Subgroups — C₂×C₁₃×#3398 #15747734

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3398	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	2	yes	maximal
5	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#464	C₂	1	2	yes	maximal
7	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#441	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₁₃×#557	—	2	4	no	—
19	C₁₃×#557	C₂²	1	8	yes	complemented
20	C₁₃×#556	—	2	4	no	—
21	C₁₃×#556	C₂²	1	8	yes	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#126	—	2	2	no	—
26	C₂×C₁₃×#125	—	2	1	no	—
27	C₂×C₁₃×#125	—	2	2	no	—
28	C₂×C₁₃×#124	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₁₃×#497	C₂²	1	16	yes	—
38	C₁₃×#494	C₂²	1	8	yes	complemented
39	C₁₃×#464	C₂²	1	16	yes	—
40	C₁₃×#462	C₂²	1	16	yes	complemented
41	C₁₃×#462	C₂²	1	8	yes	complemented
42	C₁₃×#461	C₂²	1	8	yes	—
43	C₁₃×#446	C₂²	1	8	yes	complemented
44	C₁₃×#441	C₂²	1	16	yes	complemented
45	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
46	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂×C₁₃×Q₁₆	—	2	8	no	—
62	C₂×C₁₃×Q₁₆	—	4	4	no	—
63	C₂×C₁₃×Q₁₆	—	4	4	no	—
64	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
65	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
67	C₂×C₁₃×SD₁₆	—	2	4	no	—
68	C₂×C₁₃×SD₁₆	—	4	4	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	2	no	—
76	C₁₃×C₄⋊Q₈	—	2	4	no	—
77	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
80	C₁₃×#126	—	2	16	no	—
81	C₁₃×#125	—	2	8	no	—
82	C₁₃×#125	—	2	16	no	—
83	C₁₃×#124	—	2	4	no	—
84	C₁₃×#124	C₂³	1	8	yes	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	4	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	4	no	—
90	C₄×Q₈×C₁₃	D₄	1	4	yes	—
91	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
92	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	C₂³	1	4	yes	—
97	C₁₃×#117	—	2	8	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₄²×C₁₃	—	2	2	no	—
115	C₂×C₄²×C₁₃	—	2	2	no	—
116	C₂×C₄²×C₁₃	—	2	1	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₁₃×#106	C₂³	1	4	yes	—
120	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#103	C₂³	1	4	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#103	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	4	yes	—
126	C₁₃×#97	C₂³	1	8	yes	—
127	C₄×C₈×C₁₃	C₂³	1	4	yes	—
128	C₂×#3398	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
141	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	2	16	no	—
161	C₁₃×Q₁₆	—	4	8	no	—
162	C₁₃×Q₁₆	—	4	8	no	—
163	C₁₃×SD₁₆	—	2	8	no	—
164	C₁₃×SD₁₆	—	4	8	no	—
165	C₂×C₈×C₁₃	—	2	4	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	#41	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	8	no	—
176	C₁₃×C₄⋊C₄	—	2	4	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	1	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₄²×C₁₃	—	2	8	no	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃	C₂⁴	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	4	yes	—
196	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
198	#3398	C₂×C₁₃	1	16	yes	direct product factor
199	C₂×#497	C₂×C₁₃	1	2	yes	—
200	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#464	C₂×C₁₃	1	2	yes	—
202	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#462	C₂×C₁₃	1	2	yes	complemented
204	C₂×#461	C₂×C₁₃	1	1	yes	characteristic
205	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#441	C₂×C₁₃	1	2	yes	complemented
207	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	8	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	2	4	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	2	4	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	4	4	no	—
221	Q₈×C₁₃	—	4	2	no	—
222	Q₈×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	8	no	—
240	C₂×C₄×C₁₃	#137	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
247	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
249	C₈×C₁₃	—	2	4	no	—
250	C₈×C₁₃	—	2	2	no	—
251	C₈×C₁₃	C₂×#41	1	4	yes	—
252	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
253	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
254	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
257	#557	—	2	4	no	—
258	#557	C₂²×C₁₃	1	8	yes	complemented
259	#556	—	2	4	no	—
260	#556	C₂²×C₁₃	1	8	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#126	—	2	2	no	—
265	C₂×#125	—	2	1	no	—
266	C₂×#125	—	2	2	no	—
267	C₂×#124	C₂²×C₁₃	1	2	yes	—
268	C₂×C₂²⋊Q₈	—	2	1	no	—
269	C₂×C₄×Q₈	—	2	1	no	—
270	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
272	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
273	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#117	—	2	1	no	—
276	#497	C₂²×C₁₃	1	16	yes	—
277	#494	C₂²×C₁₃	1	8	yes	complemented
278	#464	C₂²×C₁₃	1	16	yes	—
279	#462	C₂²×C₁₃	1	16	yes	complemented
280	#462	C₂²×C₁₃	1	8	yes	complemented
281	#461	C₂²×C₁₃	1	8	yes	—
282	#446	C₂²×C₁₃	1	8	yes	complemented
283	#441	C₂²×C₁₃	1	16	yes	complemented
284	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
285	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃	1	2	yes	—
290	C₂×#103	C₂²×C₁₃	1	2	yes	—
291	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#97	C₂²×C₁₃	1	2	yes	—
293	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	8	4	no	—
298	C₂²×C₁₃	#550	1	2	yes	—
299	C₂²×C₁₃	C₂×#137	1	2	yes	—
300	C₂²×C₁₃	#578	1	2	yes	—
301	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
302	C₄×C₁₃	—	2	4	no	—
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	4	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	#550	1	2	yes	—
311	C₄×C₁₃	C₂×#137	1	4	yes	—
312	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
313	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂×Q₁₆	—	2	8	no	—
321	C₂×Q₁₆	—	4	4	no	—
322	C₂×Q₁₆	—	4	4	no	—
323	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
324	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
325	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	4	4	no	—
328	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
329	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	4	no	—
336	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
337	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
338	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
339	#126	—	2	16	no	—
340	#125	—	2	8	no	—
341	#125	—	2	16	no	—
342	#124	—	2	4	no	—
343	#124	C₂³×C₁₃	1	8	yes	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	8	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	D₄×C₁₃	1	4	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
351	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
352	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
353	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	C₂³×C₁₃	1	4	yes	—
356	#117	—	2	8	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
378	#106	C₂³×C₁₃	1	4	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
380	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
381	#103	C₂³×C₁₃	1	4	yes	—
382	#103	C₂³×C₁₃	1	8	yes	—
383	#103	C₂³×C₁₃	1	8	yes	—
384	#102	C₂³×C₁₃	1	4	yes	—
385	#97	C₂³×C₁₃	1	8	yes	—
386	C₄×C₈	C₂³×C₁₃	1	4	yes	—
387	C₂×C₁₃	—	8	2	no	—
388	C₂×C₁₃	#3398	1	4	yes	direct product factor
389	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
390	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
391	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
392	C₂⁴	—	2	1	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
404	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
405	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
406	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	Q₁₆	—	2	16	no	—
424	Q₁₆	—	4	8	no	—
425	Q₁₆	—	4	8	no	—
426	SD₁₆	—	2	8	no	—
427	SD₁₆	—	4	8	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	C₁₃×#41	1	4	yes	—
431	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
433	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	4	no	—
455	C₄²	C₂×D₄×C₁₃	1	2	yes	—
456	C₄²	C₂×D₄×C₁₃	1	4	yes	—
457	C₄²	C₂⁴×C₁₃	1	2	yes	—
458	C₄²	C₂⁴×C₁₃	1	4	yes	—
459	C₁₃	C₂×#3398	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	Q₈	—	2	8	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	2	4	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	4	4	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	C₁₃×#137	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
499	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
500	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	2	no	—
503	C₈	C₂×C₁₃×#41	1	4	yes	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	C₁₃×#550	1	2	yes	—
509	C₂²	C₂×C₁₃×#137	1	2	yes	—
510	C₂²	C₁₃×#578	1	2	yes	—
511	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
512	C₄	—	2	4	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	4	no	—
520	C₄	C₁₃×#550	1	2	yes	—
521	C₄	C₂×C₁₃×#137	1	4	yes	—
522	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
523	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂	—	8	2	no	—
525	C₂	C₁₃×#3398	1	4	yes	direct product factor
526	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
527	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
528	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3398	C₂	direct (N × H)
5. C₂×C₁₃×#494	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#462	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#441	C₂	semidirect
19. C₁₃×#557	C₂²	semidirect
38. C₁₃×#494	C₂²	semidirect
40. C₁₃×#462	C₂²	semidirect
41. C₁₃×#462	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₁₃×#441	C₂²	semidirect
128. C₂×#3398	C₁₃	direct (N × H)
196. C₂×#557	C₂×C₁₃	semidirect
198. #3398	C₂×C₁₃	direct (N × H)
200. C₂×#494	C₂×C₁₃	semidirect
202. C₂×#462	C₂×C₁₃	semidirect
203. C₂×#462	C₂×C₁₃	semidirect
205. C₂×#446	C₂×C₁₃	semidirect
206. C₂×#441	C₂×C₁₃	semidirect
258. #557	C₂²×C₁₃	semidirect
277. #494	C₂²×C₁₃	semidirect
279. #462	C₂²×C₁₃	semidirect
280. #462	C₂²×C₁₃	semidirect
282. #446	C₂²×C₁₃	semidirect
283. #441	C₂²×C₁₃	semidirect
388. C₂×C₁₃	#3398	direct (N × H)
459. C₁₃	C₂×#3398	direct (N × H)
525. C₂	C₁₃×#3398	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×#557	2
C₂×C₁₃×#556	2
C₁₃×#3398	2
C₂×C₁₃×#497	2
C₂×C₁₃×#494	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#461	2
C₂×C₁₃×#446	2
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3398	13

Subgroups — C2×C13×#3398 #15747734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3398 #15747734