Subgroups — #16833563

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	#14271887	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271886	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271866	C₂	1	1	yes	maximal, characteristic, complemented
4	#14271861	C₂	1	2	yes	maximal, complemented
5	#14271855	C₂	1	2	yes	maximal, complemented
6	#14271851	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271840	C₂	1	2	yes	maximal, complemented
8	#14271840	C₂	1	2	yes	maximal, complemented
9	#14271817	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271808	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271808	C₂	1	1	yes	maximal, characteristic, complemented
12	#14271787	C₂	1	1	yes	maximal, characteristic, complemented
13	#14271776	C₂	1	1	yes	maximal, characteristic, complemented
14	#14271762	C₂	1	2	yes	maximal, complemented
15	#14271753	C₂	1	2	yes	maximal, complemented
16	#14271700	C₂	1	1	yes	maximal, characteristic, complemented
17	#14271699	C₂	1	2	yes	maximal, complemented
18	#14271698	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#11745260	C₂	1	2	yes	maximal, complemented
20	#14271642	C₂	1	1	yes	maximal, characteristic, complemented
21	#14271635	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#90807	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#90807	C₂²	1	1	yes	characteristic
25	C₂×#90807	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
29	C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
30	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
31	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
32	C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
38	#11745309	C₂²	1	2	yes	—
39	#11745309	C₂²	1	1	yes	characteristic
40	#11745309	C₂²	1	2	yes	complemented
41	#11745308	C₂²	1	1	yes	characteristic, complemented
42	#11745308	C₂²	1	2	yes	complemented
43	#11745308	C₂²	1	2	yes	complemented
44	Q₈×Dic₂₉	C₂²	1	2	yes	complemented
45	D₄×Dic₂₉	C₂²	1	1	yes	characteristic
46	#11745292	C₂²	1	2	yes	—
47	#11745292	C₂²	1	2	yes	—
48	#11745292	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₂₉	C₂²	1	2	yes	complemented
52	C₂×#90781	C₂²	1	2	yes	—
53	C₂×#90781	C₂²	1	2	yes	—
54	C₂×#90781	C₂²	1	2	yes	—
55	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	complemented
56	C₂×#90779	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₂₉	C₂²	1	2	yes	complemented
58	#11745260	C₂²	1	2	yes	—
59	#11745260	C₂²	1	2	yes	—
60	#11745260	C₂²	1	2	yes	—
61	#11745260	C₂²	1	2	yes	—
62	#11745260	C₂²	1	1	yes	characteristic
63	#11745260	C₂²	1	2	yes	complemented
64	#11745260	C₂²	1	2	yes	complemented
65	#11745260	C₂²	1	2	yes	complemented
66	#11745260	C₂²	1	2	yes	complemented
67	#11745260	C₂²	1	2	yes	complemented
68	#11745260	C₂²	1	2	yes	complemented
69	#11745260	C₂²	1	1	yes	characteristic, complemented
70	#11745259	C₂²	1	1	yes	characteristic
71	#11745259	C₂²	1	1	yes	characteristic
72	#11745259	C₂²	1	1	yes	characteristic, complemented
73	#11745259	C₂²	1	1	yes	characteristic, complemented
74	#11745257	C₂²	1	1	yes	characteristic
75	#11745257	C₂²	1	1	yes	characteristic
76	#11745257	C₂²	1	1	yes	characteristic
77	#11745257	C₂²	1	2	yes	complemented
78	#11745256	C₂²	1	2	yes	—
79	#11745256	C₂²	1	1	yes	characteristic
80	#11745256	C₂²	1	2	yes	complemented
81	#11745256	C₂²	1	2	yes	complemented
82	#11745256	C₂²	1	2	yes	complemented
83	#11745256	C₂²	1	1	yes	characteristic, complemented
84	#11745255	C₂²	1	1	yes	characteristic
85	#11745255	C₂²	1	2	yes	complemented
86	#11745255	C₂²	1	2	yes	complemented
87	#11745254	C₂²	1	1	yes	characteristic
88	#11745254	C₂²	1	2	yes	complemented
89	#11745254	C₂²	1	2	yes	complemented
90	#11745254	C₂²	1	2	yes	complemented
91	#11745254	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic, complemented
93	#11745252	C₂²	1	2	yes	complemented
94	#11745252	C₂²	1	2	yes	complemented
95	#11745252	C₂²	1	2	yes	complemented
96	#11745252	C₂²	1	1	yes	characteristic, complemented
97	#11745249	C₂²	1	1	yes	characteristic, complemented
98	#11745249	C₂²	1	1	yes	characteristic, complemented
99	#11745248	C₂²	1	2	yes	—
100	#11745248	C₂²	1	2	yes	—
101	#11745248	C₂²	1	2	yes	complemented
102	#11745248	C₂²	1	2	yes	complemented
103	#11745244	C₂²	1	2	yes	—
104	#11745244	C₂²	1	2	yes	—
105	#11745243	C₂²	1	2	yes	—
106	#11745243	C₂²	1	2	yes	complemented
107	#11745243	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₂₉	C₂²	1	2	yes	—
109	#11745239	C₂²	1	2	yes	complemented
110	#11745239	C₂²	1	2	yes	complemented
111	#11745237	C₂²	1	1	yes	characteristic
112	#11745237	C₂²	1	1	yes	characteristic
113	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
114	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
115	C₄×D₁₁₆	C₂²	1	1	yes	characteristic
116	C₄×D₁₁₆	C₂²	1	1	yes	characteristic, complemented
117	#11745234	C₂²	1	1	yes	characteristic
118	#11745234	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₂₉	C₂²	1	1	yes	characteristic, complemented
120	#11745231	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₅₈	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₉	C₂³	1	2	yes	—
124	C₂×Q₈×C₂₉	C₂³	1	2	yes	—
125	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₂₉	C₂³	1	2	yes	—
133	C₂²×Dic₂₉	C₂³	1	2	yes	—
134	C₂²×Dic₂₉	C₂³	1	2	yes	—
135	C₂²×Dic₂₉	C₂³	1	2	yes	—
136	#90807	—	2	4	no	—
137	#90807	—	2	4	no	—
138	D₄×D₂₉	—	2	4	no	—
139	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
140	C₂×D₁₁₆	C₂³	1	2	yes	—
141	C₂×D₁₁₆	C₂³	1	2	yes	—
142	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
143	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
144	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₂₉	C₂³	1	2	yes	—
149	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₂₉	C₂³	1	2	yes	—
151	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₂₉	C₂³	1	2	yes	—
153	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
154	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
158	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
165	C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
169	C₄²×C₂₉	C₂³	1	1	yes	characteristic
170	C₄²×C₂₉	C₂³	1	1	yes	characteristic
171	C₄²×C₂₉	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₂₉	C₂³	1	2	yes	—
173	#90781	C₂³	1	1	yes	characteristic
174	#90781	C₂³	1	1	yes	characteristic
175	#90781	C₂³	1	1	yes	characteristic
176	#90781	C₂³	1	2	yes	—
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	1	yes	characteristic
186	#90781	C₂³	1	2	yes	—
187	#90781	C₂³	1	1	yes	characteristic
188	#90781	C₂³	1	1	yes	characteristic
189	#90781	C₂³	1	2	yes	—
190	#90781	C₂³	1	2	yes	—
191	#90781	C₂³	1	2	yes	—
192	#90781	C₂³	1	1	yes	characteristic
193	#90781	C₂³	1	2	yes	—
194	#90781	C₂³	1	1	yes	characteristic
195	#90781	C₂³	1	1	yes	characteristic
196	#90781	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₂₉	C₂³	1	2	yes	—
199	C₄⋊Dic₂₉	C₂³	1	2	yes	—
200	C₄⋊Dic₂₉	C₂³	1	2	yes	—
201	C₄⋊Dic₂₉	C₂³	1	2	yes	—
202	C₄⋊Dic₂₉	C₂³	1	2	yes	—
203	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₂₉	C₂³	1	2	yes	—
206	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
207	#90779	C₂³	1	1	yes	characteristic
208	#90779	C₂³	1	2	yes	—
209	#90779	C₂³	1	2	yes	—
210	#90779	C₂³	1	2	yes	—
211	#90779	C₂³	1	1	yes	characteristic
212	#90779	C₂³	1	2	yes	—
213	#90779	C₂³	1	1	yes	characteristic
214	#90779	C₂³	1	2	yes	—
215	#90779	C₂³	1	1	yes	characteristic
216	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
217	C₄×Dic₂₉	C₂³	1	2	yes	—
218	C₄×Dic₂₉	C₂³	1	2	yes	—
219	C₄×Dic₂₉	C₂³	1	2	yes	—
220	C₄×Dic₂₉	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₂³×C₂₉	C₂⁴	1	2	yes	—
226	C₂²×D₂₉	—	2	4	no	—
227	C₂²×D₂₉	—	4	2	no	—
228	C₂²×D₂₉	—	4	2	no	—
229	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₂₉	C₂⁴	1	2	yes	—
231	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₂₉	C₂⁴	1	1	yes	characteristic
233	Q₈×C₂₉	—	4	1	no	—
234	Q₈×C₂₉	—	4	2	no	—
235	D₄×C₂₉	#41	1	4	yes	—
236	C₂×C₄×C₂₉	—	4	2	no	—
237	C₂×C₄×C₂₉	—	4	2	no	—
238	C₂×C₄×C₂₉	—	4	2	no	—
239	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
242	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₂₉	C₂⁴	1	2	yes	—
245	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₂₉	—	2	4	no	—
250	C₂²⋊D₂₉	—	2	4	no	—
251	C₂²⋊D₂₉	—	2	4	no	—
252	C₂×Dic₂₉	—	2	4	no	—
253	C₂×Dic₂₉	—	2	4	no	—
254	C₂×Dic₂₉	—	4	2	no	—
255	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₂₉	C₂⁴	1	2	yes	—
258	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₂₉	C₂⁴	1	2	yes	—
261	C₂×Dic₂₉	C₂⁴	1	2	yes	—
262	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
263	D₁₁₆	—	2	2	no	—
264	D₁₁₆	—	4	2	no	—
265	D₁₁₆	—	4	1	no	—
266	D₁₁₆	—	4	1	no	—
267	D₁₁₆	—	4	2	no	—
268	D₁₁₆	—	4	1	no	—
269	C₄×D₂₉	—	2	2	no	—
270	C₄×D₂₉	—	2	2	no	—
271	C₄×D₂₉	—	2	2	no	—
272	C₄×D₂₉	—	4	1	no	—
273	C₄×D₂₉	—	4	2	no	—
274	C₄×D₂₉	—	4	2	no	—
275	C₄×D₂₉	—	4	2	no	—
276	C₄×D₂₉	—	4	1	no	—
277	Dic₅₈	—	2	2	no	—
278	Dic₅₈	—	2	2	no	—
279	#3521	—	29	1	no	maximal, Sylow
280	C₂²×C₂₉	—	2	2	no	—
281	C₂²×C₂₉	—	2	2	no	—
282	C₂²×C₂₉	C₂×#41	1	4	yes	—
283	C₂²×C₂₉	C₂⁵	1	1	yes	characteristic
284	C₂×D₂₉	—	2	1	no	—
285	C₂×D₂₉	—	2	1	no	—
286	C₂×D₂₉	—	2	1	no	—
287	C₂×D₂₉	—	2	2	no	—
288	C₂×D₂₉	—	2	1	no	—
289	C₂×D₂₉	—	2	1	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	1	no	—
300	C₄×C₂₉	—	2	1	no	—
301	C₄×C₂₉	—	2	2	no	—
302	C₄×C₂₉	—	2	1	no	—
303	C₄×C₂₉	—	2	2	no	—
304	C₄×C₂₉	—	2	1	no	—
305	C₄×C₂₉	—	2	1	no	—
306	C₄×C₂₉	C₂×#41	1	2	yes	—
307	Dic₂₉	—	2	2	no	—
308	Dic₂₉	—	2	2	no	—
309	Dic₂₉	—	2	1	no	—
310	Dic₂₉	—	2	1	no	—
311	Dic₂₉	—	2	1	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	D₂₉	1	1	yes	characteristic, complemented
318	#553	—	29	1	no	—
319	#553	—	29	2	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	1	no	—
332	#529	—	29	2	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	—	29	1	no	—
338	C₂×C₂₉	—	2	4	no	—
339	C₂×C₂₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₂₉	#585	1	1	yes	characteristic
341	C₂×C₂₉	#585	1	1	yes	characteristic
342	D₂₉	—	4	1	no	—
343	D₂₉	—	4	1	no	—
344	D₂₉	—	4	2	no	—
345	D₂₉	—	4	1	no	—
346	C₂×#41	—	29	1	no	—
347	C₂×#41	—	29	1	no	—
348	C₂²×D₄	—	29	1	no	—
349	C₄⋊Q₈	—	29	1	no	—
350	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
351	#126	—	29	1	no	—
352	#126	—	29	2	no	—
353	#126	—	29	2	no	—
354	#126	—	29	2	no	—
355	#126	—	29	2	no	—
356	#126	—	29	2	no	—
357	#126	—	29	2	no	—
358	#126	—	29	2	no	—
359	#126	—	29	1	no	—
360	#126	—	29	2	no	—
361	#126	—	29	2	no	—
362	#126	—	29	2	no	—
363	#125	—	29	2	no	—
364	#125	—	29	1	no	—
365	#125	—	29	2	no	—
366	#125	—	29	2	no	—
367	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
368	#125	C₂×D₂₉	1	1	yes	characteristic, complemented
369	#124	—	29	2	no	—
370	#124	—	29	1	no	—
371	#124	—	29	2	no	—
372	#124	—	29	1	no	—
373	#124	—	29	1	no	—
374	#123	—	29	2	no	—
375	#123	—	29	1	no	—
376	#123	—	29	1	no	—
377	#123	—	29	2	no	—
378	#123	—	29	2	no	—
379	#123	—	29	2	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	2	no	—
386	C₂²⋊Q₈	—	29	2	no	—
387	C₂²⋊Q₈	—	29	1	no	—
388	C₂²⋊Q₈	—	29	1	no	—
389	C₂²⋊Q₈	—	29	1	no	—
390	C₂²⋊Q₈	—	29	1	no	—
391	C₂²⋊Q₈	C₂×D₂₉	1	2	yes	complemented
392	C₂²⋊Q₈	C₂×D₂₉	1	2	yes	complemented
393	C₂²⋊Q₈	C₂×D₂₉	1	2	yes	complemented
394	#121	—	29	2	no	—
395	#121	—	29	2	no	—
396	#121	—	29	2	no	—
397	#121	—	29	1	no	—
398	#121	—	29	1	no	—
399	#121	—	29	2	no	—
400	#121	—	29	1	no	—
401	#120	—	29	2	no	—
402	#120	—	29	2	no	—
403	C₄×Q₈	—	29	2	no	—
404	C₄×Q₈	—	29	1	no	—
405	C₄×Q₈	—	29	1	no	—
406	C₄×Q₈	—	29	1	no	—
407	C₄×Q₈	—	29	1	no	—
408	C₄×Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
409	C₄×D₄	—	29	1	no	—
410	C₄×D₄	—	29	2	no	—
411	C₄×D₄	—	29	2	no	—
412	C₄×D₄	—	29	2	no	—
413	C₄×D₄	—	29	1	no	—
414	C₄×D₄	—	29	2	no	—
415	C₄×D₄	—	29	2	no	—
416	C₄×D₄	—	29	2	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	1	no	—
422	C₄×D₄	—	29	1	no	—
423	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
424	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₂₉	1	1	yes	characteristic
426	#117	—	29	1	no	—
427	#117	—	29	1	no	—
428	#117	—	29	2	no	—
429	#117	—	29	2	no	—
430	#117	—	29	2	no	—
431	#117	—	29	2	no	—
432	#117	—	29	2	no	—
433	#117	—	29	1	no	—
434	#117	—	29	1	no	—
435	C₂×C₄⋊C₄	—	29	2	no	—
436	C₂×C₄⋊C₄	—	29	2	no	—
437	C₂×C₄⋊C₄	—	29	1	no	—
438	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	complemented
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	—	29	2	no	—
444	C₂×C₄²	—	29	1	no	—
445	C₂₉	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	—	29	2	no	—
447	#41	—	58	4	no	—
448	#41	—	58	4	no	—
449	C₂×Q₈	—	29	1	no	—
450	C₂×Q₈	—	29	1	no	—
451	C₂×Q₈	C₂²×D₂₉	1	2	yes	—
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	2	no	—
456	C₂×D₄	—	29	1	no	—
457	C₂×D₄	—	29	1	no	—
458	C₂×D₄	—	29	1	no	—
459	C₂×D₄	—	29	2	no	—
460	C₂×D₄	—	29	2	no	—
461	C₂×D₄	—	29	1	no	—
462	C₂×D₄	—	58	4	no	—
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	1	no	—
470	C₂²×C₄	—	29	1	no	—
471	C₂²×C₄	—	29	1	no	—
472	C₂²×C₄	—	29	2	no	—
473	C₂²×C₄	—	29	2	no	—
474	C₂²×C₄	—	29	2	no	—
475	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
476	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
477	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
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	2	no	—
485	C₄⋊C₄	—	29	2	no	—
486	C₄⋊C₄	—	29	2	no	—
487	C₄⋊C₄	—	29	1	no	—
488	C₄⋊C₄	—	29	1	no	—
489	C₄⋊C₄	—	29	1	no	—
490	C₄⋊C₄	—	29	2	no	—
491	C₄⋊C₄	—	29	2	no	—
492	C₄⋊C₄	—	29	2	no	—
493	C₄⋊C₄	—	29	2	no	—
494	C₄⋊C₄	—	29	1	no	—
495	C₄⋊C₄	—	29	1	no	—
496	C₄⋊C₄	—	29	2	no	—
497	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
500	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
502	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
506	C₄⋊C₄	C₂²×D₂₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	29	2	no	—
509	C₂²⋊C₄	—	29	1	no	—
510	C₂²⋊C₄	—	29	2	no	—
511	C₂²⋊C₄	—	29	1	no	—
512	C₂²⋊C₄	—	29	1	no	—
513	C₂²⋊C₄	—	29	1	no	—
514	C₂²⋊C₄	—	29	2	no	—
515	C₂²⋊C₄	—	29	2	no	—
516	C₂²⋊C₄	—	29	2	no	—
517	C₂²⋊C₄	—	29	2	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	1	no	—
523	C₂²⋊C₄	—	29	2	no	—
524	C₂²⋊C₄	—	29	1	no	—
525	C₂²⋊C₄	—	29	1	no	—
526	C₂²⋊C₄	—	29	2	no	—
527	C₂²⋊C₄	—	29	2	no	—
528	C₂²⋊C₄	—	29	2	no	—
529	C₂²⋊C₄	—	29	1	no	—
530	C₂²⋊C₄	—	29	1	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	1	no	—
537	C₄²	—	29	1	no	—
538	C₄²	—	29	1	no	—
539	C₄²	—	29	2	no	—
540	C₄²	—	29	2	no	—
541	C₄²	—	29	2	no	—
542	C₄²	—	29	2	no	—
543	C₄²	—	29	2	no	—
544	C₄²	—	29	2	no	—
545	C₄²	C₂²×D₂₉	1	1	yes	characteristic
546	C₄²	C₂²×D₂₉	1	1	yes	characteristic
547	C₄²	C₂²×D₂₉	1	1	yes	characteristic
548	C₂³	—	29	1	no	—
549	C₂³	—	29	2	no	—
550	C₂³	—	29	1	no	—
551	C₂³	—	29	1	no	—
552	C₂³	—	58	4	no	—
553	C₂³	—	116	2	no	—
554	C₂³	—	116	2	no	—
555	C₂³	C₂³×D₂₉	1	2	yes	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	58	2	no	—
559	Q₈	—	58	2	no	—
560	D₄	—	58	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	1	no	—
567	D₄	—	116	2	no	—
568	D₄	—	116	1	no	—
569	D₄	#90809	1	4	yes	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	29	1	no	—
574	C₂×C₄	—	29	1	no	—
575	C₂×C₄	—	29	1	no	—
576	C₂×C₄	—	29	2	no	—
577	C₂×C₄	—	29	2	no	—
578	C₂×C₄	—	29	2	no	—
579	C₂×C₄	—	29	1	no	—
580	C₂×C₄	—	29	1	no	—
581	C₂×C₄	—	58	4	no	—
582	C₂×C₄	—	58	4	no	—
583	C₂×C₄	—	58	2	no	—
584	C₂×C₄	—	58	2	no	—
585	C₂×C₄	—	58	2	no	—
586	C₂×C₄	—	116	1	no	—
587	C₂×C₄	—	116	2	no	—
588	C₂×C₄	—	116	2	no	—
589	C₂×C₄	—	116	2	no	—
590	C₂×C₄	—	116	1	no	—
591	C₂×C₄	—	116	2	no	—
592	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
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	2	yes	—
597	C₂×C₄	C₂³×D₂₉	1	2	yes	—
598	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	58	1	no	—
605	C₂²	—	58	1	no	—
606	C₂²	—	58	1	no	—
607	C₂²	—	58	2	no	—
608	C₂²	—	58	1	no	—
609	C₂²	—	58	2	no	—
610	C₂²	—	58	1	no	—
611	C₂²	—	58	1	no	—
612	C₂²	—	58	1	no	—
613	C₂²	—	58	1	no	—
614	C₂²	—	58	2	no	—
615	C₂²	—	58	1	no	—
616	C₂²	—	232	4	no	—
617	C₂²	C₂×#90809	1	4	yes	—
618	C₂²	C₂⁴×D₂₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	58	1	no	—
629	C₄	—	58	1	no	—
630	C₄	—	58	1	no	—
631	C₄	—	58	2	no	—
632	C₄	—	58	2	no	—
633	C₄	—	58	1	no	—
634	C₄	—	58	2	no	—
635	C₄	—	58	1	no	—
636	C₄	C₂×#90809	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	116	1	no	—
639	C₂	—	116	2	no	—
640	C₂	—	116	1	no	—
641	C₂	—	116	1	no	—
642	C₂	C₂²×#90809	1	1	yes	characteristic
643	C₂	#14271998	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	C₂₉×#554	C₂
hypercenter	#554	D₂₉
hypocenter	C₂₉	#3521
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #14271887	C₂	semidirect
2. #14271886	C₂	semidirect
3. #14271866	C₂	semidirect
4. #14271861	C₂	semidirect
5. #14271855	C₂	semidirect
6. #14271851	C₂	semidirect
7. #14271840	C₂	semidirect
8. #14271840	C₂	semidirect
9. #14271817	C₂	semidirect
10. #14271808	C₂	semidirect
11. #14271808	C₂	semidirect
12. #14271787	C₂	semidirect
13. #14271776	C₂	semidirect
14. #14271762	C₂	semidirect
15. #14271753	C₂	semidirect
16. #14271700	C₂	semidirect
17. #14271699	C₂	semidirect
18. #14271698	C₂	semidirect
19. C₂×#11745260	C₂	semidirect
20. #14271642	C₂	semidirect
21. #14271635	C₂	semidirect
22. C₄×#90807	C₂	semidirect
23. C₂₉×#554	C₂	semidirect
27. C₂₉×C₄⋊Q₈	C₂²	semidirect
28. C₂₉×#125	C₂²	semidirect
29. C₂₉×#125	C₂²	semidirect
30. C₂₉×C₂²⋊Q₈	C₂²	semidirect
31. C₂₉×C₂²⋊Q₈	C₂²	semidirect
32. C₂₉×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₂₉	C₂²	semidirect
37. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
40. #11745309	C₂²	semidirect
41. #11745308	C₂²	semidirect
42. #11745308	C₂²	semidirect
43. #11745308	C₂²	semidirect
44. Q₈×Dic₂₉	C₂²	semidirect
48. #11745292	C₂²	semidirect
50. C₄×C₂²⋊D₂₉	C₂²	semidirect
51. C₄×C₂²⋊D₂₉	C₂²	semidirect
55. C₂×C₄⋊Dic₂₉	C₂²	semidirect
56. C₂×#90779	C₂²	semidirect
57. C₂×C₄×Dic₂₉	C₂²	semidirect
63. #11745260	C₂²	semidirect
64. #11745260	C₂²	semidirect
65. #11745260	C₂²	semidirect
66. #11745260	C₂²	semidirect
67. #11745260	C₂²	semidirect
68. #11745260	C₂²	semidirect
69. #11745260	C₂²	semidirect
72. #11745259	C₂²	semidirect
73. #11745259	C₂²	semidirect
77. #11745257	C₂²	semidirect
80. #11745256	C₂²	semidirect
81. #11745256	C₂²	semidirect
82. #11745256	C₂²	semidirect
83. #11745256	C₂²	semidirect
85. #11745255	C₂²	semidirect
86. #11745255	C₂²	semidirect
88. #11745254	C₂²	semidirect
89. #11745254	C₂²	semidirect
90. #11745254	C₂²	semidirect
91. #11745254	C₂²	semidirect
92. C₄⋊C₄×D₂₉	C₂²	semidirect
93. #11745252	C₂²	semidirect
94. #11745252	C₂²	semidirect
95. #11745252	C₂²	semidirect
96. #11745252	C₂²	semidirect
97. #11745249	C₂²	semidirect
98. #11745249	C₂²	semidirect
101. #11745248	C₂²	semidirect
102. #11745248	C₂²	semidirect
106. #11745243	C₂²	semidirect
107. #11745243	C₂²	semidirect
109. #11745239	C₂²	semidirect
110. #11745239	C₂²	semidirect
116. C₄×D₁₁₆	C₂²	semidirect
118. #11745234	C₂²	semidirect
119. C₄²×D₂₉	C₂²	semidirect
120. #11745231	C₂²	semidirect
121. C₄×Dic₅₈	C₂²	semidirect
122. C₄×Dic₅₈	C₂²	semidirect
317. #554	D₂₉	semidirect
350. C₄⋊Q₈	C₂×D₂₉	semidirect
367. #125	C₂×D₂₉	semidirect
368. #125	C₂×D₂₉	semidirect
391. C₂²⋊Q₈	C₂×D₂₉	semidirect
392. C₂²⋊Q₈	C₂×D₂₉	semidirect
393. C₂²⋊Q₈	C₂×D₂₉	semidirect
408. C₄×Q₈	C₂×D₂₉	semidirect
438. C₂×C₄⋊C₄	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
#14271887	2
#14271886	2
#14271866	2
#14271861	2
#14271855	2
#14271851	2
#14271840	2
#14271817	2
#14271808	2
#14271787	2
#14271776	2
#14271762	2
#14271753	2
#14271700	2
#14271699	2
#14271698	2
C₂×#11745260	2
#14271642	2
#14271635	2
C₄×#90807	2
C₂₉×#554	2
#3521	29