Subgroups — #16833560

Order 3712.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271885	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271881	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271872	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271862	C₂	1	2	yes	maximal, complemented
5	#14271857	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271854	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271846	C₂	1	2	yes	maximal, complemented
8	#14271842	C₂	1	2	yes	maximal, complemented
9	#14271837	C₂	1	2	yes	maximal, complemented
10	#14271812	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271808	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271801	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271785	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271771	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271755	C₂	1	2	yes	maximal, complemented
16	#14271746	C₂	1	2	yes	maximal, complemented
17	#14271697	C₂	1	1	yes	maximal, characteristic, complemented
18	#14271697	C₂	1	2	yes	maximal, complemented
19	#14271697	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11745238	C₂	1	2	yes	maximal, complemented
21	#14271642	C₂	1	1	yes	maximal, characteristic, complemented
22	#14271635	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×#90807	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
27	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
30	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
32	C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
33	C₂₉×#117	C₂²	1	2	yes	complemented
34	C₂₉×#117	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄²×C₂₉	C₂²	1	2	yes	complemented
36	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
37	#11745309	C₂²	1	1	yes	characteristic
38	#11745308	C₂²	1	1	yes	characteristic
39	#11745308	C₂²	1	1	yes	characteristic, complemented
40	#11745306	C₂²	1	1	yes	characteristic, complemented
41	#11745301	C₂²	1	2	yes	—
42	#11745301	C₂²	1	2	yes	complemented
43	#11745299	C₂²	1	2	yes	—
44	#11745297	C₂²	1	2	yes	complemented
45	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
46	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
47	#11745292	C₂²	1	1	yes	characteristic
48	#11745292	C₂²	1	1	yes	characteristic
49	#11745292	C₂²	1	2	yes	—
50	#11745291	C₂²	1	2	yes	—
51	#11745291	C₂²	1	1	yes	characteristic
52	#11745291	C₂²	1	2	yes	complemented
53	#11745291	C₂²	1	2	yes	complemented
54	#11745291	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₂₉	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	complemented
60	C₂×#90781	C₂²	1	2	yes	—
61	C₂×#90781	C₂²	1	2	yes	—
62	C₂×#90781	C₂²	1	2	yes	—
63	#11745286	C₂²	1	1	yes	characteristic, complemented
64	#11745286	C₂²	1	1	yes	characteristic, complemented
65	#11745286	C₂²	1	2	yes	complemented
66	C₂×#90779	C₂²	1	2	yes	complemented
67	C₂×#90779	C₂²	1	2	yes	complemented
68	C₂×#90779	C₂²	1	2	yes	complemented
69	#11745260	C₂²	1	2	yes	—
70	#11745260	C₂²	1	2	yes	complemented
71	#11745259	C₂²	1	1	yes	characteristic
72	#11745258	C₂²	1	2	yes	complemented
73	#11745258	C₂²	1	2	yes	complemented
74	#11745257	C₂²	1	1	yes	characteristic
75	#11745256	C₂²	1	2	yes	—
76	#11745256	C₂²	1	2	yes	complemented
77	#11745255	C₂²	1	1	yes	characteristic
78	#11745254	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
80	#11745252	C₂²	1	1	yes	characteristic, complemented
81	#11745251	C₂²	1	2	yes	complemented
82	#11745251	C₂²	1	2	yes	complemented
83	#11745250	C₂²	1	1	yes	characteristic, complemented
84	#11745249	C₂²	1	1	yes	characteristic, complemented
85	#11745248	C₂²	1	2	yes	—
86	#11745247	C₂²	1	2	yes	—
87	#11745246	C₂²	1	2	yes	complemented
88	#11745245	C₂²	1	2	yes	complemented
89	#11745244	C₂²	1	2	yes	—
90	#11745243	C₂²	1	2	yes	—
91	#11745243	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₂₉	C₂²	1	2	yes	—
93	#11745241	C₂²	1	2	yes	complemented
94	#11745240	C₂²	1	2	yes	complemented
95	#11745240	C₂²	1	2	yes	complemented
96	#11745239	C₂²	1	2	yes	complemented
97	#11745238	C₂²	1	2	yes	—
98	#11745238	C₂²	1	2	yes	—
99	#11745238	C₂²	1	2	yes	—
100	#11745238	C₂²	1	1	yes	characteristic
101	#11745238	C₂²	1	2	yes	complemented
102	#11745238	C₂²	1	2	yes	complemented
103	#11745238	C₂²	1	2	yes	complemented
104	#11745238	C₂²	1	2	yes	complemented
105	#11745238	C₂²	1	1	yes	characteristic, complemented
106	#11745237	C₂²	1	1	yes	characteristic
107	#11745237	C₂²	1	1	yes	characteristic
108	#11745237	C₂²	1	2	yes	complemented
109	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
110	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
111	C₄×D₁₁₆	C₂²	1	2	yes	complemented
112	#11745234	C₂²	1	1	yes	characteristic
113	#11745234	C₂²	1	1	yes	characteristic, complemented
114	#11745234	C₂²	1	2	yes	complemented
115	#11745234	C₂²	1	2	yes	complemented
116	#11745234	C₂²	1	2	yes	complemented
117	#11745232	C₂²	1	2	yes	complemented
118	#11745232	C₂²	1	1	yes	characteristic, complemented
119	#11745232	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₅₈	C₂²	1	2	yes	complemented
122	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₉	C₂³	1	2	yes	—
124	#41×C₂₉	—	2	4	no	—
125	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₉	C₂³	1	2	yes	—
127	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₉	C₂³	1	1	yes	characteristic
139	C₂²×Dic₂₉	C₂³	1	2	yes	—
140	C₂²×Dic₂₉	C₂³	1	2	yes	—
141	C₂²×Dic₂₉	C₂³	1	2	yes	—
142	#90807	—	2	4	no	—
143	D₄×D₂₉	—	2	4	no	—
144	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
145	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
146	C₂×D₁₁₆	C₂³	1	2	yes	—
147	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₂₉	C₂³	1	2	yes	—
150	C₂×C₄×D₂₉	C₂³	1	2	yes	—
151	C₂×C₄×D₂₉	C₂³	1	2	yes	—
152	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
153	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
154	C₂×Dic₅₈	C₂³	1	2	yes	—
155	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
162	C₄²×C₂₉	C₂³	1	1	yes	characteristic
163	C₄²×C₂₉	C₂³	1	2	yes	—
164	C₄²×C₂₉	C₂³	1	1	yes	characteristic
165	C₄²×C₂₉	C₂³	1	1	yes	characteristic
166	C₄²×C₂₉	C₂³	1	1	yes	characteristic
167	C₄²×C₂₉	C₂³	1	2	yes	—
168	C₄²×C₂₉	C₂³	1	2	yes	—
169	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
170	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₂₉	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
174	#90781	C₂³	1	1	yes	characteristic
175	#90781	C₂³	1	1	yes	characteristic
176	#90781	C₂³	1	1	yes	characteristic
177	#90781	C₂³	1	2	yes	—
178	#90781	C₂³	1	2	yes	—
179	#90781	C₂³	1	2	yes	—
180	#90781	C₂³	1	2	yes	—
181	#90781	C₂³	1	2	yes	—
182	#90781	C₂³	1	2	yes	—
183	#90781	C₂³	1	2	yes	—
184	#90781	C₂³	1	2	yes	—
185	#90781	C₂³	1	2	yes	—
186	#90781	C₂³	1	1	yes	characteristic
187	#90781	C₂³	1	1	yes	characteristic
188	#90781	C₂³	1	2	yes	—
189	#90781	C₂³	1	1	yes	characteristic
190	#90781	C₂³	1	1	yes	characteristic
191	#90781	C₂³	1	2	yes	—
192	#90781	C₂³	1	1	yes	characteristic
193	#90781	C₂³	1	2	yes	—
194	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₂₉	C₂³	1	2	yes	—
197	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₂₉	C₂³	1	2	yes	—
200	#90779	C₂³	1	1	yes	characteristic
201	#90779	C₂³	1	1	yes	characteristic
202	#90779	C₂³	1	1	yes	characteristic
203	#90779	C₂³	1	2	yes	—
204	#90779	C₂³	1	2	yes	—
205	#90779	C₂³	1	2	yes	—
206	#90779	C₂³	1	2	yes	—
207	#90779	C₂³	1	2	yes	—
208	#90779	C₂³	1	2	yes	—
209	#90779	C₂³	1	2	yes	—
210	#90779	C₂³	1	2	yes	—
211	#90779	C₂³	1	2	yes	—
212	#90779	C₂³	1	1	yes	characteristic
213	#90779	C₂³	1	1	yes	characteristic
214	#90779	C₂³	1	1	yes	characteristic
215	#90779	C₂³	1	2	yes	—
216	#90779	C₂³	1	1	yes	characteristic
217	#90779	C₂³	1	2	yes	—
218	#90779	C₂³	1	1	yes	characteristic
219	#90779	C₂³	1	2	yes	—
220	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₂₉	C₂³	1	2	yes	—
222	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
223	C₄×Dic₂₉	C₂³	1	2	yes	—
224	C₄×Dic₂₉	C₂³	1	2	yes	—
225	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₂₉	C₂⁴	1	2	yes	—
227	C₂²×D₂₉	—	2	4	no	—
228	C₂²×D₂₉	—	4	2	no	—
229	C₂²×D₂₉	—	4	2	no	—
230	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₂₉	C₂⁴	1	2	yes	—
232	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
233	Q₈×C₂₉	—	2	2	no	—
234	D₄×C₂₉	—	2	4	no	—
235	D₄×C₂₉	#41	1	4	yes	—
236	C₂×C₄×C₂₉	—	2	4	no	—
237	C₂×C₄×C₂₉	—	2	2	no	—
238	C₂×C₄×C₂₉	—	4	2	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	2	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₂₉	—	2	4	no	—
252	C₂²⋊D₂₉	—	2	4	no	—
253	C₂²⋊D₂₉	—	4	1	no	—
254	C₂²⋊D₂₉	—	4	2	no	—
255	C₂²⋊D₂₉	—	4	1	no	—
256	C₂×Dic₂₉	—	2	4	no	—
257	C₂×Dic₂₉	—	4	2	no	—
258	C₂×Dic₂₉	—	4	2	no	—
259	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₂₉	C₂⁴	1	2	yes	—
262	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₂₉	C₂⁴	1	2	yes	—
264	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₂₉	C₂⁴	1	2	yes	—
266	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
268	D₁₁₆	—	2	2	no	—
269	D₁₁₆	—	4	1	no	—
270	D₁₁₆	—	4	2	no	—
271	C₄×D₂₉	—	2	2	no	—
272	C₄×D₂₉	—	2	2	no	—
273	C₄×D₂₉	—	4	2	no	—
274	C₄×D₂₉	—	4	2	no	—
275	C₄×D₂₉	—	4	2	no	—
276	Dic₅₈	—	2	2	no	—
277	Dic₅₈	—	4	2	no	—
278	Dic₅₈	—	4	1	no	—
279	#3521	—	29	1	no	maximal, Sylow
280	C₂²×C₂₉	—	2	2	no	—
281	C₂²×C₂₉	—	2	2	no	—
282	C₂²×C₂₉	—	2	1	no	—
283	C₂²×C₂₉	—	2	1	no	—
284	C₂²×C₂₉	—	2	1	no	—
285	C₂²×C₂₉	C₂×#41	1	4	yes	—
286	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
287	C₂×D₂₉	—	2	1	no	—
288	C₂×D₂₉	—	2	1	no	—
289	C₂×D₂₉	—	2	2	no	—
290	C₂×D₂₉	—	2	1	no	—
291	C₂×D₂₉	—	2	2	no	—
292	C₂×D₂₉	—	2	2	no	—
293	C₂×D₂₉	—	2	1	no	—
294	C₂×D₂₉	—	2	1	no	—
295	C₂×D₂₉	—	2	1	no	—
296	C₂×D₂₉	—	8	4	no	—
297	C₄×C₂₉	—	2	1	no	—
298	C₄×C₂₉	—	2	2	no	—
299	C₄×C₂₉	—	2	2	no	—
300	C₄×C₂₉	—	2	1	no	—
301	C₄×C₂₉	—	2	1	no	—
302	C₄×C₂₉	—	2	2	no	—
303	C₄×C₂₉	—	2	1	no	—
304	C₄×C₂₉	—	2	1	no	—
305	C₄×C₂₉	C₂×#41	1	2	yes	—
306	Dic₂₉	—	2	2	no	—
307	Dic₂₉	—	2	1	no	—
308	Dic₂₉	—	2	1	no	—
309	Dic₂₉	—	2	1	no	—
310	Dic₂₉	—	2	1	no	—
311	Dic₂₉	—	2	2	no	—
312	Dic₂₉	—	2	1	no	—
313	Dic₂₉	—	2	2	no	—
314	Dic₂₉	—	2	1	no	—
315	#556	—	29	1	no	—
316	#556	—	29	1	no	—
317	#554	—	29	1	no	—
318	#553	—	29	2	no	—
319	#553	—	29	1	no	—
320	#552	—	29	1	no	—
321	#552	—	29	2	no	—
322	#551	—	29	2	no	—
323	#551	—	29	2	no	—
324	#547	—	29	1	no	—
325	#546	—	29	1	no	—
326	#546	—	29	1	no	—
327	#542	—	29	1	no	—
328	#541	—	29	1	no	—
329	#539	—	29	2	no	—
330	#538	—	29	2	no	—
331	#529	—	29	2	no	—
332	#529	—	29	1	no	—
333	#529	—	29	1	no	—
334	C₂×#126	—	29	2	no	—
335	#520	—	29	1	no	—
336	#518	—	29	1	no	—
337	C₄×#41	D₂₉	1	1	yes	characteristic, complemented
338	C₂×C₂₉	—	2	4	no	—
339	C₂×C₂₉	—	4	1	no	—
340	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
341	C₂×C₂₉	#585	1	1	yes	characteristic
342	C₂×C₂₉	#585	1	1	yes	characteristic
343	D₂₉	—	4	1	no	—
344	D₂₉	—	4	2	no	—
345	D₂₉	—	4	1	no	—
346	C₂×#41	—	29	1	no	—
347	C₂×#41	C₂×D₂₉	1	1	yes	characteristic
348	C₂²×D₄	—	29	1	no	—
349	C₄⋊Q₈	—	29	1	no	—
350	C₄⋊Q₈	—	29	1	no	—
351	#126	—	29	2	no	—
352	#126	—	29	2	no	—
353	#126	—	29	2	no	—
354	#126	—	29	1	no	—
355	#126	—	29	2	no	—
356	#126	—	29	2	no	—
357	#126	—	29	2	no	—
358	#126	—	29	2	no	—
359	#126	—	29	2	no	—
360	#126	—	29	2	no	—
361	#126	—	29	2	no	—
362	#126	—	29	1	no	—
363	#125	—	29	2	no	—
364	#125	—	29	2	no	—
365	#125	—	29	1	no	—
366	#125	—	29	2	no	—
367	#125	—	29	1	no	—
368	#125	—	29	1	no	—
369	#124	—	29	1	no	—
370	#124	—	29	2	no	—
371	#124	—	29	2	no	—
372	#124	—	29	1	no	—
373	#124	—	29	1	no	—
374	#123	—	29	2	no	—
375	#123	—	29	2	no	—
376	#123	—	29	1	no	—
377	#123	—	29	2	no	—
378	#123	—	29	2	no	—
379	#123	—	29	1	no	—
380	#123	—	29	2	no	—
381	#123	—	29	2	no	—
382	#123	—	29	2	no	—
383	#123	—	29	2	no	—
384	C₂²⋊Q₈	—	29	1	no	—
385	C₂²⋊Q₈	—	29	1	no	—
386	C₂²⋊Q₈	—	29	1	no	—
387	C₂²⋊Q₈	—	29	1	no	—
388	C₂²⋊Q₈	—	29	2	no	—
389	C₂²⋊Q₈	—	29	2	no	—
390	C₂²⋊Q₈	—	29	1	no	—
391	C₂²⋊Q₈	—	29	2	no	—
392	C₂²⋊Q₈	—	29	2	no	—
393	C₂²⋊Q₈	—	29	2	no	—
394	#121	—	29	2	no	—
395	#121	—	29	2	no	—
396	#121	—	29	1	no	—
397	#121	—	29	1	no	—
398	#121	—	29	2	no	—
399	#121	—	29	1	no	—
400	#121	—	29	2	no	—
401	#120	—	29	2	no	—
402	#120	—	29	2	no	—
403	C₄×Q₈	—	29	1	no	—
404	C₄×Q₈	—	29	1	no	—
405	C₄×Q₈	—	29	2	no	—
406	C₄×Q₈	—	29	1	no	—
407	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
408	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
409	C₄×D₄	—	29	1	no	—
410	C₄×D₄	—	29	1	no	—
411	C₄×D₄	—	29	2	no	—
412	C₄×D₄	—	29	2	no	—
413	C₄×D₄	—	29	1	no	—
414	C₄×D₄	—	29	1	no	—
415	C₄×D₄	—	29	2	no	—
416	C₄×D₄	—	29	1	no	—
417	C₄×D₄	—	29	2	no	—
418	C₄×D₄	—	29	2	no	—
419	C₄×D₄	—	29	1	no	—
420	C₄×D₄	—	29	1	no	—
421	C₄×D₄	—	29	2	no	—
422	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
423	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
424	C₄×D₄	C₂×D₂₉	1	2	yes	complemented
425	C₄×D₄	C₂×D₂₉	1	2	yes	complemented
426	#117	—	29	1	no	—
427	#117	—	29	2	no	—
428	#117	—	29	1	no	—
429	#117	—	29	1	no	—
430	#117	—	29	2	no	—
431	#117	—	29	2	no	—
432	#117	—	29	2	no	—
433	#117	C₂×D₂₉	1	2	yes	complemented
434	#117	C₂×D₂₉	1	1	yes	characteristic, complemented
435	C₂×C₄⋊C₄	—	29	2	no	—
436	C₂×C₄⋊C₄	—	29	2	no	—
437	C₂×C₄⋊C₄	—	29	2	no	—
438	C₂×C₄⋊C₄	—	29	1	no	—
439	C₂×C₂²⋊C₄	—	29	2	no	—
440	C₂×C₂²⋊C₄	—	29	2	no	—
441	C₂×C₂²⋊C₄	—	29	2	no	—
442	C₂×C₂²⋊C₄	—	29	2	no	—
443	C₂×C₄²	C₂×D₂₉	1	2	yes	complemented
444	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic, complemented
445	C₂₉	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	—	29	2	no	—
447	#41	—	2	4	no	—
448	#41	—	58	4	no	—
449	C₂×Q₈	—	29	1	no	—
450	C₂×Q₈	—	29	1	no	—
451	C₂×Q₈	—	29	2	no	—
452	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
453	C₂×D₄	—	29	2	no	—
454	C₂×D₄	—	29	2	no	—
455	C₂×D₄	—	29	1	no	—
456	C₂×D₄	—	29	2	no	—
457	C₂×D₄	—	29	1	no	—
458	C₂×D₄	—	29	1	no	—
459	C₂×D₄	—	29	1	no	—
460	C₂×D₄	—	29	2	no	—
461	C₂×D₄	—	58	4	no	—
462	C₂×D₄	C₂²×D₂₉	1	2	yes	—
463	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
464	C₂²×C₄	—	29	2	no	—
465	C₂²×C₄	—	29	2	no	—
466	C₂²×C₄	—	29	2	no	—
467	C₂²×C₄	—	29	1	no	—
468	C₂²×C₄	—	29	1	no	—
469	C₂²×C₄	—	29	2	no	—
470	C₂²×C₄	—	29	2	no	—
471	C₂²×C₄	—	29	2	no	—
472	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
473	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
476	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
478	C₄⋊C₄	—	29	1	no	—
479	C₄⋊C₄	—	29	2	no	—
480	C₄⋊C₄	—	29	1	no	—
481	C₄⋊C₄	—	29	1	no	—
482	C₄⋊C₄	—	29	2	no	—
483	C₄⋊C₄	—	29	2	no	—
484	C₄⋊C₄	—	29	1	no	—
485	C₄⋊C₄	—	29	2	no	—
486	C₄⋊C₄	—	29	2	no	—
487	C₄⋊C₄	—	29	2	no	—
488	C₄⋊C₄	—	29	2	no	—
489	C₄⋊C₄	—	29	2	no	—
490	C₄⋊C₄	—	29	2	no	—
491	C₄⋊C₄	—	29	1	no	—
492	C₄⋊C₄	—	29	1	no	—
493	C₄⋊C₄	—	29	1	no	—
494	C₄⋊C₄	—	29	1	no	—
495	C₄⋊C₄	—	29	1	no	—
496	C₄⋊C₄	—	29	2	no	—
497	C₄⋊C₄	—	29	2	no	—
498	C₄⋊C₄	—	29	2	no	—
499	C₄⋊C₄	—	29	1	no	—
500	C₄⋊C₄	—	29	2	no	—
501	C₄⋊C₄	—	29	1	no	—
502	C₄⋊C₄	—	29	1	no	—
503	C₄⋊C₄	—	29	2	no	—
504	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
508	C₂²⋊C₄	—	29	2	no	—
509	C₂²⋊C₄	—	29	2	no	—
510	C₂²⋊C₄	—	29	1	no	—
511	C₂²⋊C₄	—	29	2	no	—
512	C₂²⋊C₄	—	29	1	no	—
513	C₂²⋊C₄	—	29	1	no	—
514	C₂²⋊C₄	—	29	2	no	—
515	C₂²⋊C₄	—	29	1	no	—
516	C₂²⋊C₄	—	29	1	no	—
517	C₂²⋊C₄	—	29	1	no	—
518	C₂²⋊C₄	—	29	2	no	—
519	C₂²⋊C₄	—	29	2	no	—
520	C₂²⋊C₄	—	29	2	no	—
521	C₂²⋊C₄	—	29	2	no	—
522	C₂²⋊C₄	—	29	2	no	—
523	C₂²⋊C₄	—	29	2	no	—
524	C₂²⋊C₄	—	29	2	no	—
525	C₂²⋊C₄	—	29	2	no	—
526	C₂²⋊C₄	—	29	1	no	—
527	C₂²⋊C₄	—	29	1	no	—
528	C₂²⋊C₄	—	29	1	no	—
529	C₂²⋊C₄	—	29	2	no	—
530	C₂²⋊C₄	—	29	2	no	—
531	C₂²⋊C₄	—	29	2	no	—
532	C₂²⋊C₄	—	29	1	no	—
533	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₂₉	1	2	yes	—
536	C₄²	—	29	2	no	—
537	C₄²	—	29	2	no	—
538	C₄²	—	29	2	no	—
539	C₄²	—	29	1	no	—
540	C₄²	—	29	1	no	—
541	C₄²	C₂²×D₂₉	1	1	yes	characteristic
542	C₄²	C₂²×D₂₉	1	1	yes	characteristic
543	C₄²	C₂²×D₂₉	1	1	yes	characteristic
544	C₄²	C₂²×D₂₉	1	2	yes	—
545	C₄²	C₂²×D₂₉	1	2	yes	—
546	C₄²	C₂²×D₂₉	1	1	yes	characteristic
547	C₄²	C₂²×D₂₉	1	2	yes	—
548	C₂³	—	29	1	no	—
549	C₂³	—	29	2	no	—
550	C₂³	—	29	1	no	—
551	C₂³	—	58	4	no	—
552	C₂³	—	116	2	no	—
553	C₂³	—	116	2	no	—
554	C₂³	C₂³×D₂₉	1	1	yes	characteristic
555	C₂³	C₂³×D₂₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	58	2	no	—
558	Q₈	—	116	1	no	—
559	Q₈	—	116	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	58	4	no	—
562	D₄	—	58	4	no	—
563	D₄	—	58	2	no	—
564	D₄	—	116	1	no	—
565	D₄	—	116	2	no	—
566	D₄	—	116	2	no	—
567	D₄	—	116	1	no	—
568	D₄	—	116	1	no	—
569	D₄	#90805	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	29	1	no	—
577	C₂×C₄	—	29	2	no	—
578	C₂×C₄	—	29	1	no	—
579	C₂×C₄	—	29	2	no	—
580	C₂×C₄	—	29	1	no	—
581	C₂×C₄	—	29	1	no	—
582	C₂×C₄	—	29	2	no	—
583	C₂×C₄	—	29	1	no	—
584	C₂×C₄	—	29	1	no	—
585	C₂×C₄	—	58	4	no	—
586	C₂×C₄	—	58	2	no	—
587	C₂×C₄	—	58	2	no	—
588	C₂×C₄	—	116	2	no	—
589	C₂×C₄	—	116	2	no	—
590	C₂×C₄	—	116	2	no	—
591	C₂×C₄	—	116	2	no	—
592	C₂×C₄	—	116	2	no	—
593	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₂₉	1	2	yes	—
595	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₂₉	1	2	yes	—
599	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₂₉	1	2	yes	—
601	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	58	1	no	—
608	C₂²	—	58	1	no	—
609	C₂²	—	58	2	no	—
610	C₂²	—	58	1	no	—
611	C₂²	—	58	2	no	—
612	C₂²	—	58	2	no	—
613	C₂²	—	58	1	no	—
614	C₂²	—	58	1	no	—
615	C₂²	—	58	1	no	—
616	C₂²	—	232	4	no	—
617	C₂²	C₂×#90805	1	4	yes	—
618	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	58	1	no	—
628	C₄	—	58	1	no	—
629	C₄	—	58	2	no	—
630	C₄	—	58	2	no	—
631	C₄	—	58	1	no	—
632	C₄	—	58	1	no	—
633	C₄	—	58	2	no	—
634	C₄	—	58	1	no	—
635	C₄	—	58	1	no	—
636	C₄	C₂×#90805	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	116	1	no	—
640	C₂	—	116	2	no	—
641	C₂	—	116	1	no	—
642	C₂	C₂²×#90805	1	1	yes	characteristic
643	C₂	#14271999	1	1	yes	characteristic
644	C₂	#14271999	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁵
Fitting	C₄×#41×C₂₉	C₂
hypercenter	C₄×#41	D₂₉
hypocenter	C₂₉	#3521
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #14271885	C₂	semidirect
2. #14271881	C₂	semidirect
3. #14271872	C₂	semidirect
4. #14271862	C₂	semidirect
5. #14271857	C₂	semidirect
6. #14271854	C₂	semidirect
7. #14271846	C₂	semidirect
8. #14271842	C₂	semidirect
9. #14271837	C₂	semidirect
10. #14271812	C₂	semidirect
11. #14271808	C₂	semidirect
12. #14271801	C₂	semidirect
13. #14271785	C₂	semidirect
14. #14271771	C₂	semidirect
15. #14271755	C₂	semidirect
16. #14271746	C₂	semidirect
17. #14271697	C₂	semidirect
18. #14271697	C₂	semidirect
19. #14271697	C₂	semidirect
20. C₂×#11745238	C₂	semidirect
21. #14271642	C₂	semidirect
22. #14271635	C₂	semidirect
23. C₄×#41×C₂₉	C₂	semidirect
27. C₄×Q₈×C₂₉	C₂²	semidirect
28. C₄×Q₈×C₂₉	C₂²	semidirect
31. C₄×D₄×C₂₉	C₂²	semidirect
32. C₄×D₄×C₂₉	C₂²	semidirect
33. C₂₉×#117	C₂²	semidirect
34. C₂₉×#117	C₂²	semidirect
35. C₂×C₄²×C₂₉	C₂²	semidirect
36. C₂×C₄²×C₂₉	C₂²	semidirect
39. #11745308	C₂²	semidirect
40. #11745306	C₂²	semidirect
42. #11745301	C₂²	semidirect
44. #11745297	C₂²	semidirect
52. #11745291	C₂²	semidirect
53. #11745291	C₂²	semidirect
54. #11745291	C₂²	semidirect
57. C₄×C₂²⋊D₂₉	C₂²	semidirect
58. C₄×C₂²⋊D₂₉	C₂²	semidirect
59. C₄×C₂²⋊D₂₉	C₂²	semidirect
63. #11745286	C₂²	semidirect
64. #11745286	C₂²	semidirect
65. #11745286	C₂²	semidirect
66. C₂×#90779	C₂²	semidirect
67. C₂×#90779	C₂²	semidirect
68. C₂×#90779	C₂²	semidirect
70. #11745260	C₂²	semidirect
72. #11745258	C₂²	semidirect
73. #11745258	C₂²	semidirect
76. #11745256	C₂²	semidirect
79. C₄⋊C₄×D₂₉	C₂²	semidirect
80. #11745252	C₂²	semidirect
81. #11745251	C₂²	semidirect
82. #11745251	C₂²	semidirect
83. #11745250	C₂²	semidirect
84. #11745249	C₂²	semidirect
87. #11745246	C₂²	semidirect
88. #11745245	C₂²	semidirect
91. #11745243	C₂²	semidirect
93. #11745241	C₂²	semidirect
94. #11745240	C₂²	semidirect
95. #11745240	C₂²	semidirect
96. #11745239	C₂²	semidirect
101. #11745238	C₂²	semidirect
102. #11745238	C₂²	semidirect
103. #11745238	C₂²	semidirect
104. #11745238	C₂²	semidirect
105. #11745238	C₂²	semidirect
108. #11745237	C₂²	semidirect
111. C₄×D₁₁₆	C₂²	semidirect
113. #11745234	C₂²	semidirect
114. #11745234	C₂²	semidirect
115. #11745234	C₂²	semidirect
116. #11745234	C₂²	semidirect
117. #11745232	C₂²	semidirect
118. #11745232	C₂²	semidirect
119. #11745232	C₂²	semidirect
120. C₄×Dic₅₈	C₂²	semidirect
121. C₄×Dic₅₈	C₂²	semidirect
122. C₄×Dic₅₈	C₂²	semidirect
337. C₄×#41	D₂₉	semidirect
407. C₄×Q₈	C₂×D₂₉	semidirect
408. C₄×Q₈	C₂×D₂₉	semidirect
424. C₄×D₄	C₂×D₂₉	semidirect
425. C₄×D₄	C₂×D₂₉	semidirect
433. #117	C₂×D₂₉	semidirect
434. #117	C₂×D₂₉	semidirect
443. C₂×C₄²	C₂×D₂₉	semidirect
444. C₂×C₄²	C₂×D₂₉	semidirect
445. C₂₉	#3521	semidirect

Maximal subgroups

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

subgroup	index
#14271885	2
#14271881	2
#14271872	2
#14271862	2
#14271857	2
#14271854	2
#14271846	2
#14271842	2
#14271837	2
#14271812	2
#14271808	2
#14271801	2
#14271785	2
#14271771	2
#14271755	2
#14271746	2
#14271697	2
C₂×#11745238	2
#14271642	2
#14271635	2
C₄×#41×C₂₉	2
#3521	29