Subgroups — C₂×C₁₃×#1929 #15707408

Order 3328.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1929	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#108	—	2	4	no	—
17	C₂×C₁₃×#108	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#104	—	2	4	no	—
19	C₂×C₁₃×#104	C₂²	1	4	yes	—
20	C₁₃×#416	C₄	1	4	yes	complemented
21	C₁₃×#416	C₂²	1	4	yes	—
22	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#103	C₄	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#102	C₄	1	1	yes	characteristic, complemented
26	C₁₃×#408	—	2	2	no	—
27	C₁₃×#408	C₂²	1	4	yes	—
28	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
30	C₁₃×#405	—	2	2	no	—
31	C₁₃×#405	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#97	—	2	1	no	—
33	C₂×C₄×C₈×C₁₃	—	2	1	no	—
34	C₁₃×#339	C₂²	1	4	yes	complemented
35	C₁₃×#336	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₁₃	D₄	1	2	yes	—
68	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
72	C₁₃×#117	—	2	1	no	—
73	C₁₃×#117	—	2	1	no	—
74	C₁₃×#117	C₂×C₄	1	2	yes	—
75	C₁₃×#117	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
84	C₁₃×#108	—	2	8	no	—
85	C₁₃×#104	—	2	8	no	—
86	C₁₃×#103	C₂×C₄	1	4	yes	complemented
87	C₁₃×#103	C₂×C₄	1	4	yes	complemented
88	C₁₃×#102	C₂×C₄	1	4	yes	complemented
89	C₁₃×#102	C₂×C₄	1	4	yes	complemented
90	C₁₃×C₂²⋊C₈	—	2	4	no	—
91	C₁₃×C₂²⋊C₈	—	2	4	no	—
92	C₁₃×#97	—	2	4	no	—
93	C₄×C₈×C₁₃	—	2	4	no	—
94	C₂×#1929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₁₃×#41	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	2	yes	—
136	C₂²×C₄×C₁₃	#41	1	2	yes	—
137	C₂²×C₄×C₁₃	#41	1	2	yes	—
138	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	—	2	2	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	4	2	no	—
145	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	4	no	—
149	C₂×C₈×C₁₃	—	2	4	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	4	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₂×C₈×C₁₃	—	4	2	no	—
160	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	2	2	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	4	2	no	—
175	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
177	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#408	C₂×C₁₃	1	1	yes	characteristic
179	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1929	C₂×C₁₃	1	8	yes	direct product factor
181	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂³×C₁₃	#124	1	2	yes	—
192	C₂³×C₁₃	#126	1	2	yes	—
193	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	2	2	no	—
196	Q₈×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	2	2	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	4	2	no	—
201	D₄×C₁₃	—	4	4	no	—
202	D₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	#117	1	2	yes	—
217	C₂×C₄×C₁₃	#117	1	2	yes	—
218	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	#121	1	2	yes	—
223	C₂×C₄×C₁₃	#121	1	2	yes	—
224	C₂×C₄×C₁₃	#123	1	2	yes	—
225	C₂×C₄×C₁₃	#123	1	2	yes	—
226	C₂×C₄×C₁₃	#124	1	2	yes	—
227	C₂×C₄×C₁₃	#126	1	2	yes	—
228	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	2	4	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	4	2	no	—
240	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#108	—	2	4	no	—
248	C₂×#108	C₂²×C₁₃	1	4	yes	complemented
249	C₂×#104	—	2	4	no	—
250	C₂×#104	C₂²×C₁₃	1	4	yes	—
251	#416	C₄×C₁₃	1	4	yes	complemented
252	#416	C₂²×C₁₃	1	4	yes	—
253	C₂×#103	C₄×C₁₃	1	1	yes	characteristic, complemented
254	C₂×#103	C₄×C₁₃	1	1	yes	characteristic, complemented
255	C₂×#102	C₄×C₁₃	1	1	yes	characteristic, complemented
256	C₂×#102	C₄×C₁₃	1	1	yes	characteristic, complemented
257	#408	—	2	2	no	—
258	#408	C₂²×C₁₃	1	4	yes	—
259	C₂×C₂²⋊C₈	—	2	1	no	—
260	C₂×C₂²⋊C₈	—	2	1	no	—
261	#405	—	2	2	no	—
262	#405	C₂²×C₁₃	1	4	yes	complemented
263	C₂×#97	—	2	1	no	—
264	C₂×C₄×C₈	—	2	1	no	—
265	#339	C₂²×C₁₃	1	4	yes	complemented
266	#336	C₂²×C₁₃	1	4	yes	complemented
267	C₂²×C₁₃	—	2	4	no	—
268	C₂²×C₁₃	—	2	4	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	8	4	no	—
277	C₂²×C₁₃	#388	1	2	yes	—
278	C₂²×C₁₃	#388	1	2	yes	—
279	C₂²×C₁₃	#443	1	2	yes	—
280	C₂²×C₁₃	#444	1	2	yes	—
281	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
283	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	#388	1	2	yes	—
289	C₄×C₁₃	#388	1	2	yes	—
290	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
291	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
293	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
294	C₂×#41	—	2	1	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	2	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
301	C₂×#41	C₂³×C₁₃	1	2	yes	—
302	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
314	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
315	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
324	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
325	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
326	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	D₄×C₁₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
330	#117	—	2	1	no	—
331	#117	—	2	1	no	—
332	#117	C₂×C₄×C₁₃	1	2	yes	—
333	#117	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
342	#108	—	2	8	no	—
343	#104	—	2	8	no	—
344	#103	C₂×C₄×C₁₃	1	4	yes	complemented
345	#103	C₂×C₄×C₁₃	1	4	yes	complemented
346	#102	C₂×C₄×C₁₃	1	4	yes	complemented
347	#102	C₂×C₄×C₁₃	1	4	yes	complemented
348	C₂²⋊C₈	—	2	4	no	—
349	C₂²⋊C₈	—	2	4	no	—
350	#97	—	2	4	no	—
351	C₄×C₈	—	2	4	no	—
352	C₂×C₁₃	—	2	1	no	—
353	C₂×C₁₃	—	2	1	no	—
354	C₂×C₁₃	—	2	2	no	—
355	C₂×C₁₃	—	8	2	no	—
356	C₂×C₁₃	#1929	1	4	yes	direct product factor
357	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
358	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
360	C₂⁴	—	2	1	no	—
361	C₂⁴	C₁₃×#41	1	1	yes	characteristic
362	#41	—	2	4	no	—
363	#41	—	2	4	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	4	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₁₃×#41	1	2	yes	—
401	C₂²×C₄	C₁₃×#41	1	2	yes	—
402	C₂²×C₄	C₁₃×#41	1	2	yes	—
403	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	M₁₆	—	2	4	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	4	2	no	—
410	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	4	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
426	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
427	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
432	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	4	2	no	—
440	C₁₃	C₂×#1929	1	1	yes	characteristic, direct product factor, Sylow
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
448	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
449	C₂³	C₁₃×#124	1	2	yes	—
450	C₂³	C₁₃×#126	1	2	yes	—
451	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	C₁₃×#117	1	2	yes	—
475	C₂×C₄	C₁₃×#117	1	2	yes	—
476	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
480	C₂×C₄	C₁₃×#121	1	2	yes	—
481	C₂×C₄	C₁₃×#121	1	2	yes	—
482	C₂×C₄	C₁₃×#123	1	2	yes	—
483	C₂×C₄	C₁₃×#123	1	2	yes	—
484	C₂×C₄	C₁₃×#124	1	2	yes	—
485	C₂×C₄	C₁₃×#126	1	2	yes	—
486	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
490	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
491	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	C₁₃×#388	1	2	yes	—
509	C₂²	C₁₃×#388	1	2	yes	—
510	C₂²	C₁₃×#443	1	2	yes	—
511	C₂²	C₁₃×#444	1	2	yes	—
512	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
513	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
514	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
515	C₄	—	4	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	C₁₃×#388	1	2	yes	—
520	C₄	C₁₃×#388	1	2	yes	—
521	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
522	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
523	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
524	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	C₁₃×#1929	1	4	yes	direct product factor
530	C₂	C₂×C₁₃×#388	1	1	yes	characteristic
531	C₂	C₂×C₁₃×#443	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#108	C₂	semidirect
5. C₂×C₁₃×#405	C₂	semidirect
6. C₁₃×#1929	C₂	direct (N × H)
7. C₂×C₁₃×#339	C₂	semidirect
8. C₂×C₁₃×#336	C₂	semidirect
17. C₂×C₁₃×#108	C₂²	semidirect
20. C₁₃×#416	C₄	semidirect
22. C₂×C₁₃×#103	C₄	semidirect
23. C₂×C₁₃×#103	C₄	semidirect
24. C₂×C₁₃×#102	C₄	semidirect
25. C₂×C₁₃×#102	C₄	semidirect
31. C₁₃×#405	C₂²	semidirect
34. C₁₃×#339	C₂²	semidirect
35. C₁₃×#336	C₂²	semidirect
86. C₁₃×#103	C₂×C₄	semidirect
87. C₁₃×#103	C₂×C₄	semidirect
88. C₁₃×#102	C₂×C₄	semidirect
89. C₁₃×#102	C₂×C₄	semidirect
94. C₂×#1929	C₁₃	direct (N × H)
175. C₂²×#108	C₂×C₁₃	semidirect
179. C₂×#405	C₂×C₁₃	semidirect
180. #1929	C₂×C₁₃	direct (N × H)
181. C₂×#339	C₂×C₁₃	semidirect
182. C₂×#336	C₂×C₁₃	semidirect
248. C₂×#108	C₂²×C₁₃	semidirect
251. #416	C₄×C₁₃	semidirect
253. C₂×#103	C₄×C₁₃	semidirect
254. C₂×#103	C₄×C₁₃	semidirect
255. C₂×#102	C₄×C₁₃	semidirect
256. C₂×#102	C₄×C₁₃	semidirect
262. #405	C₂²×C₁₃	semidirect
265. #339	C₂²×C₁₃	semidirect
266. #336	C₂²×C₁₃	semidirect
344. #103	C₂×C₄×C₁₃	semidirect
345. #103	C₂×C₄×C₁₃	semidirect
346. #102	C₂×C₄×C₁₃	semidirect
347. #102	C₂×C₄×C₁₃	semidirect
356. C₂×C₁₃	#1929	direct (N × H)
440. C₁₃	C₂×#1929	direct (N × H)
529. C₂	C₁₃×#1929	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#108	2
C₂²×C₁₃×#104	2
C₂×C₁₃×#416	2
C₂×C₁₃×#408	2
C₂×C₁₃×#405	2
C₁₃×#1929	2
C₂×C₁₃×#339	2
C₂×C₁₃×#336	2
C₂×#1929	13

Subgroups — C2×C13×#1929 #15707408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1929 #15707408