₂×C₁₃	semidirect
402. #3532	C₂×C₁₃	semidirect
403. #3510	C₂×C₁₃	semidirect
404. #3508	C₂×C₁₃	semidirect
405. #3500	C₂×C₁₃	semidirect
406. #3498	C₂×C₁₃	semidirect
407. #3487	C₂×C₁₃	semidirect
408. #3485	C₂×C₁₃	semidirect
409. #3484	C₂×C₁₃	semidirect
410. #3455	C₂×C₁₃	semidirect
411. C₂×#535	C₂×C₁₃	semidirect
481. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
482. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
483. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
484. C₂²×#41	C₂²×C₁₃	semidirect
485. C₂³×D₄	C₂²×C₁₃	semidirect
486. #562	C₂²×C₁₃	semidirect
487. H(3,𝔽₄)	C₂²×C₁₃	semidirect
488. #560	C₂²×C₁₃	semidirect
489. #560	C₂²×C₁₃	semidirect
490. #560	C₂²×C₁₃	semidirect
491. #559	C₂²×C₁₃	semidirect
492. #559	C₂²×C₁₃	semidirect
493. #556	C₂²×C₁₃	semidirect
494. #553	C₂²×C₁₃	semidirect
495. #551	C₂²×C₁₃	semidirect
496. #551	C₂²×C₁₃	semidirect
497. #550	C₂²×C₁₃	semidirect
498. #550	C₂²×C₁₃	semidirect
499. #550	C₂²×C₁₃	semidirect
500. #548	C₂²×C₁₃	semidirect
501. #548	C₂²×C₁₃	semidirect
502. #547	C₂²×C₁₃	semidirect
503. #546	C₂²×C₁₃	semidirect
504. #546	C₂²×C₁₃	semidirect
505. #546	C₂²×C₁₃	semidirect
506. #546	C₂²×C₁₃	semidirect
507. #546	C₂²×C₁₃	semidirect
508. #546	C₂²×C₁₃	semidirect
509. #546	C₂²×C₁₃	semidirect
510. #546	C₂²×C₁₃	semidirect
511. D₄²	C₂²×C₁₃	semidirect
512. D₄²	C₂²×C₁₃	semidirect
513. D₄²	C₂²×C₁₃	semidirect
514. D₄²	C₂²×C₁₃	semidirect
515. D₄²	C₂²×C₁₃	semidirect
516. #542	C₂²×C₁₃	semidirect
517. #542	C₂²×C₁₃	semidirect
518. #542	C₂²×C₁₃	semidirect
519. #541	C₂²×C₁₃	semidirect
520. #540	C₂²×C₁₃	semidirect
521. #540	C₂²×C₁₃	semidirect
522. #540	C₂²×C₁₃	semidirect
523. #539	C₂²×C₁₃	semidirect
524. #539	C₂²×C₁₃	semidirect
525. #538	C₂²×C₁₃	semidirect
526. #538	C₂²×C₁₃	semidirect
527. #538	C₂²×C₁₃	semidirect
528. #538	C₂²×C₁₃	semidirect
529. #538	C₂²×C₁₃	semidirect
530. #537	C₂²×C₁₃	semidirect
531. #536	C₂²×C₁₃	semidirect
532. #536	C₂²×C₁₃	semidirect
534. #535	C₂²×C₁₃	semidirect
535. #535	C₂²×C₁₃	semidirect
536. #535	C₂²×C₁₃	semidirect
537. #535	C₂²×C₁₃	semidirect
538. #535	C₂²×C₁₃	semidirect
539. #535	C₂²×C₁₃	semidirect
540. #535	C₂²×C₁₃	semidirect
541. #535	C₂²×C₁₃	semidirect
542. #535	C₂²×C₁₃	semidirect
543. #534	C₂²×C₁₃	semidirect
544. #534	C₂²×C₁₃	semidirect
545. #534	C₂²×C₁₃	semidirect
546. #534	C₂²×C₁₃	semidirect
547. #533	C₂²×C₁₃	semidirect
548. #532	C₂²×C₁₃	semidirect
549. #532	C₂²×C₁₃	semidirect
550. #532	C₂²×C₁₃	semidirect
551. #532	C₂²×C₁₃	semidirect
552. C₂×#127	C₂²×C₁₃	semidirect
553. C₂×#127	C₂²×C₁₃	semidirect
554. #529	C₂²×C₁₃	semidirect
555. #529	C₂²×C₁₃	semidirect
556. #529	C₂²×C₁₃	semidirect
557. C₂×#124	C₂²×C₁₃	semidirect
558. C₂×#124	C₂²×C₁₃	semidirect
559. #525	C₂²×C₁₃	semidirect
560. #525	C₂²×C₁₃	semidirect
561. #525	C₂²×C₁₃	semidirect
562. C₂×#123	C₂²×C₁₃	semidirect
563. C₂×#121	C₂²×C₁₃	semidirect
564. C₂×#120	C₂²×C₁₃	semidirect
565. C₂×#120	C₂²×C₁₃	semidirect
566. #519	C₂²×C₁₃	semidirect
567. #518	C₂²×C₁₃	semidirect
568. #518	C₂²×C₁₃	semidirect
569. C₄×#41	C₂²×C₁₃	semidirect
570. C₄×#41	C₂²×C₁₃	semidirect
571. C₂×#117	C₂²×C₁₃	semidirect
611. C₂×#41	C₂³×C₁₃	semidirect
612. C₂×#41	C₂³×C₁₃	semidirect
613. C₂×#41	C₂³×C₁₃	semidirect
615. C₂²×Q₈	C₂³×C₁₃	semidirect
628. C₂²×D₄	C₂³×C₁₃	semidirect
629. C₂²×D₄	C₂³×C₁₃	semidirect
632. C₄⋊Q₈	C₂³×C₁₃	semidirect
633. C₄⋊Q₈	C₂³×C₁₃	semidirect
634. C₄⋊Q₈	C₂³×C₁₃	semidirect
641. #127	C₂³×C₁₃	semidirect
642. #127	C₂³×C₁₃	semidirect
643. #127	C₂³×C₁₃	semidirect
646. #126	C₂³×C₁₃	semidirect
647. #126	C₂³×C₁₃	semidirect
648. #126	C₂³×C₁₃	semidirect
649. #126	C₂³×C₁₃	semidirect
650. #125	C₂³×C₁₃	semidirect
651. #125	C₂³×C₁₃	semidirect
652. #125	C₂³×C₁₃	semidirect
661. #124	C₂³×C₁₃	semidirect
662. #124	C₂³×C₁₃	semidirect
663. #124	C₂³×C₁₃	semidirect
664. #124	C₂³×C₁₃	semidirect
665. #124	C₂³×C₁₃	semidirect
666. #124	C₂³×C₁₃	semidirect
667. #124	C₂³×C₁₃	semidirect
675. #123	C₂³×C₁₃	semidirect
676. #123	C₂³×C₁₃	semidirect
677. #123	C₂³×C₁₃	semidirect
678. #123	C₂³×C₁₃	semidirect
679. #123	C₂³×C₁₃	semidirect
680. #123	C₂³×C₁₃	semidirect
681. #123	C₂³×C₁₃	semidirect
682. #123	C₂³×C₁₃	semidirect
686. C₂²⋊Q₈	C₂³×C₁₃	semidirect
687. C₂²⋊Q₈	C₂³×C₁₃	semidirect
688. C₂²⋊Q₈	C₂³×C₁₃	semidirect
689. C₂²⋊Q₈	C₂³×C₁₃	semidirect
690. C₂²⋊Q₈	C₂³×C₁₃	semidirect
691. C₂²⋊Q₈	C₂³×C₁₃	semidirect
706. #121	C₂³×C₁₃	semidirect
707. #121	C₂³×C₁₃	semidirect
708. #121	C₂³×C₁₃	semidirect
709. #121	C₂³×C₁₃	semidirect
710. #121	C₂³×C₁₃	semidirect
711. #121	C₂³×C₁₃	semidirect
712. #121	C₂³×C₁₃	semidirect
713. #121	C₂³×C₁₃	semidirect
714. #121	C₂³×C₁₃	semidirect
715. #121	C₂³×C₁₃	semidirect
728. #120	C₂³×C₁₃	semidirect
729. #120	C₂³×C₁₃	semidirect
730. #120	C₂³×C₁₃	semidirect
731. C₄×Q₈	C₂³×C₁₃	semidirect
732. C₄×Q₈	C₂³×C₁₃	semidirect
733. C₄×Q₈	C₂³×C₁₃	semidirect
734. C₄×Q₈	C₂³×C₁₃	semidirect
741. C₄×D₄	C₂³×C₁₃	semidirect
742. C₄×D₄	C₂³×C₁₃	semidirect
743. C₄×D₄	C₂³×C₁₃	semidirect
744. C₄×D₄	C₂³×C₁₃	semidirect
745. C₄×D₄	C₂³×C₁₃	semidirect
746. C₄×D₄	C₂³×C₁₃	semidirect
747. C₄×D₄	C₂³×C₁₃	semidirect
748. C₄×D₄	C₂³×C₁₃	semidirect
749. C₄×D₄	C₂³×C₁₃	semidirect
755. #117	C₂³×C₁₃	semidirect
756. #117	C₂³×C₁₃	semidirect
757. #117	C₂³×C₁₃	semidirect
759. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
765. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
766. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
768. C₂×C₄²	C₂³×C₁₃	semidirect
769. C₂×C₄²	C₂³×C₁₃	semidirect
897. C₁₃	#62876	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×#3562	2
C₁₃×#3558	2
C₁₃×#3546	2
C₁₃×#3543	2
C₁₃×#3534	2
C₁₃×#3532	2
C₁₃×#3510	2
C₁₃×#3508	2
C₁₃×#3500	2
C₁₃×#3498	2
C₁₃×#3487	2
C₁₃×#3485	2
C₁₃×#3484	2
C₁₃×#3455	2
C₂×C₁₃×#535	2
#62876	13

Subgroups — C13×#62876 #15749215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62876 #15749215