Subgroups — C₂₉×#9845 #20304745

Order 7424.

478 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3170	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1994	C₂	1	2	yes	maximal
3	C₄²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1567	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1493	C₂	1	2	yes	maximal
6	C₂₉×#533	C₂²	1	2	yes	—
7	C₂₉×#500	C₄	1	1	yes	characteristic, complemented
8	C₂₉×#494	C₄	1	1	yes	characteristic, complemented
9	C₂₉×#487	C₄	1	2	yes	complemented
10	C₂₉×#467	—	2	2	no	—
11	C₄×Q₁₆×C₂₉	—	2	2	no	—
12	C₂₉×#423	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₂₉	—	2	2	no	—
14	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₄³×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#339	—	2	4	no	—
18	C₂₉×#335	—	2	2	no	—
19	C₂₉×Q₈⋊C₈	—	2	4	no	—
20	C₂×Q₁₆×C₂₉	—	2	2	no	—
21	C₂×M₁₆×C₂₉	—	2	2	no	—
22	C₂²×C₈×C₂₉	—	2	1	no	—
23	C₂²×C₈×C₂₉	D₄	1	2	yes	—
24	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
26	C₂₉×#125	—	2	2	no	—
27	C₂₉×C₂²⋊Q₈	—	2	2	no	—
28	C₂₉×C₂²⋊Q₈	—	2	2	no	—
29	C₄×Q₈×C₂₉	—	2	2	no	—
30	C₄×Q₈×C₂₉	—	2	2	no	—
31	C₂₉×#117	—	2	2	no	—
32	C₂×C₄²×C₂₉	—	2	1	no	—
33	C₂×C₄²×C₂₉	—	2	1	no	—
34	C₂×C₄²×C₂₉	D₄	1	2	yes	—
35	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
36	C₂₉×#107	—	2	2	no	—
37	C₂₉×C₄⋊C₈	—	2	2	no	—
38	C₂₉×C₄⋊C₈	—	2	2	no	—
39	C₂₉×#103	—	2	4	no	—
40	C₄×C₈×C₂₉	—	2	8	no	—
41	C₄×C₈×C₂₉	—	2	1	no	—
42	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₂₉	D₄	1	2	yes	—
45	C₄×C₈×C₂₉	D₄	1	2	yes	—
46	C₂×Q₈×C₂₉	—	2	2	no	—
47	C₂×Q₈×C₂₉	—	2	2	no	—
48	C₂²×C₄×C₂₉	—	2	2	no	—
49	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
52	Q₁₆×C₂₉	—	4	4	no	—
53	M₁₆×C₂₉	—	4	4	no	—
54	C₂×C₈×C₂₉	—	2	4	no	—
55	C₂×C₈×C₂₉	—	2	2	no	—
56	C₂×C₈×C₂₉	—	2	4	no	—
57	C₂×C₈×C₂₉	—	4	2	no	—
58	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
60	C₄⋊C₄×C₂₉	—	2	2	no	—
61	C₄⋊C₄×C₂₉	—	2	2	no	—
62	C₄⋊C₄×C₂₉	—	2	2	no	—
63	C₄⋊C₄×C₂₉	—	2	2	no	—
64	C₄⋊C₄×C₂₉	—	4	2	no	—
65	C₄⋊C₄×C₂₉	—	4	2	no	—
66	C₂²⋊C₄×C₂₉	—	4	2	no	—
67	C₄²×C₂₉	—	2	4	no	—
68	C₄²×C₂₉	—	2	4	no	—
69	C₄²×C₂₉	—	2	2	no	—
70	C₄²×C₂₉	—	4	2	no	—
71	C₄²×C₂₉	Q₁₆	1	4	yes	complemented
72	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₂₉	#41	1	1	yes	characteristic
76	#9845	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₂₉	#121	1	1	yes	characteristic
78	Q₈×C₂₉	—	4	4	no	—
79	Q₈×C₂₉	—	4	4	no	—
80	C₂×C₄×C₂₉	—	2	4	no	—
81	C₂×C₄×C₂₉	—	2	4	no	—
82	C₂×C₄×C₂₉	—	2	4	no	—
83	C₂×C₄×C₂₉	—	2	2	no	—
84	C₂×C₄×C₂₉	—	2	2	no	—
85	C₂×C₄×C₂₉	—	4	2	no	—
86	C₂×C₄×C₂₉	—	4	2	no	—
87	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
89	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₂₉	#124	1	1	yes	characteristic
92	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
93	C₂×C₄×C₂₉	C₂×Q₁₆	1	2	yes	—
94	C₂×C₄×C₂₉	#135	1	2	yes	—
95	C₈×C₂₉	—	2	4	no	—
96	C₈×C₂₉	—	2	2	no	—
97	C₈×C₂₉	—	8	2	no	—
98	C₈×C₂₉	#104	1	4	yes	—
99	#3170	C₂×C₂₉	1	1	yes	characteristic
100	#1994	C₂×C₂₉	1	2	yes	—
101	C₄²×C₈	C₂×C₂₉	1	1	yes	characteristic
102	#1567	C₂×C₂₉	1	1	yes	characteristic
103	#1493	C₂×C₂₉	1	2	yes	—
104	C₂²×C₂₉	—	2	1	no	—
105	C₂²×C₂₉	—	2	1	no	—
106	C₂²×C₂₉	#390	1	1	yes	characteristic
107	C₂²×C₂₉	#467	1	2	yes	—
108	C₄×C₂₉	—	2	8	no	—
109	C₄×C₂₉	—	2	1	no	—
110	C₄×C₂₉	—	2	1	no	—
111	C₄×C₂₉	—	8	2	no	—
112	C₄×C₂₉	—	8	2	no	—
113	C₄×C₂₉	C₂×#104	1	2	yes	—
114	C₄×C₂₉	C₄×Q₁₆	1	2	yes	—
115	C₄×C₂₉	#443	1	2	yes	—
116	C₄×C₂₉	#494	1	1	yes	characteristic
117	C₄×C₂₉	#495	1	1	yes	characteristic
118	#533	C₂²×C₂₉	1	2	yes	—
119	#500	C₄×C₂₉	1	1	yes	characteristic, complemented
120	#494	C₄×C₂₉	1	1	yes	characteristic, complemented
121	#487	C₄×C₂₉	1	2	yes	complemented
122	#467	—	2	2	no	—
123	C₄×Q₁₆	—	2	2	no	—
124	#423	C₂²×C₂₉	1	2	yes	—
125	C₂×C₄×C₈	—	2	2	no	—
126	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
128	C₄³	C₂²×C₂₉	1	1	yes	characteristic
129	#339	—	2	4	no	—
130	#335	—	2	2	no	—
131	Q₈⋊C₈	—	2	4	no	—
132	C₂×C₂₉	—	2	2	no	—
133	C₂×C₂₉	#1962	1	1	yes	characteristic
134	C₂×C₂₉	#1969	1	1	yes	characteristic
135	C₂×C₂₉	#1974	1	1	yes	characteristic
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×M₁₆	—	2	2	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	D₄×C₂₉	1	2	yes	—
140	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
141	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
142	#125	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	D₄×C₂₉	1	2	yes	—
151	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	2	8	no	—
157	C₄×C₈	—	2	1	no	—
158	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
159	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
160	C₄×C₈	D₄×C₂₉	1	2	yes	—
161	C₄×C₈	D₄×C₂₉	1	2	yes	—
162	C₂₉	#9845	1	1	yes	characteristic, direct product factor, Sylow
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
167	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
168	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
169	Q₁₆	—	4	4	no	—
170	M₁₆	—	4	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
176	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	4	2	no	—
188	C₄²	Q₁₆×C₂₉	1	4	yes	complemented
189	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
191	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
192	C₄²	#41×C₂₉	1	1	yes	characteristic
193	C₂³	C₂₉×#121	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
204	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
205	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
206	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
207	C₂×C₄	C₂₉×#124	1	1	yes	characteristic
208	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
209	C₂×C₄	C₂×Q₁₆×C₂₉	1	2	yes	—
210	C₂×C₄	C₂₉×#135	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	8	2	no	—
214	C₈	C₂₉×#104	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	C₂₉×#390	1	1	yes	characteristic
218	C₂²	C₂₉×#467	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	8	2	no	—
223	C₄	—	8	2	no	—
224	C₄	C₂×C₂₉×#104	1	2	yes	—
225	C₄	C₄×Q₁₆×C₂₉	1	2	yes	—
226	C₄	C₂₉×#443	1	2	yes	—
227	C₄	C₂₉×#494	1	1	yes	characteristic
228	C₄	C₂₉×#495	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	C₂₉×#1962	1	1	yes	characteristic
231	C₂	C₂₉×#1969	1	1	yes	characteristic
232	C₂	C₂₉×#1974	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#127
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#390
prime radical	C₂³×C₂₉	#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂₉×#500	C₄	semidirect
8. C₂₉×#494	C₄	semidirect
9. C₂₉×#487	C₄	semidirect
71. C₄²×C₂₉	Q₁₆	semidirect
76. #9845	C₂₉	direct (N × H)
119. #500	C₄×C₂₉	semidirect
120. #494	C₄×C₂₉	semidirect
121. #487	C₄×C₂₉	semidirect
162. C₂₉	#9845	direct (N × H)
188. C₄²	Q₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3170	2
C₂₉×#1994	2
C₄²×C₈×C₂₉	2
C₂₉×#1567	2
C₂₉×#1493	2
#9845	29

Subgroups — C29×#9845 #20304745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9845 #20304745