Subgroups — #34058784

Order 19072.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750353	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750352	C₂	1	2	yes	maximal, complemented
3	#23750348	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750347	C₂	1	2	yes	maximal, complemented
5	#23750316	C₂	1	2	yes	maximal, complemented
6	#23750307	C₂	1	4	yes	maximal, complemented
7	#23750290	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750290	C₂	1	2	yes	maximal, complemented
9	#23750236	C₂	1	2	yes	maximal, complemented
10	#23750234	C₂	1	4	yes	maximal, complemented
11	#23750180	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750179	C₂	1	2	yes	maximal, complemented
13	#23750162	C₂	1	1	yes	maximal, characteristic
14	#23750160	C₂	1	2	yes	maximal
15	#23750101	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#557×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₁₄₉	C₂²	1	2	yes	—
20	#18011911	C₂²	1	1	yes	characteristic
21	#18011910	C₂²	1	2	yes	—
22	#18011910	C₂²	1	4	yes	—
23	#18011909	C₂²	1	2	yes	—
24	#18011906	C₂²	1	4	yes	—
25	#18011906	C₂²	1	2	yes	—
26	#18011906	C₂²	1	4	yes	—
27	#18011906	C₂²	1	4	yes	—
28	#18011905	C₂²	1	4	yes	—
29	#18011903	C₂²	1	2	yes	—
30	#18011902	C₂²	1	1	yes	characteristic
31	#18011902	C₂²	1	2	yes	—
32	#18011901	C₂²	1	4	yes	—
33	#18011901	C₂²	1	4	yes	—
34	#18011901	C₂²	1	4	yes	—
35	#18011901	C₂²	1	4	yes	—
36	#18011900	C₂²	1	1	yes	characteristic
37	#18011899	C₂²	1	2	yes	—
38	#18011896	C₂²	1	4	yes	—
39	#18011896	C₂²	1	2	yes	—
40	#18011891	C₂²	1	2	yes	—
41	#18011889	C₂²	1	4	yes	—
42	#18011889	C₂²	1	4	yes	—
43	#18011889	C₂²	1	4	yes	—
44	#18011887	C₂²	1	1	yes	characteristic
45	#18011887	C₂²	1	2	yes	—
46	#18011887	C₂²	1	2	yes	—
47	#18011887	C₂²	1	2	yes	—
48	#18011886	C₂²	1	1	yes	characteristic
49	Q₈×Dic₁₄₉	C₂²	1	2	yes	—
50	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
51	C₄×Dic₂₉₈	C₂²	1	4	yes	—
52	C₄×Dic₂₉₈	C₂²	1	2	yes	—
53	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
54	C₄×Dic₂₉₈	C₂²	1	2	yes	—
55	C₄×Dic₂₉₈	C₂²	1	2	yes	—
56	#18011876	C₂²	1	2	yes	—
57	#18011876	C₂²	1	2	yes	—
58	#18011876	C₂²	1	2	yes	—
59	#18011876	C₂²	1	4	yes	—
60	#18011876	C₂²	1	1	yes	characteristic
61	C₄×D₅₉₆	C₂²	1	2	yes	—
62	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
63	#18011873	C₂²	1	4	yes	—
64	#18011873	C₂²	1	2	yes	—
65	#18011869	C₂²	1	4	yes	—
66	#18011869	C₂²	1	2	yes	—
67	#18011869	C₂²	1	2	yes	—
68	#18011868	C₂²	1	2	yes	—
69	#18011868	C₂²	1	4	yes	—
70	#18011868	C₂²	1	4	yes	—
71	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
73	C₄²×D₁₄₉	C₂²	1	2	yes	—
74	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
76	C₄⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
77	#125×C₁₄₉	C₂²	1	2	yes	—
78	#125×C₁₄₉	C₂²	1	4	yes	—
79	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
80	C₄×Q₈×C₁₄₉	C₂²	1	2	yes	—
81	C₄×Q₈×C₁₄₉	C₂²	1	2	yes	—
82	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
83	C₂×Dic₂₉₈	C₂³	1	2	yes	—
84	C₂×Dic₂₉₈	C₂³	1	4	yes	—
85	C₂×Dic₂₉₈	C₂³	1	2	yes	—
86	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
87	Q₈×D₁₄₉	—	2	4	no	—
88	Q₈×D₁₄₉	—	2	8	no	—
89	C₂×D₅₉₆	C₂³	1	2	yes	—
90	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
92	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
94	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
97	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
99	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
100	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
101	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
102	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
105	#14558715	C₂³	1	2	yes	—
106	#14558715	C₂³	1	4	yes	—
107	#14558715	C₂³	1	4	yes	—
108	#14558715	C₂³	1	4	yes	—
109	#14558715	C₂³	1	2	yes	—
110	#14558715	C₂³	1	4	yes	—
111	#14558715	C₂³	1	4	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	2	yes	—
114	#14558715	C₂³	1	2	yes	—
115	#14558715	C₂³	1	2	yes	—
116	#14558713	C₂³	1	2	yes	—
117	#14558713	C₂³	1	4	yes	—
118	#14558713	C₂³	1	4	yes	—
119	#14558713	C₂³	1	2	yes	—
120	#14558713	C₂³	1	4	yes	—
121	#14558713	C₂³	1	2	yes	—
122	#14558713	C₂³	1	2	yes	—
123	#14558713	C₂³	1	2	yes	—
124	#14558713	C₂³	1	4	yes	—
125	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
126	C₄×Dic₁₄₉	C₂³	1	2	yes	—
127	C₄×Dic₁₄₉	C₂³	1	4	yes	—
128	C₄×Dic₁₄₉	C₂³	1	4	yes	—
129	C₄×Dic₁₄₉	C₂³	1	2	yes	—
130	C₄×Dic₁₄₉	C₂³	1	4	yes	—
131	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₄₉	C₂³	1	2	yes	—
133	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
134	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
135	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
136	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
139	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
141	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₄²×C₁₄₉	C₂³	1	4	yes	—
147	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄²×C₁₄₉	C₂³	1	2	yes	—
149	C₄²×C₁₄₉	C₂³	1	2	yes	—
150	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
151	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
152	Dic₂₉₈	—	2	4	no	—
153	Dic₂₉₈	—	2	4	no	—
154	Dic₂₉₈	—	2	8	no	—
155	Dic₂₉₈	#41	1	4	yes	—
156	D₅₉₆	—	2	4	no	—
157	D₅₉₆	—	2	2	no	—
158	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
160	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
163	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
164	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
165	C₄×D₁₄₉	—	2	4	no	—
166	C₄×D₁₄₉	—	2	2	no	—
167	C₄×D₁₄₉	—	2	2	no	—
168	C₄×D₁₄₉	—	2	4	no	—
169	C₄×D₁₄₉	—	2	2	no	—
170	C₄×D₁₄₉	—	2	4	no	—
171	C₄×D₁₄₉	—	2	8	no	—
172	Q₈×C₁₄₉	—	2	2	no	—
173	Q₈×C₁₄₉	—	2	4	no	—
174	Q₈×C₁₄₉	—	2	2	no	—
175	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
177	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
181	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₄₉	—	2	1	no	—
185	C₂×D₁₄₉	—	2	1	no	—
186	C₂×D₁₄₉	—	2	2	no	—
187	C₂×D₁₄₉	—	2	2	no	—
188	C₂×D₁₄₉	—	2	2	no	—
189	C₂×D₁₄₉	2₋¹⁺⁴	1	2	yes	—
190	C₄×C₁₄₉	—	2	2	no	—
191	C₄×C₁₄₉	—	2	4	no	—
192	C₄×C₁₄₉	—	2	2	no	—
193	C₄×C₁₄₉	—	2	2	no	—
194	C₄×C₁₄₉	—	2	1	no	—
195	C₄×C₁₄₉	—	2	2	no	—
196	C₄×C₁₄₉	C₂×#41	1	2	yes	—
197	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
198	Dic₁₄₉	—	2	1	no	—
199	Dic₁₄₉	—	2	2	no	—
200	Dic₁₄₉	—	2	1	no	—
201	Dic₁₄₉	—	2	2	no	—
202	Dic₁₄₉	—	2	1	no	—
203	Dic₁₄₉	—	2	4	no	—
204	Dic₁₄₉	C₂×#41	1	4	yes	—
205	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
206	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	D₁₄₉	—	2	2	no	—
209	D₁₄₉	—	4	2	no	—
210	C₁₄₉	#3523	1	1	yes	characteristic, complemented, Sylow
211	#3523	—	149	1	no	maximal, Sylow
212	#557	—	149	2	no	—
213	#557	—	149	1	no	—
214	#557	D₁₄₉	1	1	yes	characteristic, complemented
215	#556	—	149	2	no	—
216	#556	—	149	1	no	—
217	#552	—	149	4	no	—
218	#552	—	149	2	no	—
219	D₄×Q₈	—	149	2	no	—
220	D₄×Q₈	—	149	1	no	—
221	#541	—	149	2	no	—
222	#541	—	149	4	no	—
223	#533	—	149	1	no	—
224	#533	—	149	2	no	—
225	#529	—	149	2	no	—
226	#529	—	149	1	no	—
227	#519	—	149	2	no	—
228	C₂×C₄×Q₈	—	149	1	no	—
229	C₂²×Q₈	—	149	1	no	—
230	C₂²×Q₈	—	149	2	no	—
231	C₄⋊Q₈	—	149	2	no	—
232	C₄⋊Q₈	—	149	2	no	—
233	C₄⋊Q₈	—	149	4	no	—
234	C₄⋊Q₈	—	149	1	no	—
235	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
236	C₄⋊Q₈	C₂×D₁₄₉	1	2	yes	—
237	#126	—	149	2	no	—
238	#126	—	149	4	no	—
239	#126	—	149	4	no	—
240	#126	—	149	4	no	—
241	#126	—	149	4	no	—
242	#125	—	149	1	no	—
243	#125	—	149	4	no	—
244	#125	—	149	2	no	—
245	#125	—	149	4	no	—
246	#125	—	149	4	no	—
247	#125	—	149	4	no	—
248	#125	—	149	2	no	—
249	#125	C₂×D₁₄₉	1	2	yes	—
250	#125	C₂×D₁₄₉	1	4	yes	—
251	#124	—	149	1	no	—
252	#124	—	149	2	no	—
253	#123	—	149	2	no	—
254	#123	—	149	4	no	—
255	C₂²⋊Q₈	—	149	1	no	—
256	C₂²⋊Q₈	—	149	2	no	—
257	C₂²⋊Q₈	—	149	2	no	—
258	C₂²⋊Q₈	—	149	2	no	—
259	C₂²⋊Q₈	—	149	2	no	—
260	C₂²⋊Q₈	—	149	4	no	—
261	C₂²⋊Q₈	—	149	4	no	—
262	C₂²⋊Q₈	—	149	4	no	—
263	#121	—	149	1	no	—
264	C₄×Q₈	—	149	1	no	—
265	C₄×Q₈	—	149	2	no	—
266	C₄×Q₈	—	149	1	no	—
267	C₄×Q₈	—	149	2	no	—
268	C₄×Q₈	—	149	4	no	—
269	C₄×Q₈	—	149	2	no	—
270	C₄×Q₈	—	149	2	no	—
271	C₄×Q₈	—	149	1	no	—
272	C₄×Q₈	—	149	2	no	—
273	C₄×Q₈	—	149	4	no	—
274	C₄×Q₈	—	149	2	no	—
275	C₄×Q₈	—	149	2	no	—
276	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
277	C₄×Q₈	C₂×D₁₄₉	1	2	yes	—
278	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
279	C₄×Q₈	C₂×D₁₄₉	1	2	yes	—
280	C₄×D₄	—	149	4	no	—
281	C₄×D₄	—	149	2	no	—
282	C₄×D₄	—	149	2	no	—
283	C₄×D₄	—	149	1	no	—
284	#117	—	149	4	no	—
285	#117	—	149	2	no	—
286	#117	—	149	2	no	—
287	#117	—	149	2	no	—
288	#117	—	149	4	no	—
289	#117	—	149	4	no	—
290	C₂×C₄⋊C₄	—	149	2	no	—
291	C₂×C₄⋊C₄	—	149	1	no	—
292	C₂×C₄²	—	149	2	no	—
293	C₂×C₄²	—	149	1	no	—
294	C₂×Q₈	—	298	4	no	—
295	C₂×Q₈	—	298	8	no	—
296	C₂×Q₈	—	149	2	no	—
297	C₂×Q₈	—	149	2	no	—
298	C₂×Q₈	—	149	4	no	—
299	C₂×Q₈	—	149	1	no	—
300	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
301	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
302	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
303	C₂×D₄	—	149	2	no	—
304	C₂×D₄	—	149	1	no	—
305	C₂²×C₄	—	149	1	no	—
306	C₂²×C₄	—	149	1	no	—
307	C₂²×C₄	—	149	2	no	—
308	C₂²×C₄	—	149	2	no	—
309	C₂²×C₄	—	149	1	no	—
310	C₂²×C₄	—	149	4	no	—
311	C₂²×C₄	—	149	2	no	—
312	C₄⋊C₄	—	149	2	no	—
313	C₄⋊C₄	—	149	2	no	—
314	C₄⋊C₄	—	149	1	no	—
315	C₄⋊C₄	—	149	2	no	—
316	C₄⋊C₄	—	149	2	no	—
317	C₄⋊C₄	—	149	4	no	—
318	C₄⋊C₄	—	149	2	no	—
319	C₄⋊C₄	—	149	2	no	—
320	C₄⋊C₄	—	149	4	no	—
321	C₄⋊C₄	—	149	2	no	—
322	C₄⋊C₄	—	149	4	no	—
323	C₄⋊C₄	—	149	4	no	—
324	C₄⋊C₄	—	149	2	no	—
325	C₄⋊C₄	—	149	1	no	—
326	C₄⋊C₄	—	149	2	no	—
327	C₄⋊C₄	—	149	4	no	—
328	C₄⋊C₄	—	149	4	no	—
329	C₄⋊C₄	—	149	4	no	—
330	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
332	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
333	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
336	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
338	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
339	C₂²⋊C₄	—	149	2	no	—
340	C₂²⋊C₄	—	149	2	no	—
341	C₂²⋊C₄	—	149	4	no	—
342	C₂²⋊C₄	—	149	4	no	—
343	C₂²⋊C₄	—	149	2	no	—
344	C₂²⋊C₄	—	149	4	no	—
345	C₂²⋊C₄	—	149	2	no	—
346	C₂²⋊C₄	—	149	4	no	—
347	C₂²⋊C₄	—	149	2	no	—
348	C₄²	—	149	1	no	—
349	C₄²	—	149	2	no	—
350	C₄²	—	149	2	no	—
351	C₄²	—	149	1	no	—
352	C₄²	—	149	2	no	—
353	C₄²	—	149	1	no	—
354	C₄²	—	149	4	no	—
355	C₄²	—	149	4	no	—
356	C₄²	—	149	4	no	—
357	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
358	C₄²	C₂²×D₁₄₉	1	2	yes	—
359	C₄²	C₂²×D₁₄₉	1	4	yes	—
360	C₄²	C₂²×D₁₄₉	1	2	yes	—
361	C₂³	—	149	2	no	—
362	C₂³	—	149	1	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	298	4	no	—
367	Q₈	—	298	8	no	—
368	Q₈	—	298	4	no	—
369	Q₈	—	149	4	no	—
370	D₄	—	298	4	no	—
371	D₄	—	298	2	no	—
372	C₂×C₄	—	298	4	no	—
373	C₂×C₄	—	298	2	no	—
374	C₂×C₄	—	298	4	no	—
375	C₂×C₄	—	298	8	no	—
376	C₂×C₄	—	298	2	no	—
377	C₂×C₄	—	298	4	no	—
378	C₂×C₄	—	298	2	no	—
379	C₂×C₄	—	149	1	no	—
380	C₂×C₄	—	149	1	no	—
381	C₂×C₄	—	149	4	no	—
382	C₂×C₄	—	149	2	no	—
383	C₂×C₄	—	149	1	no	—
384	C₂×C₄	—	149	2	no	—
385	C₂×C₄	—	149	2	no	—
386	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
387	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
388	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
389	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
390	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
391	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
392	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
394	C₂²	—	298	1	no	—
395	C₂²	—	298	1	no	—
396	C₂²	—	298	2	no	—
397	C₂²	—	298	2	no	—
398	C₂²	—	298	2	no	—
399	C₂²	—	149	2	no	—
400	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	298	1	no	—
408	C₄	—	298	2	no	—
409	C₄	—	298	1	no	—
410	C₄	—	298	2	no	—
411	C₄	—	298	1	no	—
412	C₄	—	298	4	no	—
413	C₄	—	149	4	no	—
414	C₄	#41×D₁₄₉	1	2	yes	—
415	C₄	#18011959	1	2	yes	—
416	C₂	—	298	2	no	—
417	C₂	—	596	2	no	—
418	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
419	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
420	C₂	C₂×#18011959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#557×C₁₄₉	C₂
prime radical	#18011886	C₂²
hypercenter	#557	D₁₄₉
hypocenter	C₁₄₉	#3523
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #23750353	C₂	semidirect
2. #23750352	C₂	semidirect
3. #23750348	C₂	semidirect
4. #23750347	C₂	semidirect
5. #23750316	C₂	semidirect
6. #23750307	C₂	semidirect
7. #23750290	C₂	semidirect
8. #23750290	C₂	semidirect
9. #23750236	C₂	semidirect
10. #23750234	C₂	semidirect
11. #23750180	C₂	semidirect
12. #23750179	C₂	semidirect
15. #23750101	C₂	semidirect
16. C₄×Q₈×D₁₄₉	C₂	semidirect
17. #557×C₁₄₉	C₂	semidirect
210. C₁₄₉	#3523	semidirect
214. #557	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750353	2
#23750352	2
#23750348	2
#23750347	2
#23750316	2
#23750307	2
#23750290	2
#23750236	2
#23750234	2
#23750180	2
#23750179	2
#23750162	2
#23750160	2
#23750101	2
C₄×Q₈×D₁₄₉	2
#557×C₁₄₉	2
#3523	149