Subgroups — C₂₉×#2319 #16816033

Order 3712.

540 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#390	C₂	1	2	yes	maximal
3	C₂₉×#389	C₂	1	2	yes	maximal, complemented
4	C₂₉×#388	C₂	1	4	yes	maximal, complemented
5	C₂₉×#381	C₂	1	2	yes	maximal, complemented
6	C₂₉×#380	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
11	C₄×D₄×C₂₉	C₄	1	8	yes	complemented
12	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
18	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
19	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#95	C₂²	1	1	yes	characteristic
22	C₂₉×#95	C₂²	1	1	yes	characteristic
23	C₂₉×#95	C₂²	1	2	yes	—
24	C₂₉×#95	C₂²	1	2	yes	—
25	C₂₉×#95	C₂²	1	4	yes	—
26	C₂⁴×C₂₉	C₂³	1	2	yes	—
27	C₂×D₄×C₂₉	—	2	4	no	—
28	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
29	C₂²×C₄×C₂₉	—	4	4	no	—
30	C₂²×C₄×C₂₉	C₂×C₄	1	8	yes	—
31	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
32	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
33	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
38	C₄⋊C₄×C₂₉	—	2	4	no	—
39	C₄⋊C₄×C₂₉	—	4	4	no	—
40	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
41	C₂²⋊C₄×C₂₉	—	4	4	no	—
42	C₂²⋊C₄×C₂₉	—	4	4	no	—
43	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
44	C₄²×C₂₉	—	2	4	no	—
45	C₄²×C₂₉	—	4	2	no	—
46	C₄²×C₂₉	C₂×C₄	1	4	yes	—
47	C₂³×C₂₉	—	2	4	no	—
48	C₂³×C₂₉	—	2	2	no	—
49	C₂³×C₂₉	—	2	4	no	—
50	C₂³×C₂₉	—	2	2	no	—
51	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
52	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
53	D₄×C₂₉	—	2	8	no	—
54	C₂×C₄×C₂₉	—	2	1	no	—
55	C₂×C₄×C₂₉	—	2	4	no	—
56	C₂×C₄×C₂₉	—	2	2	no	—
57	C₂×C₄×C₂₉	—	2	1	no	—
58	C₂×C₄×C₂₉	—	2	2	no	—
59	C₂×C₄×C₂₉	—	2	2	no	—
60	C₂×C₄×C₂₉	—	2	4	no	—
61	C₂×C₄×C₂₉	—	2	4	no	—
62	C₂×C₄×C₂₉	—	2	2	no	—
63	C₂×C₄×C₂₉	—	2	2	no	—
64	C₂×C₄×C₂₉	—	2	4	no	—
65	C₂×C₄×C₂₉	—	2	2	no	—
66	C₂×C₄×C₂₉	—	2	2	no	—
67	C₂×C₄×C₂₉	—	4	8	no	—
68	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₂₉	#41	1	4	yes	—
73	#2319	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂²×C₂₉	—	2	4	no	—
75	C₂²×C₂₉	—	2	4	no	—
76	C₂²×C₂₉	—	2	4	no	—
77	C₂²×C₂₉	—	4	4	no	—
78	C₂²×C₂₉	—	4	4	no	—
79	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
80	C₂²×C₂₉	C₂×#41	1	2	yes	—
81	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
82	C₂²×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
83	C₂²×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
84	C₄×C₂₉	—	2	2	no	—
85	C₄×C₂₉	—	2	4	no	—
86	C₄×C₂₉	—	2	2	no	—
87	C₄×C₂₉	—	4	2	no	—
88	C₄×C₂₉	—	4	4	no	—
89	C₄×C₂₉	—	4	2	no	—
90	C₄×C₂₉	#117	1	4	yes	—
91	C₂×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic
92	#390	C₂×C₂₉	1	2	yes	—
93	#389	C₂×C₂₉	1	2	yes	complemented
94	#388	C₂×C₂₉	1	4	yes	complemented
95	#381	C₂×C₂₉	1	2	yes	complemented
96	#380	C₂×C₂₉	1	2	yes	complemented
97	C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
98	#376	C₂×C₂₉	1	1	yes	characteristic, complemented
99	C₂×C₂₉	—	4	4	no	—
100	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
101	C₂×C₂₉	#518	1	1	yes	characteristic
102	C₂×C₂₉	#520	1	1	yes	characteristic
103	C₂×C₂₉	#540	1	2	yes	—
104	C₂×C₂₉	#542	1	2	yes	—
105	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
106	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
107	C₄×D₄	C₄×C₂₉	1	8	yes	complemented
108	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
109	C₂×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
110	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
111	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
112	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
113	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
114	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
115	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
116	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
117	#95	C₂²×C₂₉	1	1	yes	characteristic
118	#95	C₂²×C₂₉	1	1	yes	characteristic
119	#95	C₂²×C₂₉	1	2	yes	—
120	#95	C₂²×C₂₉	1	2	yes	—
121	#95	C₂²×C₂₉	1	4	yes	—
122	C₂₉	#2319	1	1	yes	characteristic, direct product factor, Sylow
123	C₂⁴	C₂³×C₂₉	1	2	yes	—
124	C₂×D₄	—	2	4	no	—
125	C₂×D₄	C₂×C₄×C₂₉	1	4	yes	—
126	C₂²×C₄	—	4	4	no	—
127	C₂²×C₄	C₂×C₄×C₂₉	1	8	yes	—
128	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
129	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
130	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
131	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
132	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
133	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
134	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
135	C₄⋊C₄	—	2	4	no	—
136	C₄⋊C₄	—	4	4	no	—
137	C₄⋊C₄	C₂×C₄×C₂₉	1	4	yes	—
138	C₂²⋊C₄	—	4	4	no	—
139	C₂²⋊C₄	—	4	4	no	—
140	C₂²⋊C₄	C₂×C₄×C₂₉	1	8	yes	—
141	C₄²	—	2	4	no	—
142	C₄²	—	4	2	no	—
143	C₄²	C₂×C₄×C₂₉	1	4	yes	—
144	C₂³	—	2	4	no	—
145	C₂³	—	2	2	no	—
146	C₂³	—	2	4	no	—
147	C₂³	—	2	2	no	—
148	C₂³	C₂²×C₄×C₂₉	1	4	yes	—
149	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
150	D₄	—	2	8	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	4	8	no	—
165	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
166	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
167	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
168	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
169	C₂×C₄	#41×C₂₉	1	4	yes	—
170	C₂²	—	2	4	no	—
171	C₂²	—	2	4	no	—
172	C₂²	—	2	4	no	—
173	C₂²	—	4	4	no	—
174	C₂²	—	4	4	no	—
175	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
176	C₂²	C₂×#41×C₂₉	1	2	yes	—
177	C₂²	C₂₉×H(5,𝔽₂)	1	2	yes	—
178	C₂²	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
179	C₂²	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
180	C₄	—	2	2	no	—
181	C₄	—	2	4	no	—
182	C₄	—	2	2	no	—
183	C₄	—	4	2	no	—
184	C₄	—	4	4	no	—
185	C₄	—	4	2	no	—
186	C₄	C₂₉×#117	1	4	yes	—
187	C₂	—	4	4	no	—
188	C₂	C₂×C₂₉×#117	1	1	yes	characteristic
189	C₂	C₂₉×#518	1	1	yes	characteristic
190	C₂	C₂₉×#520	1	1	yes	characteristic
191	C₂	C₂₉×#540	1	2	yes	—
192	C₂	C₂₉×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#389	C₂	semidirect
4. C₂₉×#388	C₂	semidirect
5. C₂₉×#381	C₂	semidirect
6. C₂₉×#380	C₂	semidirect
7. C₄×C₄⋊C₄×C₂₉	C₂	semidirect
8. C₂₉×#376	C₂	semidirect
11. C₄×D₄×C₂₉	C₄	semidirect
73. #2319	C₂₉	direct (N × H)
93. #389	C₂×C₂₉	semidirect
94. #388	C₂×C₂₉	semidirect
95. #381	C₂×C₂₉	semidirect
96. #380	C₂×C₂₉	semidirect
97. C₄×C₄⋊C₄	C₂×C₂₉	semidirect
98. #376	C₂×C₂₉	semidirect
107. C₄×D₄	C₄×C₂₉	semidirect
122. C₂₉	#2319	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×C₄×D₄×C₂₉	2
C₂₉×#390	2
C₂₉×#389	2
C₂₉×#388	2
C₂₉×#381	2
C₂₉×#380	2
C₄×C₄⋊C₄×C₂₉	2
C₂₉×#376	2
#2319	29

Subgroups — C29×#2319 #16816033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2319 #16816033