Subgroups — C₂×#13116572 #16015861

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116572	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718158	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×#41	—	2	1	no	—
7	C₂×C₁₃×#135	—	2	1	no	—
8	C₂×C₁₃×#135	—	2	2	no	—
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	—	2	2	no	—
11	C₂×C₁₃×#135	C₄	1	2	yes	complemented
12	C₂×C₁₃×#135	C₄	1	4	yes	complemented
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	4	yes	—
15	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₁₃×SD₁₆	—	2	1	no	—
17	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×#88180	—	2	1	no	—
20	#11718767	—	2	2	no	—
21	#11718767	C₂²	1	4	yes	complemented
22	C₂×#88058	—	2	1	no	—
23	C₂×#88057	C₂²	1	2	yes	complemented
24	C₂×#88052	—	2	1	no	—
25	C₂×#88052	—	2	2	no	—
26	C₂×#88052	C₂²	1	2	yes	complemented
27	C₂×#88052	C₂²	1	4	yes	complemented
28	C₂²×#6090	—	2	1	no	—
29	#11718158	C₂²	1	16	yes	complemented
30	C₂×C₁₃×#41	—	2	2	no	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	2	2	no	—
33	C₂×C₁₃×#41	—	2	4	no	—
34	C₂×C₁₃×#41	—	4	1	no	—
35	C₂×C₁₃×#41	—	4	2	no	—
36	C₂×C₁₃×#41	—	4	1	no	—
37	C₂×C₁₃×#41	—	4	2	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	4	1	no	—
41	C₂³×C₄×C₁₃	—	4	1	no	—
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₁₃×#135	—	2	4	no	—
44	C₁₃×#135	—	2	4	no	—
45	C₁₃×#135	—	2	4	no	—
46	C₁₃×#135	—	2	2	no	—
47	C₁₃×#135	—	2	4	no	—
48	C₁₃×#135	—	2	4	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	C₂×C₄	1	4	yes	—
51	C₁₃×#135	C₂×C₄	1	8	yes	complemented
52	C₁₃×#135	C₂³	1	4	yes	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	1	no	—
55	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
57	C₂×C₁₃×SD₁₆	—	2	4	no	—
58	C₂×C₁₃×SD₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₂×C₁₃×SD₁₆	—	2	4	no	—
61	C₂×C₁₃×D₈	—	2	2	no	—
62	C₂×C₁₃×D₈	—	2	1	no	—
63	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
65	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
68	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	D₄	1	2	yes	—
70	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	D₄	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
75	C₂×C₂²⋊Dic₁₃	—	4	1	no	—
76	#88180	—	2	4	no	—
77	#88180	—	4	2	no	—
78	C₂×C₄⋊Dic₁₃	—	2	2	no	—
79	C₂×C₄×Dic₁₃	—	4	1	no	—
80	#88058	—	2	4	no	—
81	#88057	—	2	2	no	—
82	#88057	C₂³	1	4	yes	complemented
83	#88052	—	2	4	no	—
84	#88052	—	2	2	no	—
85	#88052	C₂³	1	4	yes	complemented
86	C₂×#6090	—	2	2	no	—
87	C₂×#6090	—	2	4	no	—
88	C₂×#2145	—	13	1	no	maximal, Sylow
89	C₂⁴×C₁₃	—	4	1	no	—
90	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	8	no	—
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	4	4	no	—
95	C₁₃×#41	—	4	4	no	—
96	C₁₃×#41	—	4	4	no	—
97	C₁₃×#41	—	4	4	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₁₃×#41	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	4	1	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	4	no	—
109	C₂×D₄×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	4	4	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	2	no	—
118	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	D₈	1	2	yes	—
123	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×Dic₁₃	—	4	2	no	—
129	C₁₃×Q₁₆	—	2	2	no	—
130	C₁₃×Q₁₆	—	2	4	no	—
131	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	—
132	C₁₃×SD₁₆	—	2	4	no	—
133	C₁₃×SD₁₆	—	2	8	no	—
134	C₁₃×SD₁₆	—	2	4	no	—
135	C₁₃×D₈	—	2	2	no	—
136	C₁₃×D₈	—	2	4	no	—
137	C₁₃×D₈	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²⋊Dic₁₃	—	4	4	no	—
157	C₄⋊Dic₁₃	—	2	4	no	—
158	C₄⋊Dic₁₃	—	4	2	no	—
159	C₄×Dic₁₃	—	4	4	no	—
160	#6090	—	2	4	no	—
161	C₂²×#135	D₁₃	1	1	yes	characteristic
162	C₂²×M₃₂	—	13	1	no	—
163	C₂×#427	—	13	1	no	—
164	#2145	—	13	8	no	—
165	C₂×#360	—	13	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	4	no	—
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	—	8	4	no	—
170	C₂³×C₁₃	#102	1	1	yes	characteristic
171	C₂³×C₁₃	#102	1	1	yes	characteristic
172	C₂³×C₁₃	#102	1	2	yes	—
173	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂³×C₁₃	C₂×D₈	1	2	yes	—
175	Q₈×C₁₃	—	2	4	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	—	4	4	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	4	4	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	8	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	#102	1	2	yes	—
190	C₂×C₄×C₁₃	#102	1	2	yes	—
191	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
192	C₂×C₄×C₁₃	#102	1	2	yes	—
193	C₂×C₄×C₁₃	#102	1	2	yes	—
194	C₂×C₄×C₁₃	#102	1	2	yes	—
195	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×Dic₁₃	—	4	4	no	—
208	C₂×Dic₁₃	—	8	4	no	—
209	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
211	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂²×#41	—	2	1	no	—
216	C₂×#135	—	2	1	no	—
217	C₂×#135	—	2	2	no	—
218	C₂×#135	—	2	1	no	—
219	C₂×#135	—	2	2	no	—
220	C₂×#135	Dic₁₃	1	2	yes	complemented
221	C₂×#135	Dic₁₃	1	4	yes	complemented
222	C₂×#135	C₂×D₁₃	1	2	yes	—
223	C₂×#135	C₂×D₁₃	1	4	yes	—
224	C₂²×Q₁₆	Dic₁₃	1	1	yes	characteristic, complemented
225	C₂²×SD₁₆	—	2	1	no	—
226	C₂²×D₈	Dic₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
228	C₂×#117	—	26	1	no	—
229	C₂×M₃₂	—	13	2	no	—
230	C₂×M₃₂	—	13	4	no	—
231	C₂×M₃₂	—	26	1	no	—
232	C₂×M₃₂	—	26	2	no	—
233	C₂²×C₁₆	—	26	1	no	—
234	#427	—	13	4	no	—
235	#427	—	26	2	no	—
236	C₂×#107	—	26	1	no	—
237	C₂×#106	—	13	2	no	—
238	#360	—	13	16	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	4	no	—
245	C₂²×C₁₃	—	8	8	no	—
246	C₂²×C₁₃	—	8	4	no	—
247	C₂²×C₁₃	C₂×#102	1	2	yes	—
248	C₂²×C₁₃	C₂×#102	1	2	yes	—
249	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#102	1	2	yes	—
255	C₄×C₁₃	C₂×#102	1	2	yes	—
256	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
257	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
258	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
259	Dic₁₃	—	8	4	no	—
260	C₂×#41	—	2	4	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	4	no	—
264	C₂×#41	—	4	2	no	—
265	C₂×#41	—	4	1	no	—
266	C₂×#41	—	4	1	no	—
267	C₂×#41	—	4	2	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	4	1	no	—
271	C₂³×C₄	—	4	1	no	—
272	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
273	#135	—	2	4	no	—
274	#135	—	2	4	no	—
275	#135	—	2	4	no	—
276	#135	—	2	2	no	—
277	#135	—	2	4	no	—
278	#135	—	2	4	no	—
279	#135	—	2	2	no	—
280	#135	C₂×Dic₁₃	1	4	yes	—
281	#135	C₂×Dic₁₃	1	8	yes	complemented
282	#135	C₂²×D₁₃	1	4	yes	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	—	2	1	no	—
285	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
286	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	complemented
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	4	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	—	2	1	no	—
293	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
294	C₂×D₈	C₂×Dic₁₃	1	4	yes	complemented
295	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
297	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
298	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
300	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
303	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
305	#117	—	26	4	no	—
306	#117	—	52	2	no	—
307	C₂×C₄⋊C₄	—	26	2	no	—
308	C₂×C₂²⋊C₄	—	52	1	no	—
309	C₂×C₄²	—	52	1	no	—
310	M₃₂	—	13	4	no	—
311	M₃₂	—	26	4	no	—
312	M₃₂	—	26	2	no	—
313	C₂×C₁₆	—	26	2	no	—
314	C₂×C₁₆	—	26	4	no	—
315	#107	—	26	4	no	—
316	#106	—	13	4	no	—
317	#106	—	26	2	no	—
318	C₂×C₁₃	—	2	1	no	—
319	C₂×C₁₃	—	2	2	no	—
320	C₂×C₁₃	—	2	1	no	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	—	8	4	no	—
323	C₂×C₁₃	#2145	1	2	yes	complemented
324	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
325	C₂⁴	—	4	1	no	—
326	C₂⁴	#6104	1	1	yes	characteristic
327	#41	—	2	4	no	—
328	#41	—	2	8	no	—
329	#41	—	2	4	no	—
330	#41	—	4	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	#41	—	4	4	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	52	2	no	—
355	C₂²×C₄	#6104	1	2	yes	—
356	C₂²×C₄	#6104	1	1	yes	characteristic
357	C₂²×C₄	#6105	1	1	yes	characteristic
358	C₂²×C₄	#6105	1	2	yes	—
359	C₂²×C₄	#6105	1	1	yes	characteristic
360	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
362	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
365	Q₁₆	—	2	2	no	—
366	Q₁₆	—	2	4	no	—
367	Q₁₆	C₂²×Dic₁₃	1	4	yes	—
368	SD₁₆	—	2	4	no	—
369	SD₁₆	—	2	8	no	—
370	SD₁₆	—	2	4	no	—
371	D₈	—	2	2	no	—
372	D₈	—	2	4	no	—
373	D₈	C₂²×Dic₁₃	1	4	yes	—
374	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
376	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
378	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
379	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
380	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
381	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
382	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
383	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
385	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
389	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
390	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
392	C₄⋊C₄	—	26	4	no	—
393	C₄⋊C₄	—	52	2	no	—
394	C₂²⋊C₄	—	52	4	no	—
395	C₄²	—	52	4	no	—
396	C₁₆	—	26	4	no	—
397	C₁₃	C₂×#2145	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	4	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	8	4	no	—
402	C₂³	#88072	1	1	yes	characteristic
403	C₂³	#88072	1	1	yes	characteristic
404	C₂³	#88072	1	2	yes	—
405	C₂³	C₂×#6104	1	1	yes	characteristic
406	C₂³	C₂×#6104	1	2	yes	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	52	4	no	—
422	C₂×C₄	—	104	4	no	—
423	C₂×C₄	#88072	1	2	yes	—
424	C₂×C₄	#88072	1	2	yes	—
425	C₂×C₄	#88072	1	1	yes	characteristic
426	C₂×C₄	#88072	1	2	yes	—
427	C₂×C₄	#88072	1	2	yes	—
428	C₂×C₄	#88072	1	2	yes	—
429	C₂×C₄	#88072	1	1	yes	characteristic
430	C₂×C₄	C₂×#6104	1	2	yes	—
431	C₂×C₄	C₂×#6104	1	1	yes	characteristic
432	C₂×C₄	C₂×#6105	1	1	yes	characteristic
433	C₂×C₄	C₂×#6105	1	2	yes	—
434	C₂×C₄	C₂×#6105	1	1	yes	characteristic
435	C₂×C₄	C₂×#6105	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	2	yes	—
437	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	2	yes	—
440	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
441	C₈	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
442	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
443	C₈	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
444	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
445	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
446	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×#88072	1	2	yes	—
456	C₂²	C₂×#88072	1	2	yes	—
457	C₂²	C₂×#88072	1	1	yes	characteristic
458	C₂²	C₂×#88072	1	1	yes	characteristic
459	C₂²	C₂²×#6104	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	104	4	no	—
462	C₄	C₂×#88072	1	1	yes	characteristic
463	C₄	C₂×#88072	1	2	yes	—
464	C₄	C₂×#88072	1	2	yes	—
465	C₄	C₂×#88072	1	1	yes	characteristic
466	C₄	C₂²×#6105	1	1	yes	characteristic
467	C₄	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	2	no	—
472	C₂	—	8	4	no	—
473	C₂	#13116572	1	2	yes	direct product factor
474	C₂	C₂²×#88072	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88072
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting, prime radical	C₂²×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂×#102
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×#135	D₁₃
hypocenter	C₁₃	C₂×#2145
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#88052	C₂	semidirect
2. C₂×#11718767	C₂	semidirect
3. #13116572	C₂	direct (N × H)
4. C₂×#11718158	C₂	semidirect
11. C₂×C₁₃×#135	C₄	semidirect
12. C₂×C₁₃×#135	C₄	semidirect
15. C₂²×C₁₃×Q₁₆	C₄	semidirect
17. C₂²×C₁₃×D₈	C₄	semidirect
21. #11718767	C₂²	semidirect
23. C₂×#88057	C₂²	semidirect
26. C₂×#88052	C₂²	semidirect
27. C₂×#88052	C₂²	semidirect
29. #11718158	C₂²	semidirect
51. C₁₃×#135	C₂×C₄	semidirect
56. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
64. C₂×C₁₃×D₈	C₂×C₄	semidirect
82. #88057	C₂³	semidirect
85. #88052	C₂³	semidirect
220. C₂×#135	Dic₁₃	semidirect
221. C₂×#135	Dic₁₃	semidirect
224. C₂²×Q₁₆	Dic₁₃	semidirect
226. C₂²×D₈	Dic₁₃	semidirect
281. #135	C₂×Dic₁₃	semidirect
286. C₂×Q₁₆	C₂×Dic₁₃	semidirect
294. C₂×D₈	C₂×Dic₁₃	semidirect
323. C₂×C₁₃	#2145	semidirect
397. C₁₃	C₂×#2145	semidirect
473. C₂	#13116572	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#88052	2
C₂×#11718767	2
#13116572	2
C₂×#11718158	2
C₂²×C₁₃×#135	2
C₂×#2145	13

Subgroups — C2×#13116572 #16015861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116572 #16015861