Subgroups — C₂×C₂₉×#553 #16817185

Order 3712.

1252 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#553	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₂₉×#126	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#123	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#121	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₂₉	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
14	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
17	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
20	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
21	C₂₉×#126	C₂²	1	16	yes	complemented
22	C₂₉×#125	C₂²	1	8	yes	complemented
23	C₂₉×#123	C₂²	1	16	yes	complemented
24	C₂₉×#121	C₂²	1	16	yes	complemented
25	C₂₉×#121	C₂²	1	8	yes	complemented
26	C₂₉×#121	C₂²	1	8	yes	complemented
27	C₄×D₄×C₂₉	C₂²	1	16	yes	complemented
28	C₄×D₄×C₂₉	C₂²	1	8	yes	complemented
29	C₄×D₄×C₂₉	C₂²	1	8	yes	complemented
30	C₂₉×#117	C₂²	1	8	yes	complemented
31	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
34	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
36	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
38	C₂×C₄⋊C₄×C₂₉	C₂²	1	8	yes	complemented
39	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
43	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
45	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
46	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
47	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
48	C₂⁴×C₂₉	C₂³	1	2	yes	—
49	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
50	C₂×D₄×C₂₉	—	2	8	no	—
51	C₂×D₄×C₂₉	—	2	4	no	—
52	C₂×D₄×C₂₉	—	2	4	no	—
53	C₂×D₄×C₂₉	—	4	4	no	—
54	C₂×D₄×C₂₉	C₂³	1	8	yes	—
55	C₂×D₄×C₂₉	C₂³	1	4	yes	—
56	C₂×D₄×C₂₉	C₂³	1	4	yes	—
57	C₂×D₄×C₂₉	C₂³	1	8	yes	—
58	C₂²×C₄×C₂₉	—	2	4	no	—
59	C₂²×C₄×C₂₉	—	2	4	no	—
60	C₂²×C₄×C₂₉	—	4	4	no	—
61	C₂²×C₄×C₂₉	—	4	4	no	—
62	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
63	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
64	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
66	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
68	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
71	C₂²×C₄×C₂₉	C₂³	1	8	yes	—
72	C₂²×C₄×C₂₉	C₂³	1	8	yes	—
73	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
75	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
76	C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
77	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
78	C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
79	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
80	C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
82	C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
83	C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
84	C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
85	C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
86	C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
87	C₄²×C₂₉	C₂³	1	8	yes	—
88	C₄²×C₂₉	C₂³	1	4	yes	—
89	C₂³×C₂₉	—	2	2	no	—
90	C₂³×C₂₉	—	2	2	no	—
91	C₂³×C₂₉	—	2	2	no	—
92	C₂³×C₂₉	—	2	2	no	—
93	C₂³×C₂₉	—	2	4	no	—
94	C₂³×C₂₉	—	2	4	no	—
95	C₂³×C₂₉	—	2	4	no	—
96	C₂³×C₂₉	—	2	2	no	—
97	C₂³×C₂₉	#41	1	4	yes	—
98	C₂³×C₂₉	C₂⁴	1	2	yes	—
99	C₂³×C₂₉	C₂⁴	1	4	yes	—
100	C₂³×C₂₉	C₂⁴	1	2	yes	—
101	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
102	D₄×C₂₉	—	2	16	no	—
103	D₄×C₂₉	—	2	8	no	—
104	D₄×C₂₉	—	2	8	no	—
105	D₄×C₂₉	—	4	8	no	—
106	C₂×C₄×C₂₉	—	2	2	no	—
107	C₂×C₄×C₂₉	—	2	2	no	—
108	C₂×C₄×C₂₉	—	2	4	no	—
109	C₂×C₄×C₂₉	—	2	2	no	—
110	C₂×C₄×C₂₉	—	2	2	no	—
111	C₂×C₄×C₂₉	—	2	4	no	—
112	C₂×C₄×C₂₉	—	2	4	no	—
113	C₂×C₄×C₂₉	—	2	8	no	—
114	C₂×C₄×C₂₉	—	2	8	no	—
115	C₂×C₄×C₂₉	—	4	8	no	—
116	C₂×C₄×C₂₉	—	4	8	no	—
117	C₂×C₄×C₂₉	#41	1	4	yes	—
118	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
119	C₂×C₄×C₂₉	C₂⁴	1	4	yes	—
120	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
121	C₂×C₄×C₂₉	C₂⁴	1	4	yes	—
122	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
123	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
124	C₂×C₄×C₂₉	C₂⁴	1	4	yes	—
125	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
126	C₂×#553	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂²×C₂₉	—	2	8	no	—
128	C₂²×C₂₉	—	2	2	no	—
129	C₂²×C₂₉	—	2	2	no	—
130	C₂²×C₂₉	—	2	2	no	—
131	C₂²×C₂₉	—	2	2	no	—
132	C₂²×C₂₉	—	2	4	no	—
133	C₂²×C₂₉	—	2	4	no	—
134	C₂²×C₂₉	—	2	4	no	—
135	C₂²×C₂₉	—	2	2	no	—
136	C₂²×C₂₉	—	4	4	no	—
137	C₂²×C₂₉	—	4	8	no	—
138	C₂²×C₂₉	C₂×#41	1	4	yes	—
139	C₂²×C₂₉	C₂×#41	1	2	yes	—
140	C₂²×C₂₉	C₂×#41	1	2	yes	—
141	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
142	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
143	C₄×C₂₉	—	2	2	no	—
144	C₄×C₂₉	—	2	2	no	—
145	C₄×C₂₉	—	2	4	no	—
146	C₄×C₂₉	—	2	2	no	—
147	C₄×C₂₉	—	2	2	no	—
148	C₄×C₂₉	—	2	4	no	—
149	C₄×C₂₉	—	2	4	no	—
150	C₄×C₂₉	C₂×#41	1	4	yes	—
151	#553	C₂×C₂₉	1	16	yes	direct product factor
152	C₂×#126	C₂×C₂₉	1	2	yes	complemented
153	C₂×#125	C₂×C₂₉	1	1	yes	characteristic, complemented
154	C₂×#123	C₂×C₂₉	1	2	yes	complemented
155	C₂×#121	C₂×C₂₉	1	2	yes	complemented
156	C₂×#121	C₂×C₂₉	1	1	yes	characteristic, complemented
157	C₂×#121	C₂×C₂₉	1	1	yes	characteristic, complemented
158	C₂×C₄×D₄	C₂×C₂₉	1	2	yes	complemented
159	C₂×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
160	C₂×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
161	C₂×#117	C₂×C₂₉	1	1	yes	characteristic, complemented
162	C₂²×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
163	C₂×C₂₉	—	2	4	no	—
164	C₂×C₂₉	—	4	2	no	—
165	C₂×C₂₉	—	4	4	no	—
166	C₂×C₂₉	#553	1	4	yes	direct product factor
167	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
168	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
169	C₂×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
170	C₂²×D₄	C₂²×C₂₉	1	2	yes	—
171	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
172	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
173	C₂²×D₄	C₂²×C₂₉	1	2	yes	—
174	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
175	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
176	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
177	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
178	#126	C₂²×C₂₉	1	16	yes	complemented
179	#125	C₂²×C₂₉	1	8	yes	complemented
180	#123	C₂²×C₂₉	1	16	yes	complemented
181	#121	C₂²×C₂₉	1	16	yes	complemented
182	#121	C₂²×C₂₉	1	8	yes	complemented
183	#121	C₂²×C₂₉	1	8	yes	complemented
184	C₄×D₄	C₂²×C₂₉	1	16	yes	complemented
185	C₄×D₄	C₂²×C₂₉	1	8	yes	complemented
186	C₄×D₄	C₂²×C₂₉	1	8	yes	complemented
187	#117	C₂²×C₂₉	1	8	yes	complemented
188	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
189	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
191	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
193	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
195	C₂×C₄⋊C₄	C₂²×C₂₉	1	8	yes	complemented
196	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
198	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
201	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
202	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
203	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
204	C₂₉	C₂×#553	1	1	yes	characteristic, direct product factor, Sylow
205	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
206	C₂⁴	C₂³×C₂₉	1	2	yes	—
207	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
208	C₂×D₄	—	2	8	no	—
209	C₂×D₄	—	2	4	no	—
210	C₂×D₄	—	2	4	no	—
211	C₂×D₄	—	4	4	no	—
212	C₂×D₄	C₂³×C₂₉	1	8	yes	—
213	C₂×D₄	C₂³×C₂₉	1	4	yes	—
214	C₂×D₄	C₂³×C₂₉	1	4	yes	—
215	C₂×D₄	C₂³×C₂₉	1	8	yes	—
216	C₂²×C₄	—	2	4	no	—
217	C₂²×C₄	—	2	4	no	—
218	C₂²×C₄	—	4	4	no	—
219	C₂²×C₄	—	4	4	no	—
220	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
221	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
222	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
223	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
224	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
225	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
226	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
227	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
228	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
229	C₂²×C₄	C₂³×C₂₉	1	8	yes	—
230	C₂²×C₄	C₂³×C₂₉	1	8	yes	—
231	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
232	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
233	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
234	C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
235	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
236	C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
237	C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
238	C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
239	C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
240	C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
241	C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
242	C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
243	C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
244	C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
245	C₄²	C₂³×C₂₉	1	8	yes	—
246	C₄²	C₂³×C₂₉	1	4	yes	—
247	C₂³	—	2	2	no	—
248	C₂³	—	2	2	no	—
249	C₂³	—	2	2	no	—
250	C₂³	—	2	2	no	—
251	C₂³	—	2	4	no	—
252	C₂³	—	2	4	no	—
253	C₂³	—	2	4	no	—
254	C₂³	—	2	2	no	—
255	C₂³	#41×C₂₉	1	4	yes	—
256	C₂³	C₂⁴×C₂₉	1	2	yes	—
257	C₂³	C₂⁴×C₂₉	1	4	yes	—
258	C₂³	C₂⁴×C₂₉	1	2	yes	—
259	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
260	D₄	—	2	16	no	—
261	D₄	—	2	8	no	—
262	D₄	—	2	8	no	—
263	D₄	—	4	8	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	4	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	—	4	8	no	—
275	C₂×C₄	#41×C₂₉	1	4	yes	—
276	C₂×C₄	C₂⁴×C₂₉	1	2	yes	—
277	C₂×C₄	C₂⁴×C₂₉	1	4	yes	—
278	C₂×C₄	C₂⁴×C₂₉	1	2	yes	—
279	C₂×C₄	C₂⁴×C₂₉	1	4	yes	—
280	C₂×C₄	C₂⁴×C₂₉	1	2	yes	—
281	C₂×C₄	C₂⁴×C₂₉	1	2	yes	—
282	C₂×C₄	C₂⁴×C₂₉	1	4	yes	—
283	C₂×C₄	C₂⁴×C₂₉	1	2	yes	—
284	C₂²	—	2	8	no	—
285	C₂²	—	2	2	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	2	2	no	—
289	C₂²	—	2	4	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	4	no	—
292	C₂²	—	2	2	no	—
293	C₂²	—	4	4	no	—
294	C₂²	—	4	8	no	—
295	C₂²	C₂×#41×C₂₉	1	4	yes	—
296	C₂²	C₂×#41×C₂₉	1	2	yes	—
297	C₂²	C₂×#41×C₂₉	1	2	yes	—
298	C₂²	C₂₉×H(5,𝔽₂)	1	2	yes	—
299	C₂²	C₂⁵×C₂₉	1	1	yes	characteristic
300	C₄	—	2	2	no	—
301	C₄	—	2	2	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	2	no	—
304	C₄	—	2	2	no	—
305	C₄	—	2	4	no	—
306	C₄	—	2	4	no	—
307	C₄	C₂×#41×C₂₉	1	4	yes	—
308	C₂	—	2	4	no	—
309	C₂	—	4	2	no	—
310	C₂	—	4	4	no	—
311	C₂	C₂₉×#553	1	4	yes	direct product factor
312	C₂	C₂²×#41×C₂₉	1	1	yes	characteristic
313	C₂	C₂²×#41×C₂₉	1	1	yes	characteristic
314	C₂	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
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
1. C₂₉×#553	C₂	direct (N × H)
2. C₂×C₂₉×#126	C₂	semidirect
3. C₂×C₂₉×#125	C₂	semidirect
4. C₂×C₂₉×#123	C₂	semidirect
5. C₂×C₂₉×#121	C₂	semidirect
6. C₂×C₂₉×#121	C₂	semidirect
7. C₂×C₂₉×#121	C₂	semidirect
8. C₂×C₄×D₄×C₂₉	C₂	semidirect
9. C₂×C₄×D₄×C₂₉	C₂	semidirect
10. C₂×C₄×D₄×C₂₉	C₂	semidirect
11. C₂×C₂₉×#117	C₂	semidirect
12. C₂²×C₄⋊C₄×C₂₉	C₂	semidirect
21. C₂₉×#126	C₂²	semidirect
22. C₂₉×#125	C₂²	semidirect
23. C₂₉×#123	C₂²	semidirect
24. C₂₉×#121	C₂²	semidirect
25. C₂₉×#121	C₂²	semidirect
26. C₂₉×#121	C₂²	semidirect
27. C₄×D₄×C₂₉	C₂²	semidirect
28. C₄×D₄×C₂₉	C₂²	semidirect
29. C₄×D₄×C₂₉	C₂²	semidirect
30. C₂₉×#117	C₂²	semidirect
38. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
126. C₂×#553	C₂₉	direct (N × H)
151. #553	C₂×C₂₉	direct (N × H)
152. C₂×#126	C₂×C₂₉	semidirect
153. C₂×#125	C₂×C₂₉	semidirect
154. C₂×#123	C₂×C₂₉	semidirect
155. C₂×#121	C₂×C₂₉	semidirect
156. C₂×#121	C₂×C₂₉	semidirect
157. C₂×#121	C₂×C₂₉	semidirect
158. C₂×C₄×D₄	C₂×C₂₉	semidirect
159. C₂×C₄×D₄	C₂×C₂₉	semidirect
160. C₂×C₄×D₄	C₂×C₂₉	semidirect
161. C₂×#117	C₂×C₂₉	semidirect
162. C₂²×C₄⋊C₄	C₂×C₂₉	semidirect
166. C₂×C₂₉	#553	direct (N × H)
178. #126	C₂²×C₂₉	semidirect
179. #125	C₂²×C₂₉	semidirect
180. #123	C₂²×C₂₉	semidirect
181. #121	C₂²×C₂₉	semidirect
182. #121	C₂²×C₂₉	semidirect
183. #121	C₂²×C₂₉	semidirect
184. C₄×D₄	C₂²×C₂₉	semidirect
185. C₄×D₄	C₂²×C₂₉	semidirect
186. C₄×D₄	C₂²×C₂₉	semidirect
187. #117	C₂²×C₂₉	semidirect
195. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
204. C₂₉	C₂×#553	direct (N × H)
311. C₂	C₂₉×#553	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#553	2
C₂×C₂₉×#126	2
C₂×C₂₉×#125	2
C₂×C₂₉×#123	2
C₂×C₂₉×#121	2
C₂×C₄×D₄×C₂₉	2
C₂×C₂₉×#117	2
C₂²×C₄⋊C₄×C₂₉	2
C₂×#553	29

Subgroups — C2×C29×#553 #16817185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#553 #16817185