Subgroups — C₂×C₆₇×#1975 #30700490

Order 17152.

1518 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#408×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1975	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#41×C₆₇	C₂²	1	2	yes	—
8	C₂×#135×C₆₇	—	2	4	no	—
9	C₂×#135×C₆₇	—	2	4	no	—
10	C₂×#135×C₆₇	C₄	1	4	yes	complemented
11	C₂×#135×C₆₇	C₂²	1	4	yes	—
12	C₂²×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
13	C₂²×SD₁₆×C₆₇	C₄	1	2	yes	complemented
14	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
15	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
16	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#108×C₆₇	—	2	4	no	—
20	C₂×#108×C₆₇	C₂²	1	4	yes	complemented
21	C₂×#104×C₆₇	—	2	8	no	—
22	C₂×#104×C₆₇	C₂²	1	8	yes	complemented
23	#408×C₆₇	—	2	4	no	—
24	#408×C₆₇	C₂²	1	8	yes	complemented
25	C₂×C₂²⋊C₈×C₆₇	—	2	4	no	—
26	C₂×#97×C₆₇	—	2	4	no	—
27	C₂×#97×C₆₇	C₂²	1	4	yes	complemented
28	C₂×#41×C₆₇	—	2	2	no	—
29	C₂×#41×C₆₇	—	2	2	no	—
30	C₂×#41×C₆₇	—	2	4	no	—
31	C₂×#41×C₆₇	—	2	4	no	—
32	C₂×#41×C₆₇	—	2	4	no	—
33	C₂×#41×C₆₇	—	2	4	no	—
34	C₂×#41×C₆₇	C₂×C₄	1	4	yes	—
35	C₂×#41×C₆₇	C₂³	1	4	yes	—
36	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
37	C₂²×D₄×C₆₇	—	2	2	no	—
38	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₆₇	—	2	1	no	—
40	C₂³×C₄×C₆₇	—	2	2	no	—
41	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
42	#135×C₆₇	—	2	16	no	—
43	#135×C₆₇	—	2	8	no	—
44	#135×C₆₇	—	2	8	no	—
45	C₂×Q₁₆×C₆₇	—	2	4	no	—
46	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
47	C₂×SD₁₆×C₆₇	—	2	8	no	—
48	C₂×SD₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
49	C₂×D₈×C₆₇	—	2	4	no	—
50	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	complemented
51	C₂×M₁₆×C₆₇	—	2	2	no	—
52	C₂×M₁₆×C₆₇	—	2	4	no	—
53	C₂×M₁₆×C₆₇	—	2	4	no	—
54	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
55	C₂²×C₈×C₆₇	—	2	2	no	—
56	C₂²×C₈×C₆₇	—	2	2	no	—
57	C₂²×C₈×C₆₇	—	2	2	no	—
58	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₆₇	D₄	1	2	yes	—
62	C₂²×C₈×C₆₇	D₄	1	2	yes	—
63	C₂²×C₈×C₆₇	D₄	1	4	yes	—
64	C₂²×C₈×C₆₇	D₄	1	4	yes	—
65	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	—	2	1	no	—
69	C₂×C₄²×C₆₇	D₄	1	4	yes	—
70	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
71	#108×C₆₇	—	2	8	no	—
72	#104×C₆₇	—	2	16	no	—
73	C₂²⋊C₈×C₆₇	—	2	16	no	—
74	#97×C₆₇	—	2	8	no	—
75	C₂⁴×C₆₇	—	2	2	no	—
76	C₂⁴×C₆₇	#41	1	1	yes	characteristic
77	#41×C₆₇	—	2	8	no	—
78	#41×C₆₇	—	2	8	no	—
79	#41×C₆₇	—	2	4	no	—
80	#41×C₆₇	—	2	4	no	—
81	#41×C₆₇	—	2	4	no	—
82	#41×C₆₇	—	2	4	no	—
83	#41×C₆₇	—	4	4	no	—
84	#41×C₆₇	—	4	4	no	—
85	#41×C₆₇	—	4	4	no	—
86	#41×C₆₇	—	4	4	no	—
87	C₂×Q₈×C₆₇	—	2	2	no	—
88	C₂×Q₈×C₆₇	—	2	4	no	—
89	C₂×Q₈×C₆₇	—	2	4	no	—
90	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
91	C₂×D₄×C₆₇	—	2	4	no	—
92	C₂×D₄×C₆₇	—	2	4	no	—
93	C₂×D₄×C₆₇	—	2	4	no	—
94	C₂×D₄×C₆₇	—	2	4	no	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	—	4	4	no	—
97	C₂×D₄×C₆₇	—	4	4	no	—
98	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	C₂²×C₄×C₆₇	—	2	4	no	—
103	C₂²×C₄×C₆₇	—	2	4	no	—
104	C₂²×C₄×C₆₇	—	4	4	no	—
105	C₂²×C₄×C₆₇	—	4	4	no	—
106	C₂²×C₄×C₆₇	—	4	4	no	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	#41	1	2	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₆₇	—	2	8	no	—
118	SD₁₆×C₆₇	—	2	16	no	—
119	D₈×C₆₇	—	2	8	no	—
120	M₁₆×C₆₇	—	2	4	no	—
121	M₁₆×C₆₇	—	2	4	no	—
122	M₁₆×C₆₇	—	4	4	no	—
123	C₂×C₈×C₆₇	—	2	4	no	—
124	C₂×C₈×C₆₇	—	2	4	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₂×C₈×C₆₇	—	2	4	no	—
128	C₂×C₈×C₆₇	—	4	4	no	—
129	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
130	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
131	C₂×C₈×C₆₇	C₂²⋊C₄	1	8	yes	—
132	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
136	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
137	C₄²×C₆₇	—	2	4	no	—
138	C₄²×C₆₇	—	2	2	no	—
139	C₄²×C₆₇	C₂×D₄	1	4	yes	—
140	C₂³×C₆₇	—	2	4	no	—
141	C₂³×C₆₇	—	2	4	no	—
142	C₂³×C₆₇	—	4	4	no	—
143	C₂³×C₆₇	—	4	8	no	—
144	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₆₇	#121	1	2	yes	—
147	C₂³×C₆₇	#124	1	2	yes	—
148	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
149	Q₈×C₆₇	—	2	4	no	—
150	Q₈×C₆₇	—	2	4	no	—
151	Q₈×C₆₇	—	4	4	no	—
152	D₄×C₆₇	—	2	4	no	—
153	D₄×C₆₇	—	2	4	no	—
154	D₄×C₆₇	—	4	4	no	—
155	D₄×C₆₇	—	4	4	no	—
156	D₄×C₆₇	—	4	8	no	—
157	D₄×C₆₇	—	4	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	4	4	no	—
161	C₂×C₄×C₆₇	—	4	8	no	—
162	C₂×C₄×C₆₇	—	4	4	no	—
163	C₂×C₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	—	4	4	no	—
165	C₂×C₄×C₆₇	—	4	8	no	—
166	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	#121	1	2	yes	—
173	C₂×C₄×C₆₇	#121	1	2	yes	—
174	C₂×C₄×C₆₇	#121	1	2	yes	—
175	C₂×C₄×C₆₇	#124	1	2	yes	—
176	C₂×C₄×C₆₇	#127	1	2	yes	—
177	C₂×C₄×C₆₇	#127	1	2	yes	—
178	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
184	C₈×C₆₇	—	2	4	no	—
185	C₈×C₆₇	—	4	4	no	—
186	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
187	C₈×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂²×C₆₇	—	2	2	no	—
189	C₂²×C₆₇	—	2	2	no	—
190	C₂²×C₆₇	—	2	4	no	—
191	C₂²×C₆₇	—	2	4	no	—
192	C₂²×C₆₇	—	4	8	no	—
193	C₂²×C₆₇	—	4	4	no	—
194	C₂²×C₆₇	—	8	8	no	—
195	C₂²×C₆₇	#390	1	2	yes	—
196	C₂²×C₆₇	#390	1	2	yes	—
197	C₂²×C₆₇	#444	1	4	yes	—
198	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
200	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
201	C₄×C₆₇	—	4	4	no	—
202	C₄×C₆₇	—	4	4	no	—
203	C₄×C₆₇	#390	1	2	yes	—
204	C₄×C₆₇	#390	1	2	yes	—
205	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
206	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
208	C₄×C₆₇	C₂×#127	1	1	yes	characteristic
209	C₂×#1975	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂×C₆₇	—	2	1	no	—
211	C₂×C₆₇	—	2	1	no	—
212	C₂×C₆₇	—	2	2	no	—
213	C₂×C₆₇	—	8	4	no	—
214	C₂×C₆₇	#1975	1	4	yes	direct product factor
215	C₂×C₆₇	C₂×#390	1	1	yes	characteristic
216	C₂×C₆₇	C₂×#444	1	2	yes	—
217	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic
218	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic, complemented
219	C₂²×#104	C₂×C₆₇	1	2	yes	complemented
220	C₂×#408	C₂×C₆₇	1	2	yes	complemented
221	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
222	#1975	C₂×C₆₇	1	8	yes	direct product factor
223	C₆₇	C₂×#1975	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×#41	C₂²×C₆₇	1	2	yes	—
225	C₂×#135	—	2	4	no	—
226	C₂×#135	—	2	4	no	—
227	C₂×#135	C₄×C₆₇	1	4	yes	complemented
228	C₂×#135	C₂²×C₆₇	1	4	yes	—
229	C₂²×Q₁₆	C₄×C₆₇	1	1	yes	characteristic, complemented
230	C₂²×SD₁₆	C₄×C₆₇	1	2	yes	complemented
231	C₂²×D₈	C₄×C₆₇	1	1	yes	characteristic, complemented
232	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
233	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
236	C₂×#108	—	2	4	no	—
237	C₂×#108	C₂²×C₆₇	1	4	yes	complemented
238	C₂×#104	—	2	8	no	—
239	C₂×#104	C₂²×C₆₇	1	8	yes	complemented
240	#408	—	2	4	no	—
241	#408	C₂²×C₆₇	1	8	yes	complemented
242	C₂×C₂²⋊C₈	—	2	4	no	—
243	C₂×#97	—	2	4	no	—
244	C₂×#97	C₂²×C₆₇	1	4	yes	complemented
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	C₂×C₄×C₆₇	1	4	yes	—
252	C₂×#41	C₂³×C₆₇	1	4	yes	—
253	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	—	2	2	no	—
258	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
259	#135	—	2	16	no	—
260	#135	—	2	8	no	—
261	#135	—	2	8	no	—
262	C₂×Q₁₆	—	2	4	no	—
263	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
264	C₂×SD₁₆	—	2	8	no	—
265	C₂×SD₁₆	C₂×C₄×C₆₇	1	8	yes	complemented
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	C₂×C₄×C₆₇	1	4	yes	complemented
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	4	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
276	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
277	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
278	C₂²×C₈	D₄×C₆₇	1	2	yes	—
279	C₂²×C₈	D₄×C₆₇	1	2	yes	—
280	C₂²×C₈	D₄×C₆₇	1	4	yes	—
281	C₂²×C₈	D₄×C₆₇	1	4	yes	—
282	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
283	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	D₄×C₆₇	1	4	yes	—
287	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
288	#108	—	2	8	no	—
289	#104	—	2	16	no	—
290	C₂²⋊C₈	—	2	16	no	—
291	#97	—	2	8	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	#41×C₆₇	1	1	yes	characteristic
294	#41	—	2	8	no	—
295	#41	—	2	8	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	4	4	no	—
301	#41	—	4	4	no	—
302	#41	—	4	4	no	—
303	#41	—	4	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
331	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
332	C₂²×C₄	#41×C₆₇	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
334	Q₁₆	—	2	8	no	—
335	SD₁₆	—	2	16	no	—
336	D₈	—	2	8	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	4	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	4	4	no	—
346	C₂×C₈	C₂²⋊C₄×C₆₇	1	4	yes	—
347	C₂×C₈	C₂²⋊C₄×C₆₇	1	4	yes	—
348	C₂×C₈	C₂²⋊C₄×C₆₇	1	8	yes	—
349	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
352	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
353	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	C₂×D₄×C₆₇	1	4	yes	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	8	no	—
361	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
362	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
363	C₂³	#121×C₆₇	1	2	yes	—
364	C₂³	#124×C₆₇	1	2	yes	—
365	C₂³	C₂×#41×C₆₇	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
387	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
388	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
389	C₂×C₄	#121×C₆₇	1	2	yes	—
390	C₂×C₄	#121×C₆₇	1	2	yes	—
391	C₂×C₄	#121×C₆₇	1	2	yes	—
392	C₂×C₄	#124×C₆₇	1	2	yes	—
393	C₂×C₄	#127×C₆₇	1	2	yes	—
394	C₂×C₄	#127×C₆₇	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
401	C₈	—	2	4	no	—
402	C₈	—	4	4	no	—
403	C₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
404	C₈	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	8	8	no	—
412	C₂²	#390×C₆₇	1	2	yes	—
413	C₂²	#390×C₆₇	1	2	yes	—
414	C₂²	#444×C₆₇	1	4	yes	—
415	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
416	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
417	C₂²	C₂×#124×C₆₇	1	1	yes	characteristic
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	#390×C₆₇	1	2	yes	—
421	C₄	#390×C₆₇	1	2	yes	—
422	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
423	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
424	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
425	C₄	C₂×#127×C₆₇	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	2	no	—
429	C₂	—	8	4	no	—
430	C₂	C₆₇×#1975	1	4	yes	direct product factor
431	C₂	C₂×#390×C₆₇	1	1	yes	characteristic
432	C₂	C₂×#444×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×#135×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂³×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₆₇	C₂	semidirect
3. C₂²×#104×C₆₇	C₂	semidirect
4. C₂×#408×C₆₇	C₂	semidirect
5. C₂²×#97×C₆₇	C₂	semidirect
6. C₆₇×#1975	C₂	direct (N × H)
10. C₂×#135×C₆₇	C₄	semidirect
12. C₂²×Q₁₆×C₆₇	C₄	semidirect
13. C₂²×SD₁₆×C₆₇	C₄	semidirect
14. C₂²×D₈×C₆₇	C₄	semidirect
20. C₂×#108×C₆₇	C₂²	semidirect
22. C₂×#104×C₆₇	C₂²	semidirect
24. #408×C₆₇	C₂²	semidirect
27. C₂×#97×C₆₇	C₂²	semidirect
46. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
48. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
50. C₂×D₈×C₆₇	C₂×C₄	semidirect
209. C₂×#1975	C₆₇	direct (N × H)
214. C₂×C₆₇	#1975	direct (N × H)
218. C₂²×#108	C₂×C₆₇	semidirect
219. C₂²×#104	C₂×C₆₇	semidirect
220. C₂×#408	C₂×C₆₇	semidirect
221. C₂²×#97	C₂×C₆₇	semidirect
222. #1975	C₂×C₆₇	direct (N × H)
223. C₆₇	C₂×#1975	direct (N × H)
227. C₂×#135	C₄×C₆₇	semidirect
229. C₂²×Q₁₆	C₄×C₆₇	semidirect
230. C₂²×SD₁₆	C₄×C₆₇	semidirect
231. C₂²×D₈	C₄×C₆₇	semidirect
237. C₂×#108	C₂²×C₆₇	semidirect
239. C₂×#104	C₂²×C₆₇	semidirect
241. #408	C₂²×C₆₇	semidirect
244. C₂×#97	C₂²×C₆₇	semidirect
263. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
265. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
267. C₂×D₈	C₂×C₄×C₆₇	semidirect
430. C₂	C₆₇×#1975	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₆₇	2
C₂²×#108×C₆₇	2
C₂²×#104×C₆₇	2
C₂×#408×C₆₇	2
C₂²×#97×C₆₇	2
C₆₇×#1975	2
C₂×#1975	67

Subgroups — C2×C67×#1975 #30700490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1975 #30700490