Subgroups — #16828517

Order 3712.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#14271237	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271236	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271235	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271234	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271233	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271232	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271231	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271219	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271218	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271126	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271125	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11745168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₂₉	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	D₄×Dic₂₉	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
25	C₂×#90777	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#6597	C₂²	1	1	yes	characteristic, complemented
27	C₂×#90772	C₂²	1	1	yes	characteristic, complemented
28	C₂×#90772	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
31	#11745255	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₂₉	C₄	1	1	yes	characteristic
33	#11745243	C₄	1	1	yes	characteristic
34	#11745243	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×D₂₉	C₄	1	1	yes	characteristic
36	C₂²⋊C₄×D₂₉	C₄	1	1	yes	characteristic
37	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
38	C₄²×D₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊#6597	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊#6597	C₂²	1	1	yes	characteristic, complemented
45	#11745168	C₂²	1	1	yes	characteristic
46	#11745168	C₂²	1	1	yes	characteristic
47	#11745168	C₂²	1	1	yes	characteristic
48	#11745168	C₂²	1	1	yes	characteristic
49	#11745168	C₂²	1	1	yes	characteristic, complemented
50	#11745168	C₂²	1	1	yes	characteristic, complemented
51	#11745168	C₂²	1	1	yes	characteristic, complemented
52	#11745168	C₂²	1	1	yes	characteristic, complemented
53	#11745163	C₂²	1	1	yes	characteristic, complemented
54	#11745163	C₂²	1	1	yes	characteristic, complemented
55	#11745162	C₂²	1	1	yes	characteristic, complemented
56	#11745162	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊#6597	C₂²	1	1	yes	characteristic, complemented
58	#11745151	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
61	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
68	D₄×D₂₉	—	2	4	no	—
69	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₂₉	—	4	1	no	—
71	C₂×C₄×D₂₉	—	4	1	no	—
72	C₂×C₄×D₂₉	—	4	1	no	—
73	C₂×C₄×D₂₉	—	4	1	no	—
74	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
83	M₁₆×C₂₉	—	4	1	no	—
84	C₂×C₈×C₂₉	—	4	1	no	—
85	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₂₉	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
95	#90781	C₂×C₄	1	1	yes	characteristic
96	#90781	C₂×C₄	1	1	yes	characteristic
97	#90781	C₂×C₄	1	1	yes	characteristic
98	#90781	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
100	#90779	C₂×C₄	1	1	yes	characteristic
101	#90779	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
105	#90777	—	4	1	no	—
106	C₂×#6597	—	4	1	no	—
107	C₂×#6597	C₂³	1	1	yes	characteristic
108	C₂×#6597	C₂³	1	1	yes	characteristic
109	C₂×#6597	C₂³	1	1	yes	characteristic
110	C₂×#6597	C₂³	1	1	yes	characteristic
111	#90772	—	4	1	no	—
112	#90772	—	4	1	no	—
113	C₈×D₂₉	—	4	1	no	—
114	C₈×D₂₉	—	4	1	no	—
115	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₂₉	—	2	2	no	—
118	C₂²×D₂₉	—	4	1	no	—
119	C₂²×D₂₉	—	4	1	no	—
120	C₂²×D₂₉	—	4	1	no	—
121	C₂²×D₂₉	—	4	1	no	—
122	C₂²×D₂₉	M₁₆	1	4	yes	complemented
123	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
126	D₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	1	no	—
128	C₂×C₄×C₂₉	—	2	1	no	—
129	C₂×C₄×C₂₉	—	2	1	no	—
130	C₂×C₄×C₂₉	—	2	1	no	—
131	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₂₉	—	2	2	no	—
137	C₂²⋊D₂₉	—	2	2	no	—
138	C₂×Dic₂₉	—	4	1	no	—
139	C₂×Dic₂₉	—	4	1	no	—
140	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
145	D₁₁₆	—	2	2	no	—
146	C₄×D₂₉	—	2	2	no	—
147	C₄×D₂₉	—	2	1	no	—
148	C₄×D₂₉	—	2	1	no	—
149	C₄×D₂₉	—	2	1	no	—
150	C₄×D₂₉	—	2	1	no	—
151	C₄×D₂₉	—	2	1	no	—
152	C₄×D₂₉	—	2	1	no	—
153	C₄×D₂₉	—	4	1	no	—
154	C₄×D₂₉	—	4	1	no	—
155	C₄×D₂₉	—	4	1	no	—
156	C₄×D₂₉	—	4	1	no	—
157	C₄×D₂₉	—	4	1	no	—
158	C₈×C₂₉	—	2	1	no	—
159	C₈×C₂₉	—	2	1	no	—
160	C₈×C₂₉	—	2	1	no	—
161	C₈×C₂₉	—	2	1	no	—
162	#6597	—	2	1	no	—
163	#6597	—	2	1	no	—
164	#6597	—	2	1	no	—
165	#6597	—	2	1	no	—
166	#2973	—	29	1	no	maximal, Sylow
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	—	2	1	no	—
172	C₂²×C₂₉	C₂×M₁₆	1	2	yes	—
173	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₂₉	—	2	1	no	—
175	C₂×D₂₉	—	2	1	no	—
176	C₂×D₂₉	—	2	1	no	—
177	C₂×D₂₉	—	2	1	no	—
178	C₂×D₂₉	—	2	1	no	—
179	C₂×D₂₉	—	2	1	no	—
180	C₂×D₂₉	—	2	1	no	—
181	C₂×D₂₉	—	4	4	no	—
182	C₂×D₂₉	—	4	4	no	—
183	C₂×D₂₉	C₂×M₁₆	1	2	yes	—
184	C₂×D₂₉	C₂×M₁₆	1	2	yes	—
185	C₄×C₂₉	—	2	1	no	—
186	C₄×C₂₉	—	2	1	no	—
187	C₄×C₂₉	—	2	1	no	—
188	C₄×C₂₉	—	2	1	no	—
189	C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
190	C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
191	Dic₂₉	—	2	1	no	—
192	Dic₂₉	—	2	1	no	—
193	Dic₂₉	—	2	1	no	—
194	Dic₂₉	—	2	1	no	—
195	Dic₂₉	—	2	1	no	—
196	C₂×C₄×D₄	—	29	1	no	—
197	#435	—	29	1	no	—
198	#435	—	29	1	no	—
199	#435	—	29	1	no	—
200	#435	—	29	1	no	—
201	#435	—	29	1	no	—
202	#435	—	29	1	no	—
203	#435	—	29	1	no	—
204	#435	D₂₉	1	1	yes	characteristic, complemented
205	#432	—	29	1	no	—
206	#432	—	29	1	no	—
207	#407	—	29	1	no	—
208	#407	—	29	1	no	—
209	C₂×C₂²⋊C₈	—	29	1	no	—
210	C₂×C₂²⋊C₈	—	29	1	no	—
211	C₂×C₂₉	—	2	2	no	—
212	C₂×C₂₉	—	4	1	no	—
213	C₂×C₂₉	#518	1	1	yes	characteristic
214	C₂×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×C₂₉	#568	1	1	yes	characteristic
216	D₂₉	—	2	2	no	—
217	D₂₉	—	2	2	no	—
218	D₂₉	—	4	1	no	—
219	C₂²×D₄	—	29	1	no	—
220	C₂³×C₄	—	29	1	no	—
221	C₂³×C₄	—	29	1	no	—
222	C₂×M₁₆	—	29	1	no	—
223	C₂×M₁₆	—	29	1	no	—
224	C₂×M₁₆	—	29	1	no	—
225	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic, complemented
226	C₂²×C₈	—	29	1	no	—
227	C₂²×C₈	—	29	1	no	—
228	C₂²×C₈	—	29	1	no	—
229	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
230	C₄×D₄	—	29	1	no	—
231	C₄×D₄	—	29	1	no	—
232	C₄×D₄	—	29	1	no	—
233	C₄×D₄	—	29	1	no	—
234	C₄×D₄	—	29	1	no	—
235	C₄×D₄	—	29	1	no	—
236	C₄×D₄	—	29	1	no	—
237	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	—	29	1	no	—
239	C₂×C₂²⋊C₄	—	29	1	no	—
240	C₂×C₂²⋊C₄	—	29	1	no	—
241	C₂×C₄²	—	29	1	no	—
242	C₄⋊C₈	—	29	1	no	—
243	C₄⋊C₈	—	29	1	no	—
244	C₄⋊C₈	—	29	1	no	—
245	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
246	C₂²⋊C₈	—	29	1	no	—
247	C₂²⋊C₈	—	29	1	no	—
248	C₂²⋊C₈	—	29	1	no	—
249	C₂²⋊C₈	—	29	1	no	—
250	C₂²⋊C₈	—	29	1	no	—
251	C₂²⋊C₈	—	29	1	no	—
252	C₂²⋊C₈	—	29	1	no	—
253	C₂²⋊C₈	—	29	1	no	—
254	C₂²⋊C₈	—	29	1	no	—
255	C₂²⋊C₈	—	29	1	no	—
256	C₂²⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
257	C₂²⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
258	#97	—	29	1	no	—
259	#97	—	29	1	no	—
260	#97	—	29	1	no	—
261	#97	C₂×D₂₉	1	1	yes	characteristic, complemented
262	C₂₉	#2973	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	29	1	no	—
264	C₂⁴	—	29	1	no	—
265	C₂×D₄	—	29	1	no	—
266	C₂×D₄	—	29	1	no	—
267	C₂×D₄	—	29	1	no	—
268	C₂×D₄	—	58	4	no	—
269	C₂×D₄	C₄×D₂₉	1	1	yes	characteristic
270	C₂²×C₄	—	29	1	no	—
271	C₂²×C₄	—	29	1	no	—
272	C₂²×C₄	—	29	1	no	—
273	C₂²×C₄	—	29	1	no	—
274	C₂²×C₄	—	29	1	no	—
275	C₂²×C₄	—	29	1	no	—
276	C₂²×C₄	—	29	1	no	—
277	C₂²×C₄	—	29	1	no	—
278	C₂²×C₄	—	29	1	no	—
279	C₂²×C₄	—	29	1	no	—
280	C₂²×C₄	—	29	1	no	—
281	C₂²×C₄	—	116	1	no	—
282	C₂²×C₄	—	116	1	no	—
283	C₂²×C₄	—	116	1	no	—
284	C₂²×C₄	—	116	1	no	—
285	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	116	1	no	—
289	M₁₆	—	116	1	no	—
290	M₁₆	—	116	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	29	1	no	—
293	C₂×C₈	—	29	1	no	—
294	C₂×C₈	—	29	1	no	—
295	C₂×C₈	—	29	1	no	—
296	C₂×C₈	—	116	1	no	—
297	C₂×C₈	—	116	1	no	—
298	C₂×C₈	—	116	1	no	—
299	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
303	C₄⋊C₄	—	29	1	no	—
304	C₄⋊C₄	—	29	1	no	—
305	C₄⋊C₄	—	29	1	no	—
306	C₄⋊C₄	C₄×D₂₉	1	1	yes	characteristic
307	C₂²⋊C₄	—	29	1	no	—
308	C₂²⋊C₄	—	29	1	no	—
309	C₂²⋊C₄	—	29	1	no	—
310	C₂²⋊C₄	—	29	1	no	—
311	C₂²⋊C₄	—	29	1	no	—
312	C₂²⋊C₄	—	29	1	no	—
313	C₂²⋊C₄	C₄×D₂₉	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₂₉	1	1	yes	characteristic
315	C₄²	—	29	1	no	—
316	C₄²	—	29	1	no	—
317	C₄²	—	29	1	no	—
318	C₄²	C₂²×D₂₉	1	1	yes	characteristic
319	C₂³	—	29	1	no	—
320	C₂³	—	29	1	no	—
321	C₂³	—	29	4	no	—
322	C₂³	—	29	1	no	—
323	C₂³	—	58	2	no	—
324	C₂³	—	116	1	no	—
325	C₂³	—	116	1	no	—
326	C₂³	—	116	1	no	—
327	C₂³	—	116	1	no	—
328	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	58	2	no	—
332	D₄	—	58	2	no	—
333	D₄	—	58	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	29	1	no	—
339	C₂×C₄	—	29	1	no	—
340	C₂×C₄	—	29	1	no	—
341	C₂×C₄	—	29	1	no	—
342	C₂×C₄	—	29	1	no	—
343	C₂×C₄	—	58	2	no	—
344	C₂×C₄	—	58	1	no	—
345	C₂×C₄	—	58	1	no	—
346	C₂×C₄	—	58	1	no	—
347	C₂×C₄	—	58	1	no	—
348	C₂×C₄	—	58	1	no	—
349	C₂×C₄	—	58	1	no	—
350	C₂×C₄	—	116	1	no	—
351	C₂×C₄	—	116	1	no	—
352	C₂×C₄	—	116	1	no	—
353	C₂×C₄	—	116	1	no	—
354	C₂×C₄	—	116	1	no	—
355	C₂×C₄	—	116	1	no	—
356	C₂×C₄	—	116	1	no	—
357	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	58	1	no	—
367	C₈	—	58	1	no	—
368	C₈	—	58	1	no	—
369	C₈	—	58	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	29	2	no	—
376	C₂²	—	29	2	no	—
377	C₂²	—	58	1	no	—
378	C₂²	—	58	1	no	—
379	C₂²	—	58	1	no	—
380	C₂²	—	58	1	no	—
381	C₂²	—	58	1	no	—
382	C₂²	—	58	1	no	—
383	C₂²	—	58	1	no	—
384	C₂²	—	116	4	no	—
385	C₂²	—	116	4	no	—
386	C₂²	M₁₆×D₂₉	1	2	yes	—
387	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	58	1	no	—
393	C₄	—	58	1	no	—
394	C₄	—	58	1	no	—
395	C₄	—	58	1	no	—
396	C₄	—	58	1	no	—
397	C₄	#11745359	1	1	yes	characteristic
398	C₄	#11745364	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	58	2	no	—
402	C₂	—	58	2	no	—
403	C₂	—	116	1	no	—
404	C₂	#14271635	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₂₉	1	1	yes	characteristic
406	C₂	#14271928	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#435	C₂
prime radical	C₂×D₄×D₂₉	C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	#435	D₂₉
hypocenter	C₂₉	#2973
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #14271237	C₂	semidirect
3. #14271236	C₂	semidirect
4. #14271235	C₂	semidirect
5. #14271234	C₂	semidirect
6. #14271233	C₂	semidirect
7. #14271232	C₂	semidirect
8. #14271231	C₂	semidirect
9. #14271219	C₂	semidirect
10. #14271218	C₂	semidirect
11. #14271126	C₂	semidirect
12. #14271125	C₂	semidirect
13. C₂×#11745168	C₂	semidirect
14. C₂²⋊C₈×D₂₉	C₂	semidirect
15. C₂₉×#435	C₂	semidirect
19. C₂×M₁₆×C₂₉	C₂²	semidirect
20. C₂²×C₈×C₂₉	C₂²	semidirect
25. C₂×#90777	C₂²	semidirect
26. C₂²×#6597	C₂²	semidirect
27. C₂×#90772	C₂²	semidirect
28. C₂×#90772	C₂²	semidirect
29. C₂×C₈×D₂₉	C₂²	semidirect
30. C₂×C₈×D₂₉	C₂²	semidirect
39. C₂₉×C₄⋊C₈	C₂²	semidirect
40. C₂₉×C₂²⋊C₈	C₂²	semidirect
41. C₂₉×C₂²⋊C₈	C₂²	semidirect
42. C₂₉×#97	C₂²	semidirect
43. C₂²⋊#6597	C₂²	semidirect
44. C₂²⋊#6597	C₂²	semidirect
49. #11745168	C₂²	semidirect
50. #11745168	C₂²	semidirect
51. #11745168	C₂²	semidirect
52. #11745168	C₂²	semidirect
53. #11745163	C₂²	semidirect
54. #11745163	C₂²	semidirect
55. #11745162	C₂²	semidirect
56. #11745162	C₂²	semidirect
57. C₄⋊#6597	C₂²	semidirect
58. #11745151	C₂²	semidirect
122. C₂²×D₂₉	M₁₆	semidirect
204. #435	D₂₉	semidirect
225. C₂×M₁₆	C₂×D₂₉	semidirect
229. C₂²×C₈	C₂×D₂₉	semidirect
245. C₄⋊C₈	C₂×D₂₉	semidirect
256. C₂²⋊C₈	C₂×D₂₉	semidirect
257. C₂²⋊C₈	C₂×D₂₉	semidirect
261. #97	C₂×D₂₉	semidirect
262. C₂₉	#2973	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×D₄×D₂₉	2
#14271237	2
#14271236	2
#14271235	2
#14271234	2
#14271233	2
#14271232	2
#14271231	2
#14271219	2
#14271218	2
#14271126	2
#14271125	2
C₂×#11745168	2
C₂²⋊C₈×D₂₉	2
C₂₉×#435	2
#2973	29