Subgroups — C₁₃×#61934 #15748273

Order 3328.

1690 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3121	C₂	1	4	yes	maximal, complemented
15	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic
17	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#563	—	2	2	no	—
19	C₁₃×#559	C₂²	1	2	yes	—
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#557	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	C₂²	1	2	yes	—
25	C₁₃×#556	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	—	2	2	no	—
29	D₄×Q₈×C₁₃	—	2	1	no	—
30	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#542	—	2	2	no	—
32	C₁₃×#542	C₂²	1	4	yes	—
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#536	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	—	2	1	no	—
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#497	C₂²	1	4	yes	—
45	C₁₃×#495	C₂²	1	4	yes	—
46	C₁₃×#494	C₂²	1	2	yes	—
47	C₁₃×#492	C₂²	1	2	yes	—
48	C₁₃×#489	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	2	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	—
53	C₁₃×#482	C₂²	1	2	yes	—
54	C₁₃×#477	C₂²	1	1	yes	characteristic
55	C₁₃×#477	C₂²	1	4	yes	—
56	C₁₃×#476	C₂²	1	1	yes	characteristic
57	C₁₃×#475	C₂²	1	1	yes	characteristic
58	C₁₃×#475	C₂²	1	4	yes	—
59	C₁₃×#474	C₂²	1	1	yes	characteristic
60	C₁₃×#464	C₂²	1	4	yes	—
61	C₁₃×#464	C₂²	1	4	yes	—
62	C₁₃×#464	C₂²	1	4	yes	—
63	C₁₃×#463	C₂²	1	4	yes	—
64	C₁₃×#462	C₂²	1	1	yes	characteristic
65	C₁₃×#462	C₂²	1	2	yes	—
66	C₁₃×#462	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	2	yes	—
68	C₁₃×#461	C₂²	1	2	yes	—
69	C₁₃×#461	C₂²	1	4	yes	—
70	C₁₃×#461	C₂²	1	1	yes	characteristic
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#460	C₂²	1	1	yes	characteristic
73	C₁₃×#459	C₂²	1	1	yes	characteristic
74	C₁₃×#452	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	4	yes	—
76	C₁₃×#449	C₂²	1	2	yes	—
77	C₁₃×#448	C₂²	1	4	yes	—
78	C₁₃×#446	C₂²	1	2	yes	—
79	C₁₃×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
81	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
82	C₁₃×#441	C₂²	1	4	yes	—
83	C₁₃×#440	C₂²	1	4	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
85	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
87	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
88	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
89	C₄×C₁₃×D₈	C₂²	1	2	yes	—
90	C₁₃×#433	C₂²	1	4	yes	—
91	C₁₃×#431	C₂²	1	1	yes	characteristic
92	C₁₃×#431	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	1	no	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	—	2	2	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×D₈	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	—	2	4	no	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	1	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#126	—	2	4	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	D₄	1	2	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	4	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	C₂³	1	4	yes	—
133	C₁₃×#124	C₂³	1	4	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	C₂³	1	2	yes	—
151	C₄×Q₈×C₁₃	—	2	2	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	2	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	—	2	1	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	C₂³	1	4	yes	—
173	C₁₃×#117	—	2	1	no	—
174	C₁₃×#117	—	2	2	no	—
175	C₁₃×#117	—	2	2	no	—
176	C₁₃×#117	—	2	2	no	—
177	C₁₃×#117	—	2	4	no	—
178	C₁₃×#117	—	2	1	no	—
179	C₁₃×#117	C₂³	1	1	yes	characteristic
180	C₁₃×#117	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×#107	C₂³	1	2	yes	—
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#106	C₂³	1	2	yes	—
188	C₁₃×#106	C₂³	1	2	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
190	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
191	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
194	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₁₃×#103	C₂³	1	2	yes	—
196	C₁₃×#103	C₂³	1	2	yes	—
197	C₁₃×#103	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×#97	C₂³	1	4	yes	—
210	C₄×C₈×C₁₃	C₂³	1	2	yes	—
211	C₄×C₈×C₁₃	C₂³	1	2	yes	—
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61934	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃×#41	—	4	1	no	—
215	C₁₃×#41	—	4	1	no	—
216	C₁₃×#41	—	8	2	no	—
217	C₂×Q₈×C₁₃	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	4	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	4	2	no	—
222	C₂×Q₈×C₁₃	—	4	2	no	—
223	C₂×Q₈×C₁₃	—	8	4	no	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
227	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₁₃×Q₁₆	—	4	4	no	—
245	C₁₃×Q₁₆	—	4	2	no	—
246	C₁₃×Q₁₆	—	4	4	no	—
247	C₁₃×SD₁₆	—	4	4	no	—
248	C₁₃×SD₁₆	—	4	2	no	—
249	C₁₃×SD₁₆	—	4	4	no	—
250	C₁₃×SD₁₆	—	4	2	no	—
251	C₁₃×D₈	—	4	2	no	—
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	2	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₄²×C₁₃	C₂⁴	1	4	yes	—
308	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3400	C₂×C₁₃	1	2	yes	complemented
311	#3398	C₂×C₁₃	1	2	yes	complemented
312	#3394	C₂×C₁₃	1	2	yes	complemented
313	#3393	C₂×C₁₃	1	2	yes	complemented
314	#3369	C₂×C₁₃	1	2	yes	complemented
315	#3367	C₂×C₁₃	1	2	yes	complemented
316	#3363	C₂×C₁₃	1	2	yes	complemented
317	#3359	C₂×C₁₃	1	2	yes	complemented
318	#3225	C₂×C₁₃	1	4	yes	complemented
319	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3121	C₂×C₁₃	1	4	yes	complemented
322	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#3106	C₂×C₁₃	1	1	yes	characteristic
324	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂³×C₁₃	—	2	1	no	—
326	C₂³×C₁₃	—	2	2	no	—
327	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₁₃	—	2	4	no	—
329	Q₈×C₁₃	—	2	4	no	—
330	Q₈×C₁₃	—	2	1	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	4	no	—
333	Q₈×C₁₃	—	2	4	no	—
334	Q₈×C₁₃	—	2	2	no	—
335	Q₈×C₁₃	—	2	1	no	—
336	Q₈×C₁₃	—	4	4	no	—
337	Q₈×C₁₃	—	4	2	no	—
338	Q₈×C₁₃	—	8	4	no	—
339	Q₈×C₁₃	—	8	1	no	—
340	D₄×C₁₃	—	2	1	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	2	1	no	—
344	D₄×C₁₃	—	4	2	no	—
345	D₄×C₁₃	—	4	2	no	—
346	D₄×C₁₃	—	8	1	no	—
347	D₄×C₁₃	—	8	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	4	2	no	—
362	C₂×C₄×C₁₃	—	4	4	no	—
363	C₂×C₄×C₁₃	—	4	2	no	—
364	C₂×C₄×C₁₃	—	8	4	no	—
365	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
373	C₈×C₁₃	—	2	2	no	—
374	C₈×C₁₃	—	2	2	no	—
375	C₈×C₁₃	—	2	2	no	—
376	C₈×C₁₃	—	2	2	no	—
377	#563	—	2	2	no	—
378	#559	C₂²×C₁₃	1	2	yes	—
379	Q₈²	C₂²×C₁₃	1	2	yes	—
380	#557	C₂²×C₁₃	1	2	yes	—
381	#557	C₂²×C₁₃	1	2	yes	—
382	#556	—	2	1	no	—
383	#556	C₂²×C₁₃	1	2	yes	—
384	#556	C₂²×C₁₃	1	2	yes	—
385	#556	C₂²×C₁₃	1	2	yes	—
386	#552	—	2	2	no	—
387	#552	—	2	2	no	—
388	D₄×Q₈	—	2	1	no	—
389	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
390	#542	—	2	2	no	—
391	#542	C₂²×C₁₃	1	4	yes	—
392	#541	—	2	2	no	—
393	#536	—	2	2	no	—
394	#536	C₂²×C₁₃	1	2	yes	—
395	#533	—	2	1	no	—
396	#533	—	2	1	no	—
397	#533	C₂²×C₁₃	1	1	yes	characteristic
398	#533	C₂²×C₁₃	1	1	yes	characteristic
399	#532	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	#519	C₂²×C₁₃	1	2	yes	—
402	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
403	#497	C₂²×C₁₃	1	4	yes	—
404	#495	C₂²×C₁₃	1	4	yes	—
405	#494	C₂²×C₁₃	1	2	yes	—
406	#492	C₂²×C₁₃	1	2	yes	—
407	#489	C₂²×C₁₃	1	4	yes	—
408	#487	C₂²×C₁₃	1	4	yes	—
409	#487	C₂²×C₁₃	1	2	yes	—
410	#487	C₂²×C₁₃	1	2	yes	—
411	#485	C₂²×C₁₃	1	2	yes	—
412	#482	C₂²×C₁₃	1	2	yes	—
413	#477	C₂²×C₁₃	1	1	yes	characteristic
414	#477	C₂²×C₁₃	1	4	yes	—
415	#476	C₂²×C₁₃	1	1	yes	characteristic
416	#475	C₂²×C₁₃	1	1	yes	characteristic
417	#475	C₂²×C₁₃	1	4	yes	—
418	#474	C₂²×C₁₃	1	1	yes	characteristic
419	#464	C₂²×C₁₃	1	4	yes	—
420	#464	C₂²×C₁₃	1	4	yes	—
421	#464	C₂²×C₁₃	1	4	yes	—
422	#463	C₂²×C₁₃	1	4	yes	—
423	#462	C₂²×C₁₃	1	1	yes	characteristic
424	#462	C₂²×C₁₃	1	2	yes	—
425	#462	C₂²×C₁₃	1	4	yes	—
426	#462	C₂²×C₁₃	1	2	yes	—
427	#461	C₂²×C₁₃	1	2	yes	—
428	#461	C₂²×C₁₃	1	4	yes	—
429	#461	C₂²×C₁₃	1	1	yes	characteristic
430	#461	C₂²×C₁₃	1	2	yes	—
431	#460	C₂²×C₁₃	1	1	yes	characteristic
432	#459	C₂²×C₁₃	1	1	yes	characteristic
433	#452	C₂²×C₁₃	1	2	yes	—
434	#451	C₂²×C₁₃	1	4	yes	—
435	#449	C₂²×C₁₃	1	2	yes	—
436	#448	C₂²×C₁₃	1	4	yes	—
437	#446	C₂²×C₁₃	1	2	yes	—
438	#446	C₂²×C₁₃	1	2	yes	—
439	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
440	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
441	#441	C₂²×C₁₃	1	4	yes	—
442	#440	C₂²×C₁₃	1	4	yes	—
443	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
444	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
445	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
446	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
447	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
448	C₄×D₈	C₂²×C₁₃	1	2	yes	—
449	#433	C₂²×C₁₃	1	4	yes	—
450	#431	C₂²×C₁₃	1	1	yes	characteristic
451	#431	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	2	1	no	—
464	C₄×C₁₃	—	2	4	no	—
465	C₄×C₁₃	—	2	1	no	—
466	C₄×C₁₃	—	2	4	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	4	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	1	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	#577	1	2	yes	—
475	C₄×C₁₃	#578	1	2	yes	—
476	C₄×C₁₃	#585	1	1	yes	characteristic
477	C₄×C₁₃	#585	1	1	yes	characteristic
478	C₂×#41	—	2	1	no	—
479	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×Q₈	—	2	2	no	—
481	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
482	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
483	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
484	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
485	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
486	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
489	C₂×D₈	C₂³×C₁₃	1	2	yes	—
490	C₄⋊Q₈	—	2	4	no	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	1	no	—
493	C₄⋊Q₈	—	2	1	no	—
494	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
503	#127	C₂³×C₁₃	1	1	yes	characteristic
504	#126	—	2	4	no	—
505	#126	—	2	4	no	—
506	#126	—	2	4	no	—
507	#126	—	2	4	no	—
508	#125	—	2	2	no	—
509	#125	—	2	2	no	—
510	#125	—	2	4	no	—
511	#125	—	2	4	no	—
512	#125	—	2	1	no	—
513	#125	D₄×C₁₃	1	2	yes	—
514	#124	—	2	2	no	—
515	#124	—	2	4	no	—
516	#124	—	2	1	no	—
517	#124	C₂³×C₁₃	1	4	yes	—
518	#124	C₂³×C₁₃	1	4	yes	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	—	2	4	no	—
531	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
532	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
533	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	#121	—	2	1	no	—
535	#121	C₂³×C₁₃	1	2	yes	—
536	C₄×Q₈	—	2	2	no	—
537	C₄×Q₈	—	2	2	no	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
548	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
549	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
555	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₁₃	1	2	yes	—
557	C₄×D₄	C₂³×C₁₃	1	4	yes	—
558	#117	—	2	1	no	—
559	#117	—	2	2	no	—
560	#117	—	2	2	no	—
561	#117	—	2	2	no	—
562	#117	—	2	4	no	—
563	#117	—	2	1	no	—
564	#117	C₂³×C₁₃	1	1	yes	characteristic
565	#117	C₂³×C₁₃	1	2	yes	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	#107	C₂³×C₁₃	1	2	yes	—
571	#107	C₂³×C₁₃	1	2	yes	—
572	#106	C₂³×C₁₃	1	2	yes	—
573	#106	C₂³×C₁₃	1	2	yes	—
574	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
579	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
580	#103	C₂³×C₁₃	1	2	yes	—
581	#103	C₂³×C₁₃	1	2	yes	—
582	#103	C₂³×C₁₃	1	4	yes	—
583	#103	C₂³×C₁₃	1	2	yes	—
584	#103	C₂³×C₁₃	1	4	yes	—
585	#103	C₂³×C₁₃	1	2	yes	—
586	#103	C₂³×C₁₃	1	4	yes	—
587	#103	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	2	yes	—
589	#102	C₂³×C₁₃	1	2	yes	—
590	#102	C₂³×C₁₃	1	2	yes	—
591	#102	C₂³×C₁₃	1	2	yes	—
592	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
593	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
594	#97	C₂³×C₁₃	1	4	yes	—
595	C₄×C₈	C₂³×C₁₃	1	2	yes	—
596	C₄×C₈	C₂³×C₁₃	1	2	yes	—
597	C₄×C₈	C₂³×C₁₃	1	4	yes	—
598	C₂×C₁₃	—	4	1	no	—
599	C₂×C₁₃	—	8	1	no	—
600	C₂×C₁₃	—	8	2	no	—
601	C₂×C₁₃	#3487	1	1	yes	characteristic
602	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
603	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
604	#41	—	4	1	no	—
605	#41	—	4	1	no	—
606	#41	—	8	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	8	4	no	—
614	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
615	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
616	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
617	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
634	Q₁₆	—	4	4	no	—
635	Q₁₆	—	4	2	no	—
636	Q₁₆	—	4	4	no	—
637	SD₁₆	—	4	4	no	—
638	SD₁₆	—	4	2	no	—
639	SD₁₆	—	4	4	no	—
640	SD₁₆	—	4	2	no	—
641	D₈	—	4	2	no	—
642	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
643	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
644	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
645	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
665	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
666	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
667	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
669	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
686	C₄²	—	2	1	no	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	4	no	—
693	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
695	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₄²	C₂⁴×C₁₃	1	4	yes	—
698	C₁₃	#61934	1	1	yes	characteristic, direct product factor, Sylow
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
702	Q₈	—	2	4	no	—
703	Q₈	—	2	4	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	4	4	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	4	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	1	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	8	1	no	—
721	D₄	—	8	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
740	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
742	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
761	C₄	—	2	1	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	2	no	—
773	C₄	C₁₃×#577	1	2	yes	—
774	C₄	C₁₃×#578	1	2	yes	—
775	C₄	C₁₃×#585	1	1	yes	characteristic
776	C₄	C₁₃×#585	1	1	yes	characteristic
777	C₂	—	4	1	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	1	no	—
780	C₂	C₁₃×#3487	1	1	yes	characteristic
781	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
782	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3394	C₂	semidirect
6. C₁₃×#3393	C₂	semidirect
7. C₁₃×#3369	C₂	semidirect
8. C₁₃×#3367	C₂	semidirect
9. C₁₃×#3363	C₂	semidirect
10. C₁₃×#3359	C₂	semidirect
11. C₁₃×#3225	C₂	semidirect
12. C₁₃×#3209	C₂	semidirect
13. C₁₃×#3206	C₂	semidirect
14. C₁₃×#3121	C₂	semidirect
15. C₁₃×#3107	C₂	semidirect
17. C₁₃×#2986	C₂	semidirect
213. #61934	C₁₃	direct (N × H)
308. #3550	C₂×C₁₃	semidirect
309. #3509	C₂×C₁₃	semidirect
310. #3400	C₂×C₁₃	semidirect
311. #3398	C₂×C₁₃	semidirect
312. #3394	C₂×C₁₃	semidirect
313. #3393	C₂×C₁₃	semidirect
314. #3369	C₂×C₁₃	semidirect
315. #3367	C₂×C₁₃	semidirect
316. #3363	C₂×C₁₃	semidirect
317. #3359	C₂×C₁₃	semidirect
318. #3225	C₂×C₁₃	semidirect
319. #3209	C₂×C₁₃	semidirect
320. #3206	C₂×C₁₃	semidirect
321. #3121	C₂×C₁₃	semidirect
322. #3107	C₂×C₁₃	semidirect
324. #2986	C₂×C₁₃	semidirect
698. C₁₃	#61934	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×#3550	2
C₁₃×#3509	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3369	2
C₁₃×#3367	2
C₁₃×#3363	2
C₁₃×#3359	2
C₁₃×#3225	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3121	2
C₁₃×#3107	2
C₁₃×#3106	2
C₁₃×#2986	2
#61934	13

Subgroups — C13×#61934 #15748273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61934 #15748273