Subgroups — C₂×C₂₉×#3122 #20355451

Order 7424.

2338 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3122	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#447	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₉×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₂₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₂₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₂₉	C₂²	1	2	yes	—
14	C₂₉×#540	—	2	4	no	—
15	C₂₉×#540	C₂²	1	8	yes	complemented
16	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₂₉×#123	—	2	2	no	—
19	C₂×C₂₉×#121	—	2	2	no	—
20	C₂×C₂₉×#121	C₂²	1	2	yes	—
21	C₂₉×#518	—	2	4	no	—
22	C₂₉×#518	C₂²	1	8	yes	complemented
23	C₂×C₄×D₄×C₂₉	—	2	2	no	—
24	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
27	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₂₉	—	2	2	no	—
30	C₂₉×#482	C₂²	1	16	yes	complemented
31	C₂₉×#478	C₂²	1	16	yes	complemented
32	C₂₉×#459	C₂²	1	16	yes	complemented
33	C₂₉×#447	C₂²	1	16	yes	complemented
34	C₂₉×#442	C₂²	1	16	yes	complemented
35	C₄×D₈×C₂₉	C₂²	1	16	yes	complemented
36	C₂₉×#433	C₂²	1	8	yes	complemented
37	C₂×C₂₉×#107	C₂²	1	2	yes	complemented
38	C₂×C₂₉×#106	C₂²	1	2	yes	complemented
39	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₂₉×#102	C₂²	1	2	yes	—
41	C₂×C₂₉×#102	C₂²	1	2	yes	—
42	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
43	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
44	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₂₉	—	2	1	no	—
48	C₂²×D₄×C₂₉	—	2	8	no	—
49	C₂²×D₄×C₂₉	—	2	2	no	—
50	C₂²×D₄×C₂₉	—	2	1	no	—
51	C₂²×D₄×C₂₉	—	2	2	no	—
52	C₂²×D₄×C₂₉	—	2	2	no	—
53	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₂₉	—	2	2	no	—
57	C₂³×C₄×C₂₉	—	2	2	no	—
58	C₂³×C₄×C₂₉	—	2	2	no	—
59	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
60	C₂×D₈×C₂₉	—	2	8	no	—
61	C₂×D₈×C₂₉	—	2	8	no	—
62	C₂×D₈×C₂₉	C₂³	1	8	yes	—
63	C₂×D₈×C₂₉	C₂³	1	8	yes	—
64	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
65	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
66	C₂₉×#127	—	2	2	no	—
67	C₂₉×#127	C₂³	1	4	yes	complemented
68	C₂₉×#125	—	2	2	no	—
69	C₂₉×#125	C₂³	1	4	yes	complemented
70	C₂₉×#123	—	2	16	no	—
71	C₂₉×#121	—	2	4	no	—
72	C₂₉×#121	—	2	16	no	—
73	C₂₉×#121	C₂³	1	8	yes	—
74	C₄×D₄×C₂₉	—	2	16	no	—
75	C₄×D₄×C₂₉	—	2	4	no	—
76	C₄×D₄×C₂₉	—	2	4	no	—
77	C₄×D₄×C₂₉	—	2	4	no	—
78	C₄×D₄×C₂₉	C₂³	1	8	yes	—
79	C₄×D₄×C₂₉	C₂³	1	8	yes	—
80	C₄×D₄×C₂₉	C₂³	1	8	yes	complemented
81	C₂₉×#117	—	2	2	no	—
82	C₂₉×#117	D₄	1	4	yes	—
83	C₂₉×#117	C₂³	1	4	yes	—
84	C₂₉×#117	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₂₉	—	2	16	no	—
95	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
96	C₂×C₄²×C₂₉	—	2	1	no	—
97	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
99	C₂₉×#107	C₂³	1	8	yes	complemented
100	C₂₉×#106	C₂³	1	8	yes	complemented
101	C₂₉×C₄⋊C₈	C₂³	1	8	yes	complemented
102	C₂₉×#102	C₂³	1	8	yes	—
103	C₂₉×#102	C₂³	1	8	yes	—
104	C₂₉×#102	C₂³	1	8	yes	complemented
105	C₂₉×#102	C₂³	1	8	yes	complemented
106	C₂₉×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₂₉×#97	C₂³	1	4	yes	complemented
108	C₄×C₈×C₂₉	C₂³	1	4	yes	complemented
109	C₂⁴×C₂₉	—	2	8	no	—
110	C₂⁴×C₂₉	—	2	2	no	—
111	C₂⁴×C₂₉	—	2	4	no	—
112	C₂⁴×C₂₉	—	2	2	no	—
113	C₂⁴×C₂₉	—	8	4	no	—
114	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₂₉	—	2	8	no	—
116	C₂×D₄×C₂₉	—	2	16	no	—
117	C₂×D₄×C₂₉	—	2	16	no	—
118	C₂×D₄×C₂₉	—	2	8	no	—
119	C₂×D₄×C₂₉	—	2	4	no	—
120	C₂×D₄×C₂₉	—	2	2	no	—
121	C₂×D₄×C₂₉	—	2	2	no	—
122	C₂×D₄×C₂₉	—	2	8	no	—
123	C₂×D₄×C₂₉	—	2	4	no	—
124	C₂×D₄×C₂₉	—	2	4	no	—
125	C₂×D₄×C₂₉	—	2	4	no	—
126	C₂×D₄×C₂₉	—	8	4	no	—
127	C₂×D₄×C₂₉	—	8	4	no	—
128	C₂×D₄×C₂₉	#41	1	8	yes	—
129	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
130	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₂₉	—	2	4	no	—
132	C₂²×C₄×C₂₉	—	2	2	no	—
133	C₂²×C₄×C₂₉	—	2	2	no	—
134	C₂²×C₄×C₂₉	—	2	8	no	—
135	C₂²×C₄×C₂₉	—	2	8	no	—
136	C₂²×C₄×C₂₉	—	2	8	no	—
137	C₂²×C₄×C₂₉	—	8	4	no	—
138	C₂²×C₄×C₂₉	—	8	4	no	—
139	C₂²×C₄×C₂₉	—	8	4	no	—
140	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
146	D₈×C₂₉	—	2	16	no	—
147	D₈×C₂₉	—	2	16	no	—
148	C₂×C₈×C₂₉	—	2	4	no	—
149	C₂×C₈×C₂₉	—	2	4	no	—
150	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
151	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₂₉	—	2	8	no	—
153	C₄⋊C₄×C₂₉	—	2	2	no	—
154	C₄⋊C₄×C₂₉	—	2	2	no	—
155	C₄⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
156	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
157	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
158	C₂²⋊C₄×C₂₉	—	2	4	no	—
159	C₂²⋊C₄×C₂₉	—	2	8	no	—
160	C₂²⋊C₄×C₂₉	—	2	8	no	—
161	C₂²⋊C₄×C₂₉	—	2	8	no	—
162	C₂²⋊C₄×C₂₉	—	2	8	no	—
163	C₂²⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
164	C₄²×C₂₉	—	2	4	no	—
165	C₄²×C₂₉	C₂×D₄	1	2	yes	—
166	C₄²×C₂₉	C₂×D₄	1	2	yes	—
167	C₄²×C₂₉	C₂⁴	1	2	yes	—
168	C₄²×C₂₉	C₂⁴	1	2	yes	—
169	C₂×#3122	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₂₉	—	2	16	no	—
171	C₂³×C₂₉	—	2	2	no	—
172	C₂³×C₂₉	—	2	8	no	—
173	C₂³×C₂₉	—	2	4	no	—
174	C₂³×C₂₉	—	2	4	no	—
175	C₂³×C₂₉	—	2	4	no	—
176	C₂³×C₂₉	—	4	4	no	—
177	C₂³×C₂₉	—	4	4	no	—
178	C₂³×C₂₉	—	4	4	no	—
179	C₂³×C₂₉	—	4	4	no	—
180	C₂³×C₂₉	—	4	4	no	—
181	C₂³×C₂₉	—	8	8	no	—
182	C₂³×C₂₉	—	8	16	no	—
183	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
184	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
185	D₄×C₂₉	—	2	16	no	—
186	D₄×C₂₉	—	2	8	no	—
187	D₄×C₂₉	—	2	4	no	—
188	D₄×C₂₉	—	2	4	no	—
189	D₄×C₂₉	—	2	4	no	—
190	D₄×C₂₉	—	4	4	no	—
191	D₄×C₂₉	—	8	8	no	—
192	D₄×C₂₉	—	8	8	no	—
193	D₄×C₂₉	C₂×#41	1	8	yes	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	4	no	—
196	C₂×C₄×C₂₉	—	2	4	no	—
197	C₂×C₄×C₂₉	—	2	4	no	—
198	C₂×C₄×C₂₉	—	2	4	no	—
199	C₂×C₄×C₂₉	—	2	4	no	—
200	C₂×C₄×C₂₉	—	2	4	no	—
201	C₂×C₄×C₂₉	—	4	4	no	—
202	C₂×C₄×C₂₉	—	4	4	no	—
203	C₂×C₄×C₂₉	—	8	8	no	—
204	C₂×C₄×C₂₉	—	8	8	no	—
205	C₂×C₄×C₂₉	—	8	8	no	—
206	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
211	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
212	C₈×C₂₉	—	2	4	no	—
213	C₈×C₂₉	—	2	4	no	—
214	C₂×#540	C₂×C₂₉	1	1	yes	characteristic, complemented
215	C₂×#518	C₂×C₂₉	1	1	yes	characteristic, complemented
216	#3122	C₂×C₂₉	1	16	yes	direct product factor
217	C₂×#482	C₂×C₂₉	1	2	yes	complemented
218	C₂×#478	C₂×C₂₉	1	2	yes	complemented
219	C₂×#459	C₂×C₂₉	1	2	yes	complemented
220	C₂×#447	C₂×C₂₉	1	2	yes	complemented
221	C₂×#442	C₂×C₂₉	1	2	yes	complemented
222	C₂×C₄×D₈	C₂×C₂₉	1	2	yes	complemented
223	C₂×#433	C₂×C₂₉	1	1	yes	characteristic, complemented
224	C₂²×C₂₉	—	2	2	no	—
225	C₂²×C₂₉	—	2	8	no	—
226	C₂²×C₂₉	—	2	4	no	—
227	C₂²×C₂₉	—	4	4	no	—
228	C₂²×C₂₉	—	4	16	no	—
229	C₂²×C₂₉	—	4	4	no	—
230	C₂²×C₂₉	—	4	4	no	—
231	C₂²×C₂₉	—	4	4	no	—
232	C₂²×C₂₉	—	4	4	no	—
233	C₂²×C₂₉	—	4	4	no	—
234	C₂²×C₂₉	—	8	16	no	—
235	C₂²×C₂₉	—	8	8	no	—
236	C₂²×C₂₉	#525	1	2	yes	—
237	C₂²×C₂₉	#576	1	4	yes	—
238	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₂₉	—	2	2	no	—
240	C₄×C₂₉	—	2	4	no	—
241	C₄×C₂₉	—	2	4	no	—
242	C₄×C₂₉	—	4	4	no	—
243	C₄×C₂₉	—	4	4	no	—
244	C₄×C₂₉	#525	1	2	yes	—
245	C₄×C₂₉	C₂²×#41	1	2	yes	—
246	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
247	C₂²×D₈	C₂²×C₂₉	1	2	yes	—
248	C₂²×D₈	C₂²×C₂₉	1	2	yes	—
249	#540	—	2	4	no	—
250	#540	C₂²×C₂₉	1	8	yes	complemented
251	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic, complemented
252	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic, complemented
253	C₂×#123	—	2	2	no	—
254	C₂×#121	—	2	2	no	—
255	C₂×#121	C₂²×C₂₉	1	2	yes	—
256	#518	—	2	4	no	—
257	#518	C₂²×C₂₉	1	8	yes	complemented
258	C₂×C₄×D₄	—	2	2	no	—
259	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
261	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
262	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
263	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	—	2	2	no	—
265	#482	C₂²×C₂₉	1	16	yes	complemented
266	#478	C₂²×C₂₉	1	16	yes	complemented
267	#459	C₂²×C₂₉	1	16	yes	complemented
268	#447	C₂²×C₂₉	1	16	yes	complemented
269	#442	C₂²×C₂₉	1	16	yes	complemented
270	C₄×D₈	C₂²×C₂₉	1	16	yes	complemented
271	#433	C₂²×C₂₉	1	8	yes	complemented
272	C₂×#107	C₂²×C₂₉	1	2	yes	complemented
273	C₂×#106	C₂²×C₂₉	1	2	yes	complemented
274	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
275	C₂×#102	C₂²×C₂₉	1	2	yes	—
276	C₂×#102	C₂²×C₂₉	1	2	yes	—
277	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
278	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
279	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
280	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
281	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
282	C₂×C₂₉	—	4	2	no	—
283	C₂×C₂₉	—	4	8	no	—
284	C₂×C₂₉	—	8	4	no	—
285	C₂×C₂₉	#3122	1	4	yes	direct product factor
286	C₂×C₂₉	C₂×#525	1	1	yes	characteristic
287	C₂×C₂₉	C₂×#576	1	2	yes	—
288	C₂⁵	—	2	1	no	—
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
295	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
296	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
301	C₂×D₈	—	2	8	no	—
302	C₂×D₈	—	2	8	no	—
303	C₂×D₈	C₂³×C₂₉	1	8	yes	—
304	C₂×D₈	C₂³×C₂₉	1	8	yes	—
305	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
306	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
307	#127	—	2	2	no	—
308	#127	C₂³×C₂₉	1	4	yes	complemented
309	#125	—	2	2	no	—
310	#125	C₂³×C₂₉	1	4	yes	complemented
311	#123	—	2	16	no	—
312	#121	—	2	4	no	—
313	#121	—	2	16	no	—
314	#121	C₂³×C₂₉	1	8	yes	—
315	C₄×D₄	—	2	16	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	C₂³×C₂₉	1	8	yes	—
320	C₄×D₄	C₂³×C₂₉	1	8	yes	—
321	C₄×D₄	C₂³×C₂₉	1	8	yes	complemented
322	#117	—	2	2	no	—
323	#117	D₄×C₂₉	1	4	yes	—
324	#117	C₂³×C₂₉	1	4	yes	—
325	#117	C₂³×C₂₉	1	4	yes	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	16	no	—
336	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
340	#107	C₂³×C₂₉	1	8	yes	complemented
341	#106	C₂³×C₂₉	1	8	yes	complemented
342	C₄⋊C₈	C₂³×C₂₉	1	8	yes	complemented
343	#102	C₂³×C₂₉	1	8	yes	—
344	#102	C₂³×C₂₉	1	8	yes	—
345	#102	C₂³×C₂₉	1	8	yes	complemented
346	#102	C₂³×C₂₉	1	8	yes	complemented
347	C₂²⋊C₈	C₂³×C₂₉	1	8	yes	—
348	#97	C₂³×C₂₉	1	4	yes	complemented
349	C₄×C₈	C₂³×C₂₉	1	4	yes	complemented
350	C₂₉	C₂×#3122	1	1	yes	characteristic, direct product factor, Sylow
351	C₂⁴	—	2	8	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	8	4	no	—
356	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	16	no	—
359	C₂×D₄	—	2	16	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	8	4	no	—
369	C₂×D₄	—	8	4	no	—
370	C₂×D₄	#41×C₂₉	1	8	yes	—
371	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
372	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	8	4	no	—
380	C₂²×C₄	—	8	4	no	—
381	C₂²×C₄	—	8	4	no	—
382	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
388	D₈	—	2	16	no	—
389	D₈	—	2	16	no	—
390	C₂×C₈	—	2	4	no	—
391	C₂×C₈	—	2	4	no	—
392	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
393	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
398	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
399	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	2	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
406	C₄²	—	2	4	no	—
407	C₄²	C₂×D₄×C₂₉	1	2	yes	—
408	C₄²	C₂×D₄×C₂₉	1	2	yes	—
409	C₄²	C₂⁴×C₂₉	1	2	yes	—
410	C₄²	C₂⁴×C₂₉	1	2	yes	—
411	C₂³	—	2	16	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	8	8	no	—
423	C₂³	—	8	16	no	—
424	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
425	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
426	D₄	—	2	16	no	—
427	D₄	—	2	8	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	4	no	—
432	D₄	—	8	8	no	—
433	D₄	—	8	8	no	—
434	D₄	C₂×#41×C₂₉	1	8	yes	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
452	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₈	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	16	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	16	no	—
466	C₂²	—	8	8	no	—
467	C₂²	C₂₉×#525	1	2	yes	—
468	C₂²	C₂₉×#576	1	4	yes	—
469	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	C₂₉×#525	1	2	yes	—
476	C₄	C₂²×#41×C₂₉	1	2	yes	—
477	C₂	—	4	2	no	—
478	C₂	—	4	8	no	—
479	C₂	—	8	4	no	—
480	C₂	C₂₉×#3122	1	4	yes	direct product factor
481	C₂	C₂×C₂₉×#525	1	1	yes	characteristic
482	C₂	C₂×C₂₉×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#540	C₂	semidirect
2. C₂×C₂₉×#518	C₂	semidirect
3. C₂₉×#3122	C₂	direct (N × H)
4. C₂×C₂₉×#482	C₂	semidirect
5. C₂×C₂₉×#478	C₂	semidirect
6. C₂×C₂₉×#459	C₂	semidirect
7. C₂×C₂₉×#447	C₂	semidirect
8. C₂×C₂₉×#442	C₂	semidirect
9. C₂×C₄×D₈×C₂₉	C₂	semidirect
10. C₂×C₂₉×#433	C₂	semidirect
15. C₂₉×#540	C₂²	semidirect
16. C₂×C₂₉×#127	C₂²	semidirect
17. C₂×C₂₉×#125	C₂²	semidirect
22. C₂₉×#518	C₂²	semidirect
26. C₂×C₄×D₄×C₂₉	C₂²	semidirect
30. C₂₉×#482	C₂²	semidirect
31. C₂₉×#478	C₂²	semidirect
32. C₂₉×#459	C₂²	semidirect
33. C₂₉×#447	C₂²	semidirect
34. C₂₉×#442	C₂²	semidirect
35. C₄×D₈×C₂₉	C₂²	semidirect
36. C₂₉×#433	C₂²	semidirect
37. C₂×C₂₉×#107	C₂²	semidirect
38. C₂×C₂₉×#106	C₂²	semidirect
39. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
42. C₂×C₂₉×#102	C₂²	semidirect
43. C₂×C₂₉×#102	C₂²	semidirect
45. C₂×C₂₉×#97	C₂²	semidirect
46. C₂×C₄×C₈×C₂₉	C₂²	semidirect
67. C₂₉×#127	C₂³	semidirect
69. C₂₉×#125	C₂³	semidirect
80. C₄×D₄×C₂₉	C₂³	semidirect
99. C₂₉×#107	C₂³	semidirect
100. C₂₉×#106	C₂³	semidirect
101. C₂₉×C₄⋊C₈	C₂³	semidirect
104. C₂₉×#102	C₂³	semidirect
105. C₂₉×#102	C₂³	semidirect
107. C₂₉×#97	C₂³	semidirect
108. C₄×C₈×C₂₉	C₂³	semidirect
169. C₂×#3122	C₂₉	direct (N × H)
214. C₂×#540	C₂×C₂₉	semidirect
215. C₂×#518	C₂×C₂₉	semidirect
216. #3122	C₂×C₂₉	direct (N × H)
217. C₂×#482	C₂×C₂₉	semidirect
218. C₂×#478	C₂×C₂₉	semidirect
219. C₂×#459	C₂×C₂₉	semidirect
220. C₂×#447	C₂×C₂₉	semidirect
221. C₂×#442	C₂×C₂₉	semidirect
222. C₂×C₄×D₈	C₂×C₂₉	semidirect
223. C₂×#433	C₂×C₂₉	semidirect
250. #540	C₂²×C₂₉	semidirect
251. C₂×#127	C₂²×C₂₉	semidirect
252. C₂×#125	C₂²×C₂₉	semidirect
257. #518	C₂²×C₂₉	semidirect
261. C₂×C₄×D₄	C₂²×C₂₉	semidirect
265. #482	C₂²×C₂₉	semidirect
266. #478	C₂²×C₂₉	semidirect
267. #459	C₂²×C₂₉	semidirect
268. #447	C₂²×C₂₉	semidirect
269. #442	C₂²×C₂₉	semidirect
270. C₄×D₈	C₂²×C₂₉	semidirect
271. #433	C₂²×C₂₉	semidirect
272. C₂×#107	C₂²×C₂₉	semidirect
273. C₂×#106	C₂²×C₂₉	semidirect
274. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
277. C₂×#102	C₂²×C₂₉	semidirect
278. C₂×#102	C₂²×C₂₉	semidirect
280. C₂×#97	C₂²×C₂₉	semidirect
281. C₂×C₄×C₈	C₂²×C₂₉	semidirect
285. C₂×C₂₉	#3122	direct (N × H)
308. #127	C₂³×C₂₉	semidirect
310. #125	C₂³×C₂₉	semidirect
321. C₄×D₄	C₂³×C₂₉	semidirect
340. #107	C₂³×C₂₉	semidirect
341. #106	C₂³×C₂₉	semidirect
342. C₄⋊C₈	C₂³×C₂₉	semidirect
345. #102	C₂³×C₂₉	semidirect
346. #102	C₂³×C₂₉	semidirect
348. #97	C₂³×C₂₉	semidirect
349. C₄×C₈	C₂³×C₂₉	semidirect
350. C₂₉	C₂×#3122	direct (N × H)
480. C₂	C₂₉×#3122	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×#540	2
C₂×C₂₉×#518	2
C₂₉×#3122	2
C₂×C₂₉×#482	2
C₂×C₂₉×#478	2
C₂×C₂₉×#459	2
C₂×C₂₉×#447	2
C₂×C₂₉×#442	2
C₂×C₄×D₈×C₂₉	2
C₂×C₂₉×#433	2
C₂×#3122	29

Subgroups — C2×C29×#3122 #20355451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3122 #20355451