Subgroups — C₂₉×#60175 #20355075

Order 7424.

2650 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#578	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2952	C₂	1	3	yes	maximal, complemented
4	C₂₉×#2950	C₂	1	3	yes	maximal, complemented
5	C₂₉×#2947	C₂	1	6	yes	maximal, complemented
6	C₄×C₂₉×#137	C₂	1	6	yes	maximal, complemented
7	C₂₉×#2943	C₂	1	3	yes	maximal, complemented
8	C₂×C₂₉×#441	C₂	1	3	yes	maximal, complemented
9	C₂₉×#2912	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2898	C₂	1	2	yes	maximal, complemented
11	C₂₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₂₉×#578	C₄	1	16	yes	complemented
14	C₂×C₂₉×#137	C₂²	1	6	yes	—
15	C₂×C₂₉×#135	C₂²	1	3	yes	—
16	C₂²×Q₁₆×C₂₉	C₂²	1	3	yes	—
17	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
19	C₂₉×#520	—	2	6	no	—
20	C₂₉×#520	C₂²	1	6	yes	—
21	C₂₉×#520	C₂²	1	2	yes	—
22	C₂₉×#519	—	2	2	no	—
23	C₂₉×#519	C₂²	1	6	yes	—
24	C₄×#41×C₂₉	—	2	6	no	—
25	C₄×#41×C₂₉	C₂²	1	6	yes	—
26	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₉	—	2	2	no	—
28	C₂×C₄×Q₈×C₂₉	C₂²	1	6	yes	—
29	C₂₉×#442	C₂²	1	1	yes	characteristic
30	C₂₉×#442	C₂²	1	3	yes	—
31	C₂₉×#441	C₂²	1	3	yes	—
32	C₂₉×#441	C₂²	1	6	yes	—
33	C₂₉×#441	C₂²	1	6	yes	—
34	C₂₉×#441	C₂²	1	6	yes	—
35	C₂₉×#441	C₂²	1	3	yes	—
36	C₂₉×#440	C₂²	1	6	yes	—
37	C₂₉×#440	C₂²	1	6	yes	—
38	C₄×Q₁₆×C₂₉	C₂²	1	12	yes	—
39	C₄×SD₁₆×C₂₉	C₂²	1	12	yes	—
40	C₂₉×#428	C₂²	1	6	yes	—
41	C₂₉×#427	C₂²	1	3	yes	—
42	C₂×C₂₉×#106	C₂²	1	3	yes	—
43	C₂₉×#419	C₂²	1	6	yes	—
44	C₂₉×#417	C₂²	1	6	yes	—
45	C₂₉×#416	C₂²	1	6	yes	—
46	C₂×C₂₉×#103	C₂²	1	6	yes	—
47	C₂₉×#405	C₂²	1	3	yes	—
48	C₂₉×#405	C₂²	1	3	yes	—
49	C₄×M₁₆×C₂₉	C₂²	1	3	yes	—
50	C₂×C₂₉×#97	C₂²	1	3	yes	—
51	C₂₉×2₋¹⁺⁴	—	2	8	no	—
52	C₂₉×2₋¹⁺⁴	C₂×C₄	1	16	yes	complemented
53	C₂×#41×C₂₉	—	2	6	no	—
54	C₂×#41×C₂₉	C₂³	1	6	yes	—
55	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₂₉	—	2	2	no	—
57	C₂²×Q₈×C₂₉	C₂³	1	6	yes	—
58	C₂₉×#137	C₂×C₄	1	48	yes	complemented
59	C₂₉×#135	C₂×C₄	1	24	yes	complemented
60	C₂×Q₁₆×C₂₉	C₂×C₄	1	24	yes	complemented
61	C₂×Q₁₆×C₂₉	C₂³	1	6	yes	—
62	C₂×Q₁₆×C₂₉	C₂³	1	3	yes	—
63	C₂×SD₁₆×C₂₉	C₂³	1	6	yes	—
64	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂₉×#131	—	2	4	no	—
66	C₂₉×#131	C₂×C₄	1	8	yes	complemented
67	C₂×M₁₆×C₂₉	C₂³	1	3	yes	—
68	C₂×M₁₆×C₂₉	C₂³	1	3	yes	—
69	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
70	C₂²×C₈×C₂₉	C₂³	1	3	yes	—
71	C₄×Q₈×C₂₉	—	2	2	no	—
72	C₄×Q₈×C₂₉	—	2	6	no	—
73	C₄×Q₈×C₂₉	—	2	6	no	—
74	C₄×Q₈×C₂₉	—	2	6	no	—
75	C₄×Q₈×C₂₉	—	2	6	no	—
76	C₄×Q₈×C₂₉	D₄	1	2	yes	—
77	C₄×Q₈×C₂₉	C₂³	1	12	yes	—
78	C₄×Q₈×C₂₉	C₂³	1	6	yes	—
79	C₄×Q₈×C₂₉	C₂³	1	6	yes	—
80	C₄×D₄×C₂₉	—	2	6	no	—
81	C₄×D₄×C₂₉	—	2	6	no	—
82	C₄×D₄×C₂₉	—	2	6	no	—
83	C₄×D₄×C₂₉	—	2	12	no	—
84	C₄×D₄×C₂₉	D₄	1	6	yes	—
85	C₄×D₄×C₂₉	C₂³	1	6	yes	—
86	C₄×D₄×C₂₉	C₂³	1	2	yes	—
87	C₂₉×#117	—	2	6	no	—
88	C₂₉×#117	—	2	12	no	—
89	C₂₉×#117	—	2	6	no	—
90	C₂₉×#117	C₂³	1	6	yes	—
91	C₂₉×#117	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₂₉	—	2	6	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	6	no	—
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	6	yes	—
95	C₂×C₄²×C₂₉	—	2	6	no	—
96	C₂×C₄²×C₂₉	—	2	6	no	—
97	C₂×C₄²×C₂₉	C₂³	1	3	yes	—
98	C₂₉×#107	C₂³	1	6	yes	—
99	C₂₉×#106	C₂³	1	3	yes	—
100	C₂₉×#106	C₂³	1	6	yes	—
101	C₂₉×#106	C₂³	1	1	yes	characteristic
102	C₂₉×#103	C₂³	1	12	yes	—
103	C₂₉×#103	C₂³	1	6	yes	—
104	C₂₉×#103	C₂³	1	6	yes	—
105	C₂₉×#102	C₂³	1	6	yes	—
106	C₂₉×#102	C₂³	1	2	yes	—
107	C₂₉×#97	C₂³	1	3	yes	—
108	C₂₉×#97	C₂³	1	3	yes	—
109	C₂₉×#97	C₂³	1	1	yes	characteristic
110	C₂₉×#97	C₂³	1	3	yes	—
111	C₄×C₈×C₂₉	C₂³	1	6	yes	—
112	#41×C₂₉	—	2	48	no	—
113	#41×C₂₉	—	2	12	no	—
114	#41×C₂₉	C₂²×C₄	1	24	yes	—
115	#41×C₂₉	C₂²×C₄	1	4	yes	—
116	#41×C₂₉	#41	1	4	yes	—
117	C₂×Q₈×C₂₉	—	2	16	no	—
118	C₂×Q₈×C₂₉	—	2	6	no	—
119	C₂×Q₈×C₂₉	—	2	12	no	—
120	C₂×Q₈×C₂₉	C₂²×C₄	1	24	yes	—
121	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₂₉	C₂⁴	1	6	yes	—
123	C₂×D₄×C₂₉	—	2	6	no	—
124	C₂×D₄×C₂₉	C₂×D₄	1	3	yes	—
125	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₂₉	—	2	6	no	—
127	C₂²×C₄×C₂₉	—	2	6	no	—
128	C₂²×C₄×C₂₉	—	2	6	no	—
129	C₂²×C₄×C₂₉	—	2	2	no	—
130	C₂²×C₄×C₂₉	—	2	6	no	—
131	C₂²×C₄×C₂₉	C₂×D₄	1	6	yes	—
132	C₂²×C₄×C₂₉	C₂⁴	1	3	yes	—
133	Q₁₆×C₂₉	C₂²×C₄	1	12	yes	—
134	Q₁₆×C₂₉	C₂²×C₄	1	24	yes	—
135	SD₁₆×C₂₉	C₂²×C₄	1	24	yes	—
136	D₈×C₂₉	C₂²×C₄	1	4	yes	—
137	M₁₆×C₂₉	—	2	6	no	—
138	M₁₆×C₂₉	C₂²×C₄	1	12	yes	—
139	C₂×C₈×C₂₉	—	2	6	no	—
140	C₂×C₈×C₂₉	C₂²×C₄	1	12	yes	—
141	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₂₉	C₂⁴	1	3	yes	—
143	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₂₉	C₂⁴	1	3	yes	—
145	C₄⋊C₄×C₂₉	—	2	6	no	—
146	C₄⋊C₄×C₂₉	—	2	12	no	—
147	C₄⋊C₄×C₂₉	—	2	6	no	—
148	C₄⋊C₄×C₂₉	—	2	6	no	—
149	C₄⋊C₄×C₂₉	C₂×D₄	1	6	yes	—
150	C₄⋊C₄×C₂₉	C₂⁴	1	6	yes	—
151	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
152	C₂²⋊C₄×C₂₉	—	2	6	no	—
153	C₂²⋊C₄×C₂₉	—	2	2	no	—
154	C₂²⋊C₄×C₂₉	—	2	6	no	—
155	C₂²⋊C₄×C₂₉	C₂×D₄	1	6	yes	—
156	C₄²×C₂₉	—	2	6	no	—
157	C₄²×C₂₉	—	2	6	no	—
158	C₄²×C₂₉	—	2	12	no	—
159	C₄²×C₂₉	—	2	6	no	—
160	C₄²×C₂₉	C₂×D₄	1	6	yes	—
161	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
162	C₄²×C₂₉	C₂⁴	1	3	yes	—
163	#60175	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₂₉	—	2	2	no	—
165	C₂³×C₂₉	C₂²×D₄	1	3	yes	—
166	Q₈×C₂₉	—	2	24	no	—
167	Q₈×C₂₉	—	2	6	no	—
168	Q₈×C₂₉	C₄×D₄	1	4	yes	—
169	Q₈×C₂₉	C₂³×C₄	1	12	yes	—
170	D₄×C₂₉	—	2	24	no	—
171	D₄×C₂₉	—	2	2	no	—
172	D₄×C₂₉	C₄×D₄	1	12	yes	—
173	D₄×C₂₉	C₂³×C₄	1	4	yes	—
174	C₂×C₄×C₂₉	—	2	24	no	—
175	C₂×C₄×C₂₉	—	2	6	no	—
176	C₂×C₄×C₂₉	—	2	24	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	2	6	no	—
179	C₂×C₄×C₂₉	—	4	6	no	—
180	C₂×C₄×C₂₉	—	4	4	no	—
181	C₂×C₄×C₂₉	—	8	6	no	—
182	C₂×C₄×C₂₉	—	8	6	no	—
183	C₂×C₄×C₂₉	C₂³×C₄	1	6	yes	—
184	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₂₉	C₂²×D₄	1	6	yes	—
186	C₂×C₄×C₂₉	C₂²×D₄	1	3	yes	—
187	C₂×C₄×C₂₉	C₂×#41	1	6	yes	—
188	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
189	C₈×C₂₉	—	2	1	no	—
190	C₈×C₂₉	—	2	3	no	—
191	C₈×C₂₉	C₂³×C₄	1	2	yes	—
192	C₈×C₂₉	C₂³×C₄	1	6	yes	—
193	C₂×#578	C₂×C₂₉	1	1	yes	characteristic
194	C₄×2₋¹⁺⁴	C₂×C₂₉	1	2	yes	complemented
195	#2952	C₂×C₂₉	1	3	yes	complemented
196	#2950	C₂×C₂₉	1	3	yes	complemented
197	#2947	C₂×C₂₉	1	6	yes	complemented
198	C₄×#137	C₂×C₂₉	1	6	yes	complemented
199	#2943	C₂×C₂₉	1	3	yes	complemented
200	C₂×#441	C₂×C₂₉	1	3	yes	complemented
201	#2912	C₂×C₂₉	1	1	yes	characteristic, complemented
202	#2898	C₂×C₂₉	1	2	yes	complemented
203	#2875	C₂×C₂₉	1	1	yes	characteristic, complemented
204	C₂²×C₂₉	—	2	6	no	—
205	C₂²×C₂₉	—	2	4	no	—
206	C₂²×C₂₉	—	4	2	no	—
207	C₂²×C₂₉	—	4	2	no	—
208	C₂²×C₂₉	C₂×C₄×D₄	1	6	yes	—
209	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
210	C₄×C₂₉	—	2	2	no	—
211	C₄×C₂₉	—	2	6	no	—
212	C₄×C₂₉	—	2	12	no	—
213	C₄×C₂₉	—	4	2	no	—
214	C₄×C₂₉	—	4	6	no	—
215	C₄×C₂₉	C₂×C₄×D₄	1	6	yes	—
216	C₄×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
217	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
218	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	2	yes	—
219	#578	C₄×C₂₉	1	16	yes	complemented
220	C₂×#137	C₂²×C₂₉	1	6	yes	—
221	C₂×#135	C₂²×C₂₉	1	3	yes	—
222	C₂²×Q₁₆	C₂²×C₂₉	1	3	yes	—
223	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
224	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
225	#520	—	2	6	no	—
226	#520	C₂²×C₂₉	1	6	yes	—
227	#520	C₂²×C₂₉	1	2	yes	—
228	#519	—	2	2	no	—
229	#519	C₂²×C₂₉	1	6	yes	—
230	C₄×#41	—	2	6	no	—
231	C₄×#41	C₂²×C₂₉	1	6	yes	—
232	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
233	C₂×C₄×Q₈	—	2	2	no	—
234	C₂×C₄×Q₈	C₂²×C₂₉	1	6	yes	—
235	#442	C₂²×C₂₉	1	1	yes	characteristic
236	#442	C₂²×C₂₉	1	3	yes	—
237	#441	C₂²×C₂₉	1	3	yes	—
238	#441	C₂²×C₂₉	1	6	yes	—
239	#441	C₂²×C₂₉	1	6	yes	—
240	#441	C₂²×C₂₉	1	6	yes	—
241	#441	C₂²×C₂₉	1	3	yes	—
242	#440	C₂²×C₂₉	1	6	yes	—
243	#440	C₂²×C₂₉	1	6	yes	—
244	C₄×Q₁₆	C₂²×C₂₉	1	12	yes	—
245	C₄×SD₁₆	C₂²×C₂₉	1	12	yes	—
246	#428	C₂²×C₂₉	1	6	yes	—
247	#427	C₂²×C₂₉	1	3	yes	—
248	C₂×#106	C₂²×C₂₉	1	3	yes	—
249	#419	C₂²×C₂₉	1	6	yes	—
250	#417	C₂²×C₂₉	1	6	yes	—
251	#416	C₂²×C₂₉	1	6	yes	—
252	C₂×#103	C₂²×C₂₉	1	6	yes	—
253	#405	C₂²×C₂₉	1	3	yes	—
254	#405	C₂²×C₂₉	1	3	yes	—
255	C₄×M₁₆	C₂²×C₂₉	1	3	yes	—
256	C₂×#97	C₂²×C₂₉	1	3	yes	—
257	C₂×C₂₉	—	2	6	no	—
258	C₂×C₂₉	—	4	4	no	—
259	C₂×C₂₉	C₂²×C₄×D₄	1	1	yes	characteristic
260	C₂×C₂₉	#3586	1	2	yes	—
261	2₋¹⁺⁴	—	2	8	no	—
262	2₋¹⁺⁴	C₂×C₄×C₂₉	1	16	yes	complemented
263	C₂×#41	—	2	6	no	—
264	C₂×#41	C₂³×C₂₉	1	6	yes	—
265	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	C₂³×C₂₉	1	6	yes	—
268	#137	C₂×C₄×C₂₉	1	48	yes	complemented
269	#135	C₂×C₄×C₂₉	1	24	yes	complemented
270	C₂×Q₁₆	C₂×C₄×C₂₉	1	24	yes	complemented
271	C₂×Q₁₆	C₂³×C₂₉	1	3	yes	—
272	C₂×Q₁₆	C₂³×C₂₉	1	6	yes	—
273	C₂×SD₁₆	C₂³×C₂₉	1	6	yes	—
274	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
275	#131	—	2	4	no	—
276	#131	C₂×C₄×C₂₉	1	8	yes	complemented
277	C₂×M₁₆	C₂³×C₂₉	1	3	yes	—
278	C₂×M₁₆	C₂³×C₂₉	1	3	yes	—
279	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
280	C₂²×C₈	C₂³×C₂₉	1	3	yes	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	6	no	—
283	C₄×Q₈	—	2	6	no	—
284	C₄×Q₈	—	2	6	no	—
285	C₄×Q₈	—	2	6	no	—
286	C₄×Q₈	D₄×C₂₉	1	2	yes	—
287	C₄×Q₈	C₂³×C₂₉	1	6	yes	—
288	C₄×Q₈	C₂³×C₂₉	1	12	yes	—
289	C₄×Q₈	C₂³×C₂₉	1	6	yes	—
290	C₄×D₄	—	2	6	no	—
291	C₄×D₄	—	2	6	no	—
292	C₄×D₄	—	2	6	no	—
293	C₄×D₄	—	2	12	no	—
294	C₄×D₄	D₄×C₂₉	1	6	yes	—
295	C₄×D₄	C₂³×C₂₉	1	2	yes	—
296	C₄×D₄	C₂³×C₂₉	1	6	yes	—
297	#117	—	2	6	no	—
298	#117	—	2	12	no	—
299	#117	—	2	6	no	—
300	#117	C₂³×C₂₉	1	6	yes	—
301	#117	C₂³×C₂₉	1	3	yes	—
302	C₂×C₄⋊C₄	—	2	6	no	—
303	C₂×C₄⋊C₄	—	2	6	no	—
304	C₂×C₄⋊C₄	C₂³×C₂₉	1	6	yes	—
305	C₂×C₄²	—	2	6	no	—
306	C₂×C₄²	—	2	6	no	—
307	C₂×C₄²	C₂³×C₂₉	1	3	yes	—
308	#107	C₂³×C₂₉	1	6	yes	—
309	#106	C₂³×C₂₉	1	3	yes	—
310	#106	C₂³×C₂₉	1	6	yes	—
311	#106	C₂³×C₂₉	1	1	yes	characteristic
312	#103	C₂³×C₂₉	1	6	yes	—
313	#103	C₂³×C₂₉	1	12	yes	—
314	#103	C₂³×C₂₉	1	6	yes	—
315	#102	C₂³×C₂₉	1	2	yes	—
316	#102	C₂³×C₂₉	1	6	yes	—
317	#97	C₂³×C₂₉	1	1	yes	characteristic
318	#97	C₂³×C₂₉	1	3	yes	—
319	#97	C₂³×C₂₉	1	3	yes	—
320	#97	C₂³×C₂₉	1	3	yes	—
321	C₄×C₈	C₂³×C₂₉	1	6	yes	—
322	C₂₉	#60175	1	1	yes	characteristic, direct product factor, Sylow
323	#41	—	2	48	no	—
324	#41	—	2	12	no	—
325	#41	C₂²×C₄×C₂₉	1	24	yes	—
326	#41	C₂²×C₄×C₂₉	1	4	yes	—
327	#41	#41×C₂₉	1	4	yes	—
328	C₂×Q₈	—	2	16	no	—
329	C₂×Q₈	—	2	6	no	—
330	C₂×Q₈	—	2	12	no	—
331	C₂×Q₈	C₂²×C₄×C₂₉	1	24	yes	—
332	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴×C₂₉	1	6	yes	—
334	C₂×D₄	—	2	6	no	—
335	C₂×D₄	C₂×D₄×C₂₉	1	3	yes	—
336	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
337	C₂²×C₄	—	2	6	no	—
338	C₂²×C₄	—	2	6	no	—
339	C₂²×C₄	—	2	6	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	6	no	—
342	C₂²×C₄	C₂×D₄×C₂₉	1	6	yes	—
343	C₂²×C₄	C₂⁴×C₂₉	1	3	yes	—
344	Q₁₆	C₂²×C₄×C₂₉	1	12	yes	—
345	Q₁₆	C₂²×C₄×C₂₉	1	24	yes	—
346	SD₁₆	C₂²×C₄×C₂₉	1	24	yes	—
347	D₈	C₂²×C₄×C₂₉	1	4	yes	—
348	M₁₆	—	2	6	no	—
349	M₁₆	C₂²×C₄×C₂₉	1	12	yes	—
350	C₂×C₈	—	2	6	no	—
351	C₂×C₈	C₂²×C₄×C₂₉	1	12	yes	—
352	C₂×C₈	C₂⁴×C₂₉	1	3	yes	—
353	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
354	C₂×C₈	C₂⁴×C₂₉	1	3	yes	—
355	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
356	C₄⋊C₄	—	2	6	no	—
357	C₄⋊C₄	—	2	12	no	—
358	C₄⋊C₄	—	2	6	no	—
359	C₄⋊C₄	—	2	6	no	—
360	C₄⋊C₄	C₂×D₄×C₂₉	1	6	yes	—
361	C₄⋊C₄	C₂⁴×C₂₉	1	6	yes	—
362	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
363	C₂²⋊C₄	—	2	6	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	6	no	—
366	C₂²⋊C₄	C₂×D₄×C₂₉	1	6	yes	—
367	C₄²	—	2	6	no	—
368	C₄²	—	2	6	no	—
369	C₄²	—	2	12	no	—
370	C₄²	—	2	6	no	—
371	C₄²	C₂×D₄×C₂₉	1	6	yes	—
372	C₄²	C₂⁴×C₂₉	1	3	yes	—
373	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	C₂²×D₄×C₂₉	1	3	yes	—
376	Q₈	—	2	24	no	—
377	Q₈	—	2	6	no	—
378	Q₈	C₄×D₄×C₂₉	1	4	yes	—
379	Q₈	C₂³×C₄×C₂₉	1	12	yes	—
380	D₄	—	2	24	no	—
381	D₄	—	2	2	no	—
382	D₄	C₄×D₄×C₂₉	1	12	yes	—
383	D₄	C₂³×C₄×C₂₉	1	4	yes	—
384	C₂×C₄	—	2	24	no	—
385	C₂×C₄	—	2	6	no	—
386	C₂×C₄	—	2	24	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	6	no	—
389	C₂×C₄	—	4	6	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	8	6	no	—
392	C₂×C₄	—	8	6	no	—
393	C₂×C₄	C₂³×C₄×C₂₉	1	6	yes	—
394	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
395	C₂×C₄	C₂²×D₄×C₂₉	1	6	yes	—
396	C₂×C₄	C₂²×D₄×C₂₉	1	3	yes	—
397	C₂×C₄	C₂×#41×C₂₉	1	6	yes	—
398	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
399	C₈	—	2	1	no	—
400	C₈	—	2	3	no	—
401	C₈	C₂³×C₄×C₂₉	1	2	yes	—
402	C₈	C₂³×C₄×C₂₉	1	6	yes	—
403	C₂²	—	2	6	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	C₂×C₄×D₄×C₂₉	1	6	yes	—
408	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	6	no	—
411	C₄	—	2	12	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	6	no	—
414	C₄	C₂×C₄×D₄×C₂₉	1	6	yes	—
415	C₄	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
416	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
417	C₂	—	2	6	no	—
418	C₂	—	4	4	no	—
419	C₂	C₂²×C₄×D₄×C₂₉	1	1	yes	characteristic
420	C₂	C₂₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#578	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₉×2₋¹⁺⁴	C₂	semidirect
3. C₂₉×#2952	C₂	semidirect
4. C₂₉×#2950	C₂	semidirect
5. C₂₉×#2947	C₂	semidirect
6. C₄×C₂₉×#137	C₂	semidirect
7. C₂₉×#2943	C₂	semidirect
8. C₂×C₂₉×#441	C₂	semidirect
9. C₂₉×#2912	C₂	semidirect
10. C₂₉×#2898	C₂	semidirect
11. C₂₉×#2875	C₂	semidirect
13. C₂₉×#578	C₄	semidirect
52. C₂₉×2₋¹⁺⁴	C₂×C₄	semidirect
58. C₂₉×#137	C₂×C₄	semidirect
59. C₂₉×#135	C₂×C₄	semidirect
60. C₂×Q₁₆×C₂₉	C₂×C₄	semidirect
66. C₂₉×#131	C₂×C₄	semidirect
163. #60175	C₂₉	direct (N × H)
194. C₄×2₋¹⁺⁴	C₂×C₂₉	semidirect
195. #2952	C₂×C₂₉	semidirect
196. #2950	C₂×C₂₉	semidirect
197. #2947	C₂×C₂₉	semidirect
198. C₄×#137	C₂×C₂₉	semidirect
199. #2943	C₂×C₂₉	semidirect
200. C₂×#441	C₂×C₂₉	semidirect
201. #2912	C₂×C₂₉	semidirect
202. #2898	C₂×C₂₉	semidirect
203. #2875	C₂×C₂₉	semidirect
219. #578	C₄×C₂₉	semidirect
262. 2₋¹⁺⁴	C₂×C₄×C₂₉	semidirect
268. #137	C₂×C₄×C₂₉	semidirect
269. #135	C₂×C₄×C₂₉	semidirect
270. C₂×Q₁₆	C₂×C₄×C₂₉	semidirect
276. #131	C₂×C₄×C₂₉	semidirect
322. C₂₉	#60175	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×#578	2
C₄×C₂₉×2₋¹⁺⁴	2
C₂₉×#2952	2
C₂₉×#2950	2
C₂₉×#2947	2
C₄×C₂₉×#137	2
C₂₉×#2943	2
C₂×C₂₉×#441	2
C₂₉×#2912	2
C₂₉×#2898	2
C₂₉×#2875	2
#60175	29

Subgroups — C29×#60175 #20355075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60175 #20355075