Subgroups — C₁₃×#34298 #15720637

Order 3328.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2374	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2359	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2297	C₂	1	2	yes	maximal, complemented
20	C₁₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	2	yes	—
25	C₁₃×#547	C₄	1	16	yes	complemented
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#123	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#117	C₂²	1	2	yes	—
41	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#391	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	2	yes	—
51	C₁₃×#390	C₂²	1	2	yes	—
52	C₁₃×#390	C₂²	1	1	yes	characteristic
53	C₁₃×#390	C₂²	1	1	yes	characteristic
54	C₁₃×#389	C₂²	1	1	yes	characteristic
55	C₁₃×#389	C₂²	1	1	yes	characteristic
56	C₁₃×#389	C₂²	1	1	yes	characteristic
57	C₁₃×#389	C₂²	1	1	yes	characteristic
58	C₁₃×#389	C₂²	1	2	yes	—
59	C₁₃×#388	C₂²	1	1	yes	characteristic
60	C₁₃×#388	C₂²	1	1	yes	characteristic
61	C₁₃×#388	C₂²	1	2	yes	—
62	C₁₃×#388	C₂²	1	2	yes	—
63	C₁₃×#388	C₂²	1	2	yes	—
64	C₁₃×#388	C₂²	1	2	yes	—
65	C₁₃×#388	C₂²	1	2	yes	—
66	C₁₃×#388	C₂²	1	2	yes	—
67	C₁₃×#388	C₂²	1	2	yes	—
68	C₁₃×#387	C₂²	1	1	yes	characteristic
69	C₁₃×#387	C₂²	1	1	yes	characteristic
70	C₁₃×#387	C₂²	1	2	yes	—
71	C₁₃×#387	C₂²	1	2	yes	—
72	C₁₃×#387	C₂²	1	2	yes	—
73	C₁₃×#387	C₂²	1	2	yes	—
74	C₁₃×#387	C₂²	1	2	yes	—
75	C₁₃×#387	C₂²	1	2	yes	—
76	C₁₃×#387	C₂²	1	2	yes	—
77	C₁₃×#386	C₂²	1	1	yes	characteristic
78	C₁₃×#386	C₂²	1	1	yes	characteristic
79	C₁₃×#386	C₂²	1	2	yes	—
80	C₁₃×#386	C₂²	1	2	yes	—
81	C₁₃×#386	C₂²	1	2	yes	—
82	C₁₃×#386	C₂²	1	2	yes	—
83	C₁₃×#386	C₂²	1	2	yes	—
84	C₁₃×#385	C₂²	1	1	yes	characteristic
85	C₁₃×#385	C₂²	1	1	yes	characteristic
86	C₁₃×#385	C₂²	1	2	yes	—
87	C₁₃×#385	C₂²	1	2	yes	—
88	C₁₃×#382	C₂²	1	1	yes	characteristic
89	C₁₃×#381	C₂²	1	2	yes	—
90	C₁₃×#381	C₂²	1	2	yes	—
91	C₁₃×#380	C₂²	1	1	yes	characteristic
92	C₁₃×#380	C₂²	1	1	yes	characteristic
93	C₁₃×#380	C₂²	1	2	yes	—
94	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₁₃×#376	C₂²	1	1	yes	characteristic
122	C₂×C₁₃×#95	C₂²	1	2	yes	—
123	C₂×C₁₃×#95	C₂²	1	2	yes	—
124	C₂×C₁₃×#41	—	4	4	no	—
125	C₂×C₁₃×#41	—	4	4	no	—
126	C₂×C₁₃×#41	C₂×C₄	1	16	yes	complemented
127	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
142	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
143	C₁₃×#123	C₂×C₄	1	16	yes	complemented
144	C₁₃×#123	C₂×C₄	1	16	yes	complemented
145	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
146	C₁₃×#121	C₂×C₄	1	8	yes	—
147	C₁₃×#121	C₂×C₄	1	8	yes	complemented
148	C₄×D₄×C₁₃	—	2	4	no	—
149	C₄×D₄×C₁₃	—	2	4	no	—
150	C₄×D₄×C₁₃	—	4	4	no	—
151	C₄×D₄×C₁₃	—	4	4	no	—
152	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
153	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
154	C₁₃×#117	—	2	4	no	—
155	C₁₃×#117	—	2	4	no	—
156	C₁₃×#117	—	4	4	no	—
157	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
159	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
160	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₁₃	—	2	4	no	—
201	C₂×C₄²×C₁₃	—	4	4	no	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₁₃×#95	C₂³	1	1	yes	characteristic
220	C₁₃×#95	C₂³	1	2	yes	—
221	C₁₃×#95	C₂³	1	2	yes	—
222	C₁₃×#95	C₂³	1	1	yes	characteristic
223	C₁₃×#95	C₂³	1	1	yes	characteristic
224	C₁₃×#95	C₂³	1	1	yes	characteristic
225	C₁₃×#95	C₂³	1	1	yes	characteristic
226	C₁₃×#95	C₂³	1	2	yes	—
227	C₁₃×#95	C₂³	1	2	yes	—
228	C₁₃×#95	C₂³	1	2	yes	—
229	C₁₃×#95	C₂³	1	2	yes	—
230	C₁₃×#95	C₂³	1	2	yes	—
231	C₁₃×#95	C₂³	1	2	yes	—
232	C₁₃×#95	C₂³	1	2	yes	—
233	C₁₃×#95	C₂³	1	2	yes	—
234	C₁₃×#95	C₂³	1	2	yes	—
235	C₁₃×#95	C₂³	1	2	yes	—
236	C₁₃×#95	C₂³	1	1	yes	characteristic
237	C₁₃×#95	C₂³	1	1	yes	characteristic
238	C₁₃×#95	C₂³	1	2	yes	—
239	C₁₃×#95	C₂³	1	1	yes	characteristic
240	C₁₃×#95	C₂³	1	2	yes	—
241	C₁₃×#95	C₂³	1	2	yes	—
242	C₁₃×#95	C₂³	1	2	yes	—
243	C₁₃×#95	C₂³	1	1	yes	characteristic
244	C₁₃×#95	C₂³	1	2	yes	—
245	C₁₃×#95	C₂³	1	1	yes	characteristic
246	#34298	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
249	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₁₃×#41	—	4	32	no	—
251	C₂×Q₈×C₁₃	—	4	2	no	—
252	C₂×Q₈×C₁₃	—	4	2	no	—
253	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	4	2	no	—
261	C₂×D₄×C₁₃	—	4	2	no	—
262	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
263	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	2	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	4	no	—
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	—	4	1	no	—
283	C₂²×C₄×C₁₃	—	4	2	no	—
284	C₂²×C₄×C₁₃	—	4	2	no	—
285	C₂²×C₄×C₁₃	—	4	2	no	—
286	C₂²×C₄×C₁₃	—	4	2	no	—
287	C₂²×C₄×C₁₃	—	4	2	no	—
288	C₂²×C₄×C₁₃	—	4	2	no	—
289	C₂²×C₄×C₁₃	—	4	2	no	—
290	C₂²×C₄×C₁₃	—	4	2	no	—
291	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
292	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
294	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
295	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	—	2	4	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	4	1	no	—
324	C₁₃×C₄⋊C₄	—	4	2	no	—
325	C₁₃×C₄⋊C₄	—	4	2	no	—
326	C₁₃×C₄⋊C₄	—	4	2	no	—
327	C₁₃×C₄⋊C₄	—	4	2	no	—
328	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
329	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
330	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
331	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
332	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
333	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
334	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
335	C₁₃×C₄⋊C₄	#41	1	4	yes	complemented
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	4	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	4	no	—
342	C₁₃×C₂²⋊C₄	—	2	4	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	—	4	2	no	—
347	C₁₃×C₂²⋊C₄	—	4	2	no	—
348	C₁₃×C₂²⋊C₄	—	4	1	no	—
349	C₁₃×C₂²⋊C₄	—	4	2	no	—
350	C₁₃×C₂²⋊C₄	—	4	2	no	—
351	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
352	C₁₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
353	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
354	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
355	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
356	C₄²×C₁₃	—	2	2	no	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	2	no	—
359	C₄²×C₁₃	—	2	4	no	—
360	C₄²×C₁₃	—	2	2	no	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	4	2	no	—
363	C₄²×C₁₃	—	4	2	no	—
364	C₄²×C₁₃	—	4	2	no	—
365	C₄²×C₁₃	—	4	2	no	—
366	C₄²×C₁₃	—	4	2	no	—
367	C₄²×C₁₃	—	4	2	no	—
368	C₄²×C₁₃	—	4	2	no	—
369	C₄²×C₁₃	—	4	2	no	—
370	C₄²×C₁₃	—	4	2	no	—
371	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
372	C₄²×C₁₃	#41	1	4	yes	complemented
373	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
374	#2374	C₂×C₁₃	1	2	yes	complemented
375	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
376	#2368	C₂×C₁₃	1	2	yes	complemented
377	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
378	#2361	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#2359	C₂×C₁₃	1	2	yes	complemented
380	#2357	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#2352	C₂×C₁₃	1	1	yes	characteristic, complemented
382	#2345	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#2344	C₂×C₁₃	1	1	yes	characteristic, complemented
384	#2339	C₂×C₁₃	1	2	yes	complemented
385	#2335	C₂×C₁₃	1	2	yes	complemented
386	#2332	C₂×C₁₃	1	2	yes	complemented
387	#2331	C₂×C₁₃	1	1	yes	characteristic, complemented
388	#2324	C₂×C₁₃	1	1	yes	characteristic, complemented
389	C₄×#123	C₂×C₁₃	1	2	yes	complemented
390	C₄×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
391	#2297	C₂×C₁₃	1	2	yes	complemented
392	#2290	C₂×C₁₃	1	1	yes	characteristic, complemented
393	#2275	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
395	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂³×C₁₃	—	2	1	no	—
397	C₂³×C₁₃	—	2	1	no	—
398	C₂³×C₁₃	—	2	1	no	—
399	C₂³×C₁₃	—	2	1	no	—
400	C₂³×C₁₃	—	2	1	no	—
401	C₂³×C₁₃	—	2	1	no	—
402	C₂³×C₁₃	—	2	2	no	—
403	C₂³×C₁₃	—	2	2	no	—
404	C₂³×C₁₃	—	2	2	no	—
405	C₂³×C₁₃	—	2	2	no	—
406	C₂³×C₁₃	—	2	1	no	—
407	C₂³×C₁₃	—	2	1	no	—
408	C₂³×C₁₃	—	2	1	no	—
409	C₂³×C₁₃	—	2	2	no	—
410	C₂³×C₁₃	—	2	1	no	—
411	C₂³×C₁₃	—	2	2	no	—
412	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
413	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
414	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
415	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
416	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
417	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
418	Q₈×C₁₃	—	4	8	no	—
419	D₄×C₁₃	—	2	16	no	—
420	D₄×C₁₃	—	2	8	no	—
421	D₄×C₁₃	—	2	8	no	—
422	D₄×C₁₃	—	4	8	no	—
423	C₂×C₄×C₁₃	—	2	8	no	—
424	C₂×C₄×C₁₃	—	2	16	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	1	no	—
443	C₂×C₄×C₁₃	—	2	1	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	8	no	—
448	C₂×C₄×C₁₃	—	2	8	no	—
449	C₂×C₄×C₁₃	—	2	1	no	—
450	C₂×C₄×C₁₃	—	2	1	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	1	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	1	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	1	no	—
465	C₂×C₄×C₁₃	—	2	1	no	—
466	C₂×C₄×C₁₃	—	2	2	no	—
467	C₂×C₄×C₁₃	—	2	1	no	—
468	C₂×C₄×C₁₃	—	2	2	no	—
469	C₂×C₄×C₁₃	—	2	1	no	—
470	C₂×C₄×C₁₃	—	2	2	no	—
471	C₂×C₄×C₁₃	—	2	1	no	—
472	C₂×C₄×C₁₃	—	2	1	no	—
473	C₂×C₄×C₁₃	—	4	8	no	—
474	C₂×C₄×C₁₃	—	4	8	no	—
475	C₂×C₄×C₁₃	—	4	4	no	—
476	C₂×C₄×C₁₃	—	4	8	no	—
477	C₂×C₄×C₁₃	—	8	4	no	—
478	C₂×C₄×C₁₃	—	8	4	no	—
479	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
484	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
485	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
486	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
487	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
488	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
489	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
490	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
491	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
492	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
493	C₂²×#41	C₂²×C₁₃	1	2	yes	—
494	#547	C₄×C₁₃	1	16	yes	complemented
495	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×#123	C₂²×C₁₃	1	2	yes	—
497	C₂×#123	C₂²×C₁₃	1	2	yes	—
498	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
499	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
504	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
507	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
508	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
509	C₂×#117	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
511	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
512	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
513	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
514	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
515	#391	C₂²×C₁₃	1	2	yes	—
516	#391	C₂²×C₁₃	1	2	yes	—
517	#391	C₂²×C₁₃	1	2	yes	—
518	#391	C₂²×C₁₃	1	2	yes	—
519	#390	C₂²×C₁₃	1	2	yes	—
520	#390	C₂²×C₁₃	1	1	yes	characteristic
521	#390	C₂²×C₁₃	1	1	yes	characteristic
522	#390	C₂²×C₁₃	1	2	yes	—
523	#389	C₂²×C₁₃	1	1	yes	characteristic
524	#389	C₂²×C₁₃	1	1	yes	characteristic
525	#389	C₂²×C₁₃	1	1	yes	characteristic
526	#389	C₂²×C₁₃	1	2	yes	—
527	#389	C₂²×C₁₃	1	1	yes	characteristic
528	#388	C₂²×C₁₃	1	2	yes	—
529	#388	C₂²×C₁₃	1	2	yes	—
530	#388	C₂²×C₁₃	1	2	yes	—
531	#388	C₂²×C₁₃	1	2	yes	—
532	#388	C₂²×C₁₃	1	1	yes	characteristic
533	#388	C₂²×C₁₃	1	2	yes	—
534	#388	C₂²×C₁₃	1	2	yes	—
535	#388	C₂²×C₁₃	1	2	yes	—
536	#388	C₂²×C₁₃	1	1	yes	characteristic
537	#387	C₂²×C₁₃	1	2	yes	—
538	#387	C₂²×C₁₃	1	2	yes	—
539	#387	C₂²×C₁₃	1	1	yes	characteristic
540	#387	C₂²×C₁₃	1	2	yes	—
541	#387	C₂²×C₁₃	1	2	yes	—
542	#387	C₂²×C₁₃	1	2	yes	—
543	#387	C₂²×C₁₃	1	2	yes	—
544	#387	C₂²×C₁₃	1	2	yes	—
545	#387	C₂²×C₁₃	1	1	yes	characteristic
546	#386	C₂²×C₁₃	1	2	yes	—
547	#386	C₂²×C₁₃	1	2	yes	—
548	#386	C₂²×C₁₃	1	1	yes	characteristic
549	#386	C₂²×C₁₃	1	2	yes	—
550	#386	C₂²×C₁₃	1	2	yes	—
551	#386	C₂²×C₁₃	1	1	yes	characteristic
552	#386	C₂²×C₁₃	1	2	yes	—
553	#385	C₂²×C₁₃	1	2	yes	—
554	#385	C₂²×C₁₃	1	2	yes	—
555	#385	C₂²×C₁₃	1	1	yes	characteristic
556	#385	C₂²×C₁₃	1	1	yes	characteristic
557	#382	C₂²×C₁₃	1	1	yes	characteristic
558	#381	C₂²×C₁₃	1	2	yes	—
559	#381	C₂²×C₁₃	1	2	yes	—
560	#380	C₂²×C₁₃	1	1	yes	characteristic
561	#380	C₂²×C₁₃	1	2	yes	—
562	#380	C₂²×C₁₃	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
569	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
573	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
583	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
584	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
587	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
588	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
589	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
590	#376	C₂²×C₁₃	1	1	yes	characteristic
591	C₂×#95	C₂²×C₁₃	1	2	yes	—
592	C₂×#95	C₂²×C₁₃	1	2	yes	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	2	2	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	2	2	no	—
597	C₂²×C₁₃	—	2	2	no	—
598	C₂²×C₁₃	—	2	2	no	—
599	C₂²×C₁₃	—	2	2	no	—
600	C₂²×C₁₃	—	2	4	no	—
601	C₂²×C₁₃	—	2	2	no	—
602	C₂²×C₁₃	—	2	4	no	—
603	C₂²×C₁₃	—	2	2	no	—
604	C₂²×C₁₃	—	2	4	no	—
605	C₂²×C₁₃	—	4	1	no	—
606	C₂²×C₁₃	—	4	2	no	—
607	C₂²×C₁₃	—	4	2	no	—
608	C₂²×C₁₃	—	4	1	no	—
609	C₂²×C₁₃	—	4	2	no	—
610	C₂²×C₁₃	—	4	1	no	—
611	C₂²×C₁₃	—	4	1	no	—
612	C₂²×C₁₃	—	4	2	no	—
613	C₂²×C₁₃	#518	1	4	yes	—
614	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
615	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
616	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
617	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
620	C₂²×C₁₃	#585	1	1	yes	characteristic
621	C₄×C₁₃	—	2	2	no	—
622	C₄×C₁₃	—	2	2	no	—
623	C₄×C₁₃	—	2	4	no	—
624	C₄×C₁₃	—	2	4	no	—
625	C₄×C₁₃	—	2	2	no	—
626	C₄×C₁₃	—	2	4	no	—
627	C₄×C₁₃	—	2	2	no	—
628	C₄×C₁₃	—	2	2	no	—
629	C₄×C₁₃	—	2	2	no	—
630	C₄×C₁₃	—	2	2	no	—
631	C₄×C₁₃	—	2	4	no	—
632	C₄×C₁₃	—	4	1	no	—
633	C₄×C₁₃	—	4	1	no	—
634	C₄×C₁₃	—	4	1	no	—
635	C₄×C₁₃	—	4	2	no	—
636	C₄×C₁₃	—	4	2	no	—
637	C₄×C₁₃	—	4	1	no	—
638	C₄×C₁₃	—	4	1	no	—
639	C₄×C₁₃	—	4	2	no	—
640	C₄×C₁₃	C₄×#41	1	4	yes	—
641	C₂×#41	—	4	4	no	—
642	C₂×#41	—	4	4	no	—
643	C₂×#41	C₂×C₄×C₁₃	1	16	yes	complemented
644	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
645	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
647	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
649	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
651	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
655	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
656	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
657	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
658	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
659	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
660	#123	C₂×C₄×C₁₃	1	16	yes	complemented
661	#123	C₂×C₄×C₁₃	1	16	yes	complemented
662	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
663	#121	C₂×C₄×C₁₃	1	8	yes	—
664	#121	C₂×C₄×C₁₃	1	8	yes	complemented
665	C₄×D₄	—	2	4	no	—
666	C₄×D₄	—	2	4	no	—
667	C₄×D₄	—	4	4	no	—
668	C₄×D₄	—	4	4	no	—
669	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
670	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
671	#117	—	2	4	no	—
672	#117	—	2	4	no	—
673	#117	—	4	4	no	—
674	C₂×C₄⋊C₄	—	2	4	no	—
675	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
676	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
677	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
717	C₂×C₄²	—	2	4	no	—
718	C₂×C₄²	—	4	4	no	—
719	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
720	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
726	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
727	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
728	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
729	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
730	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
731	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
732	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
733	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
734	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
736	#95	C₂³×C₁₃	1	1	yes	characteristic
737	#95	C₂³×C₁₃	1	2	yes	—
738	#95	C₂³×C₁₃	1	2	yes	—
739	#95	C₂³×C₁₃	1	2	yes	—
740	#95	C₂³×C₁₃	1	2	yes	—
741	#95	C₂³×C₁₃	1	2	yes	—
742	#95	C₂³×C₁₃	1	2	yes	—
743	#95	C₂³×C₁₃	1	1	yes	characteristic
744	#95	C₂³×C₁₃	1	1	yes	characteristic
745	#95	C₂³×C₁₃	1	1	yes	characteristic
746	#95	C₂³×C₁₃	1	1	yes	characteristic
747	#95	C₂³×C₁₃	1	2	yes	—
748	#95	C₂³×C₁₃	1	1	yes	characteristic
749	#95	C₂³×C₁₃	1	2	yes	—
750	#95	C₂³×C₁₃	1	2	yes	—
751	#95	C₂³×C₁₃	1	2	yes	—
752	#95	C₂³×C₁₃	1	2	yes	—
753	#95	C₂³×C₁₃	1	2	yes	—
754	#95	C₂³×C₁₃	1	2	yes	—
755	#95	C₂³×C₁₃	1	2	yes	—
756	#95	C₂³×C₁₃	1	2	yes	—
757	#95	C₂³×C₁₃	1	1	yes	characteristic
758	#95	C₂³×C₁₃	1	1	yes	characteristic
759	#95	C₂³×C₁₃	1	2	yes	—
760	#95	C₂³×C₁₃	1	1	yes	characteristic
761	#95	C₂³×C₁₃	1	1	yes	characteristic
762	#95	C₂³×C₁₃	1	2	yes	—
763	C₂×C₁₃	—	2	4	no	—
764	C₂×C₁₃	—	4	2	no	—
765	C₂×C₁₃	—	4	4	no	—
766	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
767	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
768	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
769	C₂×C₁₃	#3492	1	1	yes	characteristic
770	C₂×C₁₃	#3494	1	1	yes	characteristic
771	C₂×C₁₃	#3513	1	1	yes	characteristic
772	C₂×C₁₃	#3522	1	1	yes	characteristic
773	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
775	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
776	#41	—	4	32	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
789	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
790	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
791	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	—	2	2	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	4	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
818	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
819	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
820	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
821	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
822	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
828	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	4	2	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	1	no	—
854	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
855	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
856	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
857	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
858	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
859	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
860	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
861	C₄⋊C₄	C₁₃×#41	1	4	yes	complemented
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	1	no	—
877	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
878	C₂²⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	4	2	no	—
889	C₄²	—	4	2	no	—
890	C₄²	—	4	2	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	2	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	2	no	—
895	C₄²	—	4	2	no	—
896	C₄²	—	4	2	no	—
897	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
898	C₄²	C₁₃×#41	1	4	yes	complemented
899	C₁₃	#34298	1	1	yes	characteristic, direct product factor, Sylow
900	C₂³	—	2	1	no	—
901	C₂³	—	2	1	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	1	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	2	no	—
916	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
917	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
918	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
919	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
920	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
921	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
922	Q₈	—	4	8	no	—
923	D₄	—	2	16	no	—
924	D₄	—	2	8	no	—
925	D₄	—	2	8	no	—
926	D₄	—	4	8	no	—
927	C₂×C₄	—	2	8	no	—
928	C₂×C₄	—	2	16	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	8	no	—
952	C₂×C₄	—	2	8	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	8	4	no	—
982	C₂×C₄	—	8	4	no	—
983	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
984	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
985	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
986	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
987	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
988	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
989	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
990	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
991	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
992	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
993	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
994	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
995	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
996	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	—	4	2	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	C₁₃×#518	1	4	yes	—
1018	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
1019	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1020	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
1021	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1022	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1023	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1024	C₂²	C₁₃×#585	1	1	yes	characteristic
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	4	no	—
1028	C₄	—	2	4	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	4	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	4	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	2	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	C₄×C₁₃×#41	1	4	yes	—
1045	C₂	—	2	4	no	—
1046	C₂	—	4	2	no	—
1047	C₂	—	4	4	no	—
1048	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
1049	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
1050	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1051	C₂	C₁₃×#3492	1	1	yes	characteristic
1052	C₂	C₁₃×#3494	1	1	yes	characteristic
1053	C₂	C₁₃×#3513	1	1	yes	characteristic
1054	C₂	C₁₃×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2374	C₂	semidirect
3. C₁₃×#2369	C₂	semidirect
4. C₁₃×#2368	C₂	semidirect
5. C₁₃×#2363	C₂	semidirect
6. C₁₃×#2361	C₂	semidirect
7. C₁₃×#2359	C₂	semidirect
8. C₁₃×#2357	C₂	semidirect
9. C₁₃×#2352	C₂	semidirect
10. C₁₃×#2345	C₂	semidirect
11. C₁₃×#2344	C₂	semidirect
12. C₁₃×#2339	C₂	semidirect
13. C₁₃×#2335	C₂	semidirect
14. C₁₃×#2332	C₂	semidirect
15. C₁₃×#2331	C₂	semidirect
16. C₁₃×#2324	C₂	semidirect
17. C₄×C₁₃×#123	C₂	semidirect
18. C₄×C₁₃×#121	C₂	semidirect
19. C₁₃×#2297	C₂	semidirect
20. C₁₃×#2290	C₂	semidirect
21. C₁₃×#2275	C₂	semidirect
22. C₁₃×#2274	C₂	semidirect
23. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
25. C₁₃×#547	C₄	semidirect
126. C₂×C₁₃×#41	C₂×C₄	semidirect
142. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
143. C₁₃×#123	C₂×C₄	semidirect
144. C₁₃×#123	C₂×C₄	semidirect
145. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
147. C₁₃×#121	C₂×C₄	semidirect
152. C₄×D₄×C₁₃	C₂×C₄	semidirect
153. C₄×D₄×C₁₃	C₂×C₄	semidirect
158. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
159. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
246. #34298	C₁₃	direct (N × H)
335. C₁₃×C₄⋊C₄	#41	semidirect
372. C₄²×C₁₃	#41	semidirect
374. #2374	C₂×C₁₃	semidirect
375. #2369	C₂×C₁₃	semidirect
376. #2368	C₂×C₁₃	semidirect
377. #2363	C₂×C₁₃	semidirect
378. #2361	C₂×C₁₃	semidirect
379. #2359	C₂×C₁₃	semidirect
380. #2357	C₂×C₁₃	semidirect
381. #2352	C₂×C₁₃	semidirect
382. #2345	C₂×C₁₃	semidirect
383. #2344	C₂×C₁₃	semidirect
384. #2339	C₂×C₁₃	semidirect
385. #2335	C₂×C₁₃	semidirect
386. #2332	C₂×C₁₃	semidirect
387. #2331	C₂×C₁₃	semidirect
388. #2324	C₂×C₁₃	semidirect
389. C₄×#123	C₂×C₁₃	semidirect
390. C₄×#121	C₂×C₁₃	semidirect
391. #2297	C₂×C₁₃	semidirect
392. #2290	C₂×C₁₃	semidirect
393. #2275	C₂×C₁₃	semidirect
394. #2274	C₂×C₁₃	semidirect
395. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
494. #547	C₄×C₁₃	semidirect
643. C₂×#41	C₂×C₄×C₁₃	semidirect
659. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
660. #123	C₂×C₄×C₁₃	semidirect
661. #123	C₂×C₄×C₁₃	semidirect
662. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
664. #121	C₂×C₄×C₁₃	semidirect
669. C₄×D₄	C₂×C₄×C₁₃	semidirect
670. C₄×D₄	C₂×C₄×C₁₃	semidirect
675. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
676. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
861. C₄⋊C₄	C₁₃×#41	semidirect
898. C₄²	C₁₃×#41	semidirect
899. C₁₃	#34298	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#547	2
C₁₃×#2374	2
C₁₃×#2369	2
C₁₃×#2368	2
C₁₃×#2363	2
C₁₃×#2361	2
C₁₃×#2359	2
C₁₃×#2357	2
C₁₃×#2352	2
C₁₃×#2345	2
C₁₃×#2344	2
C₁₃×#2339	2
C₁₃×#2335	2
C₁₃×#2332	2
C₁₃×#2331	2
C₁₃×#2324	2
C₄×C₁₃×#123	2
C₄×C₁₃×#121	2
C₁₃×#2297	2
C₁₃×#2290	2
C₁₃×#2275	2
C₁₃×#2274	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34298	13

Subgroups — C13×#34298 #15720637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34298 #15720637