Subgroups — C₁₃×#62874 #15749213

Order 3328.

7422 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3551	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3549	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3546	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3545	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3543	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3542	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3540	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3537	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3532	C₂	1	8	yes	maximal, complemented
10	C₁₃×#3494	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3493	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3449	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#563	C₂²	1	4	yes	complemented
21	C₁₃×#562	C₂²	1	8	yes	complemented
22	C₁₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
23	C₁₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
24	C₁₃×#560	C₂²	1	16	yes	complemented
25	C₁₃×#560	C₂²	1	8	yes	complemented
26	C₁₃×#560	C₂²	1	8	yes	complemented
27	C₁₃×#560	C₂²	1	8	yes	complemented
28	C₁₃×#559	C₂²	1	4	yes	complemented
29	C₁₃×#556	C₂²	1	8	yes	complemented
30	C₁₃×#555	C₂²	1	8	yes	complemented
31	C₁₃×#555	C₂²	1	8	yes	complemented
32	C₁₃×#555	C₂²	1	8	yes	complemented
33	C₁₃×#553	C₂²	1	8	yes	complemented
34	C₁₃×#553	C₂²	1	8	yes	complemented
35	C₁₃×#553	C₂²	1	8	yes	complemented
36	C₁₃×#552	C₂²	1	8	yes	complemented
37	C₁₃×#551	C₂²	1	16	yes	complemented
38	C₁₃×#551	C₂²	1	8	yes	complemented
39	C₁₃×#551	C₂²	1	8	yes	complemented
40	C₁₃×#550	C₂²	1	8	yes	complemented
41	C₁₃×#550	C₂²	1	8	yes	complemented
42	C₁₃×#548	C₂²	1	8	yes	complemented
43	C₁₃×#547	C₂²	1	8	yes	complemented
44	C₁₃×#546	C₂²	1	8	yes	complemented
45	C₁₃×#546	C₂²	1	8	yes	complemented
46	C₁₃×#546	C₂²	1	16	yes	complemented
47	C₁₃×#546	C₂²	1	16	yes	complemented
48	C₁₃×#546	C₂²	1	16	yes	complemented
49	C₁₃×#546	C₂²	1	8	yes	complemented
50	D₄²×C₁₃	C₂²	1	8	yes	complemented
51	D₄²×C₁₃	C₂²	1	8	yes	complemented
52	D₄²×C₁₃	C₂²	1	16	yes	complemented
53	D₄²×C₁₃	C₂²	1	8	yes	complemented
54	D₄²×C₁₃	C₂²	1	4	yes	complemented
55	D₄²×C₁₃	C₂²	1	8	yes	complemented
56	C₁₃×#544	C₂²	1	2	yes	complemented
57	C₁₃×#542	C₂²	1	8	yes	complemented
58	C₁₃×#542	C₂²	1	16	yes	complemented
59	C₁₃×#540	C₂²	1	8	yes	complemented
60	C₁₃×#540	C₂²	1	16	yes	complemented
61	C₁₃×#538	C₂²	1	8	yes	complemented
62	C₁₃×#538	C₂²	1	16	yes	complemented
63	C₁₃×#538	C₂²	1	16	yes	complemented
64	C₁₃×#538	C₂²	1	16	yes	complemented
65	C₁₃×#537	C₂²	1	2	yes	complemented
66	C₁₃×#537	C₂²	1	4	yes	complemented
67	C₁₃×#537	C₂²	1	4	yes	complemented
68	C₁₃×#537	C₂²	1	8	yes	complemented
69	C₁₃×#536	C₂²	1	4	yes	complemented
70	C₁₃×#536	C₂²	1	2	yes	complemented
71	C₁₃×#536	C₂²	1	2	yes	complemented
72	C₁₃×#535	C₂²	1	4	yes	complemented
73	C₁₃×#535	C₂²	1	4	yes	complemented
74	C₁₃×#535	C₂²	1	4	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×#535	C₂²	1	16	yes	complemented
79	C₁₃×#535	C₂²	1	2	yes	complemented
80	C₁₃×#535	C₂²	1	2	yes	complemented
81	C₁₃×#535	C₂²	1	16	yes	complemented
82	C₁₃×#535	C₂²	1	8	yes	complemented
83	C₁₃×#534	C₂²	1	4	yes	complemented
84	C₁₃×#534	C₂²	1	8	yes	complemented
85	C₁₃×#534	C₂²	1	4	yes	complemented
86	C₁₃×#534	C₂²	1	16	yes	complemented
87	C₁₃×#532	C₂²	1	4	yes	complemented
88	C₁₃×#532	C₂²	1	4	yes	complemented
89	C₁₃×#532	C₂²	1	8	yes	complemented
90	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
91	C₁₃×#529	C₂²	1	8	yes	complemented
92	C₁₃×#529	C₂²	1	8	yes	complemented
93	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
94	C₁₃×#525	C₂²	1	4	yes	complemented
95	C₁₃×#525	C₂²	1	4	yes	complemented
96	C₁₃×#525	C₂²	1	4	yes	complemented
97	C₁₃×#525	C₂²	1	4	yes	complemented
98	C₁₃×#525	C₂²	1	8	yes	complemented
99	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
100	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
101	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
102	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
103	C₁₃×#520	C₂²	1	4	yes	complemented
104	C₁₃×#518	C₂²	1	2	yes	complemented
105	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
107	C₂⁵×C₁₃	C₂³	1	2	yes	—
108	C₁₃×H(5,𝔽₂)	—	4	8	no	—
109	C₂×C₁₃×#41	—	4	4	no	—
110	C₂×C₁₃×#41	—	4	8	no	—
111	C₂×C₁₃×#41	C₂³	1	4	yes	—
112	C₂×C₁₃×#41	C₂³	1	2	yes	—
113	C₂×C₁₃×#41	C₂³	1	2	yes	—
114	C₂×C₁₃×#41	C₂³	1	8	yes	—
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂×C₁₃×#41	C₂³	1	2	yes	—
117	C₂×C₁₃×#41	C₂³	1	4	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	2	yes	complemented
123	C₂²×D₄×C₁₃	—	4	4	no	—
124	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
131	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
132	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
133	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
136	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
140	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
141	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
142	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
143	C₁₃×#127	C₂³	1	8	yes	—
144	C₁₃×#127	C₂³	1	4	yes	—
145	C₁₃×#127	C₂³	1	4	yes	—
146	C₁₃×#127	C₂³	1	4	yes	—
147	C₁₃×#127	C₂³	1	4	yes	—
148	C₁₃×#127	C₂³	1	8	yes	—
149	C₁₃×#127	C₂³	1	16	yes	complemented
150	C₁₃×#126	C₂³	1	16	yes	—
151	C₁₃×#126	C₂³	1	16	yes	complemented
152	C₁₃×#126	C₂³	1	16	yes	complemented
153	C₁₃×#126	C₂³	1	16	yes	complemented
154	C₁₃×#125	C₂³	1	8	yes	complemented
155	C₁₃×#125	C₂³	1	8	yes	complemented
156	C₁₃×#124	C₂³	1	8	yes	—
157	C₁₃×#124	C₂³	1	4	yes	—
158	C₁₃×#124	C₂³	1	4	yes	—
159	C₁₃×#124	C₂³	1	8	yes	—
160	C₁₃×#124	C₂³	1	4	yes	—
161	C₁₃×#124	C₂³	1	4	yes	—
162	C₁₃×#124	C₂³	1	16	yes	—
163	C₁₃×#124	C₂³	1	8	yes	complemented
164	C₁₃×#124	C₂³	1	4	yes	complemented
165	C₁₃×#124	C₂³	1	4	yes	complemented
166	C₁₃×#124	C₂³	1	16	yes	complemented
167	C₁₃×#124	C₂³	1	16	yes	complemented
168	C₁₃×#124	C₂³	1	16	yes	complemented
169	C₁₃×#123	C₂³	1	8	yes	—
170	C₁₃×#123	C₂³	1	4	yes	—
171	C₁₃×#123	C₂³	1	8	yes	—
172	C₁₃×#123	C₂³	1	4	yes	—
173	C₁₃×#123	C₂³	1	16	yes	—
174	C₁₃×#123	C₂³	1	8	yes	—
175	C₁₃×#123	C₂³	1	8	yes	—
176	C₁₃×#123	C₂³	1	4	yes	complemented
177	C₁₃×#123	C₂³	1	4	yes	complemented
178	C₁₃×#123	C₂³	1	16	yes	complemented
179	C₁₃×#123	C₂³	1	16	yes	complemented
180	C₁₃×#123	C₂³	1	16	yes	complemented
181	C₁₃×#123	C₂³	1	16	yes	complemented
182	C₁₃×#123	C₂³	1	16	yes	complemented
183	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
187	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
188	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
190	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
191	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
192	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
193	C₁₃×#121	C₂³	1	8	yes	—
194	C₁₃×#121	C₂³	1	8	yes	—
195	C₁₃×#121	C₂³	1	8	yes	—
196	C₁₃×#121	C₂³	1	8	yes	—
197	C₁₃×#121	C₂³	1	8	yes	—
198	C₁₃×#121	C₂³	1	8	yes	—
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₁₃×#121	C₂³	1	4	yes	—
201	C₁₃×#121	C₂³	1	4	yes	—
202	C₁₃×#121	C₂³	1	8	yes	—
203	C₁₃×#121	C₂³	1	8	yes	—
204	C₁₃×#121	C₂³	1	8	yes	—
205	C₁₃×#121	C₂³	1	8	yes	—
206	C₁₃×#121	C₂³	1	16	yes	—
207	C₁₃×#121	C₂³	1	16	yes	—
208	C₁₃×#121	C₂³	1	16	yes	—
209	C₁₃×#121	C₂³	1	4	yes	complemented
210	C₁₃×#121	C₂³	1	16	yes	complemented
211	C₁₃×#121	C₂³	1	8	yes	complemented
212	C₁₃×#121	C₂³	1	16	yes	complemented
213	C₁₃×#121	C₂³	1	4	yes	complemented
214	C₁₃×#121	C₂³	1	8	yes	complemented
215	C₁₃×#121	C₂³	1	8	yes	complemented
216	C₁₃×#121	C₂³	1	16	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×#120	C₂³	1	8	yes	—
223	C₁₃×#120	C₂³	1	8	yes	—
224	C₁₃×#120	C₂³	1	16	yes	—
225	C₁₃×#120	C₂³	1	16	yes	—
226	C₁₃×#120	C₂³	1	8	yes	—
227	C₁₃×#120	C₂³	1	8	yes	—
228	C₁₃×#120	C₂³	1	8	yes	—
229	C₁₃×#120	C₂³	1	16	yes	—
230	C₁₃×#120	C₂³	1	4	yes	—
231	C₁₃×#120	C₂³	1	8	yes	—
232	C₁₃×#120	C₂³	1	4	yes	—
233	C₁₃×#120	C₂³	1	8	yes	—
234	C₁₃×#120	C₂³	1	8	yes	—
235	C₁₃×#120	C₂³	1	4	yes	complemented
236	C₁₃×#120	C₂³	1	4	yes	complemented
237	C₁₃×#120	C₂³	1	16	yes	complemented
238	C₁₃×#120	C₂³	1	16	yes	complemented
239	C₁₃×#120	C₂³	1	16	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	16	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	complemented
248	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
249	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
250	C₄×D₄×C₁₃	C₂³	1	16	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	C₁₃×#117	C₂³	1	4	yes	—
256	C₁₃×#117	C₂³	1	4	yes	—
257	C₁₃×#117	C₂³	1	4	yes	—
258	C₁₃×#117	C₂³	1	4	yes	—
259	C₁₃×#117	C₂³	1	4	yes	complemented
260	C₁₃×#117	C₂³	1	2	yes	complemented
261	C₁₃×#117	C₂³	1	2	yes	complemented
262	C₁₃×#117	C₂³	1	8	yes	complemented
263	C₁₃×#117	C₂³	1	16	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	4	yes	complemented
267	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	8	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
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	#62874	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂⁴×C₁₃	—	4	4	no	—
278	C₂⁴×C₁₃	—	8	4	no	—
279	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
280	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
282	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
283	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
284	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
285	C₁₃×#41	—	2	16	no	—
286	C₁₃×#41	—	4	4	no	—
287	C₁₃×#41	—	4	4	no	—
288	C₁₃×#41	—	4	4	no	—
289	C₁₃×#41	—	4	4	no	—
290	C₁₃×#41	—	4	8	no	—
291	C₁₃×#41	—	4	8	no	—
292	C₁₃×#41	—	4	8	no	—
293	C₁₃×#41	—	4	16	no	—
294	C₁₃×#41	—	8	16	no	—
295	C₂×Q₈×C₁₃	—	4	2	no	—
296	C₂×Q₈×C₁₃	—	4	4	no	—
297	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
301	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
302	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₂×D₄×C₁₃	—	2	8	no	—
304	C₂×D₄×C₁₃	—	4	8	no	—
305	C₂×D₄×C₁₃	—	4	8	no	—
306	C₂×D₄×C₁₃	—	4	16	no	—
307	C₂×D₄×C₁₃	—	4	4	no	—
308	C₂×D₄×C₁₃	—	4	4	no	—
309	C₂×D₄×C₁₃	—	4	2	no	—
310	C₂×D₄×C₁₃	—	4	4	no	—
311	C₂×D₄×C₁₃	—	4	8	no	—
312	C₂×D₄×C₁₃	—	4	16	no	—
313	C₂×D₄×C₁₃	—	8	8	no	—
314	C₂×D₄×C₁₃	—	8	16	no	—
315	C₂×D₄×C₁₃	—	8	16	no	—
316	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
317	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
318	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
319	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
320	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
321	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
322	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
323	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
325	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
328	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
329	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
330	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
333	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
334	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
336	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
338	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
339	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃	—	2	4	no	—
341	C₂²×C₄×C₁₃	—	2	8	no	—
342	C₂²×C₄×C₁₃	—	4	8	no	—
343	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
353	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
355	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
373	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
374	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
375	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
376	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
377	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	16	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	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
390	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₄²×C₁₃	C₂⁴	1	4	yes	—
393	C₄²×C₁₃	C₂⁴	1	4	yes	—
394	C₄²×C₁₃	C₂⁴	1	4	yes	—
395	C₄²×C₁₃	C₂⁴	1	8	yes	—
396	C₄²×C₁₃	C₂⁴	1	4	yes	—
397	C₄²×C₁₃	C₂⁴	1	16	yes	—
398	#3551	C₂×C₁₃	1	4	yes	complemented
399	#3549	C₂×C₁₃	1	4	yes	complemented
400	#3546	C₂×C₁₃	1	8	yes	complemented
401	#3545	C₂×C₁₃	1	4	yes	complemented
402	#3543	C₂×C₁₃	1	4	yes	complemented
403	#3542	C₂×C₁₃	1	8	yes	complemented
404	#3540	C₂×C₁₃	1	4	yes	complemented
405	#3537	C₂×C₁₃	1	4	yes	complemented
406	#3532	C₂×C₁₃	1	8	yes	complemented
407	#3494	C₂×C₁₃	1	4	yes	complemented
408	#3493	C₂×C₁₃	1	2	yes	complemented
409	#3488	C₂×C₁₃	1	4	yes	complemented
410	#3484	C₂×C₁₃	1	2	yes	complemented
411	#3449	C₂×C₁₃	1	2	yes	complemented
412	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
413	C₂³×C₁₃	—	2	2	no	—
414	C₂³×C₁₃	—	2	4	no	—
415	C₂³×C₁₃	—	2	8	no	—
416	C₂³×C₁₃	—	4	2	no	—
417	C₂³×C₁₃	—	4	4	no	—
418	C₂³×C₁₃	—	4	8	no	—
419	C₂³×C₁₃	—	4	4	no	—
420	C₂³×C₁₃	—	4	8	no	—
421	C₂³×C₁₃	—	4	8	no	—
422	C₂³×C₁₃	—	4	16	no	—
423	C₂³×C₁₃	—	4	8	no	—
424	C₂³×C₁₃	—	4	16	no	—
425	C₂³×C₁₃	—	8	16	no	—
426	C₂³×C₁₃	C₂⁵	1	2	yes	—
427	C₂³×C₁₃	C₂⁵	1	8	yes	—
428	C₂³×C₁₃	C₂⁵	1	2	yes	—
429	C₂³×C₁₃	C₂⁵	1	8	yes	—
430	C₂³×C₁₃	C₂⁵	1	2	yes	—
431	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
432	Q₈×C₁₃	—	2	8	no	—
433	Q₈×C₁₃	—	4	1	no	—
434	Q₈×C₁₃	—	4	2	no	—
435	Q₈×C₁₃	—	4	1	no	—
436	Q₈×C₁₃	—	4	4	no	—
437	Q₈×C₁₃	—	4	8	no	—
438	D₄×C₁₃	—	2	16	no	—
439	D₄×C₁₃	—	2	16	no	—
440	D₄×C₁₃	—	2	8	no	—
441	D₄×C₁₃	—	4	4	no	—
442	D₄×C₁₃	—	4	4	no	—
443	D₄×C₁₃	—	4	16	no	—
444	D₄×C₁₃	—	4	2	no	—
445	D₄×C₁₃	—	4	2	no	—
446	D₄×C₁₃	—	4	1	no	—
447	D₄×C₁₃	—	4	2	no	—
448	D₄×C₁₃	—	4	1	no	—
449	D₄×C₁₃	—	4	2	no	—
450	D₄×C₁₃	—	4	2	no	—
451	D₄×C₁₃	—	4	4	no	—
452	D₄×C₁₃	—	4	8	no	—
453	D₄×C₁₃	—	4	8	no	—
454	D₄×C₁₃	—	4	16	no	—
455	D₄×C₁₃	—	4	8	no	—
456	D₄×C₁₃	—	4	16	no	—
457	D₄×C₁₃	—	4	8	no	—
458	D₄×C₁₃	—	4	8	no	—
459	D₄×C₁₃	—	4	16	no	—
460	D₄×C₁₃	—	4	16	no	—
461	D₄×C₁₃	—	4	8	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	4	no	—
464	C₂×C₄×C₁₃	—	2	4	no	—
465	C₂×C₄×C₁₃	—	2	4	no	—
466	C₂×C₄×C₁₃	—	2	4	no	—
467	C₂×C₄×C₁₃	—	2	4	no	—
468	C₂×C₄×C₁₃	—	2	4	no	—
469	C₂×C₄×C₁₃	—	2	4	no	—
470	C₂×C₄×C₁₃	—	2	16	no	—
471	C₂×C₄×C₁₃	—	4	4	no	—
472	C₂×C₄×C₁₃	—	4	8	no	—
473	C₂×C₄×C₁₃	—	4	8	no	—
474	C₂×C₄×C₁₃	—	4	4	no	—
475	C₂×C₄×C₁₃	—	4	16	no	—
476	C₂×C₄×C₁₃	—	4	16	no	—
477	C₂×C₄×C₁₃	—	4	8	no	—
478	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
479	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
480	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
481	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
482	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
485	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
486	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
488	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
489	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
491	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#563	C₂²×C₁₃	1	4	yes	complemented
493	#562	C₂²×C₁₃	1	8	yes	complemented
494	H(3,𝔽₄)	C₂²×C₁₃	1	8	yes	complemented
495	H(3,𝔽₄)	C₂²×C₁₃	1	4	yes	complemented
496	#560	C₂²×C₁₃	1	16	yes	complemented
497	#560	C₂²×C₁₃	1	8	yes	complemented
498	#560	C₂²×C₁₃	1	8	yes	complemented
499	#560	C₂²×C₁₃	1	8	yes	complemented
500	#559	C₂²×C₁₃	1	4	yes	complemented
501	#556	C₂²×C₁₃	1	8	yes	complemented
502	#555	C₂²×C₁₃	1	8	yes	complemented
503	#555	C₂²×C₁₃	1	8	yes	complemented
504	#555	C₂²×C₁₃	1	8	yes	complemented
505	#553	C₂²×C₁₃	1	8	yes	complemented
506	#553	C₂²×C₁₃	1	8	yes	complemented
507	#553	C₂²×C₁₃	1	8	yes	complemented
508	#552	C₂²×C₁₃	1	8	yes	complemented
509	#551	C₂²×C₁₃	1	16	yes	complemented
510	#551	C₂²×C₁₃	1	8	yes	complemented
511	#551	C₂²×C₁₃	1	8	yes	complemented
512	#550	C₂²×C₁₃	1	8	yes	complemented
513	#550	C₂²×C₁₃	1	8	yes	complemented
514	#548	C₂²×C₁₃	1	8	yes	complemented
515	#547	C₂²×C₁₃	1	8	yes	complemented
516	#546	C₂²×C₁₃	1	8	yes	complemented
517	#546	C₂²×C₁₃	1	8	yes	complemented
518	#546	C₂²×C₁₃	1	16	yes	complemented
519	#546	C₂²×C₁₃	1	16	yes	complemented
520	#546	C₂²×C₁₃	1	16	yes	complemented
521	#546	C₂²×C₁₃	1	8	yes	complemented
522	D₄²	C₂²×C₁₃	1	8	yes	complemented
523	D₄²	C₂²×C₁₃	1	8	yes	complemented
524	D₄²	C₂²×C₁₃	1	16	yes	complemented
525	D₄²	C₂²×C₁₃	1	8	yes	complemented
526	D₄²	C₂²×C₁₃	1	4	yes	complemented
527	D₄²	C₂²×C₁₃	1	8	yes	complemented
528	#544	C₂²×C₁₃	1	2	yes	complemented
529	#542	C₂²×C₁₃	1	8	yes	complemented
530	#542	C₂²×C₁₃	1	16	yes	complemented
531	#540	C₂²×C₁₃	1	8	yes	complemented
532	#540	C₂²×C₁₃	1	16	yes	complemented
533	#538	C₂²×C₁₃	1	8	yes	complemented
534	#538	C₂²×C₁₃	1	16	yes	complemented
535	#538	C₂²×C₁₃	1	16	yes	complemented
536	#538	C₂²×C₁₃	1	16	yes	complemented
537	#537	C₂²×C₁₃	1	2	yes	complemented
538	#537	C₂²×C₁₃	1	4	yes	complemented
539	#537	C₂²×C₁₃	1	4	yes	complemented
540	#537	C₂²×C₁₃	1	8	yes	complemented
541	#536	C₂²×C₁₃	1	4	yes	complemented
542	#536	C₂²×C₁₃	1	2	yes	complemented
543	#536	C₂²×C₁₃	1	2	yes	complemented
544	#535	C₂²×C₁₃	1	4	yes	complemented
545	#535	C₂²×C₁₃	1	4	yes	complemented
546	#535	C₂²×C₁₃	1	4	yes	complemented
547	#535	C₂²×C₁₃	1	4	yes	complemented
548	#535	C₂²×C₁₃	1	4	yes	complemented
549	#535	C₂²×C₁₃	1	4	yes	complemented
550	#535	C₂²×C₁₃	1	16	yes	complemented
551	#535	C₂²×C₁₃	1	2	yes	complemented
552	#535	C₂²×C₁₃	1	2	yes	complemented
553	#535	C₂²×C₁₃	1	16	yes	complemented
554	#535	C₂²×C₁₃	1	8	yes	complemented
555	#534	C₂²×C₁₃	1	4	yes	complemented
556	#534	C₂²×C₁₃	1	8	yes	complemented
557	#534	C₂²×C₁₃	1	4	yes	complemented
558	#534	C₂²×C₁₃	1	16	yes	complemented
559	#532	C₂²×C₁₃	1	4	yes	complemented
560	#532	C₂²×C₁₃	1	4	yes	complemented
561	#532	C₂²×C₁₃	1	8	yes	complemented
562	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
563	#529	C₂²×C₁₃	1	8	yes	complemented
564	#529	C₂²×C₁₃	1	8	yes	complemented
565	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
566	#525	C₂²×C₁₃	1	4	yes	complemented
567	#525	C₂²×C₁₃	1	4	yes	complemented
568	#525	C₂²×C₁₃	1	4	yes	complemented
569	#525	C₂²×C₁₃	1	4	yes	complemented
570	#525	C₂²×C₁₃	1	8	yes	complemented
571	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
572	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
573	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
574	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
575	#520	C₂²×C₁₃	1	4	yes	complemented
576	#518	C₂²×C₁₃	1	2	yes	complemented
577	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
579	C₂²×C₁₃	—	2	2	no	—
580	C₂²×C₁₃	—	2	2	no	—
581	C₂²×C₁₃	—	2	2	no	—
582	C₂²×C₁₃	—	2	2	no	—
583	C₂²×C₁₃	—	2	8	no	—
584	C₂²×C₁₃	—	2	8	no	—
585	C₂²×C₁₃	—	2	4	no	—
586	C₂²×C₁₃	—	2	8	no	—
587	C₂²×C₁₃	—	2	16	no	—
588	C₂²×C₁₃	—	2	4	no	—
589	C₂²×C₁₃	—	2	8	no	—
590	C₂²×C₁₃	—	2	4	no	—
591	C₂²×C₁₃	—	4	4	no	—
592	C₂²×C₁₃	—	8	4	no	—
593	C₂²×C₁₃	—	8	8	no	—
594	C₂²×C₁₃	—	8	8	no	—
595	C₂²×C₁₃	—	8	16	no	—
596	C₂²×C₁₃	—	16	8	no	—
597	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
598	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	1	no	—
602	C₄×C₁₃	—	2	2	no	—
603	C₄×C₁₃	—	2	8	no	—
604	C₄×C₁₃	—	2	8	no	—
605	C₄×C₁₃	—	2	8	no	—
606	C₄×C₁₃	—	2	8	no	—
607	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
608	C₂⁵	C₂³×C₁₃	1	2	yes	—
609	H(5,𝔽₂)	—	4	8	no	—
610	C₂×#41	—	4	4	no	—
611	C₂×#41	—	4	8	no	—
612	C₂×#41	C₂³×C₁₃	1	4	yes	—
613	C₂×#41	C₂³×C₁₃	1	2	yes	—
614	C₂×#41	C₂³×C₁₃	1	2	yes	—
615	C₂×#41	C₂³×C₁₃	1	8	yes	—
616	C₂×#41	C₂³×C₁₃	1	2	yes	—
617	C₂×#41	C₂³×C₁₃	1	2	yes	—
618	C₂×#41	C₂³×C₁₃	1	4	yes	—
619	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
620	C₂×#41	C₂³×C₁₃	1	4	yes	complemented
621	C₂×#41	C₂³×C₁₃	1	16	yes	complemented
622	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₂²×Q₈	C₂³×C₁₃	1	2	yes	complemented
624	C₂²×D₄	—	4	4	no	—
625	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
626	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
627	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
628	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
629	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
630	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
632	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
633	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
634	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
635	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
636	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
637	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
638	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
639	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
641	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
642	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
643	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
644	#127	C₂³×C₁₃	1	8	yes	—
645	#127	C₂³×C₁₃	1	4	yes	—
646	#127	C₂³×C₁₃	1	4	yes	—
647	#127	C₂³×C₁₃	1	4	yes	—
648	#127	C₂³×C₁₃	1	4	yes	—
649	#127	C₂³×C₁₃	1	8	yes	—
650	#127	C₂³×C₁₃	1	16	yes	complemented
651	#126	C₂³×C₁₃	1	16	yes	—
652	#126	C₂³×C₁₃	1	16	yes	complemented
653	#126	C₂³×C₁₃	1	16	yes	complemented
654	#126	C₂³×C₁₃	1	16	yes	complemented
655	#125	C₂³×C₁₃	1	8	yes	complemented
656	#125	C₂³×C₁₃	1	8	yes	complemented
657	#124	C₂³×C₁₃	1	8	yes	—
658	#124	C₂³×C₁₃	1	4	yes	—
659	#124	C₂³×C₁₃	1	4	yes	—
660	#124	C₂³×C₁₃	1	8	yes	—
661	#124	C₂³×C₁₃	1	4	yes	—
662	#124	C₂³×C₁₃	1	4	yes	—
663	#124	C₂³×C₁₃	1	16	yes	—
664	#124	C₂³×C₁₃	1	8	yes	complemented
665	#124	C₂³×C₁₃	1	4	yes	complemented
666	#124	C₂³×C₁₃	1	4	yes	complemented
667	#124	C₂³×C₁₃	1	16	yes	complemented
668	#124	C₂³×C₁₃	1	16	yes	complemented
669	#124	C₂³×C₁₃	1	16	yes	complemented
670	#123	C₂³×C₁₃	1	8	yes	—
671	#123	C₂³×C₁₃	1	4	yes	—
672	#123	C₂³×C₁₃	1	8	yes	—
673	#123	C₂³×C₁₃	1	4	yes	—
674	#123	C₂³×C₁₃	1	16	yes	—
675	#123	C₂³×C₁₃	1	8	yes	—
676	#123	C₂³×C₁₃	1	8	yes	—
677	#123	C₂³×C₁₃	1	4	yes	complemented
678	#123	C₂³×C₁₃	1	4	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	#123	C₂³×C₁₃	1	16	yes	complemented
684	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
685	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
687	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
688	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
689	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
690	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
691	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
692	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
693	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
694	#121	C₂³×C₁₃	1	8	yes	—
695	#121	C₂³×C₁₃	1	8	yes	—
696	#121	C₂³×C₁₃	1	8	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	4	yes	—
702	#121	C₂³×C₁₃	1	4	yes	—
703	#121	C₂³×C₁₃	1	8	yes	—
704	#121	C₂³×C₁₃	1	8	yes	—
705	#121	C₂³×C₁₃	1	8	yes	—
706	#121	C₂³×C₁₃	1	8	yes	—
707	#121	C₂³×C₁₃	1	16	yes	—
708	#121	C₂³×C₁₃	1	16	yes	—
709	#121	C₂³×C₁₃	1	16	yes	—
710	#121	C₂³×C₁₃	1	4	yes	complemented
711	#121	C₂³×C₁₃	1	16	yes	complemented
712	#121	C₂³×C₁₃	1	8	yes	complemented
713	#121	C₂³×C₁₃	1	16	yes	complemented
714	#121	C₂³×C₁₃	1	4	yes	complemented
715	#121	C₂³×C₁₃	1	8	yes	complemented
716	#121	C₂³×C₁₃	1	8	yes	complemented
717	#121	C₂³×C₁₃	1	16	yes	complemented
718	#121	C₂³×C₁₃	1	16	yes	complemented
719	#121	C₂³×C₁₃	1	16	yes	complemented
720	#121	C₂³×C₁₃	1	16	yes	complemented
721	#121	C₂³×C₁₃	1	16	yes	complemented
722	#121	C₂³×C₁₃	1	16	yes	complemented
723	#120	C₂³×C₁₃	1	8	yes	—
724	#120	C₂³×C₁₃	1	8	yes	—
725	#120	C₂³×C₁₃	1	16	yes	—
726	#120	C₂³×C₁₃	1	16	yes	—
727	#120	C₂³×C₁₃	1	8	yes	—
728	#120	C₂³×C₁₃	1	8	yes	—
729	#120	C₂³×C₁₃	1	8	yes	—
730	#120	C₂³×C₁₃	1	16	yes	—
731	#120	C₂³×C₁₃	1	4	yes	—
732	#120	C₂³×C₁₃	1	8	yes	—
733	#120	C₂³×C₁₃	1	4	yes	—
734	#120	C₂³×C₁₃	1	8	yes	—
735	#120	C₂³×C₁₃	1	8	yes	—
736	#120	C₂³×C₁₃	1	4	yes	complemented
737	#120	C₂³×C₁₃	1	4	yes	complemented
738	#120	C₂³×C₁₃	1	16	yes	complemented
739	#120	C₂³×C₁₃	1	16	yes	complemented
740	#120	C₂³×C₁₃	1	16	yes	complemented
741	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
742	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
743	C₄×D₄	C₂³×C₁₃	1	8	yes	—
744	C₄×D₄	C₂³×C₁₃	1	8	yes	—
745	C₄×D₄	C₂³×C₁₃	1	16	yes	—
746	C₄×D₄	C₂³×C₁₃	1	8	yes	—
747	C₄×D₄	C₂³×C₁₃	1	8	yes	—
748	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
749	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
750	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
751	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
752	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
753	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
754	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
755	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
756	#117	C₂³×C₁₃	1	4	yes	—
757	#117	C₂³×C₁₃	1	4	yes	—
758	#117	C₂³×C₁₃	1	4	yes	—
759	#117	C₂³×C₁₃	1	4	yes	—
760	#117	C₂³×C₁₃	1	4	yes	complemented
761	#117	C₂³×C₁₃	1	2	yes	complemented
762	#117	C₂³×C₁₃	1	2	yes	complemented
763	#117	C₂³×C₁₃	1	8	yes	complemented
764	#117	C₂³×C₁₃	1	16	yes	complemented
765	#117	C₂³×C₁₃	1	16	yes	complemented
766	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
769	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
775	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
776	C₂×C₄²	C₂³×C₁₃	1	4	yes	complemented
777	C₂×C₁₃	—	2	2	no	—
778	C₂×C₁₃	—	4	2	no	—
779	C₂×C₁₃	—	4	2	no	—
780	C₂×C₁₃	—	4	2	no	—
781	C₂×C₁₃	—	4	8	no	—
782	C₂×C₁₃	—	4	8	no	—
783	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
784	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
785	C₂⁴	—	4	4	no	—
786	C₂⁴	—	8	4	no	—
787	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
788	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
790	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
791	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
792	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
793	#41	—	2	16	no	—
794	#41	—	4	4	no	—
795	#41	—	4	4	no	—
796	#41	—	4	4	no	—
797	#41	—	4	4	no	—
798	#41	—	4	8	no	—
799	#41	—	4	8	no	—
800	#41	—	4	8	no	—
801	#41	—	4	16	no	—
802	#41	—	8	16	no	—
803	C₂×Q₈	—	4	2	no	—
804	C₂×Q₈	—	4	4	no	—
805	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
806	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
807	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
809	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
810	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂×D₄	—	2	8	no	—
812	C₂×D₄	—	4	8	no	—
813	C₂×D₄	—	4	8	no	—
814	C₂×D₄	—	4	16	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	—	4	4	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	4	no	—
819	C₂×D₄	—	4	8	no	—
820	C₂×D₄	—	4	16	no	—
821	C₂×D₄	—	8	8	no	—
822	C₂×D₄	—	8	16	no	—
823	C₂×D₄	—	8	16	no	—
824	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
825	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
826	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
827	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
828	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
829	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
830	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
831	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
832	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
833	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
834	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
835	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
836	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
837	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
838	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
839	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
840	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
841	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
842	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
843	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
844	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
845	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
846	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
847	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₂²×C₄	—	2	4	no	—
849	C₂²×C₄	—	2	8	no	—
850	C₂²×C₄	—	4	8	no	—
851	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
854	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
856	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
859	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
860	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
861	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
862	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
863	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
864	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
866	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
869	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
870	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
871	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
872	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
873	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
876	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
877	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
878	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
879	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
882	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
883	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
885	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
886	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
887	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
889	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
890	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
892	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
894	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
895	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
896	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
897	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
900	C₄²	C₂⁴×C₁₃	1	4	yes	—
901	C₄²	C₂⁴×C₁₃	1	4	yes	—
902	C₄²	C₂⁴×C₁₃	1	4	yes	—
903	C₄²	C₂⁴×C₁₃	1	8	yes	—
904	C₄²	C₂⁴×C₁₃	1	4	yes	—
905	C₄²	C₂⁴×C₁₃	1	16	yes	—
906	C₁₃	#62874	1	1	yes	characteristic, direct product factor, Sylow
907	C₂³	—	2	2	no	—
908	C₂³	—	2	4	no	—
909	C₂³	—	2	8	no	—
910	C₂³	—	4	2	no	—
911	C₂³	—	4	4	no	—
912	C₂³	—	4	8	no	—
913	C₂³	—	4	4	no	—
914	C₂³	—	4	8	no	—
915	C₂³	—	4	8	no	—
916	C₂³	—	4	16	no	—
917	C₂³	—	4	8	no	—
918	C₂³	—	4	16	no	—
919	C₂³	—	8	16	no	—
920	C₂³	C₂⁵×C₁₃	1	2	yes	—
921	C₂³	C₂⁵×C₁₃	1	8	yes	—
922	C₂³	C₂⁵×C₁₃	1	2	yes	—
923	C₂³	C₂⁵×C₁₃	1	8	yes	—
924	C₂³	C₂⁵×C₁₃	1	2	yes	—
925	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
926	Q₈	—	2	8	no	—
927	Q₈	—	4	1	no	—
928	Q₈	—	4	2	no	—
929	Q₈	—	4	1	no	—
930	Q₈	—	4	4	no	—
931	Q₈	—	4	8	no	—
932	D₄	—	2	16	no	—
933	D₄	—	2	16	no	—
934	D₄	—	2	8	no	—
935	D₄	—	4	4	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	16	no	—
938	D₄	—	4	2	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	1	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	8	no	—
947	D₄	—	4	8	no	—
948	D₄	—	4	16	no	—
949	D₄	—	4	8	no	—
950	D₄	—	4	16	no	—
951	D₄	—	4	8	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	16	no	—
954	D₄	—	4	16	no	—
955	D₄	—	4	8	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	4	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	4	no	—
964	C₂×C₄	—	2	16	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	8	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	16	no	—
970	C₂×C₄	—	4	16	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
973	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
974	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
975	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
976	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
977	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
978	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
979	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
980	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
981	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	8	no	—
987	C₂²	—	2	8	no	—
988	C₂²	—	2	4	no	—
989	C₂²	—	2	8	no	—
990	C₂²	—	2	16	no	—
991	C₂²	—	2	4	no	—
992	C₂²	—	2	8	no	—
993	C₂²	—	2	4	no	—
994	C₂²	—	4	4	no	—
995	C₂²	—	8	4	no	—
996	C₂²	—	8	8	no	—
997	C₂²	—	8	8	no	—
998	C₂²	—	8	16	no	—
999	C₂²	—	16	8	no	—
1000	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1001	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1002	C₄	—	2	2	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	8	no	—
1007	C₄	—	2	8	no	—
1008	C₄	—	2	8	no	—
1009	C₄	—	2	8	no	—
1010	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1011	C₂	—	2	2	no	—
1012	C₂	—	4	2	no	—
1013	C₂	—	4	8	no	—
1014	C₂	—	4	2	no	—
1015	C₂	—	4	8	no	—
1016	C₂	—	4	2	no	—
1017	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1018	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×#3551	C₂	semidirect
2. C₁₃×#3549	C₂	semidirect
3. C₁₃×#3546	C₂	semidirect
4. C₁₃×#3545	C₂	semidirect
5. C₁₃×#3543	C₂	semidirect
6. C₁₃×#3542	C₂	semidirect
7. C₁₃×#3540	C₂	semidirect
8. C₁₃×#3537	C₂	semidirect
9. C₁₃×#3532	C₂	semidirect
10. C₁₃×#3494	C₂	semidirect
11. C₁₃×#3493	C₂	semidirect
12. C₁₃×#3488	C₂	semidirect
13. C₁₃×#3484	C₂	semidirect
14. C₁₃×#3449	C₂	semidirect
15. C₂×C₁₃×#535	C₂	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
19. C₂³×D₄×C₁₃	C₂²	semidirect
20. C₁₃×#563	C₂²	semidirect
21. C₁₃×#562	C₂²	semidirect
22. C₁₃×H(3,𝔽₄)	C₂²	semidirect
23. C₁₃×H(3,𝔽₄)	C₂²	semidirect
24. C₁₃×#560	C₂²	semidirect
25. C₁₃×#560	C₂²	semidirect
26. C₁₃×#560	C₂²	semidirect
27. C₁₃×#560	C₂²	semidirect
28. C₁₃×#559	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
30. C₁₃×#555	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#555	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#553	C₂²	semidirect
35. C₁₃×#553	C₂²	semidirect
36. C₁₃×#552	C₂²	semidirect
37. C₁₃×#551	C₂²	semidirect
38. C₁₃×#551	C₂²	semidirect
39. C₁₃×#551	C₂²	semidirect
40. C₁₃×#550	C₂²	semidirect
41. C₁₃×#550	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#546	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#546	C₂²	semidirect
48. C₁₃×#546	C₂²	semidirect
49. C₁₃×#546	C₂²	semidirect
50. D₄²×C₁₃	C₂²	semidirect
51. D₄²×C₁₃	C₂²	semidirect
52. D₄²×C₁₃	C₂²	semidirect
53. D₄²×C₁₃	C₂²	semidirect
54. D₄²×C₁₃	C₂²	semidirect
55. D₄²×C₁₃	C₂²	semidirect
56. C₁₃×#544	C₂²	semidirect
57. C₁₃×#542	C₂²	semidirect
58. C₁₃×#542	C₂²	semidirect
59. C₁₃×#540	C₂²	semidirect
60. C₁₃×#540	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×#537	C₂²	semidirect
67. C₁₃×#537	C₂²	semidirect
68. C₁₃×#537	C₂²	semidirect
69. C₁₃×#536	C₂²	semidirect
70. C₁₃×#536	C₂²	semidirect
71. C₁₃×#536	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×#535	C₂²	semidirect
79. C₁₃×#535	C₂²	semidirect
80. C₁₃×#535	C₂²	semidirect
81. C₁₃×#535	C₂²	semidirect
82. C₁₃×#535	C₂²	semidirect
83. C₁₃×#534	C₂²	semidirect
84. C₁₃×#534	C₂²	semidirect
85. C₁₃×#534	C₂²	semidirect
86. C₁₃×#534	C₂²	semidirect
87. C₁₃×#532	C₂²	semidirect
88. C₁₃×#532	C₂²	semidirect
89. C₁₃×#532	C₂²	semidirect
90. C₂×C₁₃×#127	C₂²	semidirect
91. C₁₃×#529	C₂²	semidirect
92. C₁₃×#529	C₂²	semidirect
93. C₂×C₁₃×#124	C₂²	semidirect
94. C₁₃×#525	C₂²	semidirect
95. C₁₃×#525	C₂²	semidirect
96. C₁₃×#525	C₂²	semidirect
97. C₁₃×#525	C₂²	semidirect
98. C₁₃×#525	C₂²	semidirect
99. C₂×C₁₃×#121	C₂²	semidirect
100. C₂×C₁₃×#121	C₂²	semidirect
101. C₂×C₁₃×#120	C₂²	semidirect
102. C₂×C₁₃×#120	C₂²	semidirect
103. C₁₃×#520	C₂²	semidirect
104. C₁₃×#518	C₂²	semidirect
105. C₂×C₁₃×#117	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. C₂³×C₄×C₁₃	C₂³	semidirect
140. C₁₃×C₄⋊Q₈	C₂³	semidirect
141. C₁₃×C₄⋊Q₈	C₂³	semidirect
142. C₁₃×C₄⋊Q₈	C₂³	semidirect
149. C₁₃×#127	C₂³	semidirect
151. C₁₃×#126	C₂³	semidirect
152. C₁₃×#126	C₂³	semidirect
153. C₁₃×#126	C₂³	semidirect
154. C₁₃×#125	C₂³	semidirect
155. C₁₃×#125	C₂³	semidirect
163. C₁₃×#124	C₂³	semidirect
164. C₁₃×#124	C₂³	semidirect
165. C₁₃×#124	C₂³	semidirect
166. C₁₃×#124	C₂³	semidirect
167. C₁₃×#124	C₂³	semidirect
168. C₁₃×#124	C₂³	semidirect
176. C₁₃×#123	C₂³	semidirect
177. C₁₃×#123	C₂³	semidirect
178. C₁₃×#123	C₂³	semidirect
179. C₁₃×#123	C₂³	semidirect
180. C₁₃×#123	C₂³	semidirect
181. C₁₃×#123	C₂³	semidirect
182. C₁₃×#123	C₂³	semidirect
186. C₁₃×C₂²⋊Q₈	C₂³	semidirect
187. C₁₃×C₂²⋊Q₈	C₂³	semidirect
188. C₁₃×C₂²⋊Q₈	C₂³	semidirect
189. C₁₃×C₂²⋊Q₈	C₂³	semidirect
190. C₁₃×C₂²⋊Q₈	C₂³	semidirect
191. C₁₃×C₂²⋊Q₈	C₂³	semidirect
192. C₁₃×C₂²⋊Q₈	C₂³	semidirect
209. C₁₃×#121	C₂³	semidirect
210. C₁₃×#121	C₂³	semidirect
211. C₁₃×#121	C₂³	semidirect
212. C₁₃×#121	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
235. C₁₃×#120	C₂³	semidirect
236. C₁₃×#120	C₂³	semidirect
237. C₁₃×#120	C₂³	semidirect
238. C₁₃×#120	C₂³	semidirect
239. C₁₃×#120	C₂³	semidirect
240. C₄×Q₈×C₁₃	C₂³	semidirect
241. C₄×Q₈×C₁₃	C₂³	semidirect
247. C₄×D₄×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
259. C₁₃×#117	C₂³	semidirect
260. C₁₃×#117	C₂³	semidirect
261. C₁₃×#117	C₂³	semidirect
262. C₁₃×#117	C₂³	semidirect
263. C₁₃×#117	C₂³	semidirect
264. C₁₃×#117	C₂³	semidirect
266. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
267. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
273. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
275. C₂×C₄²×C₁₃	C₂³	semidirect
276. #62874	C₁₃	direct (N × H)
398. #3551	C₂×C₁₃	semidirect
399. #3549	C₂×C₁₃	semidirect
400. #3546	C₂×C₁₃	semidirect
401. #3545	C₂×C₁₃	semidirect
402. #3543	C₂×C₁₃	semidirect
403. #3542	C₂×C₁₃	semidirect
404. #3540	C₂×C₁₃	semidirect
405. #3537	C₂×C₁₃	semidirect
406. #3532	C₂×C₁₃	semidirect
407. #3494	C₂×C₁₃	semidirect
408. #3493	C₂×C₁₃	semidirect
409. #3488	C₂×C₁₃	semidirect
410. #3484	C₂×C₁₃	semidirect
411. #3449	C₂×C₁₃	semidirect
412. C₂×#535	C₂×C₁₃	semidirect
488. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
489. C₂²×#41	C₂²×C₁₃	semidirect
490. C₂²×#41	C₂²×C₁₃	semidirect
491. C₂³×D₄	C₂²×C₁₃	semidirect
492. #563	C₂²×C₁₃	semidirect
493. #562	C₂²×C₁₃	semidirect
494. H(3,𝔽₄)	C₂²×C₁₃	semidirect
495. H(3,𝔽₄)	C₂²×C₁₃	semidirect
496. #560	C₂²×C₁₃	semidirect
497. #560	C₂²×C₁₃	semidirect
498. #560	C₂²×C₁₃	semidirect
499. #560	C₂²×C₁₃	semidirect
500. #559	C₂²×C₁₃	semidirect
501. #556	C₂²×C₁₃	semidirect
502. #555	C₂²×C₁₃	semidirect
503. #555	C₂²×C₁₃	semidirect
504. #555	C₂²×C₁₃	semidirect
505. #553	C₂²×C₁₃	semidirect
506. #553	C₂²×C₁₃	semidirect
507. #553	C₂²×C₁₃	semidirect
508. #552	C₂²×C₁₃	semidirect
509. #551	C₂²×C₁₃	semidirect
510. #551	C₂²×C₁₃	semidirect
511. #551	C₂²×C₁₃	semidirect
512. #550	C₂²×C₁₃	semidirect
513. #550	C₂²×C₁₃	semidirect
514. #548	C₂²×C₁₃	semidirect
515. #547	C₂²×C₁₃	semidirect
516. #546	C₂²×C₁₃	semidirect
517. #546	C₂²×C₁₃	semidirect
518. #546	C₂²×C₁₃	semidirect
519. #546	C₂²×C₁₃	semidirect
520. #546	C₂²×C₁₃	semidirect
521. #546	C₂²×C₁₃	semidirect
522. D₄²	C₂²×C₁₃	semidirect
523. D₄²	C₂²×C₁₃	semidirect
524. D₄²	C₂²×C₁₃	semidirect
525. D₄²	C₂²×C₁₃	semidirect
526. D₄²	C₂²×C₁₃	semidirect
527. D₄²	C₂²×C₁₃	semidirect
528. #544	C₂²×C₁₃	semidirect
529. #542	C₂²×C₁₃	semidirect
530. #542	C₂²×C₁₃	semidirect
531. #540	C₂²×C₁₃	semidirect
532. #540	C₂²×C₁₃	semidirect
533. #538	C₂²×C₁₃	semidirect
534. #538	C₂²×C₁₃	semidirect
535. #538	C₂²×C₁₃	semidirect
536. #538	C₂²×C₁₃	semidirect
537. #537	C₂²×C₁₃	semidirect
538. #537	C₂²×C₁₃	semidirect
539. #537	C₂²×C₁₃	semidirect
540. #537	C₂²×C₁₃	semidirect
541. #536	C₂²×C₁₃	semidirect
542. #536	C₂²×C₁₃	semidirect
543. #536	C₂²×C₁₃	semidirect
544. #535	C₂²×C₁₃	semidirect
545. #535	C₂²×C₁₃	semidirect
546. #535	C₂²×C₁₃	semidirect
547. #535	C₂²×C₁₃	semidirect
548. #535	C₂²×C₁₃	semidirect
549. #535	C₂²×C₁₃	semidirect
550. #535	C₂²×C₁₃	semidirect
551. #535	C₂²×C₁₃	semidirect
552. #535	C₂²×C₁₃	semidirect
553. #535	C₂²×C₁₃	semidirect
554. #535	C₂²×C₁₃	semidirect
555. #534	C₂²×C₁₃	semidirect
556. #534	C₂²×C₁₃	semidirect
557. #534	C₂²×C₁₃	semidirect
558. #534	C₂²×C₁₃	semidirect
559. #532	C₂²×C₁₃	semidirect
560. #532	C₂²×C₁₃	semidirect
561. #532	C₂²×C₁₃	semidirect
562. C₂×#127	C₂²×C₁₃	semidirect
563. #529	C₂²×C₁₃	semidirect
564. #529	C₂²×C₁₃	semidirect
565. C₂×#124	C₂²×C₁₃	semidirect
566. #525	C₂²×C₁₃	semidirect
567. #525	C₂²×C₁₃	semidirect
568. #525	C₂²×C₁₃	semidirect
569. #525	C₂²×C₁₃	semidirect
570. #525	C₂²×C₁₃	semidirect
571. C₂×#121	C₂²×C₁₃	semidirect
572. C₂×#121	C₂²×C₁₃	semidirect
573. C₂×#120	C₂²×C₁₃	semidirect
574. C₂×#120	C₂²×C₁₃	semidirect
575. #520	C₂²×C₁₃	semidirect
576. #518	C₂²×C₁₃	semidirect
577. C₂×#117	C₂²×C₁₃	semidirect
578. C₂×#117	C₂²×C₁₃	semidirect
619. C₂×#41	C₂³×C₁₃	semidirect
620. C₂×#41	C₂³×C₁₃	semidirect
621. C₂×#41	C₂³×C₁₃	semidirect
623. C₂²×Q₈	C₂³×C₁₃	semidirect
636. C₂²×D₄	C₂³×C₁₃	semidirect
637. C₂²×D₄	C₂³×C₁₃	semidirect
640. C₂³×C₄	C₂³×C₁₃	semidirect
641. C₄⋊Q₈	C₂³×C₁₃	semidirect
642. C₄⋊Q₈	C₂³×C₁₃	semidirect
643. C₄⋊Q₈	C₂³×C₁₃	semidirect
650. #127	C₂³×C₁₃	semidirect
652. #126	C₂³×C₁₃	semidirect
653. #126	C₂³×C₁₃	semidirect
654. #126	C₂³×C₁₃	semidirect
655. #125	C₂³×C₁₃	semidirect
656. #125	C₂³×C₁₃	semidirect
664. #124	C₂³×C₁₃	semidirect
665. #124	C₂³×C₁₃	semidirect
666. #124	C₂³×C₁₃	semidirect
667. #124	C₂³×C₁₃	semidirect
668. #124	C₂³×C₁₃	semidirect
669. #124	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
683. #123	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
692. C₂²⋊Q₈	C₂³×C₁₃	semidirect
693. C₂²⋊Q₈	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
716. #121	C₂³×C₁₃	semidirect
717. #121	C₂³×C₁₃	semidirect
718. #121	C₂³×C₁₃	semidirect
719. #121	C₂³×C₁₃	semidirect
720. #121	C₂³×C₁₃	semidirect
721. #121	C₂³×C₁₃	semidirect
722. #121	C₂³×C₁₃	semidirect
736. #120	C₂³×C₁₃	semidirect
737. #120	C₂³×C₁₃	semidirect
738. #120	C₂³×C₁₃	semidirect
739. #120	C₂³×C₁₃	semidirect
740. #120	C₂³×C₁₃	semidirect
741. C₄×Q₈	C₂³×C₁₃	semidirect
742. C₄×Q₈	C₂³×C₁₃	semidirect
748. C₄×D₄	C₂³×C₁₃	semidirect
749. C₄×D₄	C₂³×C₁₃	semidirect
750. C₄×D₄	C₂³×C₁₃	semidirect
751. C₄×D₄	C₂³×C₁₃	semidirect
752. C₄×D₄	C₂³×C₁₃	semidirect
753. C₄×D₄	C₂³×C₁₃	semidirect
754. C₄×D₄	C₂³×C₁₃	semidirect
755. C₄×D₄	C₂³×C₁₃	semidirect
760. #117	C₂³×C₁₃	semidirect
761. #117	C₂³×C₁₃	semidirect
762. #117	C₂³×C₁₃	semidirect
763. #117	C₂³×C₁₃	semidirect
764. #117	C₂³×C₁₃	semidirect
765. #117	C₂³×C₁₃	semidirect
767. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
768. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
774. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
776. C₂×C₄²	C₂³×C₁₃	semidirect
906. C₁₃	#62874	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×#3551	2
C₁₃×#3549	2
C₁₃×#3546	2
C₁₃×#3545	2
C₁₃×#3543	2
C₁₃×#3542	2
C₁₃×#3540	2
C₁₃×#3537	2
C₁₃×#3532	2
C₁₃×#3494	2
C₁₃×#3493	2
C₁₃×#3488	2
C₁₃×#3484	2
C₁₃×#3449	2
C₂×C₁₃×#535	2
#62874	13

Subgroups — C13×#62874 #15749213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62874 #15749213