Subgroups — C₂×C₁₃×#3174 #15747017

Order 3328.

1970 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3174	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#468	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#541	—	2	4	no	—
18	C₁₃×#541	C₂²	1	8	yes	complemented
19	C₁₃×#540	—	2	4	no	—
20	C₁₃×#540	C₂²	1	8	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#126	—	2	2	no	—
24	C₂×C₁₃×#125	—	2	2	no	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#123	—	2	2	no	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₃×#121	—	2	2	no	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₁₃×#499	C₂²	1	8	yes	complemented
35	C₁₃×#492	C₂²	1	8	yes	complemented
36	C₁₃×#491	C₂²	1	8	yes	complemented
37	C₁₃×#490	C₂²	1	8	yes	complemented
38	C₁₃×#468	C₂²	1	16	yes	complemented
39	C₁₃×#465	C₂²	1	16	yes	complemented
40	C₁₃×#440	C₂²	1	16	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
42	C₂×C₁₃×#107	C₂²	1	2	yes	—
43	C₂×C₁₃×#106	C₂²	1	2	yes	—
44	C₂×C₁₃×#103	C₂²	1	2	yes	—
45	C₂×C₁₃×#103	C₂²	1	2	yes	—
46	C₂×C₁₃×#102	C₂²	1	2	yes	—
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₁₃×#405	C₂²	1	8	yes	complemented
49	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	—	2	2	no	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×SD₁₆	—	2	8	no	—
60	C₂×C₁₃×SD₁₆	—	2	8	no	—
61	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₁₃×M₁₆	—	2	4	no	—
64	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₃	—	2	4	no	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₁₃×#127	—	2	2	no	—
74	C₁₃×#127	C₂³	1	4	yes	—
75	C₁₃×#126	—	2	16	no	—
76	C₁₃×#125	—	2	16	no	—
77	C₁₃×#125	—	2	2	no	—
78	C₁₃×#125	—	2	2	no	—
79	C₁₃×#125	C₂³	1	4	yes	—
80	C₁₃×#125	C₂³	1	4	yes	—
81	C₁₃×#123	—	2	16	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	—	2	16	no	—
86	C₁₃×#121	C₂³	1	8	yes	—
87	C₄×Q₈×C₁₃	—	2	4	no	—
88	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
89	C₄×D₄×C₁₃	—	2	4	no	—
90	C₄×D₄×C₁₃	C₂³	1	8	yes	—
91	C₁₃×#117	D₄	1	4	yes	—
92	C₁₃×#117	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
105	C₂×C₄²×C₁₃	—	2	2	no	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	C₂³	1	8	yes	—
109	C₁₃×#106	C₂³	1	8	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#103	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×#102	C₂³	1	8	yes	—
114	C₁₃×#97	C₂³	1	4	yes	—
115	C₁₃×#97	C₂³	1	4	yes	—
116	C₄×C₈×C₁₃	C₂³	1	4	yes	—
117	C₄×C₈×C₁₃	C₂³	1	4	yes	—
118	C₂×#3174	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	8	4	no	—
131	C₂×D₄×C₁₃	—	8	4	no	—
132	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	8	4	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₁₃×SD₁₆	—	2	16	no	—
147	C₁₃×SD₁₆	—	2	16	no	—
148	C₁₃×M₁₆	—	2	8	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	8	no	—
152	C₂×C₈×C₁₃	#41	1	4	yes	—
153	C₂×C₈×C₁₃	#41	1	4	yes	—
154	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
155	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
156	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂⁴	1	2	yes	—
176	C₄²×C₁₃	C₂⁴	1	2	yes	—
177	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#540	C₂×C₁₃	1	1	yes	characteristic
179	#3174	C₂×C₁₃	1	16	yes	direct product factor
180	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
183	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#468	C₂×C₁₃	1	2	yes	complemented
185	C₂×#465	C₂×C₁₃	1	2	yes	complemented
186	C₂×#440	C₂×C₁₃	1	2	yes	complemented
187	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
188	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	4	no	—
198	Q₈×C₁₃	—	2	4	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	2	4	no	—
201	D₄×C₁₃	—	2	4	no	—
202	D₄×C₁₃	—	4	4	no	—
203	D₄×C₁₃	—	8	8	no	—
204	D₄×C₁₃	—	8	8	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	—	4	4	no	—
217	C₂×C₄×C₁₃	—	8	8	no	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₁₃	—	2	2	no	—
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	C₂×#41	1	4	yes	—
228	C₈×C₁₃	C₂×#41	1	4	yes	—
229	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
230	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
231	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
233	#541	—	2	4	no	—
234	#541	C₂²×C₁₃	1	8	yes	complemented
235	#540	—	2	4	no	—
236	#540	C₂²×C₁₃	1	8	yes	—
237	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#126	—	2	2	no	—
240	C₂×#125	—	2	2	no	—
241	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#123	—	2	2	no	—
244	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
245	C₂×#121	—	2	2	no	—
246	C₂×#121	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
249	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
250	#499	C₂²×C₁₃	1	8	yes	complemented
251	#492	C₂²×C₁₃	1	8	yes	complemented
252	#491	C₂²×C₁₃	1	8	yes	complemented
253	#490	C₂²×C₁₃	1	8	yes	complemented
254	#468	C₂²×C₁₃	1	16	yes	complemented
255	#465	C₂²×C₁₃	1	16	yes	complemented
256	#440	C₂²×C₁₃	1	16	yes	complemented
257	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
258	C₂×#107	C₂²×C₁₃	1	2	yes	—
259	C₂×#106	C₂²×C₁₃	1	2	yes	—
260	C₂×#103	C₂²×C₁₃	1	2	yes	—
261	C₂×#103	C₂²×C₁₃	1	2	yes	—
262	C₂×#102	C₂²×C₁₃	1	2	yes	—
263	C₂×#102	C₂²×C₁₃	1	2	yes	—
264	#405	C₂²×C₁₃	1	8	yes	complemented
265	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	8	8	no	—
276	C₂²×C₁₃	#532	1	2	yes	—
277	C₂²×C₁₃	#577	1	4	yes	—
278	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	4	no	—
281	C₄×C₁₃	—	2	4	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	#532	1	2	yes	—
286	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
287	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	—	2	8	no	—
296	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
297	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
300	C₂²×C₈	—	2	4	no	—
301	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
308	#127	—	2	2	no	—
309	#127	C₂³×C₁₃	1	4	yes	—
310	#126	—	2	16	no	—
311	#125	—	2	16	no	—
312	#125	—	2	2	no	—
313	#125	—	2	2	no	—
314	#125	C₂³×C₁₃	1	4	yes	—
315	#125	C₂³×C₁₃	1	4	yes	—
316	#123	—	2	16	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
319	#121	—	2	4	no	—
320	#121	—	2	16	no	—
321	#121	C₂³×C₁₃	1	8	yes	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	C₂³×C₁₃	1	8	yes	—
326	#117	D₄×C₁₃	1	4	yes	—
327	#117	C₂³×C₁₃	1	4	yes	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
343	#107	C₂³×C₁₃	1	8	yes	—
344	#106	C₂³×C₁₃	1	8	yes	—
345	#103	C₂³×C₁₃	1	8	yes	—
346	#103	C₂³×C₁₃	1	8	yes	—
347	#102	C₂³×C₁₃	1	8	yes	—
348	#102	C₂³×C₁₃	1	8	yes	—
349	#97	C₂³×C₁₃	1	4	yes	—
350	#97	C₂³×C₁₃	1	4	yes	—
351	C₄×C₈	C₂³×C₁₃	1	4	yes	—
352	C₄×C₈	C₂³×C₁₃	1	4	yes	—
353	C₂×C₁₃	—	4	2	no	—
354	C₂×C₁₃	—	8	4	no	—
355	C₂×C₁₃	#3174	1	4	yes	direct product factor
356	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
357	C₂×C₁₃	C₂×#577	1	2	yes	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	8	4	no	—
370	C₂×D₄	—	8	4	no	—
371	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	8	4	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
385	SD₁₆	—	2	16	no	—
386	SD₁₆	—	2	16	no	—
387	M₁₆	—	2	8	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	8	no	—
391	C₂×C₈	C₁₃×#41	1	4	yes	—
392	C₂×C₈	C₁₃×#41	1	4	yes	—
393	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
394	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
395	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
396	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
405	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
406	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
411	C₄²	—	2	8	no	—
412	C₄²	C₂×D₄×C₁₃	1	2	yes	—
413	C₄²	C₂×D₄×C₁₃	1	2	yes	—
414	C₄²	C₂⁴×C₁₃	1	2	yes	—
415	C₄²	C₂⁴×C₁₃	1	2	yes	—
416	C₁₃	C₂×#3174	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
451	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
452	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	C₂×C₁₃×#41	1	4	yes	—
456	C₈	C₂×C₁₃×#41	1	4	yes	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	8	8	no	—
464	C₂²	C₁₃×#532	1	2	yes	—
465	C₂²	C₁₃×#577	1	4	yes	—
466	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	C₁₃×#532	1	2	yes	—
474	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
475	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
476	C₂	—	4	2	no	—
477	C₂	—	8	4	no	—
478	C₂	C₁₃×#3174	1	4	yes	direct product factor
479	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#541	C₂	semidirect
3. C₁₃×#3174	C₂	direct (N × H)
4. C₂×C₁₃×#499	C₂	semidirect
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#491	C₂	semidirect
7. C₂×C₁₃×#490	C₂	semidirect
8. C₂×C₁₃×#468	C₂	semidirect
9. C₂×C₁₃×#465	C₂	semidirect
10. C₂×C₁₃×#440	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₁₃×#405	C₂	semidirect
18. C₁₃×#541	C₂²	semidirect
34. C₁₃×#499	C₂²	semidirect
35. C₁₃×#492	C₂²	semidirect
36. C₁₃×#491	C₂²	semidirect
37. C₁₃×#490	C₂²	semidirect
38. C₁₃×#468	C₂²	semidirect
39. C₁₃×#465	C₂²	semidirect
40. C₁₃×#440	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
48. C₁₃×#405	C₂²	semidirect
118. C₂×#3174	C₁₃	direct (N × H)
177. C₂×#541	C₂×C₁₃	semidirect
179. #3174	C₂×C₁₃	direct (N × H)
180. C₂×#499	C₂×C₁₃	semidirect
181. C₂×#492	C₂×C₁₃	semidirect
182. C₂×#491	C₂×C₁₃	semidirect
183. C₂×#490	C₂×C₁₃	semidirect
184. C₂×#468	C₂×C₁₃	semidirect
185. C₂×#465	C₂×C₁₃	semidirect
186. C₂×#440	C₂×C₁₃	semidirect
187. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
188. C₂×#405	C₂×C₁₃	semidirect
234. #541	C₂²×C₁₃	semidirect
250. #499	C₂²×C₁₃	semidirect
251. #492	C₂²×C₁₃	semidirect
252. #491	C₂²×C₁₃	semidirect
253. #490	C₂²×C₁₃	semidirect
254. #468	C₂²×C₁₃	semidirect
255. #465	C₂²×C₁₃	semidirect
256. #440	C₂²×C₁₃	semidirect
257. C₄×SD₁₆	C₂²×C₁₃	semidirect
264. #405	C₂²×C₁₃	semidirect
355. C₂×C₁₃	#3174	direct (N × H)
416. C₁₃	C₂×#3174	direct (N × H)
478. C₂	C₁₃×#3174	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×#541	2
C₂×C₁₃×#540	2
C₁₃×#3174	2
C₂×C₁₃×#499	2
C₂×C₁₃×#492	2
C₂×C₁₃×#491	2
C₂×C₁₃×#490	2
C₂×C₁₃×#468	2
C₂×C₁₃×#465	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#405	2
C₂×#3174	13

Subgroups — C2×C13×#3174 #15747017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3174 #15747017