Subgroups — #16828225

Order 3712.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#90772	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#14271239	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271238	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271236	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271235	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271233	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271226	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271185	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271125	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271125	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271115	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	M₁₆×D₂₉	—	2	4	no	—
28	C₂×#90772	—	2	4	no	—
29	C₂×#90772	C₂²	1	1	yes	characteristic
30	C₂×#90772	C₂²	1	1	yes	characteristic
31	C₂×#90772	C₂²	1	1	yes	characteristic
32	C₂×#90772	C₂²	1	1	yes	characteristic
33	C₂×#90772	C₂²	1	1	yes	characteristic, complemented
34	C₂×#90772	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
37	#11745255	C₄	1	1	yes	characteristic
38	C₄⋊C₄×D₂₉	C₄	1	1	yes	characteristic
39	#11745243	C₄	1	1	yes	characteristic
40	#11745243	C₄	1	1	yes	characteristic
41	C₂²⋊C₄×D₂₉	C₄	1	1	yes	characteristic
42	C₂²⋊C₄×D₂₉	C₄	1	1	yes	characteristic
43	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
44	C₄²×D₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#6597	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#6597	C₂²	1	1	yes	characteristic, complemented
51	#11745168	C₂²	1	1	yes	characteristic, complemented
52	#11745168	C₂²	1	1	yes	characteristic, complemented
53	#11745168	C₂²	1	1	yes	characteristic, complemented
54	#11745168	C₂²	1	1	yes	characteristic, complemented
55	#11745162	C₂²	1	1	yes	characteristic, complemented
56	#11745162	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₂₉	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#6597	C₂²	1	1	yes	characteristic, complemented
60	#11745151	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
62	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
63	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
70	D₄×D₂₉	—	2	4	no	—
71	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₂₉	—	2	2	no	—
73	C₂×C₄×D₂₉	—	2	2	no	—
74	C₂×C₄×D₂₉	—	2	2	no	—
75	C₂×C₄×D₂₉	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
85	M₁₆×C₂₉	—	2	2	no	—
86	C₂×C₈×C₂₉	—	2	2	no	—
87	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
94	C₄²×C₂₉	C₂³	1	1	yes	characteristic
95	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
97	#90781	C₂×C₄	1	1	yes	characteristic
98	#90781	C₂×C₄	1	1	yes	characteristic
99	#90781	C₂×C₄	1	1	yes	characteristic
100	#90781	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
102	#90779	C₂×C₄	1	1	yes	characteristic
103	#90779	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
107	#90777	—	2	2	no	—
108	C₂×#6597	—	2	2	no	—
109	C₂×#6597	C₂³	1	1	yes	characteristic
110	C₂×#6597	C₂³	1	1	yes	characteristic
111	C₂×#6597	C₂³	1	1	yes	characteristic
112	C₂×#6597	C₂³	1	1	yes	characteristic
113	#90772	—	2	2	no	—
114	#90772	—	2	2	no	—
115	#90772	—	2	2	no	—
116	#90772	—	2	2	no	—
117	#90772	—	2	2	no	—
118	#90772	D₄	1	4	yes	complemented
119	C₈×D₂₉	—	2	2	no	—
120	C₈×D₂₉	—	2	2	no	—
121	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
122	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×D₂₉	—	2	2	no	—
124	C₂²×D₂₉	—	2	2	no	—
125	C₂²×D₂₉	—	2	2	no	—
126	C₂²×D₂₉	—	2	2	no	—
127	C₂²×D₂₉	—	4	1	no	—
128	C₂²×D₂₉	—	4	1	no	—
129	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
132	D₄×C₂₉	—	2	2	no	—
133	C₂×C₄×C₂₉	—	2	1	no	—
134	C₂×C₄×C₂₉	—	2	1	no	—
135	C₂×C₄×C₂₉	—	2	1	no	—
136	C₂×C₄×C₂₉	—	2	1	no	—
137	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₂₉	—	2	2	no	—
143	C₂²⋊D₂₉	M₁₆	1	4	yes	complemented
144	C₂×Dic₂₉	—	2	2	no	—
145	C₂×Dic₂₉	—	2	2	no	—
146	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
151	D₁₁₆	—	2	2	no	—
152	C₄×D₂₉	—	2	2	no	—
153	C₄×D₂₉	—	2	2	no	—
154	C₄×D₂₉	—	2	1	no	—
155	C₄×D₂₉	—	2	1	no	—
156	C₄×D₂₉	—	2	1	no	—
157	C₄×D₂₉	—	2	1	no	—
158	C₄×D₂₉	—	2	2	no	—
159	C₄×D₂₉	—	2	2	no	—
160	C₄×D₂₉	—	2	2	no	—
161	C₄×D₂₉	—	4	1	no	—
162	C₄×D₂₉	C₂×D₄	1	2	yes	—
163	C₄×D₂₉	#41	1	2	yes	—
164	C₈×C₂₉	—	2	1	no	—
165	C₈×C₂₉	—	2	1	no	—
166	C₈×C₂₉	—	2	1	no	—
167	C₈×C₂₉	C₂×D₄	1	2	yes	complemented
168	#6597	—	2	1	no	—
169	#6597	—	2	1	no	—
170	#6597	—	2	1	no	—
171	#6597	C₂×D₄	1	2	yes	complemented
172	D₄×M₁₆	—	29	1	no	maximal, Sylow
173	C₂²×C₂₉	—	2	1	no	—
174	C₂²×C₂₉	—	2	1	no	—
175	C₂²×C₂₉	—	2	1	no	—
176	C₂²×C₂₉	—	2	1	no	—
177	C₂²×C₂₉	—	2	1	no	—
178	C₂²×C₂₉	C₂×M₁₆	1	2	yes	complemented
179	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×D₂₉	—	2	1	no	—
181	C₂×D₂₉	—	2	1	no	—
182	C₂×D₂₉	—	2	1	no	—
183	C₂×D₂₉	—	2	1	no	—
184	C₂×D₂₉	—	2	1	no	—
185	C₂×D₂₉	—	2	1	no	—
186	C₂×D₂₉	—	2	1	no	—
187	C₂×D₂₉	—	4	4	no	—
188	C₂×D₂₉	—	4	4	no	—
189	C₂×D₂₉	C₄×D₄	1	2	yes	—
190	C₂×D₂₉	C₂×M₁₆	1	2	yes	complemented
191	C₄×C₂₉	—	2	1	no	—
192	C₄×C₂₉	—	2	1	no	—
193	C₄×C₂₉	—	2	1	no	—
194	C₄×C₂₉	—	2	1	no	—
195	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
197	Dic₂₉	—	2	1	no	—
198	Dic₂₉	—	2	1	no	—
199	Dic₂₉	—	2	1	no	—
200	Dic₂₉	C₄×D₄	1	2	yes	—
201	Dic₂₉	C₂×M₁₆	1	2	yes	complemented
202	C₂²×M₁₆	—	29	1	no	—
203	C₂²×M₁₆	—	29	1	no	—
204	C₂×C₄×D₄	—	29	1	no	—
205	#436	—	29	1	no	—
206	#436	—	29	1	no	—
207	#435	—	29	1	no	—
208	#435	—	29	1	no	—
209	#435	—	29	1	no	—
210	#435	D₂₉	1	1	yes	characteristic, complemented
211	C₈×D₄	—	29	1	no	—
212	C₈×D₄	—	29	1	no	—
213	#423	—	29	1	no	—
214	#407	—	29	1	no	—
215	#407	—	29	1	no	—
216	C₄×M₁₆	—	29	1	no	—
217	C₂×C₂₉	—	2	2	no	—
218	C₂×C₂₉	—	4	1	no	—
219	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
221	C₂×C₂₉	#568	1	1	yes	characteristic
222	D₂₉	—	2	2	no	—
223	D₂₉	—	2	2	no	—
224	D₂₉	—	4	1	no	—
225	C₂²×D₄	—	29	1	no	—
226	C₂³×C₄	—	29	1	no	—
227	C₂³×C₄	—	29	1	no	—
228	C₂×M₁₆	—	29	1	no	—
229	C₂×M₁₆	—	29	1	no	—
230	C₂×M₁₆	—	29	1	no	—
231	C₂×M₁₆	—	29	1	no	—
232	C₂×M₁₆	—	29	1	no	—
233	C₂×M₁₆	—	29	1	no	—
234	C₂×M₁₆	—	29	1	no	—
235	C₂×M₁₆	—	58	4	no	—
236	C₂×M₁₆	—	58	4	no	—
237	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic, complemented
238	C₂²×C₈	—	29	1	no	—
239	C₂²×C₈	—	29	1	no	—
240	C₂²×C₈	—	29	1	no	—
241	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
242	C₄×D₄	—	29	1	no	—
243	C₄×D₄	—	29	1	no	—
244	C₄×D₄	—	29	1	no	—
245	C₄×D₄	—	29	1	no	—
246	C₄×D₄	—	29	1	no	—
247	C₄×D₄	—	29	1	no	—
248	C₄×D₄	—	29	1	no	—
249	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	29	1	no	—
251	C₂×C₂²⋊C₄	—	29	1	no	—
252	C₂×C₂²⋊C₄	—	29	1	no	—
253	C₂×C₄²	—	29	1	no	—
254	C₄⋊C₈	—	29	1	no	—
255	C₄⋊C₈	—	29	1	no	—
256	C₄⋊C₈	—	29	1	no	—
257	C₄⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	—	29	1	no	—
259	C₂²⋊C₈	—	29	1	no	—
260	C₂²⋊C₈	—	29	1	no	—
261	C₂²⋊C₈	—	29	1	no	—
262	C₂²⋊C₈	—	29	1	no	—
263	C₂²⋊C₈	—	29	1	no	—
264	C₂²⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
265	C₂²⋊C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
266	#97	—	29	1	no	—
267	#97	C₂×D₂₉	1	1	yes	characteristic, complemented
268	C₄×C₈	—	29	1	no	—
269	C₄×C₈	—	29	1	no	—
270	C₂₉	D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	29	1	no	—
272	C₂⁴	—	29	1	no	—
273	C₂×D₄	—	29	1	no	—
274	C₂×D₄	—	29	1	no	—
275	C₂×D₄	—	29	1	no	—
276	C₂×D₄	—	58	4	no	—
277	C₂×D₄	C₄×D₂₉	1	1	yes	characteristic
278	C₂²×C₄	—	29	1	no	—
279	C₂²×C₄	—	29	1	no	—
280	C₂²×C₄	—	29	1	no	—
281	C₂²×C₄	—	29	1	no	—
282	C₂²×C₄	—	29	1	no	—
283	C₂²×C₄	—	29	1	no	—
284	C₂²×C₄	—	29	1	no	—
285	C₂²×C₄	—	29	1	no	—
286	C₂²×C₄	—	29	1	no	—
287	C₂²×C₄	—	29	1	no	—
288	C₂²×C₄	—	29	1	no	—
289	C₂²×C₄	—	58	2	no	—
290	C₂²×C₄	—	58	2	no	—
291	C₂²×C₄	—	58	2	no	—
292	C₂²×C₄	—	58	2	no	—
293	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	29	4	no	—
297	M₁₆	—	58	2	no	—
298	M₁₆	—	58	2	no	—
299	M₁₆	—	58	2	no	—
300	M₁₆	—	58	2	no	—
301	M₁₆	—	58	2	no	—
302	M₁₆	—	58	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	29	1	no	—
305	C₂×C₈	—	29	1	no	—
306	C₂×C₈	—	29	1	no	—
307	C₂×C₈	—	29	1	no	—
308	C₂×C₈	—	58	2	no	—
309	C₂×C₈	—	58	2	no	—
310	C₂×C₈	—	58	2	no	—
311	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
313	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
314	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
315	C₄⋊C₄	—	29	1	no	—
316	C₄⋊C₄	—	29	1	no	—
317	C₄⋊C₄	—	29	1	no	—
318	C₄⋊C₄	C₄×D₂₉	1	1	yes	characteristic
319	C₂²⋊C₄	—	29	1	no	—
320	C₂²⋊C₄	—	29	1	no	—
321	C₂²⋊C₄	—	29	1	no	—
322	C₂²⋊C₄	—	29	1	no	—
323	C₂²⋊C₄	—	29	1	no	—
324	C₂²⋊C₄	—	29	1	no	—
325	C₂²⋊C₄	C₄×D₂₉	1	1	yes	characteristic
326	C₂²⋊C₄	C₄×D₂₉	1	1	yes	characteristic
327	C₄²	—	29	1	no	—
328	C₄²	—	29	1	no	—
329	C₄²	—	29	1	no	—
330	C₄²	C₂²×D₂₉	1	1	yes	characteristic
331	C₂³	—	29	1	no	—
332	C₂³	—	29	1	no	—
333	C₂³	—	29	1	no	—
334	C₂³	—	58	2	no	—
335	C₂³	—	58	2	no	—
336	C₂³	—	58	2	no	—
337	C₂³	—	58	2	no	—
338	C₂³	—	116	1	no	—
339	C₂³	—	116	1	no	—
340	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
341	C₂³	C₂×C₄×D₂₉	1	1	yes	characteristic
342	D₄	—	2	2	no	—
343	D₄	—	29	4	no	—
344	D₄	—	58	2	no	—
345	D₄	—	58	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	29	1	no	—
351	C₂×C₄	—	29	1	no	—
352	C₂×C₄	—	29	2	no	—
353	C₂×C₄	—	29	2	no	—
354	C₂×C₄	—	29	1	no	—
355	C₂×C₄	—	29	1	no	—
356	C₂×C₄	—	29	1	no	—
357	C₂×C₄	—	58	2	no	—
358	C₂×C₄	—	58	2	no	—
359	C₂×C₄	—	58	2	no	—
360	C₂×C₄	—	58	2	no	—
361	C₂×C₄	—	58	2	no	—
362	C₂×C₄	—	58	2	no	—
363	C₂×C₄	—	58	2	no	—
364	C₂×C₄	—	58	1	no	—
365	C₂×C₄	—	58	1	no	—
366	C₂×C₄	—	58	1	no	—
367	C₂×C₄	—	58	1	no	—
368	C₂×C₄	—	116	1	no	—
369	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
373	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	29	2	no	—
378	C₈	—	58	1	no	—
379	C₈	—	58	1	no	—
380	C₈	—	58	1	no	—
381	C₈	D₄×D₂₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	29	2	no	—
388	C₂²	—	29	2	no	—
389	C₂²	—	58	1	no	—
390	C₂²	—	58	1	no	—
391	C₂²	—	58	1	no	—
392	C₂²	—	58	1	no	—
393	C₂²	—	58	1	no	—
394	C₂²	—	58	1	no	—
395	C₂²	—	58	1	no	—
396	C₂²	—	116	4	no	—
397	C₂²	—	116	4	no	—
398	C₂²	M₁₆×D₂₉	1	2	yes	complemented
399	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	29	2	no	—
405	C₄	—	29	2	no	—
406	C₄	—	58	1	no	—
407	C₄	—	58	1	no	—
408	C₄	—	58	1	no	—
409	C₄	C₂×D₄×D₂₉	1	1	yes	characteristic
410	C₄	#41×D₂₉	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	58	2	no	—
414	C₂	—	58	2	no	—
415	C₂	—	116	1	no	—
416	C₂	C₄×D₄×D₂₉	1	1	yes	characteristic
417	C₂	C₂×M₁₆×D₂₉	1	1	yes	characteristic
418	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	D₄×M₁₆
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
1. C₂²×#90772	C₂	semidirect
2. C₂×M₁₆×D₂₉	C₂	semidirect
4. #14271239	C₂	semidirect
5. #14271238	C₂	semidirect
6. #14271236	C₂	semidirect
7. #14271235	C₂	semidirect
8. #14271233	C₂	semidirect
9. C₈×C₂²⋊D₂₉	C₂	semidirect
10. #14271226	C₂	semidirect
11. #14271185	C₂	semidirect
12. #14271125	C₂	semidirect
13. #14271125	C₂	semidirect
14. #14271115	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
33. C₂×#90772	C₂²	semidirect
34. C₂×#90772	C₂²	semidirect
35. C₂×C₈×D₂₉	C₂²	semidirect
36. C₂×C₈×D₂₉	C₂²	semidirect
45. C₂₉×C₄⋊C₈	C₂²	semidirect
46. C₂₉×C₂²⋊C₈	C₂²	semidirect
47. C₂₉×C₂²⋊C₈	C₂²	semidirect
48. C₂₉×#97	C₂²	semidirect
49. C₂²⋊#6597	C₂²	semidirect
50. C₂²⋊#6597	C₂²	semidirect
51. #11745168	C₂²	semidirect
52. #11745168	C₂²	semidirect
53. #11745168	C₂²	semidirect
54. #11745168	C₂²	semidirect
55. #11745162	C₂²	semidirect
56. #11745162	C₂²	semidirect
57. C₈×Dic₂₉	C₂²	semidirect
58. C₈×Dic₂₉	C₂²	semidirect
59. C₄⋊#6597	C₂²	semidirect
60. #11745151	C₂²	semidirect
118. #90772	D₄	semidirect
143. C₂²⋊D₂₉	M₁₆	semidirect
167. C₈×C₂₉	C₂×D₄	semidirect
171. #6597	C₂×D₄	semidirect
178. C₂²×C₂₉	C₂×M₁₆	semidirect
190. C₂×D₂₉	C₂×M₁₆	semidirect
201. Dic₂₉	C₂×M₁₆	semidirect
210. #435	D₂₉	semidirect
237. C₂×M₁₆	C₂×D₂₉	semidirect
241. C₂²×C₈	C₂×D₂₉	semidirect
257. C₄⋊C₈	C₂×D₂₉	semidirect
264. C₂²⋊C₈	C₂×D₂₉	semidirect
265. C₂²⋊C₈	C₂×D₂₉	semidirect
267. #97	C₂×D₂₉	semidirect
270. C₂₉	D₄×M₁₆	semidirect
381. C₈	D₄×D₂₉	semidirect
398. C₂²	M₁₆×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#90772	2
C₂×M₁₆×D₂₉	2
C₄×D₄×D₂₉	2
#14271239	2
#14271238	2
#14271236	2
#14271235	2
#14271233	2
C₈×C₂²⋊D₂₉	2
#14271226	2
#14271185	2
#14271125	2
#14271115	2
C₂₉×#435	2
D₄×M₁₆	29