Subgroups — C₁₃×#25142 #15711481

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3056	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2933	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2047	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2020	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1908	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×#525	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₃×#473	—	2	4	no	—
28	C₁₃×#470	—	2	1	no	—
29	C₁₃×#468	—	2	1	no	—
30	C₁₃×#467	—	2	1	no	—
31	C₁₃×#465	—	2	1	no	—
32	C₁₃×#451	—	2	1	no	—
33	C₁₃×#451	—	2	1	no	—
34	C₁₃×#451	—	2	1	no	—
35	C₁₃×#451	—	2	1	no	—
36	C₁₃×#451	—	2	1	no	—
37	C₁₃×#451	—	2	1	no	—
38	C₁₃×#448	—	2	1	no	—
39	C₁₃×#448	—	2	1	no	—
40	C₁₃×#436	—	2	1	no	—
41	C₁₃×#435	—	2	1	no	—
42	C₁₃×#435	—	2	1	no	—
43	C₈×D₄×C₁₃	—	2	1	no	—
44	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
46	C₁₃×#428	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#419	C₂²	1	1	yes	characteristic
49	C₁₃×#419	C₂²	1	1	yes	characteristic
50	C₁₃×#419	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#101	—	2	4	no	—
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
61	C₁₃×#408	C₂²	1	1	yes	characteristic
62	C₁₃×#407	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×#405	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#341	C₂²	1	1	yes	characteristic
68	C₁₃×#341	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	—	2	2	no	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₂²×Q₈×C₁₃	—	2	1	no	—
73	C₂²×Q₈×C₁₃	—	2	1	no	—
74	C₂²×Q₈×C₁₃	—	2	1	no	—
75	C₂²×Q₈×C₁₃	—	2	1	no	—
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	—	4	1	no	—
78	C₂²×Q₈×C₁₃	—	4	1	no	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#137	—	2	2	no	—
85	C₁₃×#137	—	2	2	no	—
86	C₁₃×#137	—	2	2	no	—
87	C₁₃×#137	—	4	1	no	—
88	C₁₃×#137	—	4	1	no	—
89	C₁₃×#137	—	4	1	no	—
90	C₂×C₁₃×Q₁₆	—	2	1	no	—
91	C₂×C₁₃×Q₁₆	—	2	1	no	—
92	C₂×C₁₃×Q₁₆	—	2	1	no	—
93	C₂×C₁₃×Q₁₆	—	2	2	no	—
94	C₂×C₁₃×Q₁₆	—	2	2	no	—
95	C₂×C₁₃×Q₁₆	—	2	1	no	—
96	C₂×C₁₃×Q₁₆	—	2	1	no	—
97	C₂×C₁₃×Q₁₆	—	2	1	no	—
98	C₂×C₁₃×Q₁₆	—	2	1	no	—
99	C₂×C₁₃×Q₁₆	—	4	1	no	—
100	C₂×C₁₃×Q₁₆	—	4	1	no	—
101	C₂×C₁₃×SD₁₆	—	2	1	no	—
102	C₂×C₁₃×SD₁₆	—	2	1	no	—
103	C₂×C₁₃×SD₁₆	—	2	1	no	—
104	C₁₃×#131	—	2	2	no	—
105	C₁₃×#131	—	4	1	no	—
106	C₂×C₁₃×M₁₆	—	2	1	no	—
107	C₂×C₁₃×M₁₆	—	2	1	no	—
108	C₂×C₁₃×M₁₆	—	2	1	no	—
109	C₂×C₁₃×M₁₆	—	2	2	no	—
110	C₂×C₁₃×M₁₆	—	2	2	no	—
111	C₂×C₁₃×M₁₆	—	4	1	no	—
112	C₂×C₁₃×M₁₆	—	4	1	no	—
113	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₁₃	—	2	1	no	—
120	C₂²×C₈×C₁₃	—	2	1	no	—
121	C₂²×C₈×C₁₃	—	2	1	no	—
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#123	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	—	2	1	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₁₃×#121	D₄	1	1	yes	characteristic
132	C₁₃×#121	D₄	1	1	yes	characteristic
133	C₁₃×#120	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₁₃×#117	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
140	C₁₃×#108	—	2	2	no	—
141	C₁₃×#108	—	4	1	no	—
142	C₁₃×#107	—	2	1	no	—
143	C₁₃×#106	—	2	1	no	—
144	C₁₃×C₄⋊C₈	—	2	1	no	—
145	C₁₃×C₄⋊C₈	—	2	1	no	—
146	C₁₃×#103	—	2	1	no	—
147	C₁₃×#103	—	2	1	no	—
148	C₁₃×#103	—	2	1	no	—
149	C₁₃×#103	—	2	1	no	—
150	C₁₃×#103	—	2	1	no	—
151	C₁₃×#103	—	2	1	no	—
152	C₁₃×#103	—	2	1	no	—
153	C₁₃×#103	—	2	1	no	—
154	C₁₃×#103	—	2	1	no	—
155	C₁₃×#103	—	2	1	no	—
156	C₁₃×#103	—	2	1	no	—
157	C₁₃×#102	—	2	1	no	—
158	C₁₃×#101	—	2	2	no	—
159	C₁₃×#101	—	2	2	no	—
160	C₁₃×#101	—	2	2	no	—
161	C₁₃×#101	—	2	2	no	—
162	C₁₃×#101	—	4	1	no	—
163	C₁₃×#101	D₄	1	4	yes	complemented
164	C₁₃×C₂²⋊C₈	—	2	1	no	—
165	C₁₃×C₂²⋊C₈	—	2	1	no	—
166	C₁₃×C₂²⋊C₈	—	2	1	no	—
167	C₁₃×C₂²⋊C₈	—	2	1	no	—
168	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	#25142	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂⁴×C₁₃	#41	1	1	yes	characteristic
176	C₁₃×#41	—	2	1	no	—
177	C₁₃×#41	—	2	1	no	—
178	C₁₃×#41	—	2	1	no	—
179	C₁₃×#41	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	4	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	—	2	1	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	1	no	—
191	C₂×Q₈×C₁₃	—	2	1	no	—
192	C₂×Q₈×C₁₃	—	2	1	no	—
193	C₂×Q₈×C₁₃	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	1	no	—
197	C₂×Q₈×C₁₃	—	4	2	no	—
198	C₂×Q₈×C₁₃	—	4	2	no	—
199	C₂×Q₈×C₁₃	—	4	2	no	—
200	C₂×Q₈×C₁₃	—	4	2	no	—
201	C₂×Q₈×C₁₃	—	4	2	no	—
202	C₂×Q₈×C₁₃	—	4	2	no	—
203	C₂×Q₈×C₁₃	—	4	2	no	—
204	C₂×Q₈×C₁₃	—	4	2	no	—
205	C₂×Q₈×C₁₃	—	4	2	no	—
206	C₂×Q₈×C₁₃	—	4	1	no	—
207	C₂×Q₈×C₁₃	—	4	1	no	—
208	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×Q₈×C₁₃	#41	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	4	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	1	no	—
227	C₂²×C₄×C₁₃	—	4	1	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₁₃×Q₁₆	—	4	2	no	—
235	C₁₃×Q₁₆	—	4	2	no	—
236	C₁₃×Q₁₆	—	4	2	no	—
237	C₁₃×Q₁₆	—	4	2	no	—
238	C₁₃×Q₁₆	—	4	2	no	—
239	C₁₃×Q₁₆	—	4	2	no	—
240	C₁₃×Q₁₆	—	4	2	no	—
241	C₁₃×SD₁₆	—	4	2	no	—
242	C₁₃×SD₁₆	—	4	2	no	—
243	C₁₃×SD₁₆	—	4	2	no	—
244	C₁₃×M₁₆	—	2	1	no	—
245	C₁₃×M₁₆	—	2	1	no	—
246	C₁₃×M₁₆	—	2	1	no	—
247	C₁₃×M₁₆	—	2	1	no	—
248	C₁₃×M₁₆	—	2	1	no	—
249	C₁₃×M₁₆	—	2	1	no	—
250	C₁₃×M₁₆	—	2	1	no	—
251	C₁₃×M₁₆	—	2	1	no	—
252	C₁₃×M₁₆	—	2	1	no	—
253	C₁₃×M₁₆	—	2	1	no	—
254	C₁₃×M₁₆	—	4	2	no	—
255	C₁₃×M₁₆	—	4	2	no	—
256	C₁₃×M₁₆	—	4	2	no	—
257	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
258	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
259	C₂×C₈×C₁₃	—	2	1	no	—
260	C₂×C₈×C₁₃	—	2	1	no	—
261	C₂×C₈×C₁₃	—	2	1	no	—
262	C₂×C₈×C₁₃	—	2	1	no	—
263	C₂×C₈×C₁₃	—	2	1	no	—
264	C₂×C₈×C₁₃	—	2	1	no	—
265	C₂×C₈×C₁₃	—	2	1	no	—
266	C₂×C₈×C₁₃	—	2	1	no	—
267	C₂×C₈×C₁₃	—	2	1	no	—
268	C₂×C₈×C₁₃	—	2	1	no	—
269	C₂×C₈×C₁₃	—	4	2	no	—
270	C₂×C₈×C₁₃	—	4	2	no	—
271	C₂×C₈×C₁₃	—	4	2	no	—
272	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₁₃×C₄⋊C₄	—	2	1	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	4	1	no	—
281	C₁₃×C₄⋊C₄	—	4	1	no	—
282	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
283	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	4	1	no	—
290	C₁₃×C₂²⋊C₄	—	4	1	no	—
291	C₄²×C₁₃	—	2	1	no	—
292	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3056	C₂×C₁₃	1	1	yes	characteristic
294	#3004	C₂×C₁₃	1	1	yes	characteristic
295	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2933	C₂×C₁₃	1	1	yes	characteristic
297	C₂²×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2052	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2047	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2020	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#1979	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1908	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	2	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	#121	1	1	yes	characteristic
313	C₂³×C₁₃	#121	1	1	yes	characteristic
314	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	2	1	no	—
317	Q₈×C₁₃	—	2	2	no	—
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	2	1	no	—
321	Q₈×C₁₃	—	4	4	no	—
322	Q₈×C₁₃	—	4	4	no	—
323	Q₈×C₁₃	—	4	1	no	—
324	Q₈×C₁₃	—	4	1	no	—
325	Q₈×C₁₃	—	4	1	no	—
326	Q₈×C₁₃	—	4	1	no	—
327	Q₈×C₁₃	—	4	1	no	—
328	Q₈×C₁₃	—	4	1	no	—
329	Q₈×C₁₃	—	4	1	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	D₄×C₁₃	—	2	1	no	—
332	D₄×C₁₃	—	2	1	no	—
333	D₄×C₁₃	—	4	1	no	—
334	D₄×C₁₃	—	4	1	no	—
335	D₄×C₁₃	—	4	2	no	—
336	D₄×C₁₃	—	8	1	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	4	4	no	—
353	C₂×C₄×C₁₃	—	4	4	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	1	no	—
356	C₂×C₄×C₁₃	—	4	1	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	8	1	no	—
365	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
366	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
373	C₈×C₁₃	—	2	1	no	—
374	C₈×C₁₃	—	2	1	no	—
375	C₈×C₁₃	—	2	2	no	—
376	C₈×C₁₃	—	2	2	no	—
377	C₈×C₁₃	—	2	1	no	—
378	C₈×C₁₃	—	2	1	no	—
379	C₈×C₁₃	—	4	1	no	—
380	C₈×C₁₃	—	4	1	no	—
381	C₈×C₁₃	—	4	1	no	—
382	C₈×C₁₃	—	4	1	no	—
383	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
390	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
392	#525	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
394	#473	—	2	4	no	—
395	#470	—	2	1	no	—
396	#468	—	2	1	no	—
397	#467	—	2	1	no	—
398	#465	—	2	1	no	—
399	#451	—	2	1	no	—
400	#451	—	2	1	no	—
401	#451	—	2	1	no	—
402	#451	—	2	1	no	—
403	#451	—	2	1	no	—
404	#451	—	2	1	no	—
405	#448	—	2	1	no	—
406	#448	—	2	1	no	—
407	#436	—	2	1	no	—
408	#435	—	2	1	no	—
409	#435	—	2	1	no	—
410	C₈×D₄	—	2	1	no	—
411	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
413	#428	C₂²×C₁₃	1	1	yes	characteristic
414	#424	C₂²×C₁₃	1	1	yes	characteristic
415	#419	C₂²×C₁₃	1	1	yes	characteristic
416	#419	C₂²×C₁₃	1	1	yes	characteristic
417	#419	C₂²×C₁₃	1	1	yes	characteristic
418	#417	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#101	—	2	4	no	—
422	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
428	#408	C₂²×C₁₃	1	1	yes	characteristic
429	#407	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
431	#405	C₂²×C₁₃	1	1	yes	characteristic
432	#343	C₂²×C₁₃	1	1	yes	characteristic
433	#343	C₂²×C₁₃	1	1	yes	characteristic
434	#341	C₂²×C₁₃	1	1	yes	characteristic
435	#341	C₂²×C₁₃	1	1	yes	characteristic
436	C₂²×C₁₃	—	2	1	no	—
437	C₂²×C₁₃	—	2	1	no	—
438	C₂²×C₁₃	—	2	1	no	—
439	C₂²×C₁₃	—	2	1	no	—
440	C₂²×C₁₃	—	2	1	no	—
441	C₂²×C₁₃	—	2	1	no	—
442	C₂²×C₁₃	—	2	1	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	1	no	—
446	C₂²×C₁₃	—	4	1	no	—
447	C₂²×C₁₃	—	4	1	no	—
448	C₂²×C₁₃	#473	1	2	yes	complemented
449	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
450	C₂²×C₁₃	#525	1	1	yes	characteristic
451	C₂²×C₁₃	#538	1	1	yes	characteristic
452	C₄×C₁₃	—	2	1	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	1	no	—
457	C₄×C₁₃	—	4	1	no	—
458	C₄×C₁₃	—	4	1	no	—
459	C₄×C₁₃	—	8	1	no	—
460	C₄×C₁₃	—	8	1	no	—
461	C₄×C₁₃	D₄²	1	1	yes	characteristic
462	C₄×C₁₃	D₄²	1	1	yes	characteristic
463	C₄×C₁₃	#546	1	1	yes	characteristic
464	C₄×C₁₃	#546	1	1	yes	characteristic
465	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	2	1	no	—
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	—	2	1	no	—
471	C₂²×Q₈	—	2	1	no	—
472	C₂²×Q₈	—	2	1	no	—
473	C₂²×Q₈	—	4	1	no	—
474	C₂²×Q₈	—	4	1	no	—
475	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
480	#137	—	2	2	no	—
481	#137	—	2	2	no	—
482	#137	—	2	2	no	—
483	#137	—	4	1	no	—
484	#137	—	4	1	no	—
485	#137	—	4	1	no	—
486	C₂×Q₁₆	—	2	2	no	—
487	C₂×Q₁₆	—	2	1	no	—
488	C₂×Q₁₆	—	2	1	no	—
489	C₂×Q₁₆	—	2	1	no	—
490	C₂×Q₁₆	—	2	2	no	—
491	C₂×Q₁₆	—	2	1	no	—
492	C₂×Q₁₆	—	2	1	no	—
493	C₂×Q₁₆	—	2	1	no	—
494	C₂×Q₁₆	—	2	1	no	—
495	C₂×Q₁₆	—	4	1	no	—
496	C₂×Q₁₆	—	4	1	no	—
497	C₂×SD₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	1	no	—
499	C₂×SD₁₆	—	2	1	no	—
500	#131	—	2	2	no	—
501	#131	—	4	1	no	—
502	C₂×M₁₆	—	2	1	no	—
503	C₂×M₁₆	—	2	1	no	—
504	C₂×M₁₆	—	2	1	no	—
505	C₂×M₁₆	—	2	2	no	—
506	C₂×M₁₆	—	2	2	no	—
507	C₂×M₁₆	—	4	1	no	—
508	C₂×M₁₆	—	4	1	no	—
509	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
510	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
511	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
512	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	—	2	1	no	—
516	C₂²×C₈	—	2	1	no	—
517	C₂²×C₈	—	2	1	no	—
518	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
520	#123	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
526	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
527	#121	D₄×C₁₃	1	1	yes	characteristic
528	#121	D₄×C₁₃	1	1	yes	characteristic
529	#120	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	#117	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	#108	—	2	2	no	—
537	#108	—	4	1	no	—
538	#107	—	2	1	no	—
539	#106	—	2	1	no	—
540	C₄⋊C₈	—	2	1	no	—
541	C₄⋊C₈	—	2	1	no	—
542	#103	—	2	1	no	—
543	#103	—	2	1	no	—
544	#103	—	2	1	no	—
545	#103	—	2	1	no	—
546	#103	—	2	1	no	—
547	#103	—	2	1	no	—
548	#103	—	2	1	no	—
549	#103	—	2	1	no	—
550	#103	—	2	1	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#102	—	2	1	no	—
554	#101	—	2	2	no	—
555	#101	—	2	2	no	—
556	#101	—	2	2	no	—
557	#101	—	2	2	no	—
558	#101	—	4	1	no	—
559	#101	D₄×C₁₃	1	4	yes	complemented
560	C₂²⋊C₈	—	2	1	no	—
561	C₂²⋊C₈	—	2	1	no	—
562	C₂²⋊C₈	—	2	1	no	—
563	C₂²⋊C₈	—	2	1	no	—
564	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
565	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
566	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
567	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
568	#97	—	2	1	no	—
569	C₄×C₈	—	2	1	no	—
570	C₂×C₁₃	—	2	1	no	—
571	C₂×C₁₃	—	2	1	no	—
572	C₂×C₁₃	—	2	2	no	—
573	C₂×C₁₃	—	4	1	no	—
574	C₂×C₁₃	—	8	1	no	—
575	C₂×C₁₃	#2424	1	1	yes	characteristic
576	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
577	C₂×C₁₃	#3069	1	1	yes	characteristic
578	C₂⁴	C₁₃×#41	1	1	yes	characteristic
579	#41	—	2	1	no	—
580	#41	—	2	1	no	—
581	#41	—	2	1	no	—
582	#41	—	2	1	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	—	2	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	4	2	no	—
601	C₂×Q₈	—	4	2	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×Q₈	—	4	2	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	—	4	2	no	—
606	C₂×Q₈	—	4	2	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	2	no	—
609	C₂×Q₈	—	4	1	no	—
610	C₂×Q₈	—	4	1	no	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₂×Q₈	C₁₃×#41	1	2	yes	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	4	2	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
635	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
637	Q₁₆	—	4	2	no	—
638	Q₁₆	—	4	2	no	—
639	Q₁₆	—	4	2	no	—
640	Q₁₆	—	4	2	no	—
641	Q₁₆	—	4	2	no	—
642	Q₁₆	—	4	2	no	—
643	Q₁₆	—	4	2	no	—
644	SD₁₆	—	4	2	no	—
645	SD₁₆	—	4	2	no	—
646	SD₁₆	—	4	2	no	—
647	M₁₆	—	2	1	no	—
648	M₁₆	—	2	1	no	—
649	M₁₆	—	2	1	no	—
650	M₁₆	—	2	1	no	—
651	M₁₆	—	2	1	no	—
652	M₁₆	—	2	1	no	—
653	M₁₆	—	2	1	no	—
654	M₁₆	—	2	1	no	—
655	M₁₆	—	2	1	no	—
656	M₁₆	—	2	1	no	—
657	M₁₆	—	4	2	no	—
658	M₁₆	—	4	2	no	—
659	M₁₆	—	4	2	no	—
660	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
661	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	2	1	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	4	2	no	—
673	C₂×C₈	—	4	2	no	—
674	C₂×C₈	—	4	2	no	—
675	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
678	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	1	no	—
685	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	4	1	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₄²	—	2	1	no	—
695	C₁₃	#25142	1	1	yes	characteristic, direct product factor, Sylow
696	C₂³	—	2	2	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	C₁₃×#121	1	1	yes	characteristic
702	C₂³	C₁₃×#121	1	1	yes	characteristic
703	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	4	4	no	—
711	Q₈	—	4	4	no	—
712	Q₈	—	4	1	no	—
713	Q₈	—	4	1	no	—
714	Q₈	—	4	1	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	1	no	—
717	Q₈	—	4	1	no	—
718	Q₈	—	4	1	no	—
719	Q₈	—	4	1	no	—
720	D₄	—	2	1	no	—
721	D₄	—	2	1	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	8	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
755	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
759	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
760	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	—	2	2	no	—
765	C₈	—	2	2	no	—
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₈	—	4	1	no	—
771	C₈	—	4	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	C₁₃×#473	1	2	yes	complemented
785	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
786	C₂²	C₁₃×#525	1	1	yes	characteristic
787	C₂²	C₁₃×#538	1	1	yes	characteristic
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	8	1	no	—
796	C₄	—	8	1	no	—
797	C₄	D₄²×C₁₃	1	1	yes	characteristic
798	C₄	D₄²×C₁₃	1	1	yes	characteristic
799	C₄	C₁₃×#546	1	1	yes	characteristic
800	C₄	C₁₃×#546	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	2	1	no	—
803	C₂	—	2	1	no	—
804	C₂	—	4	1	no	—
805	C₂	—	8	1	no	—
806	C₂	C₁₃×#2424	1	1	yes	characteristic
807	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
808	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#473	C₂	semidirect
4. C₂×C₁₃×#451	C₂	semidirect
6. C₂²×C₁₃×#101	C₂	semidirect
7. C₁₃×#2064	C₂	semidirect
8. C₁₃×#2052	C₂	semidirect
9. C₁₃×#2047	C₂	semidirect
10. C₁₃×#2020	C₂	semidirect
11. C₁₃×#1979	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1908	C₂	semidirect
14. C₁₃×#1901	C₂	semidirect
15. C₁₃×#1855	C₂	semidirect
163. C₁₃×#101	D₄	semidirect
174. #25142	C₁₃	direct (N × H)
292. C₂×#473	C₂×C₁₃	semidirect
295. C₂×#451	C₂×C₁₃	semidirect
297. C₂²×#101	C₂×C₁₃	semidirect
298. #2064	C₂×C₁₃	semidirect
299. #2052	C₂×C₁₃	semidirect
300. #2047	C₂×C₁₃	semidirect
301. #2020	C₂×C₁₃	semidirect
302. #1979	C₂×C₁₃	semidirect
303. #1930	C₂×C₁₃	semidirect
304. #1908	C₂×C₁₃	semidirect
305. #1901	C₂×C₁₃	semidirect
306. #1855	C₂×C₁₃	semidirect
448. C₂²×C₁₃	#473	semidirect
559. #101	D₄×C₁₃	semidirect
695. C₁₃	#25142	direct (N × H)
784. C₂²	C₁₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#473	2
C₁₃×#3056	2
C₁₃×#3004	2
C₂×C₁₃×#451	2
C₁₃×#2933	2
C₂²×C₁₃×#101	2
C₁₃×#2064	2
C₁₃×#2052	2
C₁₃×#2047	2
C₁₃×#2020	2
C₁₃×#1979	2
C₁₃×#1930	2
C₁₃×#1908	2
C₁₃×#1901	2
C₁₃×#1855	2
#25142	13

Subgroups — C13×#25142 #15711481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25142 #15711481