Subgroups — C₁₃×#34932 #15721271

Order 3328.

2428 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2553	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2537	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2496	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2489	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2427	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2422	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2285	C₂	1	2	yes	maximal, complemented
16	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₃×#529	—	2	16	no	—
20	C₂×C₁₃×#126	C₂²	1	4	yes	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	4	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	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	4	yes	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	4	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	4	yes	—
40	C₁₃×#399	C₂²	1	4	yes	—
41	C₁₃×#398	C₂²	1	4	yes	—
42	C₁₃×#397	C₂²	1	4	yes	—
43	C₁₃×#397	C₂²	1	4	yes	—
44	C₁₃×#397	C₂²	1	4	yes	—
45	C₁₃×#394	C₂²	1	4	yes	—
46	C₁₃×#394	C₂²	1	4	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#390	C₂²	1	2	yes	—
50	C₁₃×#389	C₂²	1	2	yes	—
51	C₁₃×#389	C₂²	1	2	yes	—
52	C₁₃×#389	C₂²	1	2	yes	—
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#388	C₂²	1	4	yes	—
55	C₁₃×#387	C₂²	1	4	yes	—
56	C₁₃×#386	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#384	C₂²	1	2	yes	—
59	C₁₃×#384	C₂²	1	1	yes	characteristic
60	C₁₃×#384	C₂²	1	2	yes	—
61	C₁₃×#382	C₂²	1	4	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₁₃×#380	C₂²	1	2	yes	—
64	C₁₃×#380	C₂²	1	2	yes	—
65	C₁₃×#380	C₂²	1	2	yes	—
66	C₁₃×#380	C₂²	1	4	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₄³×C₁₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₁₃×C₄⋊Q₈	—	2	4	no	—
95	C₁₃×#126	—	2	16	no	—
96	C₁₃×#125	—	2	8	no	—
97	C₁₃×#124	—	2	8	no	—
98	C₁₃×#123	—	2	16	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×C₂²⋊Q₈	—	2	8	no	—
101	C₁₃×#121	—	2	8	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₄×Q₈×C₁₃	—	2	8	no	—
104	C₄×D₄×C₁₃	—	2	4	no	—
105	C₄×D₄×C₁₃	—	2	16	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	D₄	1	8	yes	complemented
111	C₁₃×#117	—	2	16	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	—	2	8	no	—
142	C₂×C₄²×C₁₃	—	2	8	no	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	2	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	#34932	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
171	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
172	C₂×Q₈×C₁₃	—	2	4	no	—
173	C₂×Q₈×C₁₃	—	2	4	no	—
174	C₂×Q₈×C₁₃	—	2	4	no	—
175	C₂×D₄×C₁₃	—	2	8	no	—
176	C₂×D₄×C₁₃	—	2	8	no	—
177	C₂×D₄×C₁₃	—	2	2	no	—
178	C₂×D₄×C₁₃	—	2	2	no	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	4	4	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
183	C₂×D₄×C₁₃	#41	1	4	yes	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	4	2	no	—
200	C₂²×C₄×C₁₃	—	4	2	no	—
201	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	—	2	8	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	2	8	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	2	2	no	—
223	C₁₃×C₄⋊C₄	—	2	2	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	2	no	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	8	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	4	2	no	—
231	C₁₃×C₄⋊C₄	—	4	4	no	—
232	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
233	C₁₃×C₄⋊C₄	#41	1	4	yes	—
234	C₁₃×C₂²⋊C₄	—	2	8	no	—
235	C₁₃×C₂²⋊C₄	—	2	8	no	—
236	C₁₃×C₂²⋊C₄	—	2	8	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	8	no	—
239	C₁₃×C₂²⋊C₄	—	2	8	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	8	no	—
245	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
246	C₄²×C₁₃	—	2	4	no	—
247	C₄²×C₁₃	—	2	4	no	—
248	C₄²×C₁₃	—	2	4	no	—
249	C₄²×C₁₃	—	2	8	no	—
250	C₄²×C₁₃	—	2	4	no	—
251	C₄²×C₁₃	—	2	4	no	—
252	C₄²×C₁₃	—	2	4	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	—	2	2	no	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	—	4	1	no	—
257	C₄²×C₁₃	C₂×D₄	1	4	yes	—
258	C₄²×C₁₃	#41	1	4	yes	—
259	C₄²×C₁₃	#41	1	4	yes	—
260	C₂×#529	C₂×C₁₃	1	2	yes	complemented
261	#2553	C₂×C₁₃	1	4	yes	complemented
262	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2547	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2542	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2537	C₂×C₁₃	1	1	yes	characteristic
266	#2496	C₂×C₁₃	1	2	yes	complemented
267	#2489	C₂×C₁₃	1	2	yes	complemented
268	#2427	C₂×C₁₃	1	2	yes	complemented
269	#2422	C₂×C₁₃	1	2	yes	complemented
270	#2395	C₂×C₁₃	1	4	yes	complemented
271	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
273	C₄×#121	C₂×C₁₃	1	2	yes	complemented
274	#2285	C₂×C₁₃	1	2	yes	complemented
275	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
277	C₂³×C₁₃	—	2	2	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	2	2	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
290	C₂³×C₁₃	C₂×#41	1	4	yes	—
291	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
292	Q₈×C₁₃	—	4	8	no	—
293	D₄×C₁₃	—	2	8	no	—
294	D₄×C₁₃	—	2	8	no	—
295	D₄×C₁₃	—	4	16	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	16	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	4	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	4	8	no	—
329	C₂×C₄×C₁₃	—	4	8	no	—
330	C₂×C₄×C₁₃	—	4	8	no	—
331	C₂×C₄×C₁₃	—	4	8	no	—
332	C₂×C₄×C₁₃	—	4	8	no	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
335	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
340	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
341	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
342	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
343	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
344	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
346	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
347	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
348	#529	—	2	16	no	—
349	C₂×#126	C₂²×C₁₃	1	4	yes	—
350	C₂×#125	C₂²×C₁₃	1	2	yes	—
351	C₂×#124	C₂²×C₁₃	1	2	yes	—
352	C₂×#123	C₂²×C₁₃	1	4	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
354	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
355	C₂×#121	C₂²×C₁₃	1	2	yes	—
356	C₂×#121	C₂²×C₁₃	1	2	yes	—
357	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
359	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#117	C₂²×C₁₃	1	4	yes	—
366	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
367	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
368	#400	C₂²×C₁₃	1	4	yes	—
369	#399	C₂²×C₁₃	1	4	yes	—
370	#398	C₂²×C₁₃	1	4	yes	—
371	#397	C₂²×C₁₃	1	4	yes	—
372	#397	C₂²×C₁₃	1	4	yes	—
373	#397	C₂²×C₁₃	1	4	yes	—
374	#394	C₂²×C₁₃	1	4	yes	—
375	#394	C₂²×C₁₃	1	4	yes	—
376	#391	C₂²×C₁₃	1	2	yes	—
377	#391	C₂²×C₁₃	1	2	yes	—
378	#390	C₂²×C₁₃	1	2	yes	—
379	#389	C₂²×C₁₃	1	2	yes	—
380	#389	C₂²×C₁₃	1	2	yes	—
381	#389	C₂²×C₁₃	1	2	yes	—
382	#389	C₂²×C₁₃	1	2	yes	—
383	#388	C₂²×C₁₃	1	4	yes	—
384	#387	C₂²×C₁₃	1	4	yes	—
385	#386	C₂²×C₁₃	1	4	yes	—
386	#385	C₂²×C₁₃	1	4	yes	—
387	#384	C₂²×C₁₃	1	1	yes	characteristic
388	#384	C₂²×C₁₃	1	2	yes	—
389	#384	C₂²×C₁₃	1	2	yes	—
390	#382	C₂²×C₁₃	1	4	yes	—
391	#380	C₂²×C₁₃	1	2	yes	—
392	#380	C₂²×C₁₃	1	4	yes	—
393	#380	C₂²×C₁₃	1	2	yes	—
394	#380	C₂²×C₁₃	1	2	yes	—
395	#380	C₂²×C₁₃	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
399	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
400	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
404	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
412	C₄³	C₂²×C₁₃	1	1	yes	characteristic
413	C₂²×C₁₃	—	2	4	no	—
414	C₂²×C₁₃	—	2	4	no	—
415	C₂²×C₁₃	—	2	4	no	—
416	C₂²×C₁₃	—	2	4	no	—
417	C₂²×C₁₃	—	2	4	no	—
418	C₂²×C₁₃	—	2	4	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
428	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
431	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₁₃	#585	1	1	yes	characteristic
434	C₄×C₁₃	—	2	2	no	—
435	C₄×C₁₃	—	2	4	no	—
436	C₄×C₁₃	—	2	2	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	4	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	2	no	—
441	C₄×C₁₃	—	4	4	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	4	no	—
445	C₄×C₁₃	—	4	1	no	—
446	C₄×C₁₃	#529	1	4	yes	complemented
447	C₄×C₁₃	#532	1	4	yes	—
448	C₄×C₁₃	#547	1	4	yes	—
449	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
450	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
451	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
455	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
459	C₄⋊Q₈	—	2	4	no	—
460	#126	—	2	16	no	—
461	#125	—	2	8	no	—
462	#124	—	2	8	no	—
463	#123	—	2	16	no	—
464	C₂²⋊Q₈	—	2	8	no	—
465	C₂²⋊Q₈	—	2	8	no	—
466	#121	—	2	8	no	—
467	#121	—	2	8	no	—
468	C₄×Q₈	—	2	8	no	—
469	C₄×D₄	—	2	4	no	—
470	C₄×D₄	—	2	16	no	—
471	C₄×D₄	—	2	4	no	—
472	C₄×D₄	—	2	4	no	—
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	D₄×C₁₃	1	8	yes	complemented
476	#117	—	2	16	no	—
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₂×C₄²	—	2	8	no	—
507	C₂×C₄²	—	2	8	no	—
508	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
509	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
510	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
513	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
517	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
522	#95	C₂³×C₁₃	1	2	yes	—
523	#95	C₂³×C₁₃	1	2	yes	—
524	#95	C₂³×C₁₃	1	2	yes	—
525	#95	C₂³×C₁₃	1	2	yes	—
526	#95	C₂³×C₁₃	1	2	yes	—
527	#95	C₂³×C₁₃	1	2	yes	—
528	#95	C₂³×C₁₃	1	4	yes	—
529	#95	C₂³×C₁₃	1	4	yes	—
530	#95	C₂³×C₁₃	1	4	yes	—
531	#95	C₂³×C₁₃	1	4	yes	—
532	#95	C₂³×C₁₃	1	4	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	C₂×C₁₃	—	4	4	no	—
535	C₂×C₁₃	—	4	4	no	—
536	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
537	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
538	C₂×C₁₃	#3461	1	1	yes	characteristic
539	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
540	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
541	C₂×C₁₃	#3475	1	1	yes	characteristic
542	C₂×C₁₃	#3482	1	1	yes	characteristic
543	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
544	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
556	C₂×D₄	C₁₃×#41	1	4	yes	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
590	C₄⋊C₄	—	2	8	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	8	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	8	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	4	no	—
605	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
606	C₄⋊C₄	C₁₃×#41	1	4	yes	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	8	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	8	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	2	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	4	1	no	—
630	C₄²	C₂×D₄×C₁₃	1	4	yes	—
631	C₄²	C₁₃×#41	1	4	yes	—
632	C₄²	C₁₃×#41	1	4	yes	—
633	C₁₃	#34932	1	1	yes	characteristic, direct product factor, Sylow
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
647	C₂³	C₂×C₁₃×#41	1	4	yes	—
648	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
649	Q₈	—	4	8	no	—
650	D₄	—	2	8	no	—
651	D₄	—	2	8	no	—
652	D₄	—	4	16	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	16	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	8	no	—
689	C₂×C₄	—	4	8	no	—
690	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
694	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
695	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
696	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
697	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
698	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
699	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
700	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
701	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
702	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
703	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
719	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
720	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
721	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
722	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
723	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
724	C₂²	C₁₃×#585	1	1	yes	characteristic
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	1	no	—
737	C₄	C₁₃×#529	1	4	yes	complemented
738	C₄	C₁₃×#532	1	4	yes	—
739	C₄	C₁₃×#547	1	4	yes	—
740	C₂	—	4	4	no	—
741	C₂	—	4	4	no	—
742	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
743	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
744	C₂	C₁₃×#3461	1	1	yes	characteristic
745	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
746	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
747	C₂	C₁₃×#3475	1	1	yes	characteristic
748	C₂	C₁₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2537	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#2553	C₂	semidirect
3. C₁₃×#2552	C₂	semidirect
4. C₁₃×#2547	C₂	semidirect
5. C₁₃×#2542	C₂	semidirect
7. C₁₃×#2496	C₂	semidirect
8. C₁₃×#2489	C₂	semidirect
9. C₁₃×#2427	C₂	semidirect
10. C₁₃×#2422	C₂	semidirect
11. C₁₃×#2395	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₁₃×#2285	C₂	semidirect
16. C₄²×D₄×C₁₃	C₂	semidirect
17. C₄²×D₄×C₁₃	C₂	semidirect
110. C₄×D₄×C₁₃	D₄	semidirect
169. #34932	C₁₃	direct (N × H)
260. C₂×#529	C₂×C₁₃	semidirect
261. #2553	C₂×C₁₃	semidirect
262. #2552	C₂×C₁₃	semidirect
263. #2547	C₂×C₁₃	semidirect
264. #2542	C₂×C₁₃	semidirect
266. #2496	C₂×C₁₃	semidirect
267. #2489	C₂×C₁₃	semidirect
268. #2427	C₂×C₁₃	semidirect
269. #2422	C₂×C₁₃	semidirect
270. #2395	C₂×C₁₃	semidirect
271. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
272. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
273. C₄×#121	C₂×C₁₃	semidirect
274. #2285	C₂×C₁₃	semidirect
275. C₄²×D₄	C₂×C₁₃	semidirect
276. C₄²×D₄	C₂×C₁₃	semidirect
446. C₄×C₁₃	#529	semidirect
475. C₄×D₄	D₄×C₁₃	semidirect
633. C₁₃	#34932	direct (N × H)
737. C₄	C₁₃×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#529	2
C₁₃×#2553	2
C₁₃×#2552	2
C₁₃×#2547	2
C₁₃×#2542	2
C₁₃×#2537	2
C₁₃×#2496	2
C₁₃×#2489	2
C₁₃×#2427	2
C₁₃×#2422	2
C₁₃×#2395	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2285	2
C₄²×D₄×C₁₃	2
#34932	13

Subgroups — C13×#34932 #15721271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34932 #15721271