Subgroups — C₂×C₂₉×#3400 #20356297

Order 7424.

1970 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3400	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#460	C₂	1	1	yes	maximal, characteristic
9	C₂×C₂₉×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₂₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
18	C₂₉×#559	—	2	4	no	—
19	C₂₉×#559	C₂²	1	8	yes	—
20	C₂₉×#557	—	2	4	no	—
21	C₂₉×#557	C₂²	1	8	yes	complemented
22	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#125	—	2	1	no	—
26	C₂×C₂₉×#125	—	2	2	no	—
27	C₂×C₂₉×#124	—	2	1	no	—
28	C₂×C₂₉×#124	C₂²	1	2	yes	—
29	C₂×C₂₉×#123	—	2	2	no	—
30	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
31	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₉	—	2	1	no	—
36	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
37	C₂₉×#497	C₂²	1	16	yes	complemented
38	C₂₉×#492	C₂²	1	8	yes	—
39	C₂₉×#464	C₂²	1	16	yes	complemented
40	C₂₉×#462	C₂²	1	8	yes	complemented
41	C₂₉×#461	C₂²	1	16	yes	complemented
42	C₂₉×#460	C₂²	1	8	yes	—
43	C₂₉×#446	C₂²	1	8	yes	complemented
44	C₂₉×#440	C₂²	1	16	yes	complemented
45	C₄×Q₁₆×C₂₉	C₂²	1	8	yes	complemented
46	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
47	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
48	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
50	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
51	C₂×C₂₉×#103	C₂²	1	2	yes	—
52	C₂×C₂₉×#102	C₂²	1	2	yes	—
53	C₂×C₂₉×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₂₉	—	2	1	no	—
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₂₉	—	2	2	no	—
63	C₂×Q₁₆×C₂₉	—	2	4	no	—
64	C₂×Q₁₆×C₂₉	—	4	4	no	—
65	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
66	C₂×Q₁₆×C₂₉	C₂³	1	8	yes	—
67	C₂×SD₁₆×C₂₉	—	2	8	no	—
68	C₂×SD₁₆×C₂₉	—	4	4	no	—
69	C₂×SD₁₆×C₂₉	—	4	4	no	—
70	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
71	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
72	C₂×SD₁₆×C₂₉	C₂³	1	8	yes	—
73	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×C₄⋊Q₈	—	2	4	no	—
77	C₂₉×C₄⋊Q₈	—	2	2	no	—
78	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
79	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₂₉×#127	—	2	2	no	—
81	C₂₉×#127	C₂³	1	4	yes	—
82	C₂₉×#125	—	2	8	no	—
83	C₂₉×#125	—	2	16	no	—
84	C₂₉×#124	—	2	8	no	—
85	C₂₉×#124	—	2	4	no	—
86	C₂₉×#124	C₂³	1	8	yes	—
87	C₂₉×#123	—	2	16	no	—
88	C₄×Q₈×C₂₉	—	2	8	no	—
89	C₄×Q₈×C₂₉	—	2	4	no	—
90	C₄×Q₈×C₂₉	—	2	2	no	—
91	C₄×Q₈×C₂₉	—	2	2	no	—
92	C₄×Q₈×C₂₉	D₄	1	4	yes	—
93	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
94	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
95	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
96	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
97	C₄×D₄×C₂₉	—	2	8	no	—
98	C₄×D₄×C₂₉	—	2	4	no	—
99	C₄×D₄×C₂₉	C₂³	1	8	yes	—
100	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
106	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
114	C₂×C₄²×C₂₉	—	2	1	no	—
115	C₂×C₄²×C₂₉	—	2	2	no	—
116	C₂×C₄²×C₂₉	—	2	1	no	—
117	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
119	C₂₉×#107	C₂³	1	4	yes	—
120	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
121	C₂₉×C₄⋊C₈	C₂³	1	8	yes	—
122	C₂₉×#103	C₂³	1	4	yes	—
123	C₂₉×#103	C₂³	1	4	yes	—
124	C₂₉×#103	C₂³	1	8	yes	—
125	C₂₉×#102	C₂³	1	8	yes	—
126	C₂₉×#97	C₂³	1	8	yes	—
127	C₄×C₈×C₂₉	C₂³	1	4	yes	—
128	C₂⁴×C₂₉	—	2	2	no	—
129	C₂×Q₈×C₂₉	—	2	4	no	—
130	C₂×Q₈×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	—	2	2	no	—
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	4	no	—
134	C₂×Q₈×C₂₉	—	2	2	no	—
135	C₂×Q₈×C₂₉	—	2	2	no	—
136	C₂×Q₈×C₂₉	—	2	2	no	—
137	C₂×Q₈×C₂₉	—	2	4	no	—
138	C₂×Q₈×C₂₉	—	2	2	no	—
139	C₂×Q₈×C₂₉	C₂×D₄	1	4	yes	—
140	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
141	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
142	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
143	C₂×D₄×C₂₉	—	2	2	no	—
144	C₂×D₄×C₂₉	—	2	4	no	—
145	C₂×D₄×C₂₉	—	2	4	no	—
146	C₂×D₄×C₂₉	—	2	4	no	—
147	C₂×D₄×C₂₉	—	2	4	no	—
148	C₂×D₄×C₂₉	—	4	4	no	—
149	C₂×D₄×C₂₉	—	8	2	no	—
150	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₂₉	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	1	no	—
153	C₂²×C₄×C₂₉	—	2	1	no	—
154	C₂²×C₄×C₂₉	—	2	2	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	8	no	—
157	C₂²×C₄×C₂₉	—	8	4	no	—
158	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
163	Q₁₆×C₂₉	—	2	8	no	—
164	Q₁₆×C₂₉	—	4	8	no	—
165	SD₁₆×C₂₉	—	2	16	no	—
166	SD₁₆×C₂₉	—	4	8	no	—
167	SD₁₆×C₂₉	—	4	8	no	—
168	C₂×C₈×C₂₉	—	2	2	no	—
169	C₂×C₈×C₂₉	—	2	4	no	—
170	C₂×C₈×C₂₉	#41	1	4	yes	—
171	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
172	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
173	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
174	C₄⋊C₄×C₂₉	—	2	8	no	—
175	C₄⋊C₄×C₂₉	—	2	4	no	—
176	C₄⋊C₄×C₂₉	—	2	4	no	—
177	C₄⋊C₄×C₂₉	—	2	8	no	—
178	C₄⋊C₄×C₂₉	—	2	4	no	—
179	C₄⋊C₄×C₂₉	—	2	8	no	—
180	C₄⋊C₄×C₂₉	—	2	4	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₂₉	C₂×D₄	1	8	yes	—
185	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
187	C₂²⋊C₄×C₂₉	—	2	8	no	—
188	C₂²⋊C₄×C₂₉	—	2	8	no	—
189	C₂²⋊C₄×C₂₉	—	2	8	no	—
190	C₄²×C₂₉	—	2	4	no	—
191	C₄²×C₂₉	—	2	8	no	—
192	C₄²×C₂₉	—	2	4	no	—
193	C₄²×C₂₉	C₂×D₄	1	4	yes	—
194	C₄²×C₂₉	C₂×D₄	1	2	yes	—
195	C₄²×C₂₉	C₂⁴	1	4	yes	—
196	C₄²×C₂₉	C₂⁴	1	2	yes	—
197	C₂×#3400	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₂₉	—	2	4	no	—
199	C₂³×C₂₉	—	4	4	no	—
200	C₂³×C₂₉	—	4	4	no	—
201	C₂³×C₂₉	—	4	4	no	—
202	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₂₉	—	2	8	no	—
204	Q₈×C₂₉	—	2	4	no	—
205	Q₈×C₂₉	—	2	2	no	—
206	Q₈×C₂₉	—	2	2	no	—
207	Q₈×C₂₉	—	2	2	no	—
208	Q₈×C₂₉	—	2	4	no	—
209	Q₈×C₂₉	—	2	2	no	—
210	Q₈×C₂₉	—	4	2	no	—
211	Q₈×C₂₉	—	4	4	no	—
212	Q₈×C₂₉	—	4	2	no	—
213	D₄×C₂₉	—	2	4	no	—
214	D₄×C₂₉	—	2	4	no	—
215	D₄×C₂₉	—	4	4	no	—
216	D₄×C₂₉	—	4	8	no	—
217	D₄×C₂₉	—	8	4	no	—
218	C₂×C₄×C₂₉	—	2	4	no	—
219	C₂×C₄×C₂₉	—	2	4	no	—
220	C₂×C₄×C₂₉	—	2	2	no	—
221	C₂×C₄×C₂₉	—	2	2	no	—
222	C₂×C₄×C₂₉	—	2	2	no	—
223	C₂×C₄×C₂₉	—	2	2	no	—
224	C₂×C₄×C₂₉	—	2	4	no	—
225	C₂×C₄×C₂₉	—	2	2	no	—
226	C₂×C₄×C₂₉	—	4	2	no	—
227	C₂×C₄×C₂₉	—	4	4	no	—
228	C₂×C₄×C₂₉	—	4	2	no	—
229	C₂×C₄×C₂₉	—	4	2	no	—
230	C₂×C₄×C₂₉	—	4	2	no	—
231	C₂×C₄×C₂₉	—	8	8	no	—
232	C₂×C₄×C₂₉	#137	1	4	yes	—
233	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
239	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
240	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
241	C₈×C₂₉	—	2	2	no	—
242	C₈×C₂₉	—	2	4	no	—
243	C₈×C₂₉	C₂×#41	1	4	yes	—
244	C₂×#559	C₂×C₂₉	1	1	yes	characteristic
245	C₂×#557	C₂×C₂₉	1	1	yes	characteristic, complemented
246	#3400	C₂×C₂₉	1	16	yes	direct product factor
247	C₂×#497	C₂×C₂₉	1	2	yes	complemented
248	C₂×#492	C₂×C₂₉	1	1	yes	characteristic
249	C₂×#464	C₂×C₂₉	1	2	yes	complemented
250	C₂×#462	C₂×C₂₉	1	1	yes	characteristic, complemented
251	C₂×#460	C₂×C₂₉	1	1	yes	characteristic
252	C₂×#461	C₂×C₂₉	1	2	yes	complemented
253	C₂×#446	C₂×C₂₉	1	1	yes	characteristic, complemented
254	C₂×#440	C₂×C₂₉	1	2	yes	complemented
255	C₂×C₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
256	C₂²×C₂₉	—	4	4	no	—
257	C₂²×C₂₉	—	4	4	no	—
258	C₂²×C₂₉	—	4	4	no	—
259	C₂²×C₂₉	—	8	8	no	—
260	C₂²×C₂₉	#550	1	2	yes	—
261	C₂²×C₂₉	C₂×#137	1	2	yes	—
262	C₂²×C₂₉	#577	1	2	yes	—
263	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₂₉	—	2	4	no	—
265	C₄×C₂₉	—	2	4	no	—
266	C₄×C₂₉	—	2	2	no	—
267	C₄×C₂₉	—	4	2	no	—
268	C₄×C₂₉	—	4	4	no	—
269	C₄×C₂₉	—	4	2	no	—
270	C₄×C₂₉	—	4	2	no	—
271	C₄×C₂₉	—	4	2	no	—
272	C₄×C₂₉	#550	1	2	yes	—
273	C₄×C₂₉	C₂×#137	1	4	yes	—
274	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
275	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
276	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
277	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
279	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
280	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
281	#559	—	2	4	no	—
282	#559	C₂²×C₂₉	1	8	yes	—
283	#557	—	2	4	no	—
284	#557	C₂²×C₂₉	1	8	yes	complemented
285	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
286	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
287	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
288	C₂×#125	—	2	1	no	—
289	C₂×#125	—	2	2	no	—
290	C₂×#124	—	2	1	no	—
291	C₂×#124	C₂²×C₂₉	1	2	yes	—
292	C₂×#123	—	2	2	no	—
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
296	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
298	C₂×C₄×D₄	—	2	1	no	—
299	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
300	#497	C₂²×C₂₉	1	16	yes	complemented
301	#492	C₂²×C₂₉	1	8	yes	—
302	#464	C₂²×C₂₉	1	16	yes	complemented
303	#462	C₂²×C₂₉	1	8	yes	complemented
304	#461	C₂²×C₂₉	1	16	yes	complemented
305	#460	C₂²×C₂₉	1	8	yes	—
306	#446	C₂²×C₂₉	1	8	yes	complemented
307	#440	C₂²×C₂₉	1	16	yes	complemented
308	C₄×Q₁₆	C₂²×C₂₉	1	8	yes	complemented
309	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
311	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×#103	C₂²×C₂₉	1	2	yes	—
315	C₂×#102	C₂²×C₂₉	1	2	yes	—
316	C₂×#97	C₂²×C₂₉	1	2	yes	—
317	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×C₂₉	—	8	4	no	—
319	C₂×C₂₉	#3400	1	4	yes	direct product factor
320	C₂×C₂₉	C₂×#550	1	1	yes	characteristic
321	C₂×C₂₉	C₂²×#137	1	1	yes	characteristic
322	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
323	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
324	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
326	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
330	C₂³×C₄	—	2	2	no	—
331	C₂×Q₁₆	—	2	4	no	—
332	C₂×Q₁₆	—	4	4	no	—
333	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
334	C₂×Q₁₆	C₂³×C₂₉	1	8	yes	—
335	C₂×SD₁₆	—	2	8	no	—
336	C₂×SD₁₆	—	4	4	no	—
337	C₂×SD₁₆	—	4	4	no	—
338	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
339	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
340	C₂×SD₁₆	C₂³×C₂₉	1	8	yes	—
341	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
343	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
344	C₄⋊Q₈	—	2	4	no	—
345	C₄⋊Q₈	—	2	2	no	—
346	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
347	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
348	#127	—	2	2	no	—
349	#127	C₂³×C₂₉	1	4	yes	—
350	#125	—	2	8	no	—
351	#125	—	2	16	no	—
352	#124	—	2	8	no	—
353	#124	—	2	4	no	—
354	#124	C₂³×C₂₉	1	8	yes	—
355	#123	—	2	16	no	—
356	C₄×Q₈	—	2	8	no	—
357	C₄×Q₈	—	2	4	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	D₄×C₂₉	1	4	yes	—
361	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
362	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
363	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
364	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	C₂³×C₂₉	1	8	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
386	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
387	#107	C₂³×C₂₉	1	4	yes	—
388	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
389	C₄⋊C₈	C₂³×C₂₉	1	8	yes	—
390	#103	C₂³×C₂₉	1	4	yes	—
391	#103	C₂³×C₂₉	1	4	yes	—
392	#103	C₂³×C₂₉	1	8	yes	—
393	#102	C₂³×C₂₉	1	8	yes	—
394	#97	C₂³×C₂₉	1	8	yes	—
395	C₄×C₈	C₂³×C₂₉	1	4	yes	—
396	C₂₉	C₂×#3400	1	1	yes	characteristic, direct product factor, Sylow
397	C₂⁴	—	2	2	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	C₂×D₄×C₂₉	1	4	yes	—
409	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
410	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
411	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	8	4	no	—
427	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
432	Q₁₆	—	2	8	no	—
433	Q₁₆	—	4	8	no	—
434	SD₁₆	—	2	16	no	—
435	SD₁₆	—	4	8	no	—
436	SD₁₆	—	4	8	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	#41×C₂₉	1	4	yes	—
440	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
441	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
442	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
453	C₄⋊C₄	C₂×D₄×C₂₉	1	8	yes	—
454	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
455	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₄²	—	2	4	no	—
460	C₄²	—	2	8	no	—
461	C₄²	—	2	4	no	—
462	C₄²	C₂×D₄×C₂₉	1	4	yes	—
463	C₄²	C₂×D₄×C₂₉	1	2	yes	—
464	C₄²	C₂⁴×C₂₉	1	2	yes	—
465	C₄²	C₂⁴×C₂₉	1	4	yes	—
466	C₂³	—	2	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	C₂₉×#137	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
502	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
506	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
507	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
508	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
509	C₈	—	2	2	no	—
510	C₈	—	2	4	no	—
511	C₈	C₂×#41×C₂₉	1	4	yes	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	8	8	no	—
516	C₂²	C₂₉×#550	1	2	yes	—
517	C₂²	C₂×C₂₉×#137	1	2	yes	—
518	C₂²	C₂₉×#577	1	2	yes	—
519	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
520	C₄	—	2	4	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	C₂₉×#550	1	2	yes	—
529	C₄	C₂×C₂₉×#137	1	4	yes	—
530	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
531	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂	—	8	4	no	—
533	C₂	C₂₉×#3400	1	4	yes	direct product factor
534	C₂	C₂×C₂₉×#550	1	1	yes	characteristic
535	C₂	C₂²×C₂₉×#137	1	1	yes	characteristic
536	C₂	C₂×C₂₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄×Q₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#557	C₂	semidirect
3. C₂₉×#3400	C₂	direct (N × H)
4. C₂×C₂₉×#497	C₂	semidirect
6. C₂×C₂₉×#464	C₂	semidirect
7. C₂×C₂₉×#462	C₂	semidirect
9. C₂×C₂₉×#461	C₂	semidirect
10. C₂×C₂₉×#446	C₂	semidirect
11. C₂×C₂₉×#440	C₂	semidirect
12. C₂×C₄×Q₁₆×C₂₉	C₂	semidirect
21. C₂₉×#557	C₂²	semidirect
37. C₂₉×#497	C₂²	semidirect
39. C₂₉×#464	C₂²	semidirect
40. C₂₉×#462	C₂²	semidirect
41. C₂₉×#461	C₂²	semidirect
43. C₂₉×#446	C₂²	semidirect
44. C₂₉×#440	C₂²	semidirect
45. C₄×Q₁₆×C₂₉	C₂²	semidirect
197. C₂×#3400	C₂₉	direct (N × H)
245. C₂×#557	C₂×C₂₉	semidirect
246. #3400	C₂×C₂₉	direct (N × H)
247. C₂×#497	C₂×C₂₉	semidirect
249. C₂×#464	C₂×C₂₉	semidirect
250. C₂×#462	C₂×C₂₉	semidirect
252. C₂×#461	C₂×C₂₉	semidirect
253. C₂×#446	C₂×C₂₉	semidirect
254. C₂×#440	C₂×C₂₉	semidirect
255. C₂×C₄×Q₁₆	C₂×C₂₉	semidirect
284. #557	C₂²×C₂₉	semidirect
300. #497	C₂²×C₂₉	semidirect
302. #464	C₂²×C₂₉	semidirect
303. #462	C₂²×C₂₉	semidirect
304. #461	C₂²×C₂₉	semidirect
306. #446	C₂²×C₂₉	semidirect
307. #440	C₂²×C₂₉	semidirect
308. C₄×Q₁₆	C₂²×C₂₉	semidirect
319. C₂×C₂₉	#3400	direct (N × H)
396. C₂₉	C₂×#3400	direct (N × H)
533. C₂	C₂₉×#3400	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×#559	2
C₂×C₂₉×#557	2
C₂₉×#3400	2
C₂×C₂₉×#497	2
C₂×C₂₉×#492	2
C₂×C₂₉×#464	2
C₂×C₂₉×#462	2
C₂×C₂₉×#460	2
C₂×C₂₉×#461	2
C₂×C₂₉×#446	2
C₂×C₂₉×#440	2
C₂×C₄×Q₁₆×C₂₉	2
C₂×#3400	29

Subgroups — C2×C29×#3400 #20356297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3400 #20356297