Subgroups — C₂×C₁₃×#1654 #15704835

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 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	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1654	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂²×C₁₃×SD₁₆	—	2	1	no	—
11	C₁₃×#547	—	2	2	no	—
12	C₁₃×#547	—	2	2	no	—
13	C₁₃×#547	—	2	2	no	—
14	C₁₃×#547	C₂²	1	4	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#123	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×#121	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₁₃×#498	—	2	2	no	—
24	C₁₃×#498	C₂²	1	4	yes	complemented
25	C₁₃×#474	—	2	2	no	—
26	C₁₃×#474	C₂²	1	4	yes	complemented
27	C₁₃×#461	—	2	2	no	—
28	C₁₃×#461	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#107	—	2	1	no	—
30	C₂×C₁₃×#106	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	—	2	1	no	—
34	C₂×C₁₃×#102	—	2	1	no	—
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#332	C₂²	1	4	yes	complemented
37	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
38	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×C₁₃×#41	—	2	4	no	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	4	4	no	—
42	C₂×C₁₃×#41	—	4	4	no	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	2	no	—
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	4	no	—
52	C₂×C₁₃×SD₁₆	—	4	4	no	—
53	C₂²×C₈×C₁₃	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	1	no	—
55	C₂²×C₈×C₁₃	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	—	2	1	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×#123	—	2	8	no	—
65	C₁₃×#123	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	4	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#121	—	2	4	no	—
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	1	no	—
73	C₄×D₄×C₁₃	—	2	1	no	—
74	C₄×D₄×C₁₃	D₄	1	2	yes	—
75	C₄×D₄×C₁₃	D₄	1	2	yes	—
76	C₄×D₄×C₁₃	C₂³	1	2	yes	—
77	C₄×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#107	—	2	4	no	—
92	C₁₃×#106	—	2	8	no	—
93	C₁₃×C₄⋊C₈	—	2	1	no	—
94	C₁₃×C₄⋊C₈	—	2	1	no	—
95	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#102	—	2	4	no	—
99	C₄×C₈×C₁₃	—	2	1	no	—
100	C₄×C₈×C₁₃	C₂³	1	2	yes	—
101	C₂×#1654	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₁₃×#41	—	4	8	no	—
105	C₁₃×#41	—	4	16	no	—
106	C₁₃×#41	—	4	8	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	4	1	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	—	4	2	no	—
113	C₂×Q₈×C₁₃	—	4	2	no	—
114	C₂×Q₈×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	4	8	no	—
122	C₂×D₄×C₁₃	SD₁₆	1	4	yes	complemented
123	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	4	8	no	—
134	C₂²×C₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₁₃×SD₁₆	—	4	8	no	—
143	C₂×C₈×C₁₃	—	2	4	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	4	2	no	—
148	C₂×C₈×C₁₃	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	4	1	no	—
158	C₁₃×C₄⋊C₄	—	4	1	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	2	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
172	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#1654	C₂×C₁₃	1	8	yes	direct product factor
176	C₂×#332	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	#120	1	1	yes	characteristic
188	Q₈×C₁₃	—	4	2	no	—
189	Q₈×C₁₃	—	4	2	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	4	2	no	—
193	Q₈×C₁₃	—	8	2	no	—
194	D₄×C₁₃	—	2	2	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	2	2	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	4	16	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	C₂×SD₁₆	1	4	yes	complemented
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	4	16	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	4	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	4	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	2	no	—
217	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
221	C₂×C₄×C₁₃	#135	1	2	yes	—
222	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₁₃	—	2	4	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₂²×#41	—	2	1	no	—
231	C₂²×SD₁₆	—	2	1	no	—
232	#547	—	2	2	no	—
233	#547	—	2	2	no	—
234	#547	—	2	2	no	—
235	#547	C₂²×C₁₃	1	4	yes	—
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#123	—	2	2	no	—
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×#121	—	2	1	no	—
241	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	—	2	1	no	—
244	#498	—	2	2	no	—
245	#498	C₂²×C₁₃	1	4	yes	complemented
246	#474	—	2	2	no	—
247	#474	C₂²×C₁₃	1	4	yes	complemented
248	#461	—	2	2	no	—
249	#461	C₂²×C₁₃	1	4	yes	complemented
250	C₂×#107	—	2	1	no	—
251	C₂×#106	—	2	2	no	—
252	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#103	—	2	1	no	—
255	C₂×#102	—	2	1	no	—
256	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
257	#332	C₂²×C₁₃	1	4	yes	complemented
258	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
259	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
260	C₂²×C₁₃	—	2	4	no	—
261	C₂²×C₁₃	—	4	8	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	8	4	no	—
268	C₂²×C₁₃	#449	1	2	yes	—
269	C₂²×C₁₃	#450	1	2	yes	—
270	C₂²×C₁₃	#456	1	2	yes	—
271	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	4	4	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	8	2	no	—
278	C₄×C₁₃	#449	1	2	yes	—
279	C₄×C₁₃	#450	1	2	yes	—
280	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
281	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
282	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂×#41	—	2	4	no	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	—	4	4	no	—
287	C₂×#41	—	4	4	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
292	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×SD₁₆	—	4	4	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
308	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
309	#123	—	2	8	no	—
310	#123	—	2	8	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	#121	—	2	4	no	—
314	#121	—	2	4	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₁₃	1	2	yes	—
320	C₄×D₄	D₄×C₁₃	1	2	yes	—
321	C₄×D₄	C₂³×C₁₃	1	2	yes	—
322	C₄×D₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	#107	—	2	4	no	—
337	#106	—	2	8	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
341	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
342	#103	—	2	4	no	—
343	#102	—	2	4	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	C₂³×C₁₃	1	2	yes	—
346	C₂×C₁₃	—	4	4	no	—
347	C₂×C₁₃	—	8	2	no	—
348	C₂×C₁₃	#1654	1	4	yes	direct product factor
349	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
350	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
351	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	2	1	no	—
354	#41	—	4	16	no	—
355	#41	—	4	8	no	—
356	#41	—	4	8	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂×D₄	C₁₃×SD₁₆	1	4	yes	complemented
373	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	4	8	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	SD₁₆	—	4	8	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	4	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₁₃	C₂×#1654	1	1	yes	characteristic, direct product factor, Sylow
422	C₂³	—	2	4	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	C₁₃×#120	1	1	yes	characteristic
431	Q₈	—	4	4	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	16	no	—
442	D₄	—	4	2	no	—
443	D₄	C₂×C₁₃×SD₁₆	1	4	yes	complemented
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	16	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
461	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
462	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
464	C₂×C₄	C₁₃×#135	1	2	yes	—
465	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
466	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₁₃×#449	1	2	yes	—
482	C₂²	C₁₃×#450	1	2	yes	—
483	C₂²	C₁₃×#456	1	2	yes	—
484	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	2	no	—
491	C₄	C₁₃×#449	1	2	yes	—
492	C₄	C₁₃×#450	1	2	yes	—
493	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
494	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
495	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
496	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
497	C₂	—	4	4	no	—
498	C₂	—	8	2	no	—
499	C₂	C₁₃×#1654	1	4	yes	direct product factor
500	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
501	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#498	C₂	semidirect
3. C₂×C₁₃×#474	C₂	semidirect
4. C₂×C₁₃×#461	C₂	semidirect
5. C₁₃×#1654	C₂	direct (N × H)
6. C₂×C₁₃×#332	C₂	semidirect
7. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
8. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
24. C₁₃×#498	C₂²	semidirect
26. C₁₃×#474	C₂²	semidirect
28. C₁₃×#461	C₂²	semidirect
36. C₁₃×#332	C₂²	semidirect
37. C₁₃×D₄⋊C₈	C₂²	semidirect
38. C₁₃×D₄⋊C₈	C₂²	semidirect
101. C₂×#1654	C₁₃	direct (N × H)
122. C₂×D₄×C₁₃	SD₁₆	semidirect
172. C₂×#498	C₂×C₁₃	semidirect
173. C₂×#474	C₂×C₁₃	semidirect
174. C₂×#461	C₂×C₁₃	semidirect
175. #1654	C₂×C₁₃	direct (N × H)
176. C₂×#332	C₂×C₁₃	semidirect
177. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
178. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
200. D₄×C₁₃	C₂×SD₁₆	semidirect
245. #498	C₂²×C₁₃	semidirect
247. #474	C₂²×C₁₃	semidirect
249. #461	C₂²×C₁₃	semidirect
257. #332	C₂²×C₁₃	semidirect
258. D₄⋊C₈	C₂²×C₁₃	semidirect
259. D₄⋊C₈	C₂²×C₁₃	semidirect
348. C₂×C₁₃	#1654	direct (N × H)
372. C₂×D₄	C₁₃×SD₁₆	semidirect
421. C₁₃	C₂×#1654	direct (N × H)
443. D₄	C₂×C₁₃×SD₁₆	semidirect
499. C₂	C₁₃×#1654	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
C₂×C₁₃×#498	2
C₂×C₁₃×#474	2
C₂×C₁₃×#461	2
C₁₃×#1654	2
C₂×C₁₃×#332	2
C₂×C₁₃×D₄⋊C₈	2
C₂×#1654	13

Subgroups — C2×C13×#1654 #15704835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1654 #15704835