Subgroups — C₂×C₁₃×#3222 #15747131

Order 3328.

2214 conjugacy classes of subgroups.

The subgroup lattice has 556 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×#535	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3222	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#541	—	2	4	no	—
20	C₁₃×#541	C₂²	1	8	yes	complemented
21	C₁₃×#535	—	2	4	no	—
22	C₁₃×#535	C₂²	1	8	yes	—
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#126	—	2	2	no	—
27	C₂×C₁₃×#125	—	2	2	no	—
28	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₁₃×#120	—	2	2	no	—
34	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#497	C₂²	1	8	yes	complemented
37	C₁₃×#492	C₂²	1	8	yes	complemented
38	C₁₃×#490	C₂²	1	8	yes	complemented
39	C₁₃×#488	C₂²	1	8	yes	complemented
40	C₁₃×#464	C₂²	1	16	yes	complemented
41	C₁₃×#460	C₂²	1	16	yes	complemented
42	C₁₃×#452	C₂²	1	16	yes	complemented
43	C₁₃×#450	C₂²	1	16	yes	complemented
44	C₁₃×#433	C₂²	1	8	yes	complemented
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
46	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#102	C₂²	1	2	yes	—
48	C₂×C₁₃×#102	C₂²	1	2	yes	—
49	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₁₃	—	2	1	no	—
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	4	4	no	—
56	C₂×C₁₃×#41	C₂³	1	4	yes	—
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	4	4	no	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×Q₁₆	—	4	4	no	—
72	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	complemented
73	C₂×C₁₃×SD₁₆	—	4	4	no	—
74	C₂×C₁₃×SD₁₆	—	4	4	no	—
75	C₂×C₁₃×SD₁₆	—	4	4	no	—
76	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
78	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
79	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	—	2	2	no	—
82	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	C₂³	1	4	yes	—
86	C₁₃×#127	C₂³	1	4	yes	—
87	C₁₃×#126	—	2	16	no	—
88	C₁₃×#125	—	2	16	no	—
89	C₁₃×#125	—	2	2	no	—
90	C₁₃×#125	C₂³	1	4	yes	complemented
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	4	yes	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₁₃×#121	—	2	16	no	—
98	C₁₃×#120	—	2	16	no	—
99	C₄×Q₈×C₁₃	—	2	4	no	—
100	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
101	C₁₃×#117	D₄	1	4	yes	—
102	C₁₃×#117	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
113	C₂×C₄²×C₁₃	—	2	2	no	—
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
117	C₁₃×#103	C₂³	1	8	yes	complemented
118	C₁₃×#102	C₂³	1	8	yes	—
119	C₁₃×#102	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	8	yes	complemented
121	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₁₃×#97	C₂³	1	4	yes	complemented
123	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
124	C₂×#3222	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	1	no	—
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂⁴×C₁₃	—	2	4	no	—
129	C₂⁴×C₁₃	—	4	4	no	—
130	C₂⁴×C₁₃	—	8	4	no	—
131	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₁₃×#41	—	4	8	no	—
133	C₁₃×#41	—	4	8	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	1	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	C₂⁴	1	2	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	8	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	4	8	no	—
152	C₂×D₄×C₁₃	—	4	4	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	4	no	—
155	C₂×D₄×C₁₃	—	8	4	no	—
156	C₂×D₄×C₁₃	—	8	4	no	—
157	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×Q₁₆	—	4	8	no	—
173	C₁₃×SD₁₆	—	4	8	no	—
174	C₁₃×SD₁₆	—	4	8	no	—
175	C₁₃×SD₁₆	—	4	8	no	—
176	C₂×C₈×C₁₃	—	2	4	no	—
177	C₂×C₈×C₁₃	—	2	4	no	—
178	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
191	C₄²×C₁₃	—	2	8	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₄²×C₁₃	C₂⁴	1	2	yes	—
195	C₄²×C₁₃	C₂⁴	1	2	yes	—
196	C₂×#541	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#535	C₂×C₁₃	1	1	yes	characteristic
198	#3222	C₂×C₁₃	1	16	yes	direct product factor
199	C₂×#497	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#488	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#464	C₂×C₁₃	1	2	yes	complemented
204	C₂×#460	C₂×C₁₃	1	2	yes	complemented
205	C₂×#452	C₂×C₁₃	1	2	yes	complemented
206	C₂×#450	C₂×C₁₃	1	2	yes	complemented
207	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	4	8	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	4	4	no	—
218	C₂³×C₁₃	—	4	4	no	—
219	C₂³×C₁₃	—	4	4	no	—
220	C₂³×C₁₃	—	8	8	no	—
221	C₂³×C₁₃	—	8	16	no	—
222	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	4	no	—
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	2	4	no	—
227	Q₈×C₁₃	—	4	4	no	—
228	Q₈×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	2	4	no	—
232	D₄×C₁₃	—	4	8	no	—
233	D₄×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	8	8	no	—
238	D₄×C₁₃	—	8	8	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	4	8	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
257	C₈×C₁₃	—	2	4	no	—
258	C₈×C₁₃	—	2	4	no	—
259	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
260	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
262	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
263	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
264	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
265	#541	—	2	4	no	—
266	#541	C₂²×C₁₃	1	8	yes	complemented
267	#535	—	2	4	no	—
268	#535	C₂²×C₁₃	1	8	yes	—
269	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
270	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#126	—	2	2	no	—
273	C₂×#125	—	2	2	no	—
274	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
275	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
278	C₂×#121	—	2	2	no	—
279	C₂×#120	—	2	2	no	—
280	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
281	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
282	#497	C₂²×C₁₃	1	8	yes	complemented
283	#492	C₂²×C₁₃	1	8	yes	complemented
284	#490	C₂²×C₁₃	1	8	yes	complemented
285	#488	C₂²×C₁₃	1	8	yes	complemented
286	#464	C₂²×C₁₃	1	16	yes	complemented
287	#460	C₂²×C₁₃	1	16	yes	complemented
288	#452	C₂²×C₁₃	1	16	yes	complemented
289	#450	C₂²×C₁₃	1	16	yes	complemented
290	#433	C₂²×C₁₃	1	8	yes	complemented
291	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
292	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
293	C₂×#102	C₂²×C₁₃	1	2	yes	—
294	C₂×#102	C₂²×C₁₃	1	2	yes	—
295	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
296	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
297	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	8	16	no	—
309	C₂²×C₁₃	—	8	4	no	—
310	C₂²×C₁₃	—	8	4	no	—
311	C₂²×C₁₃	—	8	4	no	—
312	C₂²×C₁₃	#535	1	2	yes	—
313	C₂²×C₁₃	#577	1	4	yes	—
314	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	4	no	—
317	C₄×C₁₃	—	2	4	no	—
318	C₄×C₁₃	—	4	2	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	—	4	4	no	—
321	C₄×C₁₃	#535	1	2	yes	—
322	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
323	C₂⁵	—	2	1	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	4	4	no	—
326	C₂×#41	C₂³×C₁₃	1	4	yes	—
327	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
328	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	4	4	no	—
335	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×Q₁₆	—	4	4	no	—
342	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	complemented
343	C₂×SD₁₆	—	4	4	no	—
344	C₂×SD₁₆	—	4	4	no	—
345	C₂×SD₁₆	—	4	4	no	—
346	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
347	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
348	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
349	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
350	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
353	#127	—	2	2	no	—
354	#127	—	2	2	no	—
355	#127	C₂³×C₁₃	1	4	yes	—
356	#127	C₂³×C₁₃	1	4	yes	—
357	#126	—	2	16	no	—
358	#125	—	2	16	no	—
359	#125	—	2	2	no	—
360	#125	C₂³×C₁₃	1	4	yes	complemented
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	C₂³×C₁₃	1	4	yes	—
364	#124	C₂³×C₁₃	1	4	yes	—
365	C₂²⋊Q₈	—	2	4	no	—
366	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
367	#121	—	2	16	no	—
368	#120	—	2	16	no	—
369	C₄×Q₈	—	2	4	no	—
370	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
371	#117	D₄×C₁₃	1	4	yes	—
372	#117	C₂³×C₁₃	1	4	yes	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
387	#103	C₂³×C₁₃	1	8	yes	complemented
388	#102	C₂³×C₁₃	1	8	yes	—
389	#102	C₂³×C₁₃	1	8	yes	—
390	#102	C₂³×C₁₃	1	8	yes	complemented
391	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
392	#97	C₂³×C₁₃	1	4	yes	complemented
393	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
394	C₂×C₁₃	—	4	2	no	—
395	C₂×C₁₃	—	8	2	no	—
396	C₂×C₁₃	—	8	2	no	—
397	C₂×C₁₃	—	8	2	no	—
398	C₂×C₁₃	#3222	1	4	yes	direct product factor
399	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#577	1	2	yes	—
401	C₂⁴	—	2	1	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	4	4	no	—
406	C₂⁴	—	8	4	no	—
407	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
408	#41	—	4	8	no	—
409	#41	—	4	8	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
416	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	4	8	no	—
428	C₂×D₄	—	4	4	no	—
429	C₂×D₄	—	4	8	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	8	4	no	—
432	C₂×D₄	—	8	4	no	—
433	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
435	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
448	Q₁₆	—	4	8	no	—
449	SD₁₆	—	4	8	no	—
450	SD₁₆	—	4	8	no	—
451	SD₁₆	—	4	8	no	—
452	C₂×C₈	—	2	4	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
455	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
462	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
467	C₄²	—	2	8	no	—
468	C₄²	C₂×D₄×C₁₃	1	2	yes	—
469	C₄²	C₂×D₄×C₁₃	1	2	yes	—
470	C₄²	C₂⁴×C₁₃	1	2	yes	—
471	C₄²	C₂⁴×C₁₃	1	2	yes	—
472	C₁₃	C₂×#3222	1	1	yes	characteristic, direct product factor, Sylow
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	4	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	8	8	no	—
486	C₂³	—	8	16	no	—
487	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	4	8	no	—
498	D₄	—	4	8	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	8	no	—
503	D₄	—	8	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
521	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
522	C₈	—	2	4	no	—
523	C₈	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	16	no	—
534	C₂²	—	8	4	no	—
535	C₂²	—	8	4	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₁₃×#535	1	2	yes	—
538	C₂²	C₁₃×#577	1	4	yes	—
539	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
540	C₄	—	2	4	no	—
541	C₄	—	2	4	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	C₁₃×#535	1	2	yes	—
547	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
548	C₂	—	4	2	no	—
549	C₂	—	8	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₁₃×#3222	1	4	yes	direct product factor
553	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
554	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×#535	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×#3222	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#490	C₂	semidirect
7. C₂×C₁₃×#488	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#460	C₂	semidirect
10. C₂×C₁₃×#452	C₂	semidirect
11. C₂×C₁₃×#450	C₂	semidirect
12. C₂×C₁₃×#433	C₂	semidirect
15. C₂²×C₁₃×Q₁₆	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₁₃×#541	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#125	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#497	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#490	C₂²	semidirect
39. C₁₃×#488	C₂²	semidirect
40. C₁₃×#464	C₂²	semidirect
41. C₁₃×#460	C₂²	semidirect
42. C₁₃×#452	C₂²	semidirect
43. C₁₃×#450	C₂²	semidirect
44. C₁₃×#433	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
46. C₂×C₁₃×#103	C₂²	semidirect
49. C₂×C₁₃×#102	C₂²	semidirect
51. C₂×C₁₃×#97	C₂²	semidirect
52. C₂×C₄×C₈×C₁₃	C₂²	semidirect
72. C₂×C₁₃×Q₁₆	C₂³	semidirect
78. C₂×C₁₃×SD₁₆	C₂³	semidirect
82. C₁₃×C₄⋊Q₈	C₂³	semidirect
90. C₁₃×#125	C₂³	semidirect
100. C₄×Q₈×C₁₃	C₂³	semidirect
116. C₁₃×C₄⋊C₈	C₂³	semidirect
117. C₁₃×#103	C₂³	semidirect
120. C₁₃×#102	C₂³	semidirect
122. C₁₃×#97	C₂³	semidirect
123. C₄×C₈×C₁₃	C₂³	semidirect
124. C₂×#3222	C₁₃	direct (N × H)
196. C₂×#541	C₂×C₁₃	semidirect
198. #3222	C₂×C₁₃	direct (N × H)
199. C₂×#497	C₂×C₁₃	semidirect
200. C₂×#492	C₂×C₁₃	semidirect
201. C₂×#490	C₂×C₁₃	semidirect
202. C₂×#488	C₂×C₁₃	semidirect
203. C₂×#464	C₂×C₁₃	semidirect
204. C₂×#460	C₂×C₁₃	semidirect
205. C₂×#452	C₂×C₁₃	semidirect
206. C₂×#450	C₂×C₁₃	semidirect
207. C₂×#433	C₂×C₁₃	semidirect
261. C₂²×Q₁₆	C₂²×C₁₃	semidirect
264. C₂²×SD₁₆	C₂²×C₁₃	semidirect
266. #541	C₂²×C₁₃	semidirect
269. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
274. C₂×#125	C₂²×C₁₃	semidirect
280. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
282. #497	C₂²×C₁₃	semidirect
283. #492	C₂²×C₁₃	semidirect
284. #490	C₂²×C₁₃	semidirect
285. #488	C₂²×C₁₃	semidirect
286. #464	C₂²×C₁₃	semidirect
287. #460	C₂²×C₁₃	semidirect
288. #452	C₂²×C₁₃	semidirect
289. #450	C₂²×C₁₃	semidirect
290. #433	C₂²×C₁₃	semidirect
291. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
292. C₂×#103	C₂²×C₁₃	semidirect
295. C₂×#102	C₂²×C₁₃	semidirect
297. C₂×#97	C₂²×C₁₃	semidirect
298. C₂×C₄×C₈	C₂²×C₁₃	semidirect
342. C₂×Q₁₆	C₂³×C₁₃	semidirect
348. C₂×SD₁₆	C₂³×C₁₃	semidirect
352. C₄⋊Q₈	C₂³×C₁₃	semidirect
360. #125	C₂³×C₁₃	semidirect
370. C₄×Q₈	C₂³×C₁₃	semidirect
386. C₄⋊C₈	C₂³×C₁₃	semidirect
387. #103	C₂³×C₁₃	semidirect
390. #102	C₂³×C₁₃	semidirect
392. #97	C₂³×C₁₃	semidirect
393. C₄×C₈	C₂³×C₁₃	semidirect
398. C₂×C₁₃	#3222	direct (N × H)
472. C₁₃	C₂×#3222	direct (N × H)
552. C₂	C₁₃×#3222	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×#535	2
C₁₃×#3222	2
C₂×C₁₃×#497	2
C₂×C₁₃×#492	2
C₂×C₁₃×#490	2
C₂×C₁₃×#488	2
C₂×C₁₃×#464	2
C₂×C₁₃×#460	2
C₂×C₁₃×#452	2
C₂×C₁₃×#450	2
C₂×C₁₃×#433	2
C₂×#3222	13

Subgroups — C2×C13×#3222 #15747131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3222 #15747131