Subgroups — C₆₇×#61726 #30740977

Order 17152.

1860 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3357	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3346	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3338	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3193	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3190	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×#480×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	#555×C₆₇	C₂²	1	1	yes	characteristic
19	#554×C₆₇	—	2	1	no	—
20	#554×C₆₇	—	2	2	no	—
21	#554×C₆₇	—	2	1	no	—
22	#554×C₆₇	C₂²	1	2	yes	—
23	#554×C₆₇	C₂²	1	1	yes	characteristic
24	#554×C₆₇	C₂²	1	4	yes	complemented
25	#554×C₆₇	C₂²	1	2	yes	complemented
26	#553×C₆₇	—	2	1	no	—
27	#553×C₆₇	C₂²	1	2	yes	—
28	#550×C₆₇	C₂²	1	1	yes	characteristic
29	#546×C₆₇	—	2	2	no	—
30	#546×C₆₇	C₂²	1	2	yes	—
31	D₄²×C₆₇	—	2	1	no	—
32	D₄²×C₆₇	C₂²	1	1	yes	characteristic
33	#540×C₆₇	—	2	1	no	—
34	#538×C₆₇	—	2	2	no	—
35	#532×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#529×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#125×C₆₇	—	2	1	no	—
39	#525×C₆₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
41	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#121×C₆₇	C₂²	1	2	yes	—
43	#518×C₆₇	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×D₄×C₆₇	—	2	1	no	—
46	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
48	#501×C₆₇	C₂²	1	2	yes	complemented
49	#500×C₆₇	C₂²	1	2	yes	complemented
50	#489×C₆₇	C₂²	1	2	yes	complemented
51	#486×C₆₇	C₂²	1	2	yes	complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#484×C₆₇	C₂²	1	4	yes	complemented
54	#484×C₆₇	C₂²	1	4	yes	complemented
55	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#483×C₆₇	C₂²	1	2	yes	complemented
57	#481×C₆₇	C₂²	1	4	yes	complemented
58	#480×C₆₇	C₂²	1	1	yes	characteristic
59	#480×C₆₇	C₂²	1	2	yes	—
60	#480×C₆₇	C₂²	1	4	yes	complemented
61	#480×C₆₇	C₂²	1	4	yes	complemented
62	#480×C₆₇	C₂²	1	2	yes	complemented
63	#480×C₆₇	C₂²	1	2	yes	complemented
64	#480×C₆₇	C₂²	1	2	yes	complemented
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#477×C₆₇	C₂²	1	2	yes	complemented
67	#477×C₆₇	C₂²	1	2	yes	complemented
68	#476×C₆₇	C₂²	1	2	yes	complemented
69	#474×C₆₇	C₂²	1	4	yes	complemented
70	#468×C₆₇	C₂²	1	4	yes	complemented
71	#468×C₆₇	C₂²	1	4	yes	complemented
72	#467×C₆₇	C₂²	1	4	yes	complemented
73	#465×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	2	yes	complemented
75	#460×C₆₇	C₂²	1	2	yes	complemented
76	#452×C₆₇	C₂²	1	4	yes	complemented
77	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#450×C₆₇	C₂²	1	4	yes	complemented
79	#448×C₆₇	C₂²	1	1	yes	characteristic
80	#448×C₆₇	C₂²	1	2	yes	complemented
81	#440×C₆₇	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
84	#436×C₆₇	C₂²	1	2	yes	complemented
85	#435×C₆₇	C₂²	1	4	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	—
87	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#428×C₆₇	C₂²	1	4	yes	complemented
90	C₂×#107×C₆₇	C₂²	1	4	yes	complemented
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₆₇	—	2	1	no	—
98	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₇	—	2	2	no	—
100	C₂²×D₄×C₆₇	—	2	1	no	—
101	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₆₇	—	2	2	no	—
104	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
105	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
108	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₆₇	—	2	1	no	—
111	C₄⋊Q₈×C₆₇	—	2	1	no	—
112	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	#127×C₆₇	—	2	1	no	—
116	#127×C₆₇	C₂³	1	1	yes	characteristic
117	#126×C₆₇	—	2	2	no	—
118	#126×C₆₇	—	2	1	no	—
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	—	2	2	no	—
121	#125×C₆₇	—	2	4	no	—
122	#125×C₆₇	—	2	1	no	—
123	#125×C₆₇	C₂³	1	1	yes	characteristic
124	#124×C₆₇	—	2	2	no	—
125	#124×C₆₇	—	2	1	no	—
126	#124×C₆₇	C₂³	1	1	yes	characteristic
127	#123×C₆₇	—	2	2	no	—
128	#123×C₆₇	—	2	1	no	—
129	#123×C₆₇	—	2	2	no	—
130	#123×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	2	no	—
133	C₂²⋊Q₈×C₆₇	—	2	4	no	—
134	C₂²⋊Q₈×C₆₇	—	2	4	no	—
135	C₂²⋊Q₈×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	—	2	2	no	—
138	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
139	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
141	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	1	no	—
144	#121×C₆₇	—	2	2	no	—
145	#121×C₆₇	—	2	2	no	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	—	2	1	no	—
148	#121×C₆₇	—	2	2	no	—
149	#121×C₆₇	—	2	2	no	—
150	#121×C₆₇	C₂³	1	1	yes	characteristic
151	#121×C₆₇	C₂³	1	2	yes	—
152	#121×C₆₇	C₂³	1	2	yes	—
153	#121×C₆₇	C₂³	1	2	yes	—
154	#121×C₆₇	C₂³	1	2	yes	—
155	#120×C₆₇	—	2	2	no	—
156	#120×C₆₇	—	2	2	no	—
157	#120×C₆₇	—	2	2	no	—
158	C₄×Q₈×C₆₇	—	2	1	no	—
159	C₄×Q₈×C₆₇	—	2	1	no	—
160	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
162	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	1	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	2	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
174	C₄×D₄×C₆₇	D₄	1	2	yes	—
175	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₇	C₂³	1	2	yes	—
180	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
181	#117×C₆₇	—	2	1	no	—
182	#117×C₆₇	—	2	1	no	—
183	#117×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
185	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
187	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
188	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
200	C₂×C₄²×C₆₇	—	2	1	no	—
201	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
202	#107×C₆₇	C₂³	1	4	yes	—
203	#107×C₆₇	C₂³	1	4	yes	—
204	#107×C₆₇	C₂³	1	4	yes	—
205	#107×C₆₇	C₂³	1	4	yes	—
206	#107×C₆₇	C₂³	1	2	yes	—
207	#106×C₆₇	C₂³	1	4	yes	—
208	#106×C₆₇	C₂³	1	2	yes	—
209	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	#103×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	4	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#102×C₆₇	C₂³	1	4	yes	—
217	#102×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	#97×C₆₇	C₂³	1	2	yes	—
227	C₄×C₈×C₆₇	C₂³	1	2	yes	—
228	C₂⁴×C₆₇	—	2	2	no	—
229	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
230	#41×C₆₇	—	4	4	no	—
231	#41×C₆₇	—	8	2	no	—
232	C₂×Q₈×C₆₇	—	2	1	no	—
233	C₂×Q₈×C₆₇	—	2	2	no	—
234	C₂×Q₈×C₆₇	—	2	2	no	—
235	C₂×Q₈×C₆₇	—	2	1	no	—
236	C₂×Q₈×C₆₇	—	4	2	no	—
237	C₂×Q₈×C₆₇	—	8	2	no	—
238	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
239	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	2	no	—
242	C₂×D₄×C₆₇	—	2	2	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	—	2	2	no	—
245	C₂×D₄×C₆₇	—	2	2	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	1	no	—
248	C₂×D₄×C₆₇	—	2	1	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	4	4	no	—
251	C₂×D₄×C₆₇	—	4	4	no	—
252	C₂×D₄×C₆₇	—	8	4	no	—
253	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	—	2	1	no	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	4	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	2	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	4	4	no	—
268	C₂²×C₄×C₆₇	—	8	4	no	—
269	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	Q₁₆×C₆₇	—	4	2	no	—
278	SD₁₆×C₆₇	—	4	4	no	—
279	SD₁₆×C₆₇	—	4	2	no	—
280	M₁₆×C₆₇	—	4	4	no	—
281	C₂×C₈×C₆₇	—	4	4	no	—
282	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
283	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
284	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₆₇	—	2	1	no	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	2	4	no	—
288	C₄⋊C₄×C₆₇	—	2	2	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	2	no	—
291	C₄⋊C₄×C₆₇	—	2	2	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	2	no	—
296	C₄⋊C₄×C₆₇	—	2	1	no	—
297	C₄⋊C₄×C₆₇	—	2	1	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	1	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	1	no	—
302	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	1	no	—
315	C₂²⋊C₄×C₆₇	—	2	1	no	—
316	C₂²⋊C₄×C₆₇	—	2	1	no	—
317	C₂²⋊C₄×C₆₇	—	2	2	no	—
318	C₂²⋊C₄×C₆₇	—	2	2	no	—
319	C₂²⋊C₄×C₆₇	—	2	2	no	—
320	C₂²⋊C₄×C₆₇	—	2	1	no	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	1	no	—
323	C₂²⋊C₄×C₆₇	—	2	2	no	—
324	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
328	C₄²×C₆₇	—	2	2	no	—
329	C₄²×C₆₇	—	2	2	no	—
330	C₄²×C₆₇	—	2	2	no	—
331	C₄²×C₆₇	—	2	1	no	—
332	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂³×C₆₇	—	2	4	no	—
337	C₂³×C₆₇	—	2	4	no	—
338	C₂³×C₆₇	—	2	1	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	4	2	no	—
341	C₂³×C₆₇	—	4	4	no	—
342	C₂³×C₆₇	—	8	2	no	—
343	C₂³×C₆₇	—	8	2	no	—
344	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
345	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₆₇	—	2	2	no	—
348	Q₈×C₆₇	—	2	2	no	—
349	Q₈×C₆₇	—	2	2	no	—
350	Q₈×C₆₇	—	4	2	no	—
351	Q₈×C₆₇	—	8	2	no	—
352	Q₈×C₆₇	—	8	2	no	—
353	Q₈×C₆₇	—	8	1	no	—
354	D₄×C₆₇	—	2	4	no	—
355	D₄×C₆₇	—	2	2	no	—
356	D₄×C₆₇	—	2	2	no	—
357	D₄×C₆₇	—	2	4	no	—
358	D₄×C₆₇	—	4	4	no	—
359	D₄×C₆₇	—	4	2	no	—
360	D₄×C₆₇	—	4	4	no	—
361	D₄×C₆₇	—	4	2	no	—
362	D₄×C₆₇	—	8	2	no	—
363	D₄×C₆₇	—	8	1	no	—
364	D₄×C₆₇	—	8	2	no	—
365	D₄×C₆₇	—	8	2	no	—
366	D₄×C₆₇	—	8	2	no	—
367	D₄×C₆₇	#137	1	4	yes	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	4	no	—
371	C₂×C₄×C₆₇	—	2	4	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	1	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	4	2	no	—
381	C₂×C₄×C₆₇	—	4	2	no	—
382	C₂×C₄×C₆₇	—	4	2	no	—
383	C₂×C₄×C₆₇	—	4	2	no	—
384	C₂×C₄×C₆₇	—	4	2	no	—
385	C₂×C₄×C₆₇	—	4	4	no	—
386	C₂×C₄×C₆₇	—	4	2	no	—
387	C₂×C₄×C₆₇	—	8	2	no	—
388	C₂×C₄×C₆₇	—	8	2	no	—
389	C₂×C₄×C₆₇	—	8	4	no	—
390	C₂×C₄×C₆₇	—	8	4	no	—
391	C₂×C₄×C₆₇	—	8	2	no	—
392	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
400	C₈×C₆₇	—	2	2	no	—
401	C₈×C₆₇	—	2	4	no	—
402	C₈×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	1	no	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	1	no	—
406	C₂²×C₆₇	—	2	2	no	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	4	8	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	1	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	2	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	1	no	—
417	C₂²×C₆₇	—	16	4	no	—
418	C₂²×C₆₇	C₂×#137	1	4	yes	—
419	C₂²×C₆₇	#576	1	2	yes	—
420	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₆₇	—	2	1	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	—	2	1	no	—
425	C₄×C₆₇	—	2	1	no	—
426	C₄×C₆₇	—	2	1	no	—
427	C₄×C₆₇	—	4	2	no	—
428	C₄×C₆₇	—	4	1	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	4	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	C₂×#137	1	2	yes	—
435	C₄×C₆₇	#585	1	2	yes	—
436	#61726	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂×C₆₇	—	2	2	no	—
438	C₂×C₆₇	—	2	4	no	—
439	C₂×C₆₇	—	4	2	no	—
440	C₂×C₆₇	—	8	2	no	—
441	C₂×C₆₇	—	8	1	no	—
442	C₂×C₆₇	#3485	1	1	yes	characteristic
443	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
444	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
445	#3519	C₂×C₆₇	1	1	yes	characteristic
446	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#3357	C₂×C₆₇	1	2	yes	complemented
448	#3346	C₂×C₆₇	1	4	yes	complemented
449	#3338	C₂×C₆₇	1	2	yes	complemented
450	#3333	C₂×C₆₇	1	2	yes	complemented
451	#3314	C₂×C₆₇	1	4	yes	complemented
452	#3295	C₂×C₆₇	1	2	yes	complemented
453	#3238	C₂×C₆₇	1	1	yes	characteristic, complemented
454	#3226	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#3193	C₂×C₆₇	1	2	yes	complemented
456	#3190	C₂×C₆₇	1	2	yes	complemented
457	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#3092	C₂×C₆₇	1	2	yes	complemented
460	C₂×#480	C₂×C₆₇	1	2	yes	complemented
461	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
462	C₆₇	#61726	1	1	yes	characteristic, direct product factor, Sylow
463	#555	C₂²×C₆₇	1	1	yes	characteristic
464	#554	—	2	1	no	—
465	#554	—	2	2	no	—
466	#554	—	2	1	no	—
467	#554	C₂²×C₆₇	1	1	yes	characteristic
468	#554	C₂²×C₆₇	1	2	yes	—
469	#554	C₂²×C₆₇	1	2	yes	complemented
470	#554	C₂²×C₆₇	1	4	yes	complemented
471	#553	—	2	1	no	—
472	#553	C₂²×C₆₇	1	2	yes	—
473	#550	C₂²×C₆₇	1	1	yes	characteristic
474	#546	—	2	2	no	—
475	#546	C₂²×C₆₇	1	2	yes	—
476	D₄²	—	2	1	no	—
477	D₄²	C₂²×C₆₇	1	1	yes	characteristic
478	#540	—	2	1	no	—
479	#538	—	2	2	no	—
480	#532	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#529	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×#125	—	2	1	no	—
484	#525	C₂²×C₆₇	1	2	yes	—
485	C₂×C₂²⋊Q₈	—	2	2	no	—
486	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
487	C₂×#121	C₂²×C₆₇	1	2	yes	—
488	#518	—	2	1	no	—
489	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
490	C₂×C₄×D₄	—	2	1	no	—
491	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
492	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
493	#501	C₂²×C₆₇	1	2	yes	complemented
494	#500	C₂²×C₆₇	1	2	yes	complemented
495	#489	C₂²×C₆₇	1	2	yes	complemented
496	#486	C₂²×C₆₇	1	2	yes	complemented
497	#485	C₂²×C₆₇	1	4	yes	complemented
498	#484	C₂²×C₆₇	1	4	yes	complemented
499	#484	C₂²×C₆₇	1	4	yes	complemented
500	#483	C₂²×C₆₇	1	1	yes	characteristic, complemented
501	#483	C₂²×C₆₇	1	2	yes	complemented
502	#481	C₂²×C₆₇	1	4	yes	complemented
503	#480	C₂²×C₆₇	1	1	yes	characteristic
504	#480	C₂²×C₆₇	1	2	yes	—
505	#480	C₂²×C₆₇	1	4	yes	complemented
506	#480	C₂²×C₆₇	1	2	yes	complemented
507	#480	C₂²×C₆₇	1	4	yes	complemented
508	#480	C₂²×C₆₇	1	2	yes	complemented
509	#480	C₂²×C₆₇	1	2	yes	complemented
510	#479	C₂²×C₆₇	1	2	yes	complemented
511	#477	C₂²×C₆₇	1	2	yes	complemented
512	#477	C₂²×C₆₇	1	2	yes	complemented
513	#476	C₂²×C₆₇	1	2	yes	complemented
514	#474	C₂²×C₆₇	1	4	yes	complemented
515	#468	C₂²×C₆₇	1	4	yes	complemented
516	#468	C₂²×C₆₇	1	4	yes	complemented
517	#467	C₂²×C₆₇	1	4	yes	complemented
518	#465	C₂²×C₆₇	1	4	yes	complemented
519	#464	C₂²×C₆₇	1	2	yes	complemented
520	#460	C₂²×C₆₇	1	2	yes	complemented
521	#452	C₂²×C₆₇	1	4	yes	complemented
522	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
523	#450	C₂²×C₆₇	1	4	yes	complemented
524	#448	C₂²×C₆₇	1	1	yes	characteristic
525	#448	C₂²×C₆₇	1	2	yes	complemented
526	#440	C₂²×C₆₇	1	4	yes	complemented
527	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
528	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
529	#436	C₂²×C₆₇	1	2	yes	complemented
530	#435	C₂²×C₆₇	1	4	yes	complemented
531	C₈×D₄	C₂²×C₆₇	1	2	yes	—
532	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
533	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	#428	C₂²×C₆₇	1	4	yes	complemented
535	C₂×#107	C₂²×C₆₇	1	4	yes	complemented
536	#417	C₂²×C₆₇	1	4	yes	complemented
537	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
538	#407	C₂²×C₆₇	1	2	yes	complemented
539	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#41	—	2	1	no	—
541	C₂×#41	C₂³×C₆₇	1	2	yes	—
542	C₂²×Q₈	—	2	1	no	—
543	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×D₄	—	2	2	no	—
545	C₂²×D₄	—	2	1	no	—
546	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
547	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
548	C₂³×C₄	—	2	2	no	—
549	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
552	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
553	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
554	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
560	#127	—	2	1	no	—
561	#127	C₂³×C₆₇	1	1	yes	characteristic
562	#126	—	2	2	no	—
563	#126	—	2	1	no	—
564	#125	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	2	4	no	—
567	#125	—	2	1	no	—
568	#125	C₂³×C₆₇	1	1	yes	characteristic
569	#124	—	2	2	no	—
570	#124	—	2	1	no	—
571	#124	C₂³×C₆₇	1	1	yes	characteristic
572	#123	—	2	2	no	—
573	#123	—	2	1	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	—	2	4	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
584	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
585	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
586	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
587	#121	—	2	2	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	C₂³×C₆₇	1	1	yes	characteristic
596	#121	C₂³×C₆₇	1	2	yes	—
597	#121	C₂³×C₆₇	1	2	yes	—
598	#121	C₂³×C₆₇	1	2	yes	—
599	#121	C₂³×C₆₇	1	2	yes	—
600	#120	—	2	2	no	—
601	#120	—	2	2	no	—
602	#120	—	2	2	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
606	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
607	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
619	C₄×D₄	D₄×C₆₇	1	2	yes	—
620	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₆₇	1	2	yes	—
623	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₆₇	1	2	yes	—
625	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
626	#117	—	2	1	no	—
627	#117	—	2	1	no	—
628	#117	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	—	2	2	no	—
642	C₂×C₂²⋊C₄	—	2	2	no	—
643	C₂×C₂²⋊C₄	—	2	2	no	—
644	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
647	#107	C₂³×C₆₇	1	2	yes	—
648	#107	C₂³×C₆₇	1	4	yes	—
649	#107	C₂³×C₆₇	1	4	yes	—
650	#107	C₂³×C₆₇	1	4	yes	—
651	#107	C₂³×C₆₇	1	4	yes	—
652	#106	C₂³×C₆₇	1	2	yes	—
653	#106	C₂³×C₆₇	1	4	yes	—
654	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
655	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
656	#103	C₂³×C₆₇	1	2	yes	—
657	#103	C₂³×C₆₇	1	4	yes	—
658	#103	C₂³×C₆₇	1	2	yes	—
659	#103	C₂³×C₆₇	1	2	yes	—
660	#103	C₂³×C₆₇	1	4	yes	—
661	#102	C₂³×C₆₇	1	2	yes	—
662	#102	C₂³×C₆₇	1	4	yes	—
663	#102	C₂³×C₆₇	1	4	yes	—
664	#102	C₂³×C₆₇	1	4	yes	—
665	#102	C₂³×C₆₇	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
667	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
668	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
669	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
671	#97	C₂³×C₆₇	1	2	yes	—
672	C₄×C₈	C₂³×C₆₇	1	2	yes	—
673	C₂⁴	—	2	2	no	—
674	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
675	#41	—	4	4	no	—
676	#41	—	8	2	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	8	2	no	—
683	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
684	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	8	4	no	—
698	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
700	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
701	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	—	8	4	no	—
714	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	Q₁₆	—	4	2	no	—
723	SD₁₆	—	4	4	no	—
724	SD₁₆	—	4	2	no	—
725	M₁₆	—	4	4	no	—
726	C₂×C₈	—	4	4	no	—
727	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
728	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
729	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
778	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
779	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
780	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
781	C₂³	—	2	4	no	—
782	C₂³	—	2	4	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	8	2	no	—
788	C₂³	—	8	2	no	—
789	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
790	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
791	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	—	8	2	no	—
797	Q₈	—	8	2	no	—
798	Q₈	—	8	1	no	—
799	D₄	—	2	4	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	4	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	2	no	—
807	D₄	—	8	2	no	—
808	D₄	—	8	1	no	—
809	D₄	—	8	2	no	—
810	D₄	—	8	2	no	—
811	D₄	—	8	2	no	—
812	D₄	#137×C₆₇	1	4	yes	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	8	2	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
840	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	16	4	no	—
863	C₂²	C₂×#137×C₆₇	1	4	yes	—
864	C₂²	#576×C₆₇	1	2	yes	—
865	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
866	C₄	—	2	1	no	—
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	4	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	1	no	—
879	C₄	C₂×#137×C₆₇	1	2	yes	—
880	C₄	#585×C₆₇	1	2	yes	—
881	C₂	—	2	2	no	—
882	C₂	—	2	4	no	—
883	C₂	—	4	2	no	—
884	C₂	—	8	1	no	—
885	C₂	—	8	2	no	—
886	C₂	C₆₇×#3485	1	1	yes	characteristic
887	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic
888	C₂	C₂×#576×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#554×C₆₇	C₂	semidirect
3. C₆₇×#3357	C₂	semidirect
4. C₆₇×#3346	C₂	semidirect
5. C₆₇×#3338	C₂	semidirect
6. C₆₇×#3333	C₂	semidirect
7. C₆₇×#3314	C₂	semidirect
8. C₆₇×#3295	C₂	semidirect
9. C₆₇×#3238	C₂	semidirect
10. C₆₇×#3226	C₂	semidirect
11. C₆₇×#3193	C₂	semidirect
12. C₆₇×#3190	C₂	semidirect
13. C₆₇×#3112	C₂	semidirect
14. C₆₇×#3108	C₂	semidirect
15. C₆₇×#3092	C₂	semidirect
16. C₂×#480×C₆₇	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
24. #554×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
41. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
44. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
48. #501×C₆₇	C₂²	semidirect
49. #500×C₆₇	C₂²	semidirect
50. #489×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #484×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
55. #483×C₆₇	C₂²	semidirect
56. #483×C₆₇	C₂²	semidirect
57. #481×C₆₇	C₂²	semidirect
60. #480×C₆₇	C₂²	semidirect
61. #480×C₆₇	C₂²	semidirect
62. #480×C₆₇	C₂²	semidirect
63. #480×C₆₇	C₂²	semidirect
64. #480×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #477×C₆₇	C₂²	semidirect
67. #477×C₆₇	C₂²	semidirect
68. #476×C₆₇	C₂²	semidirect
69. #474×C₆₇	C₂²	semidirect
70. #468×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #467×C₆₇	C₂²	semidirect
73. #465×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #460×C₆₇	C₂²	semidirect
76. #452×C₆₇	C₂²	semidirect
77. #451×C₆₇	C₂²	semidirect
78. #450×C₆₇	C₂²	semidirect
80. #448×C₆₇	C₂²	semidirect
81. #440×C₆₇	C₂²	semidirect
82. C₄×Q₁₆×C₆₇	C₂²	semidirect
83. C₄×SD₁₆×C₆₇	C₂²	semidirect
84. #436×C₆₇	C₂²	semidirect
85. #435×C₆₇	C₂²	semidirect
87. #432×C₆₇	C₂²	semidirect
88. #431×C₆₇	C₂²	semidirect
89. #428×C₆₇	C₂²	semidirect
90. C₂×#107×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. C₂×#102×C₆₇	C₂²	semidirect
93. #407×C₆₇	C₂²	semidirect
94. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
436. #61726	C₆₇	direct (N × H)
446. C₂×#554	C₂×C₆₇	semidirect
447. #3357	C₂×C₆₇	semidirect
448. #3346	C₂×C₆₇	semidirect
449. #3338	C₂×C₆₇	semidirect
450. #3333	C₂×C₆₇	semidirect
451. #3314	C₂×C₆₇	semidirect
452. #3295	C₂×C₆₇	semidirect
453. #3238	C₂×C₆₇	semidirect
454. #3226	C₂×C₆₇	semidirect
455. #3193	C₂×C₆₇	semidirect
456. #3190	C₂×C₆₇	semidirect
457. #3112	C₂×C₆₇	semidirect
458. #3108	C₂×C₆₇	semidirect
459. #3092	C₂×C₆₇	semidirect
460. C₂×#480	C₂×C₆₇	semidirect
461. #2974	C₂×C₆₇	semidirect
462. C₆₇	#61726	direct (N × H)
469. #554	C₂²×C₆₇	semidirect
470. #554	C₂²×C₆₇	semidirect
481. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
486. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
489. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
492. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
493. #501	C₂²×C₆₇	semidirect
494. #500	C₂²×C₆₇	semidirect
495. #489	C₂²×C₆₇	semidirect
496. #486	C₂²×C₆₇	semidirect
497. #485	C₂²×C₆₇	semidirect
498. #484	C₂²×C₆₇	semidirect
499. #484	C₂²×C₆₇	semidirect
500. #483	C₂²×C₆₇	semidirect
501. #483	C₂²×C₆₇	semidirect
502. #481	C₂²×C₆₇	semidirect
505. #480	C₂²×C₆₇	semidirect
506. #480	C₂²×C₆₇	semidirect
507. #480	C₂²×C₆₇	semidirect
508. #480	C₂²×C₆₇	semidirect
509. #480	C₂²×C₆₇	semidirect
510. #479	C₂²×C₆₇	semidirect
511. #477	C₂²×C₆₇	semidirect
512. #477	C₂²×C₆₇	semidirect
513. #476	C₂²×C₆₇	semidirect
514. #474	C₂²×C₆₇	semidirect
515. #468	C₂²×C₆₇	semidirect
516. #468	C₂²×C₆₇	semidirect
517. #467	C₂²×C₆₇	semidirect
518. #465	C₂²×C₆₇	semidirect
519. #464	C₂²×C₆₇	semidirect
520. #460	C₂²×C₆₇	semidirect
521. #452	C₂²×C₆₇	semidirect
522. #451	C₂²×C₆₇	semidirect
523. #450	C₂²×C₆₇	semidirect
525. #448	C₂²×C₆₇	semidirect
526. #440	C₂²×C₆₇	semidirect
527. C₄×Q₁₆	C₂²×C₆₇	semidirect
528. C₄×SD₁₆	C₂²×C₆₇	semidirect
529. #436	C₂²×C₆₇	semidirect
530. #435	C₂²×C₆₇	semidirect
532. #432	C₂²×C₆₇	semidirect
533. #431	C₂²×C₆₇	semidirect
534. #428	C₂²×C₆₇	semidirect
535. C₂×#107	C₂²×C₆₇	semidirect
536. #417	C₂²×C₆₇	semidirect
537. C₂×#102	C₂²×C₆₇	semidirect
538. #407	C₂²×C₆₇	semidirect
539. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3519	2
C₂×#554×C₆₇	2
C₆₇×#3357	2
C₆₇×#3346	2
C₆₇×#3338	2
C₆₇×#3333	2
C₆₇×#3314	2
C₆₇×#3295	2
C₆₇×#3238	2
C₆₇×#3226	2
C₆₇×#3193	2
C₆₇×#3190	2
C₆₇×#3112	2
C₆₇×#3108	2
C₆₇×#3092	2
C₂×#480×C₆₇	2
C₆₇×#2974	2
#61726	67

Subgroups — C67×#61726 #30740977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61726 #30740977