Subgroups — C₂₉×#33648 #20328548

Order 7424.

632 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2234	C₂	1	4	yes	maximal, complemented
4	C₂₉×#2233	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2232	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2159	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2140	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₂₉×#121	—	2	1	no	—
12	C₂×C₂₉×#117	—	2	1	no	—
13	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
14	C₂₉×#466	—	2	1	no	—
15	C₂₉×#466	—	2	1	no	—
16	C₂₉×#466	C₂²	1	2	yes	—
17	C₂₉×#466	C₂²	1	2	yes	—
18	C₂₉×#427	—	2	1	no	—
19	C₂₉×#427	—	2	1	no	—
20	C₂₉×#427	C₂²	1	2	yes	—
21	C₂₉×#427	C₂²	1	2	yes	complemented
22	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₉×#106	—	2	1	no	—
26	C₂×C₂₉×#102	—	2	1	no	—
27	C₂₉×#367	C₂²	1	4	yes	complemented
28	C₂₉×#366	C₂²	1	4	yes	complemented
29	C₂₉×#357	C₂²	1	4	yes	complemented
30	C₂₉×#357	C₂²	1	4	yes	complemented
31	C₂₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₂²×D₄×C₂₉	—	2	1	no	—
34	C₂²×D₄×C₂₉	—	4	1	no	—
35	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
36	C₂×D₈×C₂₉	—	2	1	no	—
37	C₂×D₈×C₂₉	—	2	4	no	—
38	C₂×D₈×C₂₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₂₉	—	2	4	no	—
40	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
46	C₂₉×#121	—	2	2	no	—
47	C₂₉×#121	—	2	2	no	—
48	C₂₉×#121	—	4	1	no	—
49	C₂₉×#121	—	4	1	no	—
50	C₂₉×#117	—	2	2	no	—
51	C₂₉×#117	—	2	2	no	—
52	C₂₉×#117	—	4	1	no	—
53	C₂₉×#117	—	4	1	no	—
54	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
58	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
59	C₂×C₄²×C₂₉	—	4	1	no	—
60	C₂₉×M₃₂	—	2	4	no	—
61	C₂×C₁₆×C₂₉	C₂³	1	4	yes	—
62	C₂₉×#107	—	2	1	no	—
63	C₂₉×#107	—	2	1	no	—
64	C₂₉×#107	—	2	1	no	—
65	C₂₉×#107	C₂³	1	2	yes	—
66	C₂₉×#107	C₂³	1	2	yes	—
67	C₂₉×#107	C₂³	1	2	yes	—
68	C₂₉×#106	—	2	2	no	—
69	C₂₉×#106	—	2	2	no	—
70	C₂₉×#102	—	2	2	no	—
71	C₂₉×#102	—	2	2	no	—
72	C₂⁴×C₂₉	—	4	1	no	—
73	C₂⁴×C₂₉	D₈	1	1	yes	characteristic
74	C₂×D₄×C₂₉	—	2	2	no	—
75	C₂×D₄×C₂₉	—	4	2	no	—
76	C₂×D₄×C₂₉	—	4	2	no	—
77	C₂×D₄×C₂₉	—	4	2	no	—
78	C₂×D₄×C₂₉	—	4	1	no	—
79	C₂×D₄×C₂₉	—	4	2	no	—
80	C₂×D₄×C₂₉	—	8	4	no	—
81	C₂²×C₄×C₂₉	—	2	2	no	—
82	C₂²×C₄×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	4	1	no	—
84	C₂²×C₄×C₂₉	—	4	1	no	—
85	C₂²×C₄×C₂₉	—	4	1	no	—
86	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
92	D₈×C₂₉	—	2	4	no	—
93	D₈×C₂₉	—	4	2	no	—
94	C₂×C₈×C₂₉	—	2	2	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	—	2	2	no	—
97	C₂×C₈×C₂₉	—	2	2	no	—
98	C₂×C₈×C₂₉	—	2	2	no	—
99	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₂₉	#41	1	4	yes	—
103	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₂₉	—	2	2	no	—
105	C₄⋊C₄×C₂₉	—	2	2	no	—
106	C₄⋊C₄×C₂₉	—	2	2	no	—
107	C₄⋊C₄×C₂₉	—	4	1	no	—
108	C₄⋊C₄×C₂₉	—	4	1	no	—
109	C₄⋊C₄×C₂₉	—	4	1	no	—
110	C₂²⋊C₄×C₂₉	—	4	2	no	—
111	C₂²⋊C₄×C₂₉	—	4	2	no	—
112	C₂²⋊C₄×C₂₉	—	4	2	no	—
113	C₂²⋊C₄×C₂₉	—	4	2	no	—
114	C₄²×C₂₉	—	4	2	no	—
115	C₄²×C₂₉	—	4	2	no	—
116	C₁₆×C₂₉	—	2	4	no	—
117	#33648	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	—	2	2	no	—
120	C₂³×C₂₉	—	4	1	no	—
121	C₂³×C₂₉	—	4	2	no	—
122	C₂³×C₂₉	—	8	2	no	—
123	C₂³×C₂₉	—	8	2	no	—
124	C₂³×C₂₉	—	8	2	no	—
125	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
126	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
127	C₂³×C₂₉	C₂×D₈	1	1	yes	characteristic
128	D₄×C₂₉	—	4	2	no	—
129	D₄×C₂₉	—	4	2	no	—
130	D₄×C₂₉	—	8	4	no	—
131	D₄×C₂₉	—	8	4	no	—
132	D₄×C₂₉	—	8	2	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	2	1	no	—
135	C₂×C₄×C₂₉	—	2	1	no	—
136	C₂×C₄×C₂₉	—	2	1	no	—
137	C₂×C₄×C₂₉	—	2	1	no	—
138	C₂×C₄×C₂₉	—	2	2	no	—
139	C₂×C₄×C₂₉	—	2	2	no	—
140	C₂×C₄×C₂₉	—	4	2	no	—
141	C₂×C₄×C₂₉	—	4	2	no	—
142	C₂×C₄×C₂₉	—	4	2	no	—
143	C₂×C₄×C₂₉	—	8	2	no	—
144	C₂×C₄×C₂₉	—	8	2	no	—
145	C₂×C₄×C₂₉	—	8	2	no	—
146	C₂×C₄×C₂₉	#123	1	2	yes	—
147	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₂₉	#137	1	2	yes	—
151	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
152	C₈×C₂₉	—	2	1	no	—
153	C₈×C₂₉	—	2	1	no	—
154	C₈×C₂₉	#123	1	2	yes	—
155	C₈×C₂₉	C₂×#41	1	2	yes	—
156	C₂×#466	C₂×C₂₉	1	1	yes	characteristic
157	C₂×#427	C₂×C₂₉	1	1	yes	characteristic, complemented
158	#2234	C₂×C₂₉	1	4	yes	complemented
159	#2233	C₂×C₂₉	1	2	yes	complemented
160	#2232	C₂×C₂₉	1	2	yes	complemented
161	#2159	C₂×C₂₉	1	2	yes	complemented
162	#2140	C₂×C₂₉	1	2	yes	complemented
163	#2112	C₂×C₂₉	1	1	yes	characteristic, complemented
164	C₂²×C₂₉	—	2	1	no	—
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	1	no	—
168	C₂²×C₂₉	—	2	1	no	—
169	C₂²×C₂₉	—	2	1	no	—
170	C₂²×C₂₉	—	2	1	no	—
171	C₂²×C₂₉	—	4	4	no	—
172	C₂²×C₂₉	—	8	2	no	—
173	C₂²×C₂₉	—	8	2	no	—
174	C₂²×C₂₉	—	8	2	no	—
175	C₂²×C₂₉	—	16	4	no	—
176	C₂²×C₂₉	#480	1	2	yes	—
177	C₂²×C₂₉	#509	1	2	yes	—
178	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	8	2	no	—
182	C₄×C₂₉	—	8	2	no	—
183	C₄×C₂₉	—	8	2	no	—
184	C₄×C₂₉	#480	1	2	yes	—
185	C₄×C₂₉	C₂×#123	1	1	yes	characteristic
186	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
187	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
189	C₂×#121	—	2	1	no	—
190	C₂×#117	—	2	1	no	—
191	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
192	#466	—	2	1	no	—
193	#466	—	2	1	no	—
194	#466	C₂²×C₂₉	1	2	yes	—
195	#466	C₂²×C₂₉	1	2	yes	—
196	#427	—	2	1	no	—
197	#427	—	2	1	no	—
198	#427	C₂²×C₂₉	1	2	yes	—
199	#427	C₂²×C₂₉	1	2	yes	complemented
200	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
201	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
202	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
203	C₂×#106	—	2	1	no	—
204	C₂×#102	—	2	1	no	—
205	#367	C₂²×C₂₉	1	4	yes	complemented
206	#366	C₂²×C₂₉	1	4	yes	complemented
207	#357	C₂²×C₂₉	1	4	yes	complemented
208	#357	C₂²×C₂₉	1	4	yes	complemented
209	C₂²⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
210	C₂²⋊C₁₆	C₂²×C₂₉	1	2	yes	complemented
211	C₂×C₂₉	—	2	2	no	—
212	C₂×C₂₉	—	2	2	no	—
213	C₂×C₂₉	—	4	1	no	—
214	C₂×C₂₉	—	16	2	no	—
215	C₂×C₂₉	C₂×#480	1	1	yes	characteristic
216	C₂×C₂₉	C₂×#509	1	1	yes	characteristic
217	C₂×C₂₉	#3414	1	1	yes	characteristic
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	—	4	1	no	—
220	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
221	C₂×D₈	—	2	1	no	—
222	C₂×D₈	—	2	4	no	—
223	C₂×D₈	C₂³×C₂₉	1	2	yes	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
226	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
227	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
231	#121	—	2	2	no	—
232	#121	—	2	2	no	—
233	#121	—	4	1	no	—
234	#121	—	4	1	no	—
235	#117	—	2	2	no	—
236	#117	—	2	2	no	—
237	#117	—	4	1	no	—
238	#117	—	4	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	4	1	no	—
243	C₂×C₂²⋊C₄	—	4	1	no	—
244	C₂×C₄²	—	4	1	no	—
245	M₃₂	—	2	4	no	—
246	C₂×C₁₆	C₂³×C₂₉	1	4	yes	—
247	#107	—	2	1	no	—
248	#107	—	2	1	no	—
249	#107	—	2	1	no	—
250	#107	C₂³×C₂₉	1	2	yes	—
251	#107	C₂³×C₂₉	1	2	yes	—
252	#107	C₂³×C₂₉	1	2	yes	—
253	#106	—	2	2	no	—
254	#106	—	2	2	no	—
255	#102	—	2	2	no	—
256	#102	—	2	2	no	—
257	C₂₉	#33648	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁴	—	4	1	no	—
259	C₂⁴	D₈×C₂₉	1	1	yes	characteristic
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	2	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	8	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	D₈×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
278	D₈	—	2	4	no	—
279	D₈	—	4	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
287	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
288	C₂×C₈	#41×C₂₉	1	4	yes	—
289	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₁₆	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	8	2	no	—
308	C₂³	—	8	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
311	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
312	C₂³	C₂×D₈×C₂₉	1	1	yes	characteristic
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	8	4	no	—
316	D₄	—	8	4	no	—
317	D₄	—	8	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₂₉×#123	1	2	yes	—
332	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
333	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
334	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
335	C₂×C₄	C₂₉×#137	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	C₂₉×#123	1	2	yes	—
340	C₈	C₂×#41×C₂₉	1	2	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	16	4	no	—
353	C₂²	C₂₉×#480	1	2	yes	—
354	C₂²	C₂₉×#509	1	2	yes	—
355	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	C₂₉×#480	1	2	yes	—
362	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
363	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	—	4	1	no	—
367	C₂	—	16	2	no	—
368	C₂	C₂×C₂₉×#480	1	1	yes	characteristic
369	C₂	C₂×C₂₉×#509	1	1	yes	characteristic
370	C₂	C₂₉×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#427	C₂	semidirect
3. C₂₉×#2234	C₂	semidirect
4. C₂₉×#2233	C₂	semidirect
5. C₂₉×#2232	C₂	semidirect
6. C₂₉×#2159	C₂	semidirect
7. C₂₉×#2140	C₂	semidirect
8. C₂₉×#2112	C₂	semidirect
21. C₂₉×#427	C₂²	semidirect
23. C₂×C₂₉×#107	C₂²	semidirect
24. C₂×C₂₉×#107	C₂²	semidirect
27. C₂₉×#367	C₂²	semidirect
28. C₂₉×#366	C₂²	semidirect
29. C₂₉×#357	C₂²	semidirect
30. C₂₉×#357	C₂²	semidirect
31. C₂₉×C₂²⋊C₁₆	C₂²	semidirect
32. C₂₉×C₂²⋊C₁₆	C₂²	semidirect
117. #33648	C₂₉	direct (N × H)
157. C₂×#427	C₂×C₂₉	semidirect
158. #2234	C₂×C₂₉	semidirect
159. #2233	C₂×C₂₉	semidirect
160. #2232	C₂×C₂₉	semidirect
161. #2159	C₂×C₂₉	semidirect
162. #2140	C₂×C₂₉	semidirect
163. #2112	C₂×C₂₉	semidirect
199. #427	C₂²×C₂₉	semidirect
201. C₂×#107	C₂²×C₂₉	semidirect
202. C₂×#107	C₂²×C₂₉	semidirect
205. #367	C₂²×C₂₉	semidirect
206. #366	C₂²×C₂₉	semidirect
207. #357	C₂²×C₂₉	semidirect
208. #357	C₂²×C₂₉	semidirect
209. C₂²⋊C₁₆	C₂²×C₂₉	semidirect
210. C₂²⋊C₁₆	C₂²×C₂₉	semidirect
257. C₂₉	#33648	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×C₂₉×#466	2
C₂×C₂₉×#427	2
C₂₉×#2234	2
C₂₉×#2233	2
C₂₉×#2232	2
C₂₉×#2159	2
C₂₉×#2140	2
C₂₉×#2112	2
#33648	29

Subgroups — C29×#33648 #20328548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33648 #20328548