Subgroups — C₂×C₁₃×#3354 #15747586

Order 3328.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3354	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×#41	—	2	1	no	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₁₃×#555	—	2	4	no	—
17	C₁₃×#555	C₂²	1	8	yes	complemented
18	C₁₃×#547	—	2	4	no	—
19	C₁₃×#547	C₂²	1	8	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	2	no	—
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	—	2	1	no	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#498	C₂²	1	8	yes	complemented
35	C₁₃×#482	C₂²	1	16	yes	complemented
36	C₁₃×#481	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#474	C₂²	1	8	yes	complemented
39	C₁₃×#469	C₂²	1	16	yes	complemented
40	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
41	C₁₃×#436	C₂²	1	8	yes	complemented
42	C₁₃×#428	C₂²	1	16	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	2	yes	—
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#106	C₂²	1	2	yes	—
46	C₂×C₁₃×#106	C₂²	1	2	yes	—
47	C₂×C₁₃×#106	C₂²	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#102	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#41	—	2	8	no	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	2	no	—
60	C₂²×D₄×C₁₃	—	2	2	no	—
61	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂×C₁₃×D₈	—	2	4	no	—
69	C₂×C₁₃×D₈	C₂³	1	4	yes	—
70	C₂×C₁₃×M₁₆	—	2	8	no	—
71	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×#124	—	2	16	no	—
80	C₁₃×#123	—	2	16	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	4	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	C₂³	1	8	yes	—
86	C₁₃×#121	C₂³	1	8	yes	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	D₄	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₄×D₄×C₁₃	C₂³	1	4	yes	—
93	C₁₃×#117	—	2	4	no	—
94	C₁₃×#117	—	2	8	no	—
95	C₁₃×#117	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
112	C₂×C₄²×C₁₃	—	2	2	no	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₁₃×#107	C₂³	1	4	yes	—
115	C₁₃×#107	C₂³	1	8	yes	—
116	C₁₃×#106	C₂³	1	8	yes	—
117	C₁₃×#106	C₂³	1	8	yes	—
118	C₁₃×#106	C₂³	1	8	yes	—
119	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×#102	C₂³	1	4	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×#102	C₂³	1	8	yes	—
124	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
125	C₄×C₈×C₁₃	C₂³	1	4	yes	—
126	C₂×#3354	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	1	no	—
129	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×#41	—	4	32	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	4	4	no	—
134	C₂×Q₈×C₁₃	—	8	2	no	—
135	C₂×D₄×C₁₃	—	2	8	no	—
136	C₂×D₄×C₁₃	—	2	8	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	4	8	no	—
145	C₂×D₄×C₁₃	—	8	4	no	—
146	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	4	8	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×D₈	—	2	8	no	—
168	C₁₃×M₁₆	—	2	16	no	—
169	C₂×C₈×C₁₃	—	2	4	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	#41	1	4	yes	complemented
172	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
173	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
174	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
193	C₄²×C₁₃	—	2	8	no	—
194	C₄²×C₁₃	C₂×D₄	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	2	yes	—
196	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3354	C₂×C₁₃	1	16	yes	direct product factor
199	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#481	C₂×C₁₃	1	2	yes	complemented
201	C₂×#482	C₂×C₁₃	1	2	yes	complemented
202	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#469	C₂×C₁₃	1	2	yes	complemented
205	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#428	C₂×C₁₃	1	2	yes	complemented
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	4	2	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
220	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃	—	4	8	no	—
222	Q₈×C₁₃	—	8	4	no	—
223	D₄×C₁₃	—	2	8	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	4	16	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	8	8	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	4	16	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	8	no	—
247	C₂×C₄×C₁₃	—	4	8	no	—
248	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
254	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
256	C₈×C₁₃	—	2	4	no	—
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	C₂×#41	1	4	yes	complemented
259	C₂²×#41	—	2	1	no	—
260	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
262	#555	—	2	4	no	—
263	#555	C₂²×C₁₃	1	8	yes	complemented
264	#547	—	2	4	no	—
265	#547	C₂²×C₁₃	1	8	yes	complemented
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#124	—	2	2	no	—
269	C₂×#123	—	2	2	no	—
270	C₂×C₂²⋊Q₈	—	2	1	no	—
271	C₂×#121	—	2	1	no	—
272	C₂×#121	C₂²×C₁₃	1	2	yes	—
273	C₂×#121	C₂²×C₁₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#117	—	2	1	no	—
278	C₂×#117	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
280	#498	C₂²×C₁₃	1	8	yes	complemented
281	#482	C₂²×C₁₃	1	16	yes	complemented
282	#481	C₂²×C₁₃	1	16	yes	complemented
283	#476	C₂²×C₁₃	1	8	yes	complemented
284	#474	C₂²×C₁₃	1	8	yes	complemented
285	#469	C₂²×C₁₃	1	16	yes	complemented
286	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
287	#436	C₂²×C₁₃	1	8	yes	complemented
288	#428	C₂²×C₁₃	1	16	yes	complemented
289	C₂×#107	C₂²×C₁₃	1	2	yes	—
290	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#106	C₂²×C₁₃	1	2	yes	—
292	C₂×#106	C₂²×C₁₃	1	2	yes	—
293	C₂×#106	C₂²×C₁₃	1	2	yes	—
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#102	C₂²×C₁₃	1	2	yes	—
297	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₃	1	2	yes	—
299	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₁₃	—	2	4	no	—
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	4	no	—
304	C₂²×C₁₃	—	4	8	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	8	4	no	—
312	C₂²×C₁₃	—	8	4	no	—
313	C₂²×C₁₃	#547	1	2	yes	—
314	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
315	C₂²×C₁₃	#577	1	2	yes	—
316	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
317	C₄×C₁₃	—	2	4	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	4	2	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	4	4	no	—
322	C₄×C₁₃	—	4	4	no	—
323	C₄×C₁₃	#547	1	2	yes	—
324	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
325	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
326	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	C₂×#41	—	2	8	no	—
328	C₂×#41	—	4	8	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	—	2	2	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂×D₈	—	2	4	no	—
341	C₂×D₈	C₂³×C₁₃	1	4	yes	—
342	C₂×M₁₆	—	2	8	no	—
343	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
344	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
350	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
351	#124	—	2	16	no	—
352	#123	—	2	16	no	—
353	C₂²⋊Q₈	—	2	8	no	—
354	#121	—	2	8	no	—
355	#121	—	2	4	no	—
356	#121	—	2	4	no	—
357	#121	C₂³×C₁₃	1	8	yes	—
358	#121	C₂³×C₁₃	1	8	yes	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	D₄×C₁₃	1	4	yes	—
362	C₄×D₄	C₂³×C₁₃	1	4	yes	—
363	C₄×D₄	C₂³×C₁₃	1	4	yes	—
364	C₄×D₄	C₂³×C₁₃	1	4	yes	—
365	#117	—	2	4	no	—
366	#117	—	2	8	no	—
367	#117	C₂³×C₁₃	1	8	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	#107	C₂³×C₁₃	1	4	yes	—
387	#107	C₂³×C₁₃	1	8	yes	—
388	#106	C₂³×C₁₃	1	8	yes	—
389	#106	C₂³×C₁₃	1	8	yes	—
390	#106	C₂³×C₁₃	1	8	yes	—
391	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
392	#102	C₂³×C₁₃	1	4	yes	—
393	#102	C₂³×C₁₃	1	4	yes	—
394	#102	C₂³×C₁₃	1	8	yes	—
395	#102	C₂³×C₁₃	1	8	yes	—
396	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
397	C₄×C₈	C₂³×C₁₃	1	4	yes	—
398	C₂×C₁₃	—	4	4	no	—
399	C₂×C₁₃	—	8	2	no	—
400	C₂×C₁₃	—	8	2	no	—
401	C₂×C₁₃	#3354	1	4	yes	direct product factor
402	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
403	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
405	C₂⁴	—	2	1	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
408	#41	—	4	32	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	—	8	2	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	4	8	no	—
423	C₂×D₄	—	8	4	no	—
424	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	4	8	no	—
437	C₂²×C₄	—	4	4	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	D₈	—	2	8	no	—
446	M₁₆	—	2	16	no	—
447	C₂×C₈	—	2	4	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	C₁₃×#41	1	4	yes	complemented
450	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
451	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
452	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
463	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
471	C₄²	—	2	8	no	—
472	C₄²	C₂×D₄×C₁₃	1	2	yes	—
473	C₄²	C₂⁴×C₁₃	1	2	yes	—
474	C₁₃	C₂×#3354	1	1	yes	characteristic, direct product factor, Sylow
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
487	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	Q₈	—	4	8	no	—
489	Q₈	—	8	4	no	—
490	D₄	—	2	8	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	16	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	8	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	16	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
521	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
522	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
523	C₈	—	2	4	no	—
524	C₈	—	2	2	no	—
525	C₈	C₂×C₁₃×#41	1	4	yes	complemented
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	4	no	—
537	C₂²	—	8	4	no	—
538	C₂²	C₁₃×#547	1	2	yes	—
539	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
540	C₂²	C₁₃×#577	1	2	yes	—
541	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	C₁₃×#547	1	2	yes	—
549	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
550	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
551	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂	—	4	4	no	—
553	C₂	—	8	2	no	—
554	C₂	—	8	2	no	—
555	C₂	C₁₃×#3354	1	4	yes	direct product factor
556	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
557	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
558	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#555	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3354	C₂	direct (N × H)
4. C₂×C₁₃×#498	C₂	semidirect
5. C₂×C₁₃×#481	C₂	semidirect
6. C₂×C₁₃×#482	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
8. C₂×C₁₃×#474	C₂	semidirect
9. C₂×C₁₃×#469	C₂	semidirect
10. C₂×C₄×C₁₃×D₈	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#428	C₂	semidirect
17. C₁₃×#555	C₂²	semidirect
19. C₁₃×#547	C₂²	semidirect
34. C₁₃×#498	C₂²	semidirect
35. C₁₃×#482	C₂²	semidirect
36. C₁₃×#481	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#469	C₂²	semidirect
40. C₄×C₁₃×D₈	C₂²	semidirect
41. C₁₃×#436	C₂²	semidirect
42. C₁₃×#428	C₂²	semidirect
126. C₂×#3354	C₁₃	direct (N × H)
171. C₂×C₈×C₁₃	#41	semidirect
196. C₂×#555	C₂×C₁₃	semidirect
197. C₂×#547	C₂×C₁₃	semidirect
198. #3354	C₂×C₁₃	direct (N × H)
199. C₂×#498	C₂×C₁₃	semidirect
200. C₂×#481	C₂×C₁₃	semidirect
201. C₂×#482	C₂×C₁₃	semidirect
202. C₂×#476	C₂×C₁₃	semidirect
203. C₂×#474	C₂×C₁₃	semidirect
204. C₂×#469	C₂×C₁₃	semidirect
205. C₂×C₄×D₈	C₂×C₁₃	semidirect
206. C₂×#436	C₂×C₁₃	semidirect
207. C₂×#428	C₂×C₁₃	semidirect
258. C₈×C₁₃	C₂×#41	semidirect
263. #555	C₂²×C₁₃	semidirect
265. #547	C₂²×C₁₃	semidirect
280. #498	C₂²×C₁₃	semidirect
281. #482	C₂²×C₁₃	semidirect
282. #481	C₂²×C₁₃	semidirect
283. #476	C₂²×C₁₃	semidirect
284. #474	C₂²×C₁₃	semidirect
285. #469	C₂²×C₁₃	semidirect
286. C₄×D₈	C₂²×C₁₃	semidirect
287. #436	C₂²×C₁₃	semidirect
288. #428	C₂²×C₁₃	semidirect
401. C₂×C₁₃	#3354	direct (N × H)
449. C₂×C₈	C₁₃×#41	semidirect
474. C₁₃	C₂×#3354	direct (N × H)
525. C₈	C₂×C₁₃×#41	semidirect
555. C₂	C₁₃×#3354	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×#555	2
C₂×C₁₃×#547	2
C₁₃×#3354	2
C₂×C₁₃×#498	2
C₂×C₁₃×#481	2
C₂×C₁₃×#482	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₂×C₁₃×#469	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#436	2
C₂×C₁₃×#428	2
C₂×#3354	13

Subgroups — C2×C13×#3354 #15747586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3354 #15747586