Subgroups — C₂₉×#19362 #20314262

Order 7424.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1697	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1677	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
14	C₂₉×#529	C₂²	1	1	yes	characteristic
15	C₂₉×#501	—	2	1	no	—
16	C₂₉×#496	—	2	1	no	—
17	C₂₉×#490	—	2	1	no	—
18	C₂₉×#489	—	2	1	no	—
19	C₂₉×#486	—	2	1	no	—
20	C₂₉×#486	—	2	1	no	—
21	C₂₉×#486	C₂²	1	2	yes	—
22	C₂₉×#486	C₂²	1	2	yes	—
23	C₂₉×#483	—	2	1	no	—
24	C₂₉×#480	—	2	1	no	—
25	C₂₉×#477	C₂²	1	2	yes	complemented
26	C₂₉×#476	C₂²	1	2	yes	complemented
27	C₂₉×#460	C₂²	1	2	yes	—
28	C₂₉×#459	C₂²	1	2	yes	—
29	C₂₉×#450	—	2	1	no	—
30	C₂₉×#447	—	2	1	no	—
31	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
32	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
33	C₂₉×#436	C₂²	1	1	yes	characteristic, complemented
34	C₂₉×#435	—	2	1	no	—
35	C₈×D₄×C₂₉	—	2	1	no	—
36	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#433	—	2	1	no	—
38	C₂₉×#432	C₂²	1	1	yes	characteristic
39	C₂₉×#432	C₂²	1	1	yes	characteristic
40	C₂₉×#432	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#102	—	2	1	no	—
42	C₂×C₂₉×#102	—	2	1	no	—
43	C₂₉×#405	—	2	1	no	—
44	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#335	C₂²	1	2	yes	complemented
46	C₂₉×#334	C₂²	1	2	yes	complemented
47	C₂₉×#333	C₂²	1	2	yes	complemented
48	C₂₉×#333	C₂²	1	2	yes	complemented
49	C₂₉×#331	C₂²	1	2	yes	—
50	C₂₉×#331	C₂²	1	2	yes	—
51	C₂²×Q₈×C₂₉	—	2	1	no	—
52	C₂²×D₄×C₂₉	—	2	1	no	—
53	C₂²×D₄×C₂₉	—	2	1	no	—
54	C₂²×D₄×C₂₉	—	2	1	no	—
55	C₂×SD₁₆×C₂₉	—	2	2	no	—
56	C₂×D₈×C₂₉	—	2	2	no	—
57	C₂×M₁₆×C₂₉	—	2	1	no	—
58	C₂²×C₈×C₂₉	—	2	1	no	—
59	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
61	C₂₉×C₄⋊Q₈	—	2	1	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₂₉×#127	—	2	1	no	—
66	C₂₉×#127	—	2	1	no	—
67	C₂₉×#127	—	2	1	no	—
68	C₂₉×#127	C₂³	1	2	yes	—
69	C₂₉×#126	—	2	1	no	—
70	C₂₉×#125	D₄	1	1	yes	characteristic
71	C₂₉×#124	D₄	1	1	yes	characteristic
72	C₂₉×#123	—	2	1	no	—
73	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
74	C₂₉×#121	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₂₉	—	2	1	no	—
77	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₂₉×#117	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×#107	—	2	2	no	—
83	C₂₉×#106	—	2	2	no	—
84	C₂₉×C₄⋊C₈	—	2	1	no	—
85	C₂₉×C₄⋊C₈	—	2	1	no	—
86	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₂₉×#103	—	2	2	no	—
91	C₂₉×#102	—	2	2	no	—
92	C₂₉×#102	—	2	2	no	—
93	C₂₉×#102	—	2	2	no	—
94	C₂₉×#102	—	2	2	no	—
95	C₂₉×#102	—	2	2	no	—
96	C₂₉×#102	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×C₂²⋊C₈	—	2	1	no	—
99	C₂₉×C₂²⋊C₈	—	2	1	no	—
100	C₂₉×C₂²⋊C₈	—	2	1	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×#97	—	2	1	no	—
104	C₂₉×#97	—	2	1	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₂₉×#97	—	2	1	no	—
107	C₄×C₈×C₂₉	—	2	1	no	—
108	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
110	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
112	C₂⁴×C₂₉	—	4	1	no	—
113	C₂×Q₈×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	4	1	no	—
115	C₂×Q₈×C₂₉	—	8	2	no	—
116	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₂₉	—	2	1	no	—
118	C₂×D₄×C₂₉	—	2	2	no	—
119	C₂×D₄×C₂₉	—	2	2	no	—
120	C₂×D₄×C₂₉	—	2	2	no	—
121	C₂×D₄×C₂₉	—	4	2	no	—
122	C₂×D₄×C₂₉	—	4	2	no	—
123	C₂×D₄×C₂₉	—	4	1	no	—
124	C₂×D₄×C₂₉	—	4	1	no	—
125	C₂×D₄×C₂₉	—	4	1	no	—
126	C₂×D₄×C₂₉	—	8	2	no	—
127	C₂×D₄×C₂₉	—	8	2	no	—
128	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	4	1	no	—
131	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
134	SD₁₆×C₂₉	—	8	2	no	—
135	D₈×C₂₉	—	8	2	no	—
136	M₁₆×C₂₉	—	4	2	no	—
137	C₂×C₈×C₂₉	—	2	1	no	—
138	C₂×C₈×C₂₉	—	2	1	no	—
139	C₂×C₈×C₂₉	—	2	2	no	—
140	C₂×C₈×C₂₉	—	2	2	no	—
141	C₂×C₈×C₂₉	—	4	1	no	—
142	C₂×C₈×C₂₉	—	4	1	no	—
143	C₂×C₈×C₂₉	—	4	2	no	—
144	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₄⋊C₄×C₂₉	—	2	2	no	—
153	C₄⋊C₄×C₂₉	—	2	2	no	—
154	C₄⋊C₄×C₂₉	—	4	1	no	—
155	C₄⋊C₄×C₂₉	—	4	1	no	—
156	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊C₄×C₂₉	—	2	1	no	—
159	C₂²⋊C₄×C₂₉	—	2	1	no	—
160	C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₄²×C₂₉	—	2	1	no	—
164	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₉	#41	1	1	yes	characteristic
167	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
168	#19362	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₂₉	—	2	1	no	—
170	C₂³×C₂₉	—	4	2	no	—
171	C₂³×C₂₉	—	8	2	no	—
172	C₂³×C₂₉	—	8	2	no	—
173	C₂³×C₂₉	—	8	2	no	—
174	C₂³×C₂₉	#121	1	1	yes	characteristic
175	Q₈×C₂₉	—	2	2	no	—
176	Q₈×C₂₉	—	8	2	no	—
177	Q₈×C₂₉	—	8	2	no	—
178	D₄×C₂₉	—	2	2	no	—
179	D₄×C₂₉	—	4	2	no	—
180	D₄×C₂₉	—	4	2	no	—
181	D₄×C₂₉	—	4	2	no	—
182	D₄×C₂₉	—	4	2	no	—
183	D₄×C₂₉	—	4	2	no	—
184	D₄×C₂₉	—	8	2	no	—
185	D₄×C₂₉	—	8	2	no	—
186	D₄×C₂₉	—	8	2	no	—
187	D₄×C₂₉	—	8	2	no	—
188	C₂×C₄×C₂₉	—	2	2	no	—
189	C₂×C₄×C₂₉	—	2	1	no	—
190	C₂×C₄×C₂₉	—	2	1	no	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	1	no	—
193	C₂×C₄×C₂₉	—	2	1	no	—
194	C₂×C₄×C₂₉	—	2	1	no	—
195	C₂×C₄×C₂₉	—	4	1	no	—
196	C₂×C₄×C₂₉	—	4	1	no	—
197	C₂×C₄×C₂₉	—	4	2	no	—
198	C₂×C₄×C₂₉	—	8	2	no	—
199	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
202	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
205	C₈×C₂₉	—	2	1	no	—
206	C₈×C₂₉	—	2	1	no	—
207	C₈×C₂₉	—	2	1	no	—
208	C₈×C₂₉	—	2	1	no	—
209	C₈×C₂₉	—	4	1	no	—
210	C₈×C₂₉	—	4	1	no	—
211	C₈×C₂₉	—	4	2	no	—
212	C₈×C₂₉	—	4	2	no	—
213	#3238	C₂×C₂₉	1	1	yes	characteristic, complemented
214	#3217	C₂×C₂₉	1	1	yes	characteristic
215	C₂×#486	C₂×C₂₉	1	1	yes	characteristic, complemented
216	#2966	C₂×C₂₉	1	1	yes	characteristic, complemented
217	#1698	C₂×C₂₉	1	2	yes	complemented
218	#1697	C₂×C₂₉	1	2	yes	complemented
219	#1678	C₂×C₂₉	1	2	yes	complemented
220	#1677	C₂×C₂₉	1	2	yes	complemented
221	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#1558	C₂×C₂₉	1	1	yes	characteristic, complemented
223	#1555	C₂×C₂₉	1	1	yes	characteristic, complemented
224	C₂²×C₂₉	—	2	1	no	—
225	C₂²×C₂₉	—	2	1	no	—
226	C₂²×C₂₉	—	4	1	no	—
227	C₂²×C₂₉	—	4	1	no	—
228	C₂²×C₂₉	—	4	1	no	—
229	C₂²×C₂₉	—	8	2	no	—
230	C₂²×C₂₉	—	8	2	no	—
231	C₂²×C₂₉	—	8	2	no	—
232	C₂²×C₂₉	—	16	4	no	—
233	C₂²×C₂₉	#472	1	2	yes	—
234	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
235	C₄×C₂₉	—	2	1	no	—
236	C₄×C₂₉	—	2	1	no	—
237	C₄×C₂₉	—	2	1	no	—
238	C₄×C₂₉	—	2	1	no	—
239	C₄×C₂₉	—	4	1	no	—
240	C₄×C₂₉	—	4	1	no	—
241	C₄×C₂₉	—	4	1	no	—
242	C₄×C₂₉	—	8	2	no	—
243	C₄×C₂₉	#575	1	1	yes	characteristic
244	C₄×C₂₉	#575	1	1	yes	characteristic
245	C₄×C₂₉	#577	1	2	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
247	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
248	#529	C₂²×C₂₉	1	1	yes	characteristic
249	#501	—	2	1	no	—
250	#496	—	2	1	no	—
251	#490	—	2	1	no	—
252	#489	—	2	1	no	—
253	#486	—	2	1	no	—
254	#486	—	2	1	no	—
255	#486	C₂²×C₂₉	1	2	yes	—
256	#486	C₂²×C₂₉	1	2	yes	—
257	#483	—	2	1	no	—
258	#480	—	2	1	no	—
259	#477	C₂²×C₂₉	1	2	yes	complemented
260	#476	C₂²×C₂₉	1	2	yes	complemented
261	#460	C₂²×C₂₉	1	2	yes	—
262	#459	C₂²×C₂₉	1	2	yes	—
263	#450	—	2	1	no	—
264	#447	—	2	1	no	—
265	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
266	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
267	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
268	#435	—	2	1	no	—
269	C₈×D₄	—	2	1	no	—
270	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
271	#433	—	2	1	no	—
272	#432	C₂²×C₂₉	1	1	yes	characteristic
273	#432	C₂²×C₂₉	1	1	yes	characteristic
274	#432	C₂²×C₂₉	1	1	yes	characteristic
275	C₂×#102	—	2	1	no	—
276	C₂×#102	—	2	1	no	—
277	#405	—	2	1	no	—
278	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
279	#335	C₂²×C₂₉	1	2	yes	complemented
280	#334	C₂²×C₂₉	1	2	yes	complemented
281	#333	C₂²×C₂₉	1	2	yes	complemented
282	#333	C₂²×C₂₉	1	2	yes	complemented
283	#331	C₂²×C₂₉	1	2	yes	—
284	#331	C₂²×C₂₉	1	2	yes	—
285	C₂×C₂₉	—	2	2	no	—
286	C₂×C₂₉	—	8	1	no	—
287	C₂×C₂₉	—	16	2	no	—
288	C₂×C₂₉	#3040	1	1	yes	characteristic
289	C₂×C₂₉	#3057	1	1	yes	characteristic
290	C₂×C₂₉	C₂×#472	1	1	yes	characteristic
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×D₈	—	2	2	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
300	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
305	#127	—	2	1	no	—
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	C₂³×C₂₉	1	2	yes	—
309	#126	—	2	1	no	—
310	#125	D₄×C₂₉	1	1	yes	characteristic
311	#124	D₄×C₂₉	1	1	yes	characteristic
312	#123	—	2	1	no	—
313	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
314	#121	D₄×C₂₉	1	1	yes	characteristic
315	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
318	#117	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
322	#107	—	2	2	no	—
323	#106	—	2	2	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
329	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
330	#103	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	2	2	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	#97	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
349	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
350	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
351	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
352	C₂₉	#19362	1	1	yes	characteristic, direct product factor, Sylow
353	C₂⁴	—	4	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
374	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
375	SD₁₆	—	8	2	no	—
376	D₈	—	8	2	no	—
377	M₁₆	—	4	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	—	4	1	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
407	C₄²	#41×C₂₉	1	1	yes	characteristic
408	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	C₂₉×#121	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	8	2	no	—
417	Q₈	—	8	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
440	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
441	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	16	4	no	—
462	C₂²	C₂₉×#472	1	2	yes	—
463	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	8	2	no	—
472	C₄	C₂₉×#575	1	1	yes	characteristic
473	C₄	C₂₉×#575	1	1	yes	characteristic
474	C₄	C₂₉×#577	1	2	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	8	1	no	—
477	C₂	—	16	2	no	—
478	C₂	C₂₉×#3040	1	1	yes	characteristic
479	C₂	C₂₉×#3057	1	1	yes	characteristic
480	C₂	C₂×C₂₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3217	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3238	C₂	semidirect
3. C₂×C₂₉×#486	C₂	semidirect
4. C₂₉×#2966	C₂	semidirect
5. C₂₉×#1698	C₂	semidirect
6. C₂₉×#1697	C₂	semidirect
7. C₂₉×#1678	C₂	semidirect
8. C₂₉×#1677	C₂	semidirect
9. C₂₉×#1568	C₂	semidirect
10. C₂₉×#1558	C₂	semidirect
11. C₂₉×#1555	C₂	semidirect
25. C₂₉×#477	C₂²	semidirect
26. C₂₉×#476	C₂²	semidirect
31. C₂₉×#446	C₂²	semidirect
32. C₈×Q₈×C₂₉	C₂²	semidirect
33. C₂₉×#436	C₂²	semidirect
36. C₈×D₄×C₂₉	C₂²	semidirect
45. C₂₉×#335	C₂²	semidirect
46. C₂₉×#334	C₂²	semidirect
47. C₂₉×#333	C₂²	semidirect
48. C₂₉×#333	C₂²	semidirect
168. #19362	C₂₉	direct (N × H)
213. #3238	C₂×C₂₉	semidirect
215. C₂×#486	C₂×C₂₉	semidirect
216. #2966	C₂×C₂₉	semidirect
217. #1698	C₂×C₂₉	semidirect
218. #1697	C₂×C₂₉	semidirect
219. #1678	C₂×C₂₉	semidirect
220. #1677	C₂×C₂₉	semidirect
221. #1568	C₂×C₂₉	semidirect
222. #1558	C₂×C₂₉	semidirect
223. #1555	C₂×C₂₉	semidirect
259. #477	C₂²×C₂₉	semidirect
260. #476	C₂²×C₂₉	semidirect
265. #446	C₂²×C₂₉	semidirect
266. C₈×Q₈	C₂²×C₂₉	semidirect
267. #436	C₂²×C₂₉	semidirect
270. C₈×D₄	C₂²×C₂₉	semidirect
279. #335	C₂²×C₂₉	semidirect
280. #334	C₂²×C₂₉	semidirect
281. #333	C₂²×C₂₉	semidirect
282. #333	C₂²×C₂₉	semidirect
352. C₂₉	#19362	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×#3238	2
C₂₉×#3217	2
C₂×C₂₉×#486	2
C₂₉×#2966	2
C₂₉×#1698	2
C₂₉×#1697	2
C₂₉×#1678	2
C₂₉×#1677	2
C₂₉×#1568	2
C₂₉×#1558	2
C₂₉×#1555	2
#19362	29

Subgroups — C29×#19362 #20314262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19362 #20314262